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Injection Mold Design Engineering D. Kazmar

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David O. Kazmer
Injection Mold Design Engineering

David O. Kazmer

Injection
Mold Design
Engineering

Hanser Publishers, Munich • Hanser Gardner Publications, Cincinnati

The Author:
David O. Kazmer, P.E., Ph.D. Department of Plastics Engineering, 1 University Avenue, Lowell, MA 01854, USA
Distributed in the USA and in Canada by
Hanser Gardner Publications, Inc.
6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA
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www.hansergardner.com
Distributed in all other countries by
Carl Hanser Verlag
Postfach 86 04 20, 81631 München, Germany
Fax: +49 (89) 98 48 09
www.hanser.de
Your use of the information provided herein is conditioned upon your agreement, and the agreement of your employer or
any third party to whom you provide information, to make use of these materials only in accordance with and subject to
the following terms and conditions.
The information provided herein is made available“as is” without warranty of any kind, either express or implied, including
but not limited to the implied warranties of merchantability, fitness for a particular purpose, satisfactory quality, or noninfringement. We may in the future modify, improve or make other changes to the information made available. All the
included information may include technical or typographical errors and we will not be responsible for any such errors.
Any pricing and other information about products and services contained herein is not an offer to provide such goods or
services.
You agree not to bring any legal action against the author or publisher based on your use of the provided information. You
agree to indemnify and hold the copyright holder and its affiliates, officers, agents, and employees harmless from any claim
or demand, including reasonable attorneys‘ fees, made by any third party due to or arising out of your use of the provided
information. The sole and maximum liability of the copyright holder, its affiliates and subsidiaries for any reason, and your
exclusive remedy for any cause whatsoever, shall be limited to the amount paid, if any, for the provided information.
Library of Congress Cataloging-in-Publication Data
Kazmer, David.
Injection mold design engineering / David O. Kazmer.
p. cm.
ISBN-13: 978-1-56990-417-6 (hardcover)
ISBN-10: 1-56990-417-0 (hardcover)
1. Injection molding of plastics. I. Title.
TP1150.K39 2007
668.4‘12--dc22
2007018765
Bibliografische Information Der Deutschen Bibliothek
Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie;
detaillierte bibliografische Daten sind im Internet über <http://dnb.d-nb.de> abrufbar.
ISBN 978-3-446-41266-8
All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or
mechanical, including photocopying or by any information storage and retrieval system, without permission in wirting
from the publisher.
© Carl Hanser Verlag, Munich 2007
Production Management: Oswald Immel
Typeset by Manuela Treindl, Laaber, Germany
Coverconcept: Marc Müller-Bremer, Rebranding, München, Germany
Coverillustration by David O. Kazmer, Lowell, USA
Coverdesign: MCP • Susanne Kraus GbR, Holzkirchen, Germany
Printed and bound by Druckhaus “Thomas Müntzer” GmbH, Bad Langensalza, Germany

Preface
Mold design has been more of a technical trade than an engineering process. Traditionally,
practitioners have shared standard practices and learned tricks of the trade to develop
sophisticated molds that often exceed customer expectations.
However, the lack of fundamental engineering analysis during mold design frequently results
in molds that may fail and require extensive rework, produce moldings of inferior quality,
or are less cost effective than may have been possible. Indeed, it has been estimated that on
average 49 out of 50 molds require some modifications during the mold start-up process.
Many times, mold designers and end-users may not know how much money was “left on
the table”.
The word“engineering”in the title of this book implies a methodical and analytical approach to
mold design. The engineer who understands the causality between design decisions and mold
performance has the ability to make better and more informed decisions on an application by
application basis. Such decision making competence is a competitive enabler by supporting
the development of custom mold designs that outperform molds developed according to
standard practices. The proficient engineer also avoids the cost and time needed to delegate
decision to other parties, who are not necessarily more competent.
The book has been written as a teaching text, but is geared towards professionals working in
a tightly integrated supply chain including product designers, mold designers, and injection
molders. Compared to most handbooks, this textbook provides worked examples with
rigorous analysis and detailed discussion of vital mold engineering concepts. It should be
understood that this textbook purposefully investigates the prevalent and fundamental aspects
of injection mold engineering.
I hope that Injection Mold Design Engineering is accessible and useful to all who read it. I
welcome your feedback and partnership for future improvements.
Best wishes,
David Kazmer, P. E., Ph. D.
Lowell, Massachusetts
June 1, 2007

Contents
Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XV
1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview of the Injection Molding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Mold Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Mold Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.1 External View of Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 View of Mold during Part Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.3 Mold Section and Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Other Common Mold Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Three Plate, Multi-Cavity Family Mold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 Hot Runner, Multi-Gated, Single Cavity Mold . . . . . . . . . . . . . . . . . . . . . 11
1.4.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 The Mold Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2

Plastic Part Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 The Product Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Product Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Product Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Business and Production Development . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.4 Scale-Up and Launch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.5 Role of Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Application Engineering Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Production Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 End Use Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Product Design Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Plastic Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Design for Injection Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Uniform Wall Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Rib Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Boss Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Corner Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Surface Finish and Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.6 Draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.7 Undercuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17
17
18
18
19
19
19
20
20
21
22
24
26
28
28
29
29
30
31
33
34
35

VIII

Contents

3

Mold Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 The Mold Quoting Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Cost Drivers for Molded Parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Effect of Production Quantity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Break-Even Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Mold Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Cavity Cost Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.1 Cavity Set Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.2 Cavity Materials Cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.3 Cavity Machining Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.4 Cavity Discount Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1.5 Cavity Finishing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Mold Base Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Mold Customization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Part Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Mold Cost per Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Material Cost per Part. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Processing Cost per Part. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.4 Defect Cost per Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37
37
39
40
41
43
44
45
45
46
51
51
53
55
60
60
61
62
65
66

4

Mold Layout Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1 Parting Plane Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Determine Mold Opening Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Determine Parting Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Parting Plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 Shut-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Cavity and Core Insert Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Height Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Length and Width Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Mold Base Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Cavity Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Mold Base Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Molding Machine Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Mold Base Suppliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Mold Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Strength vs. Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Hardness vs. Machinability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 Mold-Maker’s Cost vs. Molder’s Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.4 Material Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67
67
67
70
71
73
74
74
75
76
77
77
79
81
83
84
84
85
86
88
89

Contents

IX

5

Cavity Filling Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2 Objectives in Cavity Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2.1 Complete Filling of Mold Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2.2 Avoid Uneven Filling or Over-Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.2.3 Control the Melt Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Viscous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3.1 Shear Stress, Shear Rate, and Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.3.2 Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.3 Rheological Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.4 Newtonian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3.5 Power Law Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.5 Cavity Filling Analyses and Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.5.1 Estimating the Processing Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.5.2 Estimating the Filling Pressure and Minimum Wall Thickness . . . . . . 107
5.5.3 Estimating Clamp Tonnage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.5.4 Predicting Filling Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.5.5 Designing Flow Leaders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.6 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6

Feed System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2 Objectives in Feed System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.2.1 Conveying the Polymer Melt from Machine to Cavities . . . . . . . . . . . . 119
6.2.2 Impose Minimal Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.2.3 Consume Minimal Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2.4 Control Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.3 Feed System Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.3.1 Two-Plate Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.3.2 Three-Plate Mold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3.3 Hot Runner Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.4 Feed System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4.1 Determine Type of Feed System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.2 Determine Feed System Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.4.3 Estimate Pressure Drops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.4.4 Calculate Runner Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.4.5 Optimize Runner Diameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
6.4.6 Balance Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.4.7 Estimate Runner Cooling Times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.4.8 Estimate Residence Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.5 Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.5.1 Runner Cross-Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.5.2 Sucker Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

X

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6.6

6.5.3 Runner Shut-Offs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.5.4 Standard Runner Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.5.5 Steel Safe Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7

Gating Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.1 Objectives of Gating Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.1.1 Connecting the Runner to the Mold Cavity . . . . . . . . . . . . . . . . . . . . . . . 161
7.1.2 Provide Automatic De-Gating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
7.1.3 Provide Aesthetic De-Gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.1.4 Avoid Excessive Shear or Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.1.5 Control Pack Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.2 Common Gate Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.2.1 Sprue Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.2.2 Pin-Point Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.2.3 Edge Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.2.4 Tab Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.2.5 Fan Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.2.6 Flash/Diaphragm Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7.2.7 Tunnel/Submarine Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.2.8 Thermal Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.2.9 Valve Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.3 The Gating Design Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.3.1 Determine Type of Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.3.2 Calculate Shear Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.3.3 Calculate Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
7.3.4 Calculate Gate Freeze Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
7.3.5 Adjust Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

8

Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.1 Venting Design Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.1.1 Release Compressed Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.1.2 Contain Plastic Melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.1.3 Minimize Maintenance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8.2 Venting Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8.2.1 Estimate Air Displacement and Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8.2.2 Identify Number and Location of Vents . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8.2.3 Specify Vent Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.3 Venting Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.3.1 Vents on Parting Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.3.2 Vents around Ejector Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.3.3 Vents in Dead Pockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
8.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Contents

9

XI

Cooling System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.1 Objectives in Cooling System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.1.1 Maximize Heat Transfer Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.1.2 Maintain Uniform Wall Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
9.1.3 Minimize Mold Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
9.1.4 Minimize Volume and Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
9.1.5 Minimize Stress and Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
9.1.6 Facilitate Mold Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
9.2 The Cooling System Design Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
9.2.1 Calculate the Required Cooling Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
9.2.2 Evaluate Required Heat Transfer Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
9.2.3 Assess Coolant Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
9.2.4 Assess Cooling Line Diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
9.2.5 Select Cooling Line Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
9.2.6 Select Cooling Line Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
9.2.7 Cooling Line Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
9.3 Cooling System Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.3.1 Cooling Line Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.3.2 Cooling Inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
9.3.3 Conformal Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
9.3.4 Highly Conductive Inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
9.3.5 Cooling of Slender Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
9.3.5.1 Cooling Insert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
9.3.5.2 Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
9.3.5.3 Bubblers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
9.3.5.4 Heat Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
9.3.5.5 Conductive Pin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
9.3.5.6 Interlocking Core with Air Channel . . . . . . . . . . . . . . . . . . . . . . 229
9.3.6 One-Sided Heat Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
9.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

10 Shrinkage and Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
10.1 The Shrinkage Analysis Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
10.1.1 Estimate Process Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
10.1.2 Model Compressibility Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
10.1.3 Assess Volumetric Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
10.1.4 Evaluate Isotropic Linear Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
10.1.5 Evaluate Anisotropic Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
10.1.6 Assess Shrinkage Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
10.1.7 Establishing Final Shrinkage Recommendations . . . . . . . . . . . . . . . . . . 245
10.2 Shrinkage Analysis and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
10.2.1 Numerical Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
10.2.2 “Steel Safe” Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
10.2.3 Processing Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

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10.2.4 Semi-Crystalline Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
10.2.5 Effect of Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
10.3 Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
10.3.1 Sources of Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
10.3.2 Warpage Avoidance Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
10.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
11 Ejection System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
11.1 Objectives in Ejection System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
11.1.1 Allow Mold to Open . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
11.1.2 Transmit Ejection Forces to Moldings. . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
11.1.3 Minimize Distortion of Moldings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
11.1.4 Actuate Quickly and Reliably . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
11.1.5 Minimize Cooling Interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
11.1.6 Minimize Impact on Part Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
11.1.7 Minimize Complexity and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
11.2 The Ejector System Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
11.2.1 Identify Mold Parting Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
11.2.2 Estimate Ejection Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
11.2.3 Determine Ejector Push Area and Perimeter . . . . . . . . . . . . . . . . . . . . . . 269
11.2.4 Specify Type, Number, and Size of Ejectors . . . . . . . . . . . . . . . . . . . . . . . 271
11.2.5 Layout Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
11.2.6 Detail Ejectors and Related Components . . . . . . . . . . . . . . . . . . . . . . . . . 276
11.3 Ejector System Analyses and Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
11.3.1 Ejector Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
11.3.2 Ejector Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
11.3.3 Ejector Sleeves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
11.3.4 Stripper Plates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
11.3.5 Elastic Deformation around Undercuts . . . . . . . . . . . . . . . . . . . . . . . . . . 285
11.3.6 Core Pulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
11.3.7 Slides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
11.3.8 Early Ejector Return Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
11.3.9 Advanced Ejection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
11.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
12 Structural System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
12.1 Objectives in Structural System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
12.1.1 Minimize Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
12.1.2 Minimize Mold Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
12.1.3 Minimize Mold Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
12.2 Analysis and Design of Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
12.2.1 Plate Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
12.2.2 Plate Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
12.2.3 Support Pillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

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XIII

12.2.4 Shear Stress in Side Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
12.2.5 Interlocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
12.2.6 Stress Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
12.3 Analysis and Design of Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
12.3.1 Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
12.3.2 Compressive Hoop Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
12.3.3 Core Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
12.4 Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
12.4.1 Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
12.4.2 Socket Head Cap Screws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
12.4.3 Dowels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
12.5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340
13 Mold Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
13.2 Coinjection Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
13.2.1 Coinjection Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
13.2.2 Coinjection Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
13.2.3 Gas Assist/Water Assist Molding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
13.3 Insert Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
13.3.1 Low Pressure Compression Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
13.3.2 Insert Mold with Wall Temperature Control . . . . . . . . . . . . . . . . . . . . . . 351
13.3.3 Lost Core Molding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
13.4 Injection Blow Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.4.1 Injection Blow Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.4.2 Multilayer Injection Blow Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
13.5 Multi-Shot Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
13.5.1 Overmolding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
13.5.2 Core-Back Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
13.5.3 Multi-Station Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
13.6 Feed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
13.6.1 Insulated Runner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
13.6.2 Stack Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
13.6.3 Branched Runners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
13.6.4 Dynamic Melt Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
13.7 Mold Wall Temperature Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
13.7.1 Pulsed Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
13.7.2 Conduction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
13.7.3 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
13.7.4 Managed Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
13.8 In-Mold Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
13.8.1 Statically Charged Film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
13.8.2 Indexed Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
13.9 Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

XIV

Contents

13.9.1 Split Cavity Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
13.9.2 Collapsible Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
13.9.3 Rotating Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
13.9.4 Reverse Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
13.10 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Appendix A: Plastic Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
Appendix B: Mold Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
B.1
Non-Ferrous Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
B.2
Common Mold Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
B.3
Other Mold Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
B.4
Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
Appendix C: Properties of Coolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
Appendix D: Statistical Labor Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
D.1
United States Labor Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
D.2
International Labor Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
D.3
Trends in International Manufacturing Costs . . . . . . . . . . . . . . . . . . . . . 401
Appendix E: Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
E.1
Length Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
E.2
Mass/Force Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
E.3
Pressure Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
E.4
Flow Rate Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
E.5
Viscosity Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
E.6
Energy Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
Appendix F: Advanced Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

Nomenclature
Mold engineering requires analysis, and so an extensive nomenclature has been developed.
L, W, and H refer to the length, width, and height dimensions as shown in Figure 1.

Figure 1:

Length, width, and height nomenclature

Variable names have been selected and consistently used as expected (e.g., T for temperature,
C for cost, P for pressure, etc.). R refers to rate-related constants (with time dependence)
and κ refers to monetary constants (with cost dependence). To provide clarity, subscripts are
unabbreviated throughout most of the book. The nomenclature for many of the variables
and their units are as follows.
Table 1: Nomenclature

Variable

Meaning

α

Thermal diffusivity [m2/s]

β

Compressibility [1/MPa]

δ

Deflection [m]

δbending

Deflection due to bending [m]

δcompression

Deflection due to compression [m]

δtotal

Deflection due to bending and compression [m]

ε

Strain [m/m]

XVI

Nomenclature

Variable

Meaning

εplastic

Plastic’s strain to failure [%]

γ

Shear rate [1/s]

γ max

Maximum allowable shear rate for a plastic melt being molded [1/s]

η

Viscosity [Pa s]

κ

Thermal conductivity [W/m°C]

κinsert

Cost per unit volume of core and cavity insert materials [$/m3]

κmold

Cost of mold metal per kilogram [$/kg]

κplastic

Cost of plastic per kilogram [$/kg]

λ

Tolerance limit [m]

μ

Apparent viscosity for Newtonian model [Pa]

μstatic

Coefficient of static friction [–]

ρ

Density [kg/m3]

ρinsert

Density of core and cavity insert materials [kg/m3]

ρplastic

Density of plastic [kg/m3]

φ

Draft angle [°]

θ

Draft angle [°]

σbuckling

Stress level at which column buckles [MPa]

σcyclic

Imposed cyclic stress [MPa]

σendurance

Maximum allowable stress given cyclic loading [MPa]

σhoop

Hoop stress [MPa]

σlimit

Maximum allowable stress given cyclic loading or yielding [MPa]

σyield

Maximum allowable stress given yield failure [MPa]

τ

Shear stress [Pa]

ν

Specific volume [–]

Ωejectors

Total perimeter of all ejectors [m]

Acavity_Projected

Projected area of the mold cavity [m2]

Acompression

Area exposed to compressive stress [m2]

Aeff

Effective area under stress [m2]

Aejectors

Total area of all ejectors [m2]

Apart

Total surface area of the molded part

Ashear

Area exposed to shear stress [m2]

C

Tolerance coefficient for a standard fit [m2/3]

Cauxiliaries

Total cost of all auxiliaries [$]

Nomenclature

Variable

Meaning

Cinserts

Total cost of all cavities [$]

Cinsert_finishing

Cost of finishing one set of core and cavity inserts [$]

Cinsert_machining

Cost of machining one set of core and cavity inserts [$]

Cinsert_materials

Cost of materials for one set of core and cavity inserts [$]

Cmold

Total cost of purchasing mold [$]

Cmold/part

Cost of purchasing mold amortized across total production quantity [$]

Cmold_base

Total cost of mold base and modifications [$]

XVII

Cmold_customization Total cost of all customizations of mold base [$]
Cmold_steel

Initial purchase cost of mold base or steel [$]

Cpart

Total cost per molded part [$]

Cplastic/part

Cost of material used in molding one part [$]

Cprocess/part

Cost of machinery and labor used to mold one part [$]

CPplastic

Plastic’s specific heat [J/kg °C]

CTE

Coefficient of thermal expansion [1/°C]

CVTE

Coefficient of volumetric thermal expansion [1/°C]

D

Diameter [m]

Dhydraulic

Hydraulic diameter of runner segment [m]

Dpin

Diameter of ejector pin [m]

E

Elastic modulus [GPa]

f

Factory of safety [–]

fcavity_complexity

Factor related to the complexity of the cavity

fcavity_discount

Discount factor related to production of multiple sets of core and cavity inserts

fcycle_efficiency

Factor associated with the efficiency of operating the molding machine

fefficiency

Factor related to the overall efficiency of all machining operations

ffeed_waste

Factor associated with material wasted in molding the feed system

f
f
f

i
cavity_customizing
i
finishing
i
mold_customizing

Factor associated with customization of one set of core and cavity inserts
Percentage of the molded part’s surface area to be finished in the manner i
Factor associated with customizing mold base

fmachine

Factor associated with cost of operating different molding machines and
auxiliaries

fmachining

Factor related to the average material removal rate of all machining processes
relative to standard milling

fmaintenance

Mold lifetime maintenance factor

fwear

Factor associated with maintenance due to mold wear

XVIII

Nomenclature

Variable

Meaning

fyield

Fraction of molded parts that are good

F

Force [N]

Fbuckling

Critical load at which column buckles [N]

Fclamp

Mold force tonnage [metric tons, t]

Feject

Ejection force [N]

Finsertion

Insertion force for interference fit [N]

Ftensile

Maximum tensile force for a socket head cap screw [N]

h

Nominal cavity wall thickness [m]

h∞

Heat transfer coefficient [W/°C]

Hcavity

Height of cavity inserts [m]

Hcore

Height of core inserts [m]

Hinserts

Combined height of core and cavity inserts [m]

HLine

Distance from cavity surface to the center of cooling line [m]

Hmold

Total stack height of mold [m]

Hpart

Maximum height of molded part [m]

I

Moment of inertia [m4]

K

Stress concentration factor [–]

k, n

Reference viscosity and power law index per the power law model [Pan, –]

kplastic

Plastic’s thermal conductivity [W/m °C]

Linserts

Length of core and cavity inserts [m]

Lmold

Length of mold [m]

Lpart

Maximum length of molded part [m]

MFI

Plastic’s melt flow index [g/min]

Mmold

Total mass of mold base [kg]

ncycles

Number of molding cycles [–]

n, τ*, D1, D2, D3, WLF model coefficients
A1, A3
ncavities

Number of cavities in mold [–]

ncavities_length

Number of cavities in the length direction [–]

ncavities_width

Number of cavities in the width direction [–]

ncycles

Total number of mold cycles that a mold is operated [–]

nj

Number of j-th portions of mold cavity in mold [–]

nlines

Number of cooling lines [–]

Nomenclature

Variable

Meaning

nparts

Total production quantity of parts to be molded [–]

P

Pressure [Pa]

Pinject

Pressure required to fill the cavity [Pa]

Qmolding

Total thermal energy of moldings [J]

Q line
Q

molding

XIX

Cooling power per cooling line [W]
Cooling power [W]

rv

Relative change in the specific volume [–]

R

Radius [m]

Re

Reynold’s number [–]

Rfinishing_cost

Hourly cost of finishing [$/h]

Rifinishing

Rate of finishing the part’s surface in the manner i [m2/h]

Rmachining_cost

Hourly rate of machining [$/h]

Rmachining_area

Rate of machining per unit area [m2/h]

Rmachining_volume

Rate of machining per unit volume [m3/h]

Rmolding_cost

Hourly cost of operating molding machine and operator if required [$/h]

RW

Radius of curvature due to warpage [m]

s

Linear shrinkage rate [m/m]

s⊥

Shrinkage rate perpendicular to flow [m/m]

s//

Shrinkage rate parallel to flow [m/m]

save

Average shrinkage rate [m/m]

tc

Cooling time [s]

tcycle

Cycle time of molding machine [s]

tinsert_area

Time required to machine the cavity surface area for one set of core and cavity
inserts [h]

tinsert_finishing

Time required to completely finish one set of core and cavity inserts [h]

tinsert_machining

Time required to perform all machining for one set of core and cavity inserts [h]

tinsert_volume

Time required to machine the cavity volume for one set of core and cavity inserts
[h]

tp

Packing time before gate solidification [s]

tresidence

Residence time of the polymer melt [s]

Tc

Mold coolant temperature [°C]

Te

Plastic’s ejection temperature [°C]

Tg

Plastic’s glass transition temperature [°C]

XX

Nomenclature

Variable

Meaning

THDT

Plastic’s heat deflection temperature [°C]

Tmelt

Melt temperature [°C]

Twall

Mold wall temperature [°C]

v

Linear melt velocity [m/s]

Vinserts

Combined volume of one set of core and cavity inserts [m3]

Vj

Volume of the j-th portion of mold cavity [m3]

Vpart

Volume of molded part [m3]

V

Volumetric flow rate [m3/s]

Wcavity

Width of core and cavity inserts [m]

Wcheek

Distance from cavity side wall to side of mold [m]

Wmold

Width of mold [m]

Wpart

Maximum width of molded part [m]

Wpitch

Distance between parallel cooling lines [m]

1

Introduction

Injection molding is a fantastic process, capable of economically making extremely complex
parts to tight tolerances. Before any parts can be molded, however, a suitable injection mold
must be designed, manufactured, and commissioned. The injection mold is itself a very
complex system comprised of multiple components that are subjected to many cycles of
temperatures and stresses.
Engineers should design injection molds that are “fit for purpose”, which means that the mold
should produce parts of maximal quality at minimal cost while taking a minimum amount of
time and money to develop. Accordingly, this chapter proceeds as follows. First, an overview
of the injection molding process is provided so that the mold design engineer can estimate
the operating conditions of the mold during mold design. Next, the layout and components
in a few of the mold common mold designs are presented; this book assumes that the mold
design engineer is familiar with both injection molding and the structure and basic function
of these molds. Finally, the mold engineering design methodology is discussed.

1.1

Overview of the Injection Molding Process

An operating injection molding machine is depicted in Figure 1.1. Injection molding is called
a net shape manufacturing process because it forces the polymer melt into an evacuated mold
cavity, after which it cools to the final desired shape.
While molding processes can differ substantially in design and operation, most injection
molding processes generally include plastication, injection, packing, cooling, and mold
resetting stages. During the plastication stage, the polymer melt is plasticized from solid
granules or pellets through the combined affect of heat conduction from the heated barrel
and the internal viscous heating caused by molecular deformation with the rotation of an
internal screw. During the filling stage, the polymer melt is forced from the barrel of the
molding machine and into the mold. The molten resin travels down a feed system, through
one or more gates, and throughout one or more mold cavities where it will form one or more
desired products.
After the mold cavity is filled with the polymer melt, the packing stage provides additional
material into the mold cavity as the molten plastic melt cools and contracts. The plastic’s
volumetric shrinkage varies with the material properties and application requirements, but
the molding machine typically forces 1 to 10% additional melt into the mold cavity during
the packing stage. After the polymer melt ceases to flow, the cooling stage provides additional
time for the resin in the cavity to solidify and become sufficiently rigid for ejection. Then, the
molding machine actuates the necessary cores, slides, and pins to open the mold and remove
the molded part(s) during the mold resetting stage.

2

1 Introduction

Figure 1.1: Depiction of the injection molding process

Filling
Packing
Cooling
Plastication
Mold opening
Part ejection
Mold closing
0

10
Time (s)

20

30

Figure 1.2: Injection molding process timings

A chart plotting the approximate duration of the molding process is shown in Figure 1.2 for
a molded part approximately 2 mm thick. The filling time is a small part of the cycle and so is
often optimized to minimize the injection pressure and molded-in stresses. The packing time
is of moderate duration, and is often minimized through shot weight stability studies to end
with freeze-off of the polymer melt in the gate. In general, the cooling stage of the molding
process dominates the cycle time since the rate of heat flow from the polymer melt to the
colder mold steel is limited by the low thermal diffusivity of the plastic melt. However, the

1.2 Mold Functions

3

plastication time may exceed the cooling time for very large shot volumes with low plastication
rates. Mold reset time is also very important to minimize since it provides negligible added
value to the molded product. To minimize the molding cycle time and costs, molders strive
to operate fully automatic processes with minimum mold opening and ejector strokes.
Variants of the molding process (such as gas assist molding, water assist molding, insert
molding, two shot molding, coinjection molding, injection compression molding, and others
discussed in Chapter 13) are used to provide significant product differentiation with respect to
part properties, but may increase risk and limit the number of qualified suppliers. In any case,
the molding processes are generally similar in that each includes the injection, cooling, and
ejection of the plastic part. The cost estimation and mold design of these different processes
is also very similar; significant differences in the mold design and molding processes will be
later discussed.

1.2

Mold Functions

The injection mold is a complex system that must simultaneously meet many demands
imposed by the injection molding process. The primary function of the mold is to contain
the polymer melt within the mold cavity so that the mold cavity can be completely filled to
form a plastic component whose shape replicates the mold cavity. A second primary function
of the mold is to efficiently transfer heat from the hot polymer melt to the cooler mold steel,
such that injection molded products may be produced as uniformly and economically as
possible. A third primary function of the mold is to eject the part from the mold in a rapid
but repeatable manner, so that subsequent moldings may be produced efficiently.
These three primary functions – contain the melt, transfer the heat, and eject the molded
part(s) – also place secondary requirements on the injection mold. Figure 1.3 provides a partial
hierarchy of the functions of an injection mold. For example, the function of containing the
melt within the mold requires that



the mold resist the enormous forces that will tend to cause the mold to open or deflect,
and
the mold contain a feed system connecting the nozzle of the molding machine to one or
more cavities in the mold for the transfer of the polymer melt.

These secondary functions may also give rise to tertiary functions that are fulfilled with the
use of specific mold components or features.
It should be understood that Figure 1.3 does not provide a comprehensive list of all functions
of an injection mold, but just some of the essential primary and secondary functions that
must be considered during the engineering design of injection molds. Even so, a skilled
designer might recognize that conflicting requirements are placed on the mold design by
various functions. For instance, the desire for efficient cooling may be satisfied by the use of

4

1 Introduction

Injection Mold

Contain melt

Resist displacement

Transfer heat

Lead heat from part

Eject part(s)

Open mold

Large support pillars

Many cooling lines

Parting plane

Thick plates

Tight pitch & depth

Core pulls

Multiple interlocks

Conductive inserts

Guide melt

Lead heat from mold

Remove part(s)
Slides & lifters

Feed system

High coolant flow rate

Ejector pins

Flow leaders

Large diameter lines

Robotic assist

Figure 1.3: Function hierarchy for injection molds

multiple, tightly spaced cooling lines that conform to the mold cavity. However, the need for
part removal may require the use of multiple ejector pins at locations that conflict with the
desired cooling line placement. It is up to the mold designer to consider the relative importance
of the conflicting requirements, and ultimately deliver a mold design that is satisfactory. The
tendency among novice designers, when in doubt, is to over design. This tendency should be
avoided since it tends to lead to large, costly, and inefficient molds.

1.3

Mold Structures

An injection mold has many structures to accomplish the functions required by the injection
molding process. Since there are many different types of molds, the structure of a simple
two plate mold is first discussed. It is important for the mold designer to know the names
and functions of the mold components since later chapters will assume this knowledge.
The design of these components and more complex molds will be analyzed and designed in
subsequent chapters.

1.3.1

External View of Mold

An isometric view of a two plate mold is provided in Figure 1.4. From this view, it is observed
that a mold is constructed of a number of plates, bolted together with socket head cap screws.

1.3 Mold Structures

5

Figure 1.4: View of a closed two-plate mold

These plates commonly include the top clamp plate, the cavity insert retainer plate or “A”
plate, the core insert retainer plate or “B” plate, a support plate, and a rear clamp plate or
ejector housing. Some mold components are referred to with multiple names. For instance,
the “A” plate is sometimes referred to as the cavity insert retainer plate since this plate retains
the cavity inserts. As another example, the ejector housing is sometimes referred to as the
rear clamp plate since it clamps to the moving platen located towards the rear of the molding
machine.
This type of mold is called a “two plate” mold since it uses only two plates to contain the
polymer melt. Mold designs may vary significantly while performing the same functions. For
example, some mold designs integrate the “B” plate and the support plate into one extra thick
plate. As another example, some mold designs may split up the ejector housing, which has
a “U” shaped profile to house the ejection mechanism and clamping slots, into a rear clamp
plate and tall rails (also known as risers). The use of an integrated ejector housing as shown
in Figure 1.4 provides for a compact mold design, while the use of separate rear clamp plate
and rails provides for greater design flexibility.
To hold the mold in the injection molding machine, toe clamps are inserted in slots milled
in the top and rear clamp plates and bolted to the stationary and moving platens of the

6

1 Introduction

molding machine. A locating ring, usually found at the center of the mold, closely mates with
an opening in the molding machine’s stationary platen to fully orient the mold. The use of
the locating ring is necessary for at least two reasons. First, the inlet of the melt to the mold
(at the sprue bushing) must mate with the outlet of the melt from the nozzle of the molding
machine. Second, the ejector knockout bar(s) actuated from behind the moving platen of the
molding machine must mate with the ejector system of the mold. Molding machine and mold
suppliers have developed standard locating ring specifications to facilitate mold to machine
compatibility, with the most common locating ring diameter being 100 mm (4 in).
When the molding machine’s moving platen is actuated, all plates attached to the rear clamp
plates will be similarly actuated and cause the mold to separate at the parting plane. When
the mold is closed, guide pins and bushings are used to closely locate the “A” and the “B”
plates on separate sides of the parting plane, which is crucial to the primary mold function
of containing the melt. Improper construction of the mold components may cause improper
alignment of the “A” and “B” plates, poor quality of the molded parts, and accelerated wear
of the injection mold.

1.3.2

View of Mold during Part Ejection

Another isometric view of the mold is shown in Figure 1.5, oriented from left to right for
operation in a horizontal injection molding machine. The plastic melt has been injected and
cooled in the mold, such that the moldings are now ready for ejection. To perform ejection, the
mold is opened by at least the height of the moldings. Then, the ejector plate and associated
pins are moved forward to push the moldings off the core. From this view, many of the mold
components are observed including the “B” or core insert retainer plate, two different core
inserts, feed system, ejector pins, and the guide pins and bushings.
This mold is called a two plate, two cavity family mold. The term“family mold”refers to a mold
in which multiple components, either in an assembly a mold in which multiple components
of varying shapes and/or sizes are produced at the same time. The term “two cavity” refers
to the fact that the mold has two cavities to produce two moldings in each molding cycle.
Such multi-cavity molds are used to rapidly and economically produce high quantities of
molded products. Molds with eight or more cavities are common. The number of mold
cavities is a critical design decision that impacts the technology, cost, size, and complexity
of the mold; a cost estimation method will be provided in Chapter 3 to provide a guideline
for mold design.
In a multi-cavity mold, the cavities are placed across the parting plane to provide room
between the mold cavities for the feed system, cooling lines, and other components. It is
generally desired to place the mold cavities as close together as possible while not sacrificing
other functions such as cooling, ejection, etc. This usually results in a smaller mold that is
not only less expensive, but is also easier for the molder and can be used in more molding
machines. The number of mold cavities in a mold can be significantly increased by not only
using a larger mold, but also by using different types of molds such as a hot runner mold,
three plate mold, or stack mold as later discussed.

1.3 Mold Structures

7

Figure 1.5: View of molding ejected from injection mold

1.3.3

Mold Section and Function

Figure 1.6 shows the top view of the mold, along with the view that would result if the mold
was physically cut along the section line A-A and viewed in the direction of the arrows.Various
hatch patterns have been applied to different components to facilitate identification of the
components. It is very important to understand these components and how they interact
with each other and the molding process.
Consider now the stages of the molding process relative to the mold components. During
the filling stage, the polymer melt flows from the nozzle of the molding machine through the
orifice of the sprue bushing. The melt flows down the length of the sprue bushing and into
the runners located on the parting plane. The flow then traverses across the parting plane and
enters the mold cavities through small gates. The melt flow continues until all mold cavities
are completely filled.
After the polymer melt flows to the end of the cavity, additional material is packed into the
cavity at high pressure to compensate for volumetric shrinkage. The mold plates and support
pillars must be designed to resist deflection when subjected to high melt pressures. The
duration of the packing phase is controlled by the size and freeze-off of the gate between the
runner and the cavity. During the packing and cooling stages, heat from the hot polymer melt

8

1 Introduction

Figure 1.6: Top and cross section views of a two-plate mold

1.4 Other Common Mold Types

9

is transferred to the coolant circulating in the cooling lines. The heat transfer properties of
the mold components, together with the size and placement of the cooling lines, determines
the rate of heat transfer and the cooling time required to solidify the plastic.
After the part has cooled, the molding machine’s moving platen is actuated and the moving
half of the mold (consisting of the “B” plate, the core inserts the support plate, the ejector
housing, and related components) moves away from the stationary half (consisting of the top
clamp plate, the “A” plate, the cavity inserts, and other components). Typically, the moldings
stay with the moving half since they have shrunken onto the core.
After the mold opens, the ejector plate is pushed forward by the molding machine. The ejector
pins are driven forward and push the moldings off the core. The moldings may then drop out
of the mold or be picked up by an operator or robot. Afterwards, the ejector plate is retracted
and the mold closes to receive the melt during the next molding cycle.

1.4

Other Common Mold Types

A simple two-plate mold has been used to introduce the basic components and functions of
an injection mold. About half of all molds closely follow this design, since the mold is simple
to design and economical to produce. However, the two-plate mold has many limitations,
including:







restriction of the feed system route to the parting plane;
limited gating options from the feed system into the mold cavity or cavities;
restriction on the tight spacing of cavities;
additional forces imposed on the mold by the melt flowing through the feed system;
increased material waste incurred by the solidification of the melt in the feed system;
and
increased cycle time related to the plastication and cooling of the melt in the feed
system.

For these reasons, molding applications requiring high production quantities often do not
use two-plate mold designs, but may instead utilize mold designs that are more complex yet
provide for lower cost production of the molded components. Such designs include three
plate molds, hot runner molds, stack molds, and others. Three plate molds and hot runner
molds are the next most common types of injection molds, and so are next introduced.

1.4.1

Three Plate, Multi-Cavity Family Mold

The three plate mold is so named since it provides a third plate that floats between the mold
cavities and the top clamp plate.

10

1 Introduction

Figure 1.7: Section of an open three plate mold

Figure 1.7 shows a section of a three plate mold that is fully open with the moldings still on
the core inserts. As shown in Figure 1.7, the addition of the third plate provides a second
parting plane between the “A” plate assembly and the top clamp plate for the provision of a
feed system. During molding, the plastic melt flows out the nozzle of the molding machine,
down the sprue bushing, across the primaries, down the sprues, and into the mold cavities.
The feed system then freezes in place with the moldings.
When the mold is opened, the molded cold runner will stay on the stripper plate due to the
inclusion of sprue pullers that protrude into the primary runner. As the mold continues to
open, the stripper bolt connected to the “B” plate assembly will pull the “A” plate assembly
away from the top clamp plate. Another set of stripper bolts will then pull the stripper plate
away from the top clamp plate, stripping the molded cold runner off the sprue pullers. The
stripper plate may then be actuated to force the moldings off the core.
The three plate mold eliminates two significant limitations of the two plate molds. First, the
three plate mold allows for primary and secondary runners to be located in a plane above
the mold cavities so that the plastic melt in the cavities can be gated at any location. Such
gating flexibility is vital to improving the cost and quality of the moldings. Second, the three
plate mold provides for the automatic separation of the feed system from the mold cavities.
Automatic degating facilitates the operation the molding machine with a fully automatic
molding cycle to reduce the cycle times.

1.4 Other Common Mold Types

11

There are at least three significant potential issues with three plate molds, however. First and
most significantly, the cold runner is molded and ejected with each molding cycle. If the
cold runner is large compared to the molded parts, then the molding of the cold runner may
increase the material consumption and cycle time, thereby increasing the molded part cost.
Second, the three plate mold requires additional plates and components for the formation
and ejection of the cold runner, which increases the cost of the mold. Third, a large mold
opening stroke is needed to eject the cold runner. The large mold opening height (from the
top of the top clamp plate to the back of the rear clamp) may be problematic and require
a molding machine with larger “daylight” between the machine platens than required for a
two plate or hot runner mold.

1.4.2

Hot Runner, Multi-Gated, Single Cavity Mold

Hot runner molds provide the benefits of three plate molds without their disadvantages,
yet give rise to other issues. The term “hot runner” is used since the feed system remains
in a molten state throughout the entire molding cycle. As a result, the hot runner does not
consume any material or cycle time associated with conveying the melt from the molding
machine to the mold cavities.
A section of a multi-gated, single cavity mold is provided in Figure 1.8. This mold contains a
single cavity, which is designed to produce the front housing or “bezel” for a laptop computer.
The hot runner system includes a hot sprue bushing, a hot manifold, two hot runner nozzles
as well as heaters, cabling, and other components related for heating. The hot runner system
is carefully designed to minimize the heat transfer between the hot runner system and the
surrounding mold through the use of air gaps and minimal contact area. Like the three plate
mold design, the primary and secondary runners are routed in the manifold above the mold
cavities to achieve flexibility in gating locations. Since the polymer melt stays molten, hot
runners can be designed to provide larger flow bores and excellent pressure transmission
from the molding machine to the mold cavities. As such, hot runner system can facilitate the
molding of thinner parts with faster cycle times than either two plate or three plate molds,
while also avoiding the scrap associated with cold runners.
During the molding process, the material injected from the machine nozzle into the hot sprue
bushing pushes the existing material in the hot runner system into the mold cavity. When
the mold cavities fill, the thermal gates are designed to solidify and prevent the leakage of
the hot polymer melt from inside the hot runner system to the outside of the mold when the
mold is opened. The melt pressure developed inside the hot runner system will cause these
thermal gates to rupture at the start of the next molding cycle.
There are many different hot runner and gating designs. While they provide many advantages,
including gating flexibility, improved pressure transmission, reduced material consumption,
and increased molding productivity, there are also two significant disadvantages. First, hot
runner systems require added investment for the provision and control of temperature. The
added investment can be a significant portion of the total mold cost, and not all molders
have the auxiliary equipment or expertise to operate and maintain hot runner molds. The

12

1 Introduction

Figure 1.8: Section of hot runner mold

second disadvantage of hot runner systems is extended change-over times associated with
the purging of the contained plastic melt. In short run production applications having
aesthetic requirements, the number of cycles required to start-up or change resins may be
unacceptable.

1.4.3

Comparison

The type of feed system is a critical decision that is made early in the development of the
mold design. From a mold designer’s perspective, the choice of feed system has a critical role
in the design of the mold, the procurement of materials, and the mold making, assembly, and
testing processes. From the molder’s perspective, the choice of feed system largely determines
the purchase cost, molding productivity, and operating cost of the mold.

1.5 The Mold Development Process

13

Table 1.1: Feed system comparison

Performance measure

Two plate

Three plate

Hot runner

Gating flexibility

Poor

Excellent

Excellent

Material consumption

Good

Poor

Excellent

Cycle times

Good

Poor

Excellent

Initial investment

Excellent

Good

Poor

Start-up times

Excellent

Good

Poor

Maintenance cost

Excellent

Good

Poor

Table 1.1 compares the different types of molds with respect to several performance measures.
In general, hot runner molds are excellent with respect to molding cycle performance, but
poor with respect to initial investment, start-up, and on-going maintenance. By comparison,
two plate molds have lower costs, but provided limited in-cycle performance.
The evaluation of three plate molds in Table 1.1 warrants some further discussion. Specifically,
three plate molds do not provide as high a level of in-cycle performance compared to hot
runner molds, and at the same time have higher costs than two plate molds. For this reason,
there has been a trend away from three plate molds with the penetration of lower cost hot
runner systems.

1.5

The Mold Development Process

Given that there is substantial interplay between the product design, mold design, and the
injection molding process, an iterative mold development process is frequently used as shown
in Figure 1.9. To reduce the product development time, the product design and mold design
are often performed concurrently. In fact, a product designer may receive a reasonable cost
estimate for a preliminary part design given only the part’s overall dimensions, thickness,
material, and production quantity. Given this information, the mold designer develops a
preliminary mold design and provides a preliminary quote as discussed in Chapter 3. This
preliminary quote requires the molder and mold maker to not only develop a rough mold
design but also to estimate important processing variables such as the required clamp tonnage,
machine hourly rate, and cycle times.
Once a quote is accepted, the engineering design of the mold can begin in earnest as indicated
by the listed steps on the right side of Figure 1.9. First, the mold designer will layout the mold
design by specifying the type of mold, the number and position of the mold cavities, and
the size and thickness of the mold. Afterwards, each of the required sub-systems of the mold
is designed, which sometimes requires the redesign of previously designed subsystems. For
example, the placement of ejector(s) may require a redesign of the cooling system.

14

1 Introduction

Initial design

Review part design
and specifications
Develop preliminary
mold design & quote

Layout design

Feed system design

Cooling system design

Ejector system design
No

Project OK?
Structural system design
Machining, polishing,
assembly, & trials

Moldings OK?

No

Close project

Figure 1.9: A mold development process

To reduce the development time, the mold base and other materials may be ordered and
customized as the mold design is being fully detailed. Such concurrent engineering should
not be applied to fuzzy aspects of the design. However, many mold-makers do order the
mold base and plates upon confirmation of the order. As a result of concurrent engineering
practices, mold development times are now typically measured in weeks rather than months
[1]. Customers have traditionally placed a premium on quick mold delivery, and mold-makers
have traditionally charged more for faster service. With competition, however, customers
are increasingly requiring guarantees on mold delivery and quality, with penalties applied to
missed delivery times or poor quality levels.
After the mold is designed, machined, polished, and assembled, molding trials are performed
to verify the basic functionality of the mold. If no significant deficiencies are present, the
moldings are sampled and their quality assessed relative to specifications. Usually, the mold
and molding process are sound but must be tweaked to improve the product quality and
reduce the product cost. However, sometimes molds include “fatal flaws” that are not easily
correctable and may necessitate the scrapping of the mold and a complete redesign.

1.6 Chapter Review

1.6

15

Chapter Review

After reading this chapter, you should understand:
• The basic stages of the injection molding process,
• The primary functions of an injection mold,
• The most common types of injection molds
(two plate, three plate, hot runner, single cavity, multi-cavity, and multi-gated mold),
• The key components in an injection mold, and
• The mold development process.
In the next chapter, the typical requirements of a molded part are described along with
guidelines for design. Afterwards, the mold layout design and detailed design of the various
systems of a mold are presented.

2

Plastic Part Design

2.1

The Product Development Process

Mold design is one significant activity in a much larger product development process. Since
product and mold design are inter-dependent, it is useful for both product and mold design
engineers to understand the plastic part development process and the role of mold design
and mold making. A typical product development process is presented in Figure 2.1, which
includes different stages for product definition, product design, business and production
development, ramp-up, and launch.

Team assembled

Mold quoting

Concept development

Mold design

Budgeting

Approval?
Design for assembly

Fits & tolerances

Mold making

Sales forecasting

Detailed design,
performance analyses,
rapid prototyping, &
preliminary testing

Design for manufacturing

Geometry & material

Approval?

Business development

Tooling fabrication

Alpha test

Production planning

Quality & training plans

Approval?

Pilot production

Launch

Scale-up

Development

Product design

Product definition

Market analysis

Figure 2.1: A product development process

Beta install & test

Approval?
Production release

18

2 Plastic Part Design

While there are many product development processes, most share two critical attributes:
• a structured development plan to ensure tracking and completeness of the design and
manufacturing, and
• a toll-gate process to mitigate risk by allocating larger budgets only after significant reviews
at project milestones.
The product development process shown in Figure 2.1 is split into multiple stages separated
by approval toll-gates. An overview of each stage is next provided.

2.1.1

Product Definition

The product development process frequently begins with an analysis of the market, benchmarking of competitors, definition of the product specifications, and assessment of potential
profitability. If management agrees that a new product is to be developed, then an appropriate
team is assembled to perform the early concept design and business development. During this
first stage, the approximate size, properties, and cost of the product are estimated. Sketches,
mock-ups, and prototypes may be produced to communicate and assess the viability of the
concept.
With respect to profitability, market studies during the early product development stage
will strive to predict the potential sales at varying price points. At the same time, manpower
and project cost estimates will establish the budget required to develop and bring the
product to market. A management review of the concept design, sales forecast, and budget
is usually performed to assess the likelihood of the commercial success of continued product
development. At this time, the proposed product development project may be declined,
shelved, or modified accordingly.

2.1.2

Product Design

If the project is approved and a budget is allocated, then the product development process
continues, usually with additional resources to perform further analysis and design. During
this second stage, each component in the product is designed in detail. The design of plastic
components may include the consideration of aesthetic, structural, thermal, manufacturing,
and other issues. Design for manufacturing methods may be used to identify issues that would
inhibit the effective manufacturing of the components. Design for assembly methods may
be used to reduce the number of components, specify tolerances on critical dimensions, and
ensure the economic assembly of the finished product.
The outcome of the initial product design stage (through the second management approval
in Figure 2.1) is a detailed and validated product design. The term “detailed design” implies
that every component is fully specified with respect to material, geometric form, surface
finish, tolerances, supplier, and cost. If a custom plastic component is required, then quotes
for these molded parts are often requested during this stage. These costs are presented to

2.1 The Product Development Process

19

management along with the detailed design for approval. If the product design and costs are
acceptable, then the required budget is allocated and the product development now focuses
on manufacturing.

2.1.3

Business and Production Development

While mold design and mold making are a focus of those in the plastics industry, all these
activities are encompassed by the single activity titled “Tooling Fabrication” in Figure 2.1. At
the same time, important business development and production planning is being performed.
Specifically, business development is required to fully define the supply chain and establish
initial orders to support the product launch. Production planning is required to layout assembly lines, define manpower requirements, and develop the manufacturing infrastructure.
When the mold tooling is completed, “alpha” parts are produced, tested, and assembled. The
resulting alpha product undergoes a battery of tests to verify performance levels, regulatory
compliance, and user satisfaction. If the assembled alpha product is not satisfactory, then the
manufacturing processes, associated tooling, and detailed component designs are adjusted
as appropriate. Concurrently, the operations staff develops detailed plans governing quality
control and worker training.

2.1.4

Scale-Up and Launch

A management review is often used to verify that the developed product designs and production plans are satisfactory. If so, a pilot production run may be used to manufacture a moderate
quantity of products according to the standard manufacturing conditions. The manufactured
“beta” products are frequently provided to the marketing department, sales force, and key
customers to ensure product acceptability. As before, the design and manufacturing of the
product may be revised to address significant issues. When all stakeholders (marketing, sales,
manufacturing, critical suppliers, and critical customers) are ready, the pilot production
processes are ramped up to build an initial inventory of the product after which the product
is released for sale.

2.1.5

Role of Mold Design

Mold quoting, mold design, and mold making support the larger product development
process. Requests for mold and/or part cost quotes are usually made towards the end of the
concept design stage or near the beginning of the detailed design stage. It is somewhat unusual
for the molder or the mold-maker to be given fully detailed designs at this time, since 1) much
of the mold design could have been performed concurrently with a less developed product
design, and 2) the mold engineering process may suggest significant changes in the design
related to manufacturability or part performance.

20

2 Plastic Part Design

The mold development process (first introduced in Figure 1.9) often begins with a preliminary
design that is lacking in detail and would result in an unsatisfactory product if used directly.
The critical part design information required to begin a mold design includes just the part
size, wall thickness, and expected production quantity. Given just this information, the mold
designer can develop initial mold layouts, cost estimates, and product design improvements.
To accelerate the product development process, mold design can be performed concurrently
with the procurement and customization of the mold components.
For better or for worse, mold making and commissioning occurs near the end of the product
development process. For this reason, there can be significant pressure on mold suppliers
and molders to provide high quality moldings as soon as possible. This task can be extremely
challenging given potential mistakes made earlier in the product design process. As such, mold
designers may be required to redesign and change portions of the mold and work closely with
molders to qualify the mold for production.

2.2

Design Requirements

There are many requirements of an injection molded part which need to be considered during
the mold design. The following sections provide some useful tables to gather the required
information, along with some relevant discussion.
The information in this section is largely motivated for two reasons. First, detailed and
available documentation will improve the design and reduce the cost of the mold engineering.
Second, ISO and other regulatory agencies often require formal documentation and approval
of product development. Accordingly, the mold design engineer should not consider these
worksheets as static pages, but rather as living documents that are linked to design decisions
and decision making processes with routing from and to the right people for information
and approval.

2.2.1

Application Engineering Information

The mold design engineer should understand the overall application and development
schedule as documented in Table 2.1. This information includes the project name and part or
project number which should be referenced on all project documentation. There are several
critical milestones that should be tracked, including the dates for project initiation, machined
cavities, mold testing, and volume production. These dates are frequently negotiated since
they are related to technical feasibility, market success, and also payment terms.
It is also useful to record the contact information for the technical contact at the customer as
indicated in Table 2.2. Ideally, this person should understand the requirements of the molded
part or be able to refer the mold designer to other more knowledgeable people. Alternatively, it
may be preferable for the mold designer to first call an internal sales or applications engineer

2.2 Design Requirements

21

Table 2.1: Application engineering worksheet

Project name:
Part/project number:
Product/assembly name:
Date project initiated:
Date cavities required:
Date mold trial required:
Date volume production required:
Target material cost per part:
Target mold cost per part:
Target processing cost per part:
Target total cost per part:

Table 2.2: Contact information worksheet

Customer name:
Customer technical contact name:
Customer technical contact information:
Internal sales/application engineer name:
Internal sales contact information:

responsible for supporting the customer so as to avoid continuously contacting the customer
regarding what may be considered as potentially trivial issues.

2.2.2

Production Data

The production data requested in Table 2.3 is very important with respect to the selection of the
mold layout and mold technology. In particular, the application lifetime and total production
quantity is related to the selection of the mold materials and treatments as well as the detailed
design of the mold. The minimum and maximum monthly production quantity, together
with the expected cycle time of the molding process, will help to determine the number of
cavities and number of molds required.
It should be noted that the cycle time and other mold design data in Table 2.3 may not be
available at the start of the mold design process. In fact, these data are intermediate results from

22

2 Plastic Part Design

Table 2.3: Production data worksheet

Application lifetime [yr]:
Total lifetime production quantity:
Number of available molding hours per year per machine [h/yr]:
Minimum production rate [moldings/h]:
Maximum production rate [moldings/h]:
Expected cycle time of molding process:
Number of cavities per mold:
Family mold [yes/no] and number of parts:
Number of molds required:

the mold design process. However, some customers will provide these details as specifications
that the mold designer must satisfy. If these items are not specified by the customer, then the
mold designer should perform iterative design with cost analyses to provide the customer
with the most efficient mold designs.

2.2.3

End Use Requirements

A typical molded part may have literally dozens, if not hundreds, of specifications. A few
common end-use requirements are provided in Table 2.4. Some of these requirements drive
the geometry, material selection, and other design details about which the mold design
engineer may seem to have little control. Even so, the mold designer should be generally aware
of how the moldings will be used, as it may effect the design and performance evaluation of
some mold details.
Table 2.4: End-use requirements worksheet

End use temperature:
End use loading:
Allowable deflection:
Required yield stress:
Required strain to failure:
Required impact resistance:
Water absorption:
Chemical resistance:

2.2 Design Requirements

23

Table 2.5: Regulatory compliance worksheet

ANSI (C1461, D1972, D1975, …):
FDA (Class I, II, III, …):
IEC (ICS 20, 83, …):
MIL-SPEC (M25098, N18352, P46060, …):
ISO (9000, 9001, 13 458, …):
UL (94, 696, 746, …):

Manufacturers are generally required to use basic controls to ensure that the product being
designed and manufactured will perform as intended when commercially distributed. In many
segments of the plastics industry, such as medical devices, regulatory agencies have developed
extensive standards governing the design, manufacturing, and testing of plastic products.
A detailed discussion of regulatory compliance is well beyond the scope of this book. However,
the mold designer should be aware of any regulatory compliance issues that may affect the
mold engineering. A few common regulatory agencies and their compliance programs are
provided in Table 2.5. These include the American National Standards Institute (ANSI, http://
www.ansi.org/), the U.S. Food and Drug Administration (FDA, http://www.fda.gov/), the
International Electrotechnical Commission (IEC, www.iec.ch/), U.S. Department of Defense
Index of Specifications and Standards (MIL-SPEC, http://stinet.dtic. mil/), the International
Standards Organization (ISO, http://www.iso. org/), the Underwriters Laboratories (UL,
http://www.ul.com/), and many others.
The mold design engineer does not usually need to know every detail of these specifications
since they generally pertain to the use of the molded product and not specifically to the
injection mold. However, the mold designer should inquire about any governing regulations
that may affect the mold design. Ideally, the customer should provide a copy of any such
regulations and highlight the specific requirements related to the mold design.
The specification of dimensions and tolerances is of critical importance to the mold designer
and injection molder. Tolerance specifications should include a general relative tolerance,
specified as a percentage of the nominal dimension. For instance, a typical tolerance may
be considered as ± 0.4%, such that a 100 mm length would be specified as 100 ± 0.4 mm.
A tight tolerance may be considered as ± 0.1%, such that a 10 mm diameter may be specified
as 10 ± 0.01 mm.
The ability for a molded product to meet a specified tolerance is a function of the mold
design, the molding process, and the material properties. For this reason, product designers
are encouraged to specify a single general tolerance governing most dimensions along with
only a few tighter tolerances on specific dimensions that are critical to product function as
indicated in Table 2.6. Just because a tolerance is specified does not mean that it is achievable.
In fact, it is not uncommon for product designers to over-specify the tolerances on many
dimensions [2]. Mold designers should discuss tight tolerance specifications with the product

24

2 Plastic Part Design

Table 2.6: Dimensional tolerances worksheet

General tolerance (% mm/mm):
Critical tolerance 1:
Critical tolerance 2:
Critical tolerance 3:

Table 2.7: Product aesthetics worksheet

Color (DIN, RAL, Munsell, AFNOR, NCS, Pantone, other):
Color match across assembly?
Gloss level (%):
Surface finish (SPI D-3 to A-1):
Mold surface texture (supplier/number):
Critical aesthetic surfaces:

development team, and communicate that such specifications may require prototype molding
to characterize the shrinkage behavior, non-uniform profiling of shrinkage rates in different
areas of the mold, and mold modifications during mold commissioning.
Product designers will often provide specifications on the aesthetics, including requirements
on color, color matching across multiple components, and gloss levels as listed in Table 2.7.
It is common for the product design to specify the mold surface finish and mold surface
texture, which may add significant cost to the injection mold. Also, the mold design engineer
should be made aware of critical aesthetic surfaces in which aesthetic defects (such as from
knit-lines, gate blemish, sink, witness marks, etc.) should be avoided.

2.2.4

Product Design Methodology

Ideally, the mold design engineer should be involved with the product design from the early
stage of concept design. Such involvement often provides for significantly improved plastic
part designs that are more functional and efficient. Unfortunately, mold designers are often
provided “finished” product designs that are really substandard with respect to design for
injection molding and assembly. Rather than assume that the product design is finished and
unchangeable, the mold designer should check that the part has been specifically designed for
injection molding. Some common guidelines for injection molded part design are provided
in Table 2.8 [3, 4]; these guidelines can significant improve the function and reduce the cost
of the molded product, and so will be discussed in Section 2.3.

2.2 Design Requirements

25

Table 2.8: Design for injection molding worksheet

Uniform/minimum wall thickness:
Sharp corners avoided:
Effective rib design:
Effective boss design:
Draft applied:
Undercuts avoided:
Tolerances achievable:
Gate locations specified:
Flow length required:

Table 2.9: Design for assembly worksheet

Number of parts in assembly minimized:
Top down assembly achieved:
Snap fits designed/avoided:
Uniform fastener type utilized:
Parts symmetric or obvious asymmetric:
Molded part take-out requirements:

Table 2.9 provides some common design for assembly guidelines [5, 6]. The mold designer
should inspect the part design(s) that have been provided and check that the design for
assembly is reasonable. There are two goals for this task. First, it may be possible to improve
the overall design of the product by consolidating multiple components, facilitating topdown assembly, etc. Second, the mold designer can reduce the number of late design
changes that can cost money and time by verifying that such design considerations have
been performed.
Some mold designers may be aware of product design issues, yet choose to directly implement
molds for the provided designs. For instance, a mold designer may understand that the cost
of the mold could be reduced by slightly changing an angle on a surface to eliminate an
undercut but remain silent to justify the need for a core pull and a higher priced mold. While
such a strategy may result in additional work and profit for the mold designer in the short
term, it is a losing long term strategy. Rather, the most successful mold suppliers seek to add
value to their customers by providing services that improve the quality and reduce the cost
of their customers’ products.

26

2 Plastic Part Design

2.2.5

Plastic Material Properties

The plastic material is usually specified by the customer, not the mold-designer. However, the
mold designer needs to know the specific properties of the plastic requested in Table 2.10,
which will govern the function of the mold. Sample data for some generic grades of plastic
are provided in Appendix A. Other sources from which to gather this information include
resin suppliers and database suppliers (such as http://www.ides.com and http://www.matweb.
com).

Table 2.10:

Plastic material properties worksheet1

Material supplier:
Material trade name:
Material type:
Cost ($/kg):
Modulus (MPa):
Yield strength (MPa):
Strain to yield (%):
DTUL (C, 0.45 MPa, ASTM D648):
No flow Temperature (°C):
Melt temperature range (°C):
Coolant temperature range (°C):
Density (kg/m3):
Specific heat (J/kg°C):
Thermal conductivity (W/m°C):
Thermal diffusivity (m2/s):
Thermal expansion coefficient (m/m°C):
Shrinkage range (% m/m):
Maximum shear rate (1/s):
Viscosity and PvT coefficients:

1

Mold engineering is made simpler and more efficient through the consistent use of a unit system and
material properties. The analyses in this book will utilize the International System of units. Appendix E
provides conversions from these units to other common measurement systems.

2.2 Design Requirements

27

The materials used in mold construction are usually specified by the mold-designer, not the
customer. Materials selection will be discussed in Chapter 4; sample data for some commonly
used metals are provided in Appendix B. The mold designer should verify the mold material
properties listed in Table 2.11 with the material supplier, and document the assumed material
properties that govern the mold design.

Table 2.11:

Mold material properties worksheet

Material supplier:
Material trade name:
Material type:
Material composition:
Cost ($/kg):
Density (kg/m3):
Modulus (MPa):
Yield stress (MPa):
Fatigue limit stress (MPa):
Hardness, Brinell:
Strain to yield (%):
Density (kg/m3):
Specific heat (J/kg°C):
Thermal conductivity (W/m°C):
Thermal diffusivity (m2/s):
Recommended cutting speed (fpm, carbide tool):
Recommended feed per tooth (in, 3/4″ diameter):
Feed per tooth (mm):
Cutting speed (m/h):
Volume machining rate (m3/h):
Area machining rate (m2/h):

28

2 Plastic Part Design

2.3

Design for Injection Molding

A detailed review of the plastic part design should be conducted prior to the design and
manufacture of the injection mold. The design review should consider the fundamentals of
plastic part design, as well as other concerns related specifically to mold design. These part
design considerations are next discussed.

2.3.1

Uniform Wall Thickness

Parts of varying wall thickness should be avoided due to reasons related to both cost and
quality. The fundamental issue is that thick and thin wall sections will cool at different rates:
thicker sections will take longer to cool than thinner sections. When ejected, parts with varying
wall thickness will exhibit higher temperatures near the thick sections and lower temperatures
near the thin sections. These temperature differences and the associated differential shrinkage
can result in significant geometric distortion of the part given the high coefficient of thermal
expansion for plastics. Extreme differences in wall thicknesses should be avoided if at all
possible since internal voids may be formed internal to the part due to excessive shrinkage
in the thick sections even with extended packing and cooling times.
Figure 2.2 provides a progression of mold designs with different thicknesses across the part.
The worst part design, shown at left, has the melt flowing from a thin section to a thick
section with a sharp transition. This design may lead to moldings with poor surface finish
due to jetting of the melt from the thin section into the thick section, as well as poor surface
replication and dimensional control in the thick section related to premature solidification of
the plastic molded in the thin section. The design may be improved by reversing the direction
of melt flow, since the thicker section is unlikely to solidify before packing out the thinner
section. The design may be further improved by gradually transitioning the thick section to
the thin section. Even so, any mold design with significant variations in wall thickness will
exhibit extended cooling times and different shrinkage rates in the thick and thin sections.

Figure 2.2: Wall thickness design

2.3 Design for Injection Molding

29

A standard approach is to increase the nominal thickness of the molded part so as to eliminate
the need for thick sections in local areas. The decision to increase the wall thickness will
eliminate many issues related to part quality, but can lead to excessive material consumption
and extended cooling times. For this design, the best design may be to use a thinner wall
thickness together with vertical ribs in areas requiring stiffening. The height and/or density
of the ribs may be altered to change the relative stiffness throughout the part [7].

2.3.2

Rib Design

A typical rib design is shown in Figure 2.3. In this design, the base thickness of the rib is 70%
of the wall thickness of the part and the height of the rib is four times the wall thickness of
the part. The ribs are spaced at ten times the wall thickness of the part. Analysis of this design
indicates that this design has a stiffness equivalent to the part that is 30% thicker but does
not have ribs. However, the 30% thicker part will consume approximately 15% more material
and have a 70% longer cycle time than the thinner part with ribs.

Figure 2.3: Effective rib design

Ribs thicker than 70% of the wall thickness will tend to draw material away from the center
of the opposite wall when the rib cools. The volumetric shrinkage in this region will cause
internal voids or sink to appear on the side of the part opposite the rib. In non-aesthetic
applications that use highly filled materials with lower shrinkage, the rib thickness can be
increased. Otherwise, a rib thickness less than 70% of the nominal thickness should be used
in molding applications with unfilled materials [8].

2.3.3

Boss Design

Bosses are typically used to secure multiple components together with the use of self-threading
screws. Some different boss designs are provided in Figure 2.4. The left-most design provides
a boss near a corner with two ribs and a gusset placed at 120°. The center design shows a
boss on a rib with two gussets at 90°. The right-most design shows a free-standing boss with
gusseted ribs that provide for an elevated assembly surface. All boss designs utilize a boss,
rib, and gusset thickness of 70% times the nominal wall thickness.
Designed bosses must be able to withstand the torque applied during insertion of the selfthreading screws as well as the potential tensile pull-out forces applied during end-use. At the
same time, however, bosses should not be designed with overly thick sections that may require

30

2 Plastic Part Design

Figure 2.4: Effective boss design

extended cycle times or cause aesthetic problems. In the designs of Figure 2.4, no draft was
utilized on the bosses and gussets. These design features are vital to the structural integrity
of the part, yet are relatively small relative to the entire part. As such, using less draft on these
features can aid in increasing the stiffness and strength of the molding without significantly
increasing the ejection forces.

2.3.4

Corner Design

Sharp corners are often specified in product design to maximize the interior volume of
a component, facilitate mating between components, or for aesthetic reasons. However,
sharp corners in molded products should be avoided for many reasons related to product
performance, mold design, and injection molding:





Relative to product performance, sharp corners will result in a stress concentration that
may cause many (and especially brittle) materials to fail under load. Furthermore, a box
with sharp corners and tall sides may not have the torsional stiffness of a rounded box
with shorter sides.
Relative to mold design, sharp corners can be very difficult to produce, requiring the use
of special machining processes or the use of multiple cutting tools of decreasing size.
Relative to the molding process, sharp corners greatly restrict the heat flow from the
polymer melt to the core insert (inside the part) while facilitating heat transfer to the cavity
insert (outside the part). The result is often differential shrinkage across the thickness of
the part near the corner and significant warpage of the molded part.

Some common guidelines for filleting and chamfering corners are provided in Figure 2.5. As
shown, the fillet radius on an external corner should be 150% of the wall thickness. To maintain
the same thickness around the corner, the fillet on the internal corner is set to 50% of the wall
thickness. In most modern, solids-based design programs, these fillets can be readily achieved
by filleting the outside edges prior to shelling of the part. These fillet recommendations are
only guidelines. In fact, even larger fillets should be used if possible. Also, the mold designer
should suggest a fillet radius that corresponds to readily available tooling geometry so that
custom tools need not be custom made.

2.3 Design for Injection Molding

31

Figure 2.5: Comparison of fillets

Figure 2.6: Comparison of chamfers

Chamfers are often used to break sharp corners with a single beveled surface connecting the
outer surfaces, often at a 45 degree angle. As shown in Figure 2.6, a chamfer of one half the
wall thickness is often utilized on the internal corner to provide for adequate relief while
avoiding potential negative issues related to melt flow and part strength. Similar to fillets,
large chamfers may be applied prior to shelling to provide improved part stiffness and heat
transfer near the corners.

2.3.5

Surface Finish and Textures

Surface finish and texture are commonly specified by the part designer, yet have a significant
impact on the mold design and cost. Most mold making companies are capable of providing

32

2 Plastic Part Design

Table 2.12:

SPI Finish

SPI surface finishes and roughness

Finishing method

Microfinish (μm)

Surface roughness (μm)

A-1

#3 diamond polish

~1

~0.01

A-3

#15 diamond polish

~2

~0.04

~6

~0.12

~12

~0.3
~0.8

B-3

#320 grit cloth

C-3

#320 stone

D-2

#240 oxide blast

~30

D-3

#24 oxide blast

~160

~4

high quality surface finishes, though polishing can be outsourced to lower cost companies
and countries due to its high labor content. Surface texturing requires a higher level of skill
and technology, with a relatively small subset of companies providing a significant portion
of the mold texturing.
Surface finishes are commonly evaluated according to standards of the Society of the Plastics
Industry (http://www.plasticsindustry. org/). These finishes range from the D-3, which has a
sand-blasted appearance, to A-1, which has a mirror finish. Table 2.12 provides some common
SPI finishes, the finishing method, and the measurable surface roughness.
The cost of molded parts can increase dramatically with higher levels of surface finish. The
reason is that to effective apply a given surface finishing method, the mold maker must
successively apply all lower level finishing methods. For example, to obtain an SPI C-3 finish,
the mold would first be treated with coarse and fine bead blasts followed by polishing with a
#320 stone. For this reason, higher levels of surface finish cost significantly more than lower
levels. Furthermore, molds with high levels of finish can produce moldings in which defects
are highly visible, thus adding cost to the injection molding process and mold maintenance
requirements.
As an alternative to smooth surface finishes, many product designs specify a textured finish.
One common reason is that textures may be used to impart the appearance of wood, leather,
or other materials as shown in Table 2.13. As a result, textures may increase the perceived value
of the plastic molding by the end-user [9]. Another reason is that textured surfaces provide
an uneven depth which may be used to hide defects such as knit-lines, blemishes, or other
flaws. In addition, textures may be used to improve the function of the product, for instance,
by providing a surface that is easy to grip or hiding scratches during end-use.
Texturing does add significantly to the cost of the mold. To apply a texture, mold surfaces
must first be finished typically to SPI class B for shallow textures (in which the texture depth
is on the order of a few microns) or class C for rough textures. Otherwise, the underlying
poor surface finish may be visible after the applied texture. After surface finishing, the texture
is imbued to the mold surfaces using chemical etching or laser machining processes. Since
dedicated processing equipment is required, the mold development process must provide
adequate time and money for the mold texturing.

2.3 Design for Injection Molding

Table 2.13:

Texture examples

Texture

Image

Sand

Texture depth

SPI finish required

50 μm

B

Leather

125 μm

C

Netting

150 μm

C

Wood grain

250 μm

D

2.3.6

33

Draft

Draft refers to the angle of incline placed between the vertical surfaces of the plastic moldings
and the mold opening direction. Draft is normally applied to facilitate ejection of the moldings
from the mold. Product designers frequently avoid the application of significant draft, since
it alters the aesthetic form of the design and reduces the molding’s internal volume. Even
so, draft is commonly applied to plastic moldings to avoid ejection issues and extremely
complex mold designs.
Draft angles on ribs must be carefully specified. In the previous rib design shown in Figure 2.3,
for instance, a 2° draft angle was applied to facilitate the ejection of the molded part from
the mold. In terms of product functionality, a lesser draft angle may be desired since this
allows taller and thicker ribs with greater stiffness. Unfortunately, lower draft angles (such as
½ or 1°) may cause the part to excessively stick in the mold. This issue of sticking upon part

34

2 Plastic Part Design

Table 2.14:

Draft examples

Surface finish

Resin

Class A-1

Acrylic

Roughness (μm)

Class B-3

ABS

12

1.5°

Sand texture

20% GF PC

12



Leather texture

Soft PVC

125



Leather texture

ABS

125

7.5°

0.01

Draft
0.5°

ejection can be compounded when molding with mica and/or glass filled materials that have
low shrinkage and high surface roughness. As such, the allowable draft angle is a complex
function of the material behavior, processing conditions, and surface finish.
A minimum draft angle of 0.5° is usually necessary, with 1 to 2° commonly applied according
to material supplier recommendations. Rough and textured surfaces typically require
additional draft, with an additional 1° of draft commonly applied per 20 μm of surface
roughness or texture depth. Table 2.14 provides some recommended draft angles for a few
different surface finishes and materials; the recommended draft angle increases with the
surface roughness. With respect to the material properties, the draft angle should increase for
glass filled and/or low shrinkage materials but may be decreased for highly flexible materials
such as soft PVC.

2.3.7

Undercuts

An undercut is a feature in the product design that that interferes with the ejection of the
molding from the mold. Four typical design features that require undercuts are shown in
Figure 2.7. These design features include, for example, a window in a side wall, an overhang
above the bottom wall of the part, a horizontal boss, and a snap finger. Much of the time, the
product designer is unaware of the difficulties associated with these undercuts.

Figure 2.7: Some common features with undercuts

2.4 Chapter Review

35

When possible, undercuts should be avoided since complex mold mechanisms must be
designed and machined for the forming and ejection of the part. These additional mold
components can make the mold more difficult to use, and even damage the mold if used
improperly. For these reasons, the mold design engineer should identify undercuts, alert the
customer, and work with the product design engineer to remove the undercuts. However,
undercuts should not be designed out of the product if the function provided by the feature
with the undercut is vital to the product or the removal of the undercut would necessitate
additional post-molding operations or the redesign of a single part into multiple pieces.

2.4

Chapter Review

After reading this chapter, you should understand:
• The basic stages of the molded part development process including the role of management
reviews,
• What information is needed to begin the mold design process,
• The common specifications on a molded product,
• Where to find additional information relevant to product and mold design, and
• Basic part design guidelines for injection molding.
In the next chapter, the mold cost and the part cost will be analyzed with respect to critical
mold design decisions. The results of this analysis will be used to design the layout of the
mold. In later chapters, the design and analysis of various mold subsystems are conducted.

3

Mold Cost Estimation

3.1

The Mold Quoting Process

The quoting process for plastic parts can be difficult for both the mold customer and
supplier. Consider the view of the mold customer. The procurement specialist for the product
development team sends out requests for quotes (RFQs) to several mold makers. After waiting
days or weeks, the quotes come back and the customer discovers that the development time
and cost of the mold may vary by a factor of 3 or more. In such a case, prospective mold
purchasers should ask about the details of the provided quotes, and check if the costs can be
reduced through product redesign. To reduce uncertainty related to pricing and capability,
many prospective customers maintain a list of qualified suppliers, who tend to provide faster
turn-around, more uniform quality, and better pricing across multiple projects. Long-term,
trusting partnerships can provide for rapid application and mold development by avoiding
the quoting process altogether and invoicing on a labor cost plus materials cost (referred to
as “cost plus”) basis.
Now consider the view of the mold supplier. The mold designer must invest significant time
developing a quote that may have a relatively small chance of being accepted. Sometimes,
the mold designer may have to redesign the product and perform extensive analysis to
provide the quote. While the quote may seem high to the prospective customer, the design
may correspond to a mold of higher quality materials and workmanship that can provide a
higher production rate and longer working life than some other lower cost mold. This more
expensive mold may quickly recoup its added costs during production.
From time to time, mold-makers and molders will adjust their quote based on whether
or not they want the business. If the supplier is extremely busy or idle, then the estimated
number of hours and/or hourly rate may be adjusted to either entice or to discourage the
potential customer from accepting the quote. Such adjustments should be avoided since the
provided quote does not represent the true costs of the supplier, which would become the
basis in a long term and mutually beneficial partnership between the mold supplier and the
customer.
The provided quote typically provides payment and delivery terms for the mold(s) and
perhaps even the molded part(s). A typical mold purchase agreement may specify that the
cost of a mold is paid in three installments:


the first third: on acceptance of the quote (after which the mold base and key materials
are typically purchased);



the second third: half-way through the mold making project (often when cavity inserts
have been machined); and



the final third: upon acceptance of the quality of the molded parts.

38

3 Mold Cost Estimation

Figure 3.1: Schedule of mold and molding expenses

After the mold is purchased, molds are typically shipped to the specified molder or the
customer’s facility where the parts are molded and marginal costs are incurred on a per part
basis. The cash outlays for a typical project are plotted in Figure 3.1 on a monthly basis.
The material and processing costs in month 3 are related to molding trials to validate and
improve the mold design; a hundred or so pre-production parts may be sampled at this time
for marketing and testing purposes. Later, monthly costs are incurred related to production.
Maintenance costs may appear intermittently throughout production to maintain the quality
of the mold and moldings.
There has been a trend in the industry towards large, vertically integrated molders with
tightly integrated supply chains who can supply molded parts (and even complete product
assemblies). As such, the structure of the quote can vary substantially with the structure of
the business. With a vertically integrated supplier, there is typically an up-front fee for the
costs associated with the development of the mold, followed by a fee for each molded part.
To protect the supplier, contracts are typically developed that specify minimum production
quantities with discounts and/or fees related to changes in the production schedule.
Since the structure and magnitude of quotes will vary substantially by supplier(s), a prospective
buyer of plastic parts should solicit quotes from multiple vendors and select the quote from
the supplier that provides the most preferable combination of molded part quality, payment
terms, delivery terms, and service.

39

3.2 Cost Drivers for Molded Parts

3.2

Cost Drivers for Molded Parts

There are three main drivers of the cost of a molded part:




the cost of the mold and its maintenance,
the materials cost, and
the processing cost.

Figure 3.2 provides a breakdown of these primary cost drivers and their underlying components. It is important to note that these costs do not include indirect costs such as overhead
or profits. However, such indirect costs may be accounted through the adjustment of hourly
rates and other costs.

Molded part
cost

Material
cost

Amortized
mold cost

Mold base
cost

Part weight

Cost per
kilogram

Yield

Machining

Finishing

Regrind

Figure 3.2: Cost drivers for a commodity and specialty part

Figure 3.3: Cost drivers for a commodity and specialty part

Processing
cost

Rework

Production
quantity

Processing
time

Hourly
rate

Finishing

40

3 Mold Cost Estimation

Even though most molded products have the same cost drivers, the proportion of costs varies
widely by application. Figure 3.3 shows the cost breakdown for a commodity application
(such as a cable tie with a production volume of 10 million pieces) and a specialty application
(such as a custom electrical connector with a production volume of 100,000 pieces). While
these two products are approximately the same weight, it is observed that the magnitude and
proportion of costs are vastly different.

3.2.1

Effect of Production Quantity

Minimization of the total molded part cost is not a simple task since injection molds and
molding processes are optimally designed for different target production quantities. Typically,
there is a trade off between the upfront investment in the mold and later potential savings
related to the processing and material costs per part. Consider the data provided in Table 3.1
for a molding application with production quantities of 50,000 and 5,000,000 pieces. As
indicated, the lower production quantity may be satisfied with a two cavity, cold runner
mold. By comparison, the mold design for the higher production quantity utilizes a hot
runner system allowing the simultaneous molding of 32 cavities with a lower cycle time and
reduced material consumption.
In theory, the production quantities should be known beforehand and used to design an
“optimal” mold for the specified quantity. In reality, the production schedules and quantities
are not precisely known, so the molder and customer must carefully consider the possible
result of using molds that are over or under designed. For this reason, break-even analysis
should be utilized to consider the sensitivity of different mold designs to the total molded
part cost.
Table 3.1: Part cost data for low and high production quantities

Production quantity

50,000

5,000,000

Number of mold cavities

2

32

Runner system

Cold runner

Hot runner

Mold cost

$10,000

$250,000

Cycle time

30 s

20 s

Effective cycle time/part

15 s

0.6 s

Processing cost/part

$0.40

$0.04

Mold cost/part

$0.20

$0.05

Material cost/part

$0.15

$0.12

Total cost/part

$0.75

$0.21

3.2 Cost Drivers for Molded Parts

3.2.2

41

Break-Even Analysis

Break-even analysis should be applied to ensure the design an appropriate mold. Consider the
previous case for the two molds described in Table 3.1. It is useful to consider the total costs
incurred to produce a given quantity. The total costs, Ctotal, may be computed as:
Ctotal = Cfixed + ntotal ⋅ Cmarginal

(3.1)

where Cfixed is the total cost of the mold and its maintenance, ntotal is the total production
quantity across the life of the mold, and Cmarginal is the total marginal cost of the resin, machine,
labor, and energy on a per part basis. For a given mold design, the marginal cost per piece will
remain fairly constant across the life of the application (though there may be cost decreases
related to elimination of defects, reductions in cycle times, etc. as well as cost increases due
to material pricing or shipping costs). To provide the best possible mold design and quote,
multiple mold designs should be developed for different target production quantities, and
the total production costs estimated and compared via break-even analysis.
Example: Consider the cost data provided in Table 3.1. Calculate the production volume
where a hot runner mold becomes more economical than a cold runner mold.
Equation (3.1) is used to calculate the costs with the cold runner and hot runner as:
cold_runner
cold_runner
cold_runner
= Cfixed
+ ntotal ⋅ Cmarginal
Ctotal
hot_runner
hot_runner
hot_runner
= Cfixed
+ ntotal ⋅ Cmarginal
Ctotal

Equating these two costs and solving for the production volume provides the break-even
quantity:
breakeven
ntotal
=

hot_runner
cold_runner
Cfixed
− Cfixed
cold_runner
hot_runner
Cmarginal − Cmarginal

The analysis assumes that the marginal cost per molded part consists primarily of the
processing and material costs. Then, the marginal costs for the cold and hot runners are
$0.55 and $0.16, respectively. Substituting these values provides:
breakeven
ntotal
=

$250,000 − $10,000
$240,000
=
= 615,000 parts
$0.55/part − $0.16/part $0.39/part

The costs for the cold and hot runner mold designs are provided in Figure 3.4. While the
cost function of Eq. (3.1) is linear, a log-log scale has been used in the figure to provide
better resolution of the cost across a wide range of production volumes. In this example,
the total cost for the 2 cavity cold runner mold and the 32 cavity hot runner mold are
plotted as a function of the “realized” production quantity, Q. For this example, the 2
cavity cold runner mold has a lower total cost up to the 615,000 part quantity, after which
the 32 cavity hot runner mold provides a lower total cost.

42

3 Mold Cost Estimation

10,000,000
2 cavity cold runner
32 cavity hot runner

Total cost for ntotal pieces

1,000,000

100,000

10,000

1,000
1,000

10,000

100,000

1,000,000

10,000,000

Total production quantity, n total

Figure 3.4: Break-even analysis

The cost analysis will typically indicate the need for different mold designs at extremely low
and extremely high production quantities. In the previous example, the upfront cost of the
32 cavity hot runner system can not be justified at low or moderate production quantities.
At very high production quantities, however, a hot runner system is essential to maximizing
profitability since the marginal costs of operating the hot runner mold are significantly less
than those of the cold runner mold. While the breakeven analysis supports clear design decisions at very low and very high production quantities, the mold design can be less certain
at intermediate production volumes. If the production quantity is on the order of 500,000
parts, then the best mold design may utilize neither 2 nor 32 cavities for this application, but
rather an intermediate quantity of 4, 8, or 16 cavities with or without a hot runner. As such,
multiple designs and cost estimates should be developed until a good balance is achieved
between higher upfront investment and lower marginal costs. If necessary, the customer can
be given more than one design to select the design that they think will ultimately be best.
Many molders and customers require a quick return on investment, and so will examine
the total cost curve to accept the use of a hot runner system with high cavitation only if a
desirably short payback period can be achieved. Sometimes, however, mold design decisions
are not based solely on economics but rather by other concerns such as:



The need for a mold to permit rapid color changes, for which a hot runner feed system may
not be desirable. The color change issue in hot runners will be revisited in Section 6.4.8.
The capability and preference of the molder that will use the mold. If the molder does
not have the experience or auxiliaries required to utilize a hot runner system, then a cold
runner mold may best be utilized.

3.3 Mold Cost Estimation



43

The lean manufacturing strategies of the molders to reduce costs and improve quality.
For instance, it is not uncommon for molders to standardize on a specific type and size
of mold to maximize production flexibility and reduce setup times.

As a general practice, the mold should be designed to maximize the molder’s capability unless
the application requirements and cost constraints dictate otherwise. When an advanced
molding application has special requirements, it may be critical to select a molder with a
specialized set of molding capabilities and standard operating procedures. Chapter 13 provides
a survey of mold technologies, many of which require special molder capabilities.

3.3

Mold Cost Estimation

Many cost estimation methods have been developed for molded plastic parts with varying
degrees of causality and accuracy [10–21]. The following cost estimation method was
developed to include the main effects of the part design and molding process while being
relatively simple to use. To use the developed method, the practitioner can refer to the cost data
provided in Appendices A, B, and D, or provide more application specific data as available.
The total mold cost, Ctotal_mold, is the sum of the cost of all cavities, Ccavities, and the cost of
the mold base, Cmold_base, and the cost of the mold customization, Ccustomization:
Ctotal_mold = Ccavities + Cmold_base + Ccustomization

(3.2)

Mold maintenance costs are included as a portion of the mold amortization, and are calculated
with the part cost. To demonstrate the cost estimation method, each of these cost drivers is
analyzed for the laptop bezel shown in Figure 3.5. The example analysis assumes that 1,000,000
parts are to be molded of ABS from a single cavity, hot runner mold. The relevant application
data required to perform the cost estimation is provided in Table 3.2.

Figure 3.5: Isometric view of laptop bezel

44

3 Mold Cost Estimation

Table 3.2: Laptop design data

Parameter

Laptop bezel

Material

ABS

Production quantity

1,000,000

Lpart

240 mm

Wpart

160 mm

Hpart

10 mm

Apart_surface

45,700 mm2

Vpart

27,500 mm3

Hwall

1.5 mm

Example: Estimate the total cost of a single cavity, hot runner mold for producing the
laptop bezel. This example corresponds to the mold design shown in Figure 1.8.
Subsequent analysis will show that the cost of the core and cavity inserts are $27,900, the
cost of the mold base is $3,700, and the cost of the customizations including the purchase
of all associated components is $43,200. As such, the estimated total cost the mold is:
Ctotal_mold = Ccavities + Cmold_base + Ccustomization
= $27,900 + $3,700 + $43,200 ≈ $74,800

3.3.1

Cavity Cost Estimation

The cost of the core and cavity inserts is typically the single largest driver of the total mold
cost. The reason for their expense is that they need to contain every geometric detail of the
molded part, be made of very hard materials, and be finished to a high degree of accuracy
and quality.
The total cost of all the cavity and core inserts is driven by the cost of each set of inserts, Ccavity,
multiplied by the number of cavity sets, ncavities, and a discount factor, fcavity_discount:
Ccavities = (Ccavity ⋅ ncavities ) ⋅ f cavity_discount

(3.3)

Example: Estimate the total cost of all core and cavity insert sets for the laptop bezel.
Since there is only one cavity and no cavity discount, the cost of all inserts sets is:
Ccavities = ($27,900 ⋅ 1) ⋅ 1 = $27,900

3.3 Mold Cost Estimation

45

3.3.1.1 Cavity Set Cost
The cost of each cavity set is estimated as the sum of the materials costs, Ccavity_material, the
insert machining costs, Ccavity_machining, and the insert finishing costs, Ccavity_finishing:
Ccavity = Ccavity_material + Ccavity_machining + Ccavity_finishing

(3.4)

Example: Estimate the cost of one set of core and cavity inserts for the laptop bezel.
Subsequent analysis will show that the cost of the materials is $435, the cost of the cavity
machining is $25,800, and the cost of the cavity finishing is $1,700. As such, the total cost
for one core and cavity set is:
Ccavity = $435 + $25,800 + $1,700 ≈ $27,900
3.3.1.2 Cavity Materials Cost
The cost of the cavity insert materials is the simplest and least significant term to evaluate.
Specifically, the cavity materials cost is the volume of the cavity set, Vcavity_material, multiplied
by the density, ρcavity_material, and the cost of the material per kilogram, κcavity_material:
Ccavity_material = Vcavity_material ⋅ ρcavity_material ⋅ κcavity_material

(3.5)

Cost data for some common metals are provided in Appendix B.
The cavity insert volume is the product of the cavity length, Lcavity, the cavity width, Wcavity,
and the cavity height, Hcavity:
Vcavity_material = Lcavity ⋅ Wcavity ⋅ H cavity

(3.6)

The size of the cavity set is finalized during the mold layout design process as discussed in
Chapter 4. From generalization of the later analysis, these dimensions can be roughly estimated
as a function of the part size as follows:
Lcavity = Lpart + max [0.1 ⋅ Lpart , H part ]
Wcavity = Wpart + max [0.1 ⋅ Wpart , H part ]

(3.7)

H cavity = max [0.057,2 H part ]

It should be noted that for the formula to work with the data provided in the Appendices, all
dimensions must be stated in meters or converted with the data to another consistent set of
units. As previously suggested, the analysis should be conducted using application specific
data for the material properties, part geometry, mold geometry, or manufacturing processes
when such data is available.

46

3 Mold Cost Estimation

Example: Estimate the cost of the core and cavity insert materials for the laptop bezel.
First, the dimensions of the core and cavity inserts are estimated. From the dimensions
provided in Table 3.2, the preliminary dimensions of the inserts are:
Lcavity = 0.24 m + max [0.1 ⋅ 0.24 m, 0.01 m] = 0.268 m
Wcavity = 0.16 m + max [0.1 ⋅ 0.16 m, 0.01 m] = 0.176 m
H cavity = max [0.057,2 ⋅ 0.01 m] = 0.057 m

which provides a volume of:
Vcavity_material = 0.264 m ⋅ 0.176 m ⋅ 0.057 m = 2.65 ⋅ 10−3 m 3
To calculate the cost of the core and cavity insert materials, the type of material must be
known. Since this is a tight tolerance part with a high production quantity, tool steel D2
is selected for its wear and abrasion resistance. This material has a density of 7670 kg/m3
and a cost of 21.4 $/kg, which leads to a cost for the core and cavity insert materials of:
Ccavity_material = 2.65 ⋅ 10−3 m 3 ⋅ 7670

kg
$
⋅ 21.4
= $435
3
kg
m

3.3.1.3 Cavity Machining Cost
The cavity machining cost, Ccavity_machining, is the single most significant driver of the total
mold cost, and is a function of many variables including






the volume and geometric complexity of the part to be molded,
the core and cavity inserts’ material properties,
the machining processes,
the labor cost, and
the quality of the inserts required.

The approach used here is to estimate the cavity machining cost by multiplying the machining
time, tcavity_machining, with the machining labor rate, Rmachining_rate:
Ccavity_machining = t cavity_machining ⋅ Rmachining_rate

(3.8)

The machining labor rate, Rmachining_rate, varies substantially with the cost of living in the
location where the mold is manufactured. A mold maker in a high cost of living area (such as
Germany) will tend to have a higher labor cost than a mold maker in a low cost of living area
(such as Taiwan). Furthermore, the labor rate will also vary with the toolset, capability, and
plant utilization of the mold maker. For example, a mold maker using a 5 axis numerically
controlled milling machine will tend to have more capability and charge more than a mold
maker using manually operated 3 axis milling machines. Some approximate cost and efficiency

3.3 Mold Cost Estimation

47

data for machining and labor rates are provided in Appendix D, though application specific
data with the negotiated machinist’s rate should be used if this data is available.
The cavity machining time is driven by the size and complexity of the cavity details to be
machined, as well as the speed of the machining processes used. In theory, the exact order and
timing of the manufacturing processes can be planned to provide a precise time estimate. In
practice, however, this approach is fairly difficult unless the entire job can be automatically
processed, for instance, on a numerically controlled mill.1
The cavity machining time is estimated as the sum of the volume machining time, tcavity_volume,
and the area machining time, tcavity_area. To take application specific requirements into account,
the cavity machining time is then multiplied by a complexity factor, fcavity_complexity, to consider
geometric complexity as well as a machining factor, fmachining, then divided by an efficiency
factor, fmachining_efficiency:
⎛ t cavity_volume + t cavity_area ⎞
t cavity_machining = ⎜
⎟ ⋅ f cavity_complexity ⋅ f machining
f machining_efficiency



(3.9)

The cavity volume machining time is a function of the volume of material to be removed
and the material removal rate. To provide an approximate but conservative estimate, the
assumption is made that the removal volume is equal to the entire volume of the core and
cavity inserts. This may seem an overly conservative estimate, but in fact much of the volume
must be removed around the outside of the core insert and the inside of the cavity insert.
The material removal rate is a function of the processes that are used, the finish and tolerances
required, as well as the properties of the mold core and cavity insert materials. To simplify
the analysis, a geometric complexity factor will later be used to capture the effect of different
machining processes and tolerances needed to produce the required cavity details. As such, the
volume machining time captures only the time to require the material removal as follows:
t cavity_volume =

Vcavity_material
Rmaterial_volume

(3.10)

where Rmaterial_volume is the volumetric mold material removal rate measured in cubic meters per
hour. Machining data for different materials are provided in Appendix B, though application
specific material removal rates can be substituted if the depth of cut, speed, and feed rates
are known [22].

1

Prototype molds are, in fact, increasingly being produced in a nearly fully automatic mode on high speed
numerically controlled milling machines. Due to limitations in the process, the core and cavity inserts
are typically machined from aluminum with very small end-mills used to provide reasonably detailed
features. While this mold-making approach does provide very precise cost estimates and low costs, the
resulting molds are comparatively soft and often not appropriate for molding high quantities. Higher
strength and wear resistant aluminum alloys, however, have recently been and continue to be developed
that are increasingly cannibalizing conventionally manufactured steel molds.

48

3 Mold Cost Estimation

The cavity area machining time, tcavity_area, estimates the time required to machine all the
cavity surfaces, and is similarly evaluated as follows:
t cavity_area =

Apart_surface

(3.11)

Rmaterial_area

where Apart_surface is the total surface area of the part measured in square meters and Rmaterial_area
is the area mold material removal rate measured in square meters per hour. Modern 3D
computer aided design systems can provide exact measure of the part’s surface area and
volume.
The cavity complexity factor, fcavity_complexity, adjusts the cavity machining time to account for
the design and manufacturing of the myriad of features that will compose the mold cavity.
Some of the activities that the complexity factor accounts for include:





Decomposition of the mold cavity into multiple machining tasks;
Generation of machining tasks and NC programs including electrodes for electrical
discharge machining;
Execution of machining tasks, including multiple machine setups, electrical discharge
machining, milling, etc.;
Inspection and rework to obtain all the specified geometry.

Previous research [5, 23] has found that the complexity of the cavities is related to the total
number of dimensions and/or features specified in the design of the part to be molded. Unfortunately, these former approaches are time consuming and dependent upon the subjective
opinion as to what constitutes a dimension or feature. As such, this cost analysis uses a complexity factor that is based on the ratio of the expected volume of the part (the surface area,
Apart_surface, times the wall thickness, hwall) compared to the actual volume of the part, Vpart:
f cavity_complexity =

Apart_surface ⋅ hwall
Vpart

(3.12)

This complexity factor increases with the addition of features, since each added feature (such
as a rib, boss, or window) increases the surface area of the part without causing a significant
increase in the actual part volume. To demonstrate different levels of complexity, Table 3.3
provides the calculated complexity factors for part designs of varying complexity.
The machining factor, fmachining, accounts for the discrepancy in the material removal rates
for various type of machining. The volumetric removal rates provided in Appendix B assume
a carbide, two fluted, 19.05 mm (¾ inch) diameter end mill with a depth of cut of 3.2 mm
(0.125 inch); the surface area removal rate assumes a carbide, four fluted, 6.35 mm (¼ inch)
diameter end mill operating at half the nominal feed rate recommended for the various
materials. Since the cavity and core inserts are typically produced with a variety of machining
operations, the overall machining factor for a given application is the weighted average of
each of the machining factors provided in Table 3.4 in proportion to its use.

3.3 Mold Cost Estimation

Table 3.3: Complexity factor for various example part designs

Part design

Complexity factor

1.02

1.9

2.5

3.1

Table 3.4: Machining factor for various processes

Machining process

Machining factor

Turning

0.5

Drilling

0.5

Milling

1

Grinding

4

EDM

4

49

50

3 Mold Cost Estimation

The machining efficiency factor, fmachining_efficiency, accounts for the fraction of time that labor
and machine time are spent on non-machining activities. In theory, the efficiency of a fully
automated numerical control machining cell will approach 100%. In reality, the efficiency
rarely exceeds 50%. The reason is that a significant amount of time is required to develop
the sequence of machine operations, procure and check cutting tools, perform setups, verify
cutting paths, create electrodes, operate EDM, and other tasks. As such, a machining efficiency
rate of 25% is recommended for cost estimation reasons.
Example: Calculate the machining cost of the core and cavity inserts for the laptop
bezel.
Using the application data Table 3.2 and the removal rates for tool steel D2 from
Appendix B, the machining times are estimated as:
t cavity_volume =

t cavity_area =

2.65 ⋅ 10−3 m 3
7.00 ⋅ 10−4 m 3 /hr
0.0457 m 2

0.0170 m 2 /hr

= 3.78 h

= 2.69 h

The cavity complexity factor is evaluated as:
f cavity_complexity =

45700 mm 2 ⋅ 1.5 mm
= 2.5
27500 mm 3

Since the laptop bezel contains many narrow ribs that will be produced primarily with
EDM, a machining factor of 4 is used. An efficiency factor of 25% is also assumed. The
estimated machining time is:
⎛ 3.78 h + 2.69 h ⎞
t cavity_machining = ⎜
⎟⎠ ⋅ 2.5 ⋅ 4 = 258 h

25%
The statistical cost data in Appendix D indicates that the average hourly wage for a tool and
die maker in the United States is $23.94 per hour. This hourly wage is the direct salary to
the employee, and does not include the employee’s fringe benefits (such as medical benefits,
vacation, etc.), the cost of the equipment and plant (such as land, building, machinery,
etc.), the cost of supplies (such as cutting tools/fluids, electricity, water, etc.), and other
overhead (including management salary, profit, etc.). As such, mold makers will charge
significantly more than their employee’s direct wages. Assuming a billed hourly rate for
the machinists of 100 $/h, the estimated cavity machining costs are:
Ccavity_machining = 258 h ⋅ 100

$
= $25,800
h

3.3 Mold Cost Estimation

51

3.3.1.4 Cavity Discount Factor
The cavity discount factor stems from the fact that there are fixed costs associated with the
design and tooling of the first cavity set. Manufacturing productivity will then improve as
additional sets are machined. Accordingly, a set of discount factors is provided in Table 3.5 as
a function of the number of cavity sets to be made. For each doubling in the number of cavity
sets, the cost is reduced by 15%. However, after 16 cavities, it is difficult to further improve
manufacturing productivity. This table is based on generic human factors research [24], so
the discount factor may be replaced with application-specific data if available.
Table 3.5: Discount factor as a function of number of cavity sets

Number of cavity sets

Discount factor

1

1

2

0.85

4

0.72

8

0.61

16 or more

0.52

Example: Since the laptop bezel is produced in a single cavity mold, there is no quantity
discount and the discount factor is set to one.
3.3.1.5 Cavity Finishing Cost
The cavity finishing cost, Ccavity_finishing, is also a significant cost driver representing 5 to 30%
of the total mold cost [25]. The finishing cost is the product of the time required to finish
the cavity surface area, tcavity_finishing, and the finishing labor rate, Rfinishing_rate:
Ccavity_finishing = t cavity_finishing ⋅ Rfinishing_rate

(3.13)

i
The finishing time is a function of each area of the part to be finished, Apart_surface
, divided
i
by the rate at which the area is finished, Rcavity_finishing :

t cavity_finishing =


i

i
Apart_surface
i
Rcavity_finishing

(3.14)

Since the finishing rate depends on the surface finish and texture to be applied, the use of the
summation over the index i in Eq. (3.14) indicates that the time required to finish each portion
of the mold to various finishes must be added together. Some representative finishing rates are
provided in Table 3.6, which were adapted from Rosato [25] to account for the various finish
levels. Approximate labor rates for finishing are provided in Appendix D. Since finishing can
be quite labor intensive, the finishing of core and cavity inserts is sometimes outsourced.

52

3 Mold Cost Estimation

Table 3.6: Finishing rates

Finish

Finishing method

Finishing rate (m2/h)

Finishing rate (in2/h)

Texture

Electrochemical engraving

0.0002

0.3

SPI A-1

#3 diamond polish

0.0005

1

SPI A-3

#15 diamond polish

0.001

2

SPI B-3

#320 grit cloth

0.0025

4

SPI C-3

#320 stone

0.005

8

SPI D-2

#240 oxide blast

0.01

20

SPI D-3

#24 oxide blast

0.02

30

Example: Calculate the cavity finishing cost for the laptop bezel.
Assume that the laptop bezel is to be finished to SPI B-3 on all surfaces, which together
have a surface area of 0.0457 m2, except for an improved surface finished of SPI A-1 to
be applied to the front surface of the bezel, which has an approximate area of 0.01 m2.
The estimated finishing time is:
t cavity_finishing =

0.0457 m 2 − 0.01 m 2
0.0025 m 2 /h

+

0.01 m 2
0.0005 m 2 /h

= 34 h

In the preceding equation, the area of the front surface of the bezel is subtracted from the
total area of the bezel to avoid double computing the time to finish the front surface. If
the labor rate for finishing is 50 $/h, then the cost of cavity finishing is:
Ccavity_finishing = 34 h ⋅ 50

$
= $1,700
h

53

3.3 Mold Cost Estimation

3.3.2

Mold Base Cost Estimation

A mold base can be considered as a template or blank mold that is ready to be customized.
Referring to the mold design in Figure 1.8, the mold base includes the bulk of the mold with
the exception of the core insert, cavity insert, hot runner, and related components such as
ejector pins, support pillars, and cooling plugs.
The cost of the mold base is a function of the mass of the mold and the cost of the steel per
unit mass. Statistical cost analysis of mold bases was conducted and found that cost could
be closely modeled as:2
Cmold_base = US$830 + M mold ⋅ κmold_material

(3.14)

where Mmold is the mass of the mold base in kg, and κmold_material corresponds to the cost of
the mold material per kilogram. Cost data for some commonly used materials is provided
in Table 3.7.
Table 3.7: Mold steel cost coefficients

Material composition

Mold metal coefficient (US$/kg)

#1

SAE 1030

3.55

#2

AISI 4130

4.40

#3

AISI P20

5.25

Statistical regression of actual mold base costs was conducted for several different mold bases (from small
to large size) and the three standard materials. The cost of the mold base predicted by the provided model
is plotted against the actual cost in the following figure. The quality of the fit is certainly acceptable for
cost estimation purposes.
10000
y = 0.9948 x
R2 = 0.9791

9000
8000
Predicted mold cost ($)

2

DME#

7000
6000
5000
4000
3000
2000
1000
0
0

2000

4000

6000

Observed mold cost ($)

8000

10000

54

3 Mold Cost Estimation

Given the various mold dimensions, the mass of the mold base can be estimated statistically
as:3
M mold = 1330

kg
kg
⋅ Lmold ⋅ Wmold + 17200 3 ⋅ Lmold ⋅ Wmold ⋅ H mold
m2
m

(3.15)

While the mold dimensions are finalized during the mold layout design process, they can be
initially estimated as:
Lmold = Lcavity ⋅ ncavities_length ⋅ 1.33
Wmold = Wcavity ⋅ ncavities_width ⋅ 1.33

(3.16)

H mold = 0.189 + 2 H cavity

where ncavities_length and ncavities_width are the number of cavities across the length and width
dimensions. If they are completely unknown, they can initially be set as:
ncavities_length = ncavities_width = ceiling ( ncavities )

(3.17)

where the function ceiling(·) rounds any non-integer number up to the next integer. This
estimate will tend to make the mold have larger size and cost than might actually be realized,
but will provide at least a reasonable estimate.

For the previous validation data, the model had the following fit:
1600
y = 0.9813x
R2 = 0.999

1400
Predicted mold mass (kg)

3

1200
1000
800
600
400
200
0
0

500

1000

Observed mold mass (kg)

1500

3.3 Mold Cost Estimation

55

Example: Estimate the cost of the mold base for the laptop bezel.
To estimate the cost of the mold base, it is first necessary to estimate the size of the mold
base. Since this is a single cavity mold, the mold base dimensions are estimated as:
Lmold = 0.264 m ⋅ 1 ⋅ 1.33 = 0.351 m
Wmold = 0.176 m ⋅ 1 ⋅ 1.33 = 0.234 m
H mold = 0.189 + 2 ⋅ 0.057 m = 0.30 m
The mass of the mold is then estimated as:
kg
kg
⋅ 0.35 m ⋅ 0.23 m + 17200 3 ⋅ 0.35 m ⋅ 0.23 m ⋅ 0.30 m
2
m
m
= 538 kg

M mold = 1330

If a DME#3 (AISI P20) steel is used for the mold base construction, then the cost of the
mold is $5.25 per kg. The cost of the mold base is then estimated as:
Cmold_base = US$830 + 538 kg ⋅ 5.25

3.3.3

$
= $3,700
kg

Mold Customization

The mold base customization includes many design, machining, and assembly steps. Some
of the specific steps in the mold customization include:










Cutting pockets and bolt holes in the mold plates to receive the core and cavity inserts.
This cost is proportional to the number of mold cavities and the mold dimensions.
Milling a cold runner system into the mold plates, or purchasing a hot runner system
and modifying the mold accordingly. This cost is related to the type of feed system, the
number of gates, and the mold dimensions.
Drilling, tapping, and plugging the cooling lines in the mold. This cost is related to the
number and layout of the cooling lines, which is related to the number of cavities and
their geometry.
Drilling and reaming holes in the core inserts and support plates to accept ejector pins, and
providing appropriate counter bores in the ejector retainer plate. This cost is related to the
number of ejector pins, which is related to the number of cavities and their geometry.
Milling holes in the ejector plate and the ejector retainer plate to provide support pillars,
if needed. This cost is related to the number of cavities and their geometry.
Designing and machining other necessary mold components such as stripper plates,
slides, core pulls, etc. These costs are related to the specific part geometry and application
requirements.

56

3 Mold Cost Estimation

A detailed cost analysis of all the customizations is too lengthy to present given the necessary
discussion of the assumptions and equations. However, a review of the above customizations
indicates that the costs are generally related to the size of the mold base, the cost of the inserts,
and the specific technologies required. Accordingly, a reasonably simple model is:
i
i
(3.18)
Ccustomization = Ccavities ⋅ ∑ f cavity_customizing
+ Cmold_base ⋅ ∑ f mold_customizing
i

i

where the coefficients fcavity_customizing correspond to the factors governing the costs of
customizing the cavity inserts, and the coefficients, fmold_customizing, correspond to the factors
governing the costs of modifying the mold base. The summation over i represents the added
customization for each of the mold subsystems, with i ∈ [feed system, cooling system, ejector
system, structural system, and miscellaneous]. It should be noted that these customization factors
have been developed so as to include the procurement cost of the required components and
system assemblies, such as hot runners, fittings, core pulls, etc.
Feed systems are discussed in detail in Chapter 6. The cost factors associated with modifying the cavity inserts and mold base for accommodating different types of feed systems are
provided in Table 3.7. A simple molding application with one to four cavities might use a
two plate cold runner system with fcavity_customizing equal to 0.05 and fmold_customizing equal to
0.1. For a molding application with high production volume and sixteen or more cavities, a
thermally gated hot runner might be used with fcavity_customizing equal to 0.5 and fmold_customizing
equal to 1.0.
Cooling systems are discussed in Chapter 9. The cost factors for various cooling system designs
are provided in Table 3.8. Many molds use straight lines with o-ring and fittings, adding 5%
to the cost of the cavity inserts and 20% to the cost of the mold base. As the cooling system
becomes more complex, the implementation cost increases.
Ejector systems are discussed in Chapter 11. The cost factors for various ejection system
designs are provided in Table 3.9. Most molds can be assumed to use a mix of round ejector
pins, blades, and sleeves though ejection requirements will vary significantly depending on
the part geometry and application requirements.
Table 3.7: Feed system cost coefficients

Feed system design

Cavity cost coefficient,
feed_system
f cavity_customizing

Mold cost coefficient,
feed_system
f mold_customizing

Two plate cold runner system

0.05

0.1

Three plate cold runner system

0.1

1.0

Hot runner system with thermal gate

0.4

2.0

Hot runner system with valve gates

0.5

4.0

Hot runner stack mold with thermal gates

0.5

8.0

Hot runner stack mold with valve gates

0.9

12.0

3.3 Mold Cost Estimation

57

Table 3.8: Cooling system cost coefficients

Cooling system design

Cavity cost coefficient,
cooling_system
f cavity_customizing

Mold cost coefficient,
cooling_system
f mold_customizing

Straight lines with o-rings and fittings

0.05

0.2

Straight lines with bubblers or baffles,
o-rings, and fittings

0.10

0.2

Circuitous cooling lines with o-rings, plugs,
and fittings

0.15

0.4

Circuitous cooling lines with bubblers or
baffles, o-rings, plugs, and fittings

0.20

0.4

Complex cooling line layout with thermally
conductive inserts or contoured cooling
inserts

0.25

0.8

Cavity cost coefficient,

Mold cost coefficient,

Table 3.9: Ejector system cost coefficients

Ejector system design

ejector_system
f cavity_customizing

ejector_system
f mold_customizing

Round ejector pins

0.1

0.1

Mix of round ejector pins, blades,
and sleeves

0.2

0.2

Stripper plate

0.2

0.4

External slide or lifter

0.2

0.4

Internal slide or lifter

0.4

0.4

Actuated core pull

0.4

0.5

Reverse ejection system

0.5

1.0

The structural design of molds is detailed in Chapter 12. The cost factors for various structural
system designs are provided in Table 3.10. Most molds with high production volumes can be
assumed to use support pillars and parting plane interlocks. In this cost estimation method, the
sealing of the cavity by the core insert and cavity insert is considered as part of the structural
system. The cost of the mold will increase with the complexity of the parting surface, the
design of which will be discussed in Section 4.1.
There are many other customizations that can be performed on the mold. Some of these
factors are provided in Table 3.11, and are applied as necessary. For most molds, none of
these customizations are required.

58

3 Mold Cost Estimation

Table 3.10:

Structural system cost coefficients

Structural system design

Cavity cost coefficient,
structural_system
f cavity_customizing

Mold cost coefficient,
structural_system
f mold_customizing

No additional support structures
and planar mold parting surface

0.0

0.0

Multi-stepped parting surface

0.2

0.0

Complex, contoured parting surface

0.4

0.2

Support pillars

0.0

0.1

Support pillars and interlocks

0.1

0.2

Split cavity mold

0.5

1.0

Table 3.11:

Other customization cost coefficients

Required mold customization

Cavity cost coefficient,
miscellaneous
f cavity_customizing

Mold temperature sensors

0.05

Mold cost coefficient,
miscellaneous
f mold_customizing

0.1

Mold pressure sensors

0.05

0.1

Gas assist molding

0.2

0.5

Runner shut-offs

0.0

0.1

Dynamic melt control

0.2

1.0

Insert molding

0.4

0.4

In-mold labeling

0.4

0.4

Two-shot molding

2.0

4.0

Three-shot molding

3.0

6.0

Example: Estimate the cost of customizing the mold base and inserts for the laptop
bezel.
The mold will use a hot runner with thermal gates, so the appropriate customization
factors are:
feed_system
f cavity_customizing
= 0.4
feed_system
f mold_customizing
= 2.0

The mold will use a cooling system with circuitous cooling lines, o-rings, and plugs so
the appropriate customization factors are:

3.3 Mold Cost Estimation

59

cooling_system
f cavity_customizing
= 0.15
cooling_system
f mold_customizing
= 0.4

The mold will use an ejector system with a mix of round ejector pins, blades, and sleeves,
so the appropriate customization factors are:
ejector_system
= 0.2
f cavity_customizing
ejector_system
= 0.2
f mold_customizing

The mold will use a structural system with support pillars and interlocks. Also, the mold
will require a stepped parting plane to form the details along the side of the molding as
shown in Figure 3.5. As such, the appropriate customization factors are:
structural_system
f cavity_customizing
= 0.1 + 0.2 = 0.3
structural_system
f mold_customizing
= 0.2 + 0.0 = 0.2

The mold will use a melt thermocouple at the end of flow and a melt pressure transducer
near the gate for process control purposes, so additional customization factors are:
miscellaneous
f cavity_customizing
= 0.05 + 0.05 = 0.1
miscellaneous
f mold_customizing
= 0.1 + 0.1 = 0.2

The cost of all customizations may then be calculated as:
Ccustomizations = $27,900 ⋅ (0.4 + 0.15 + 0.2 + 0.3 + 0.1)
+ $3700 ⋅ (2 + 0.4 + 0.2 + 0.2 + 0.2) = $43,200
To summarize the above analysis, the total cost of the mold is estimated as:
Ctotal_mold = Ccavities + Cmold_base + Ccustomization
= $27,900 + $3,700 + $43,200 ≈ $74,800
The estimate seems reasonable for a mold produced in the United States. On the other
hand, this result may over estimate the cost of the mold if made in Asia, especially if not
including a hot runner system. Accordingly, the analysis could be repeated for a cold
runner mold with different labor cost coefficients from Appendix D.

60

3 Mold Cost Estimation

3.4

Part Cost Estimation

The total cost of a molded part, Cpart, can be estimated as:
Cpart =

Cmold/part + Cmaterial/part + Cprocess/part
yield

(3.19)

where Cmold/part is the amortized cost of the mold and maintenance per part, Cmaterial/part is
the material cost per part, Cprocess/part is the processing cost per part, and yield is the fraction
of molded parts that are acceptable. Each of these terms will next be estimated, after which
an example will be provided.
Example: Estimate the total cost per molded laptop bezel.
Subsequent analysis estimates a mold cost per part of $0.22, a material cost per part of
$0.06, and a processing cost per part of $0.19. If the yield is assumed to be 98%, then the
total part cost is estimated as:
Cpart =

3.4.1

$0.22 + $0.06 + $0.19
= $0.48
0.98

Mold Cost per Part

Having estimated the total mold cost, Ctotal_mold, the cost per part can be assessed as:
Cmold/part =

Ctotal_mold
⋅ f maintenance
ntotal

(3.20)

where ntotal is the total production quantity of parts to be molded, and fmaintenance is a factor
associated with maintaining the mold. Most molders perform several levels of maintenance
including:





preventive maintenance after every molding run,
inspections and minor repairs on an intermittent basis,
scheduled general mold maintenance on a quarterly or semi-annual basis,
and mold rebuilding as necessary.

The need for mold maintenance and repair is related to the number of molding cycles
performed, the properties of the plastic and mold materials, the processing conditions, and the
quality of the mold. It is well known that the maintenance costs can far exceed the purchase
cost across the operational lifetime of the mold. As the resin becomes more abrasive relative to
the hardness of the mold, the wear of the mold accelerates and more maintenance is required.

61

3.4 Part Cost Estimation

Table 3.11:

Mold maintenance coefficient

Unfilled,
low viscosity
plastic

High viscosity
or particulate
filled plastic

High viscosity
and fiber filled
plastic

Soft mold material,
such as aluminum or mild steel

3

10

20

Standard mold steel,
such as P20

2

5

10

Hardened surface or tool steel,
such as H13

2

2

3

Conversely, a well designed, hardened mold should exhibit lower maintenance costs when used
with an unfilled, low viscosity plastic. Table 3.11 provides some maintenance estimates.
Example: Estimate the amortized cost of the mold base per molded laptop bezel.
ABS is a moderate viscosity, unfilled material. If the mold is D2 tool steel with a hardened
surface, then the maintenance coefficient will fall between 2 and 5 – a factor of 3 is
estimated. Given that the mold has a single cavity, one million cycles are required. The
amortized cost of the mold per molded laptop bezel (including the initial purchase cost
and maintenance costs) is then estimated as:
Cmold/part =

3.4.2

$74,800
$
⋅ 3 = 0.22
1,000,000 parts
part

Material Cost per Part

The cost of the material per part can be estimated as:
Cmaterial/part = Vpart ⋅ ρplastic_material ⋅ κplastic_material ⋅ f feed_waste

(3.21)

where Vpart is the volume of the molded part, ρplastic is the density of the molded plastic, κplastic
is the cost of the molded plastic per unit volume, and ffeed_waste is the total percentage of the
material that is consumed including the scrap associated with the feed system.
Table 3.12 provides estimates of the total material consumption for various types of feed
systems. A cold runner is simple and low cost, but results in molded plastic that must be
either discarded or recycled. Utilizing the recycled plastic as regrind reduces the waste, but
incurs some cost related to the labor and energy of recycling. Hot runners have the potential
to significantly reduce material costs, but consume significant material during start-up and
so are less effective in short runs.

62

3 Mold Cost Estimation

Table 3.12:

Material waste coefficient

Type of feed design

Feed system waste factor,
ffeed_waste

Cold runner

1.25

Cold runner, fully utilizing regrind

1.08

Hot runner with short runs

1.05

Hot runner with long runs

1.02

Example: Estimate the cost of the plastic material per molded laptop bezel.
Since a hot runner system is used and the production quantity is one million parts,
large production runs are assumed with a feed waste factor of 1.02. Using the cost and
density from Appendix A, the cost of the plastic material per molded part is estimated
as:
3

kg
$
$
⎛ 0.01 m ⎞
⋅ 1044 3 ⋅ 2.16
⋅ 1.02 = 0.063
Cmaterial/part = 27.5 cc ⋅ ⎜
⎝ cm ⎟⎠
kg
part
m
The cost of the plastic material per part is quite low since the part has a very low thickness
(1.5 mm) and low part weight (28.7 g).

3.4.3

Processing Cost per Part

The processing cost per part is a function of the number of mold cavities, the cycle time, tcycle,
and the hourly rate of the machinery and labor, Rmolding_machine:
Cprocess/part =

t cycle
ncavities



Rmolding_machine
3600 s/h

(3.22)

The cycle time is effected primarily by the thickness of the part, hwall, and to a lesser extent by
the size of the part and the type of feed system. While the cycle time will be more accurately
estimated during the cooling system design, a reasonable estimate is provided by:
⎡ s ⎤
t cycle = 4 ⎢
(hwall [mm])2 ⋅ f cycle_efficiency
⎣ mm 2 ⎥⎦

(3.23)

where the cycle efficiency, fcycle_efficiency, is a function of the type of feed system and process
that is being operated according to Table 3.13. While it is desirable to operate a fully automatic
molding cell with a hot runner, many molders continue to use cold runner molds operating
in semi-automatic mode.

3.4 Part Cost Estimation

Table 3.13:

63

Cycle efficiency coefficient

Type of feed system and mold operation

Cycle efficiency factor,
fcycle_efficiency,

Cycle efficiency factor,
fcycle_efficiency,

cold runner

hot runner

Semi-automatic molding with operator
removal of molded parts

2.5

3.0

Semi-automatic molding with gravity drop
or high speed robotic take-out

1.5

2.0

Fully automatic molding

1.0

1.5

The hourly rate for the molding machine is a function of the clamp tonnage, technological
capability, and any associated labor. The following model was developed relating the clamp
tonnage and capability to the machine hourly rate:4
Rmolding_machine = [47.0 + 0.073 ⋅ Fclamp − 4.7 ln(Fclamp )] ⋅ f machine

(3.24)

where Fclamp is the clamp tonnage in metric tons, and fmachine is a factor relating to the capability
of the machine and the associated labor.

The analysis was conducted using published U.S. national hourly rate data for twelve different sized
molding machines ranging from 20 to 3500 metric tons. The described model has the fit:
300

Predicted molding machine hourly rate ($/h)

4

y = 0.9893x
R2 = 0.9881

250

200

150

100

50

0
0

50

100

150

200

Observed molding machine hourly rate ($/h)

250

300

64

3 Mold Cost Estimation

Table 3.13:

Molding machine capability

Type of molding machine and labor required

Machine factor,
fmachine

Old hydraulic machine (purchased before 1985) without operator or profit

0.8

Standard hydraulic machine or older electric machine (before 1998)
operator or profit

1.0

Modern electric machine without operator or profit

1.1

Molder profit

Add 0.1

Take-out robot and conveyor

Add 0.05

Hot runner temperature control

Add 0.05

Gas assist control

Add 0.1

Injection-compression control

Add 0.1

Dedicated operator/assembler

Add 0.15

Two-shot molding machine

Add 1.0

Three-shot molding machine

Add 1.4

The machine capability factor is provided in Table 3.13. In general, molding machines with
advanced capabilities and higher clamp tonnage cost more to purchase and operate, and so
command a price premium. Machines with specialized capability (such as multiple injection
units or very high injection pressures/velocities) are more expensive to purchase and so
likewise command a price premium per hour of operation.
The cost of all auxiliaries should be added to the appropriate machine coefficient. While
the machine and auxiliary technology increases the hourly rate of the molding process, they
should provide a net savings by improving quality and reducing the processing and materials
costs.
The clamp tonnage will be analyzed during the filling system design. However, the clamp
tonnage can be conservatively estimated assuming an average melt pressure of 75 MPa against
the projected area of the mold cavities as:
Fclamp = 75 ⋅ 106 [Pa] ⋅ (ncavities ⋅ Lpart ⋅ Wpart [m 2 ]) ⋅

[mTon]
9800 [N]

(3.25)

Example: Estimate the processing cost per molded laptop bezel.
The analysis assumes that a hot runner system is used with a take-out robot to fully
automate the molding process. The corresponding cycle efficiency factor is 1.5. The cycle
time is then estimated as:
⎡ s ⎤
t cycle = 4 ⎢
(1.5 [mm])2 ⋅ 1.5 = 13.5 s
2⎥
⎣ mm ⎦

3.4 Part Cost Estimation

65

If a modern electric machine is used with a take-out robot, conveyor, and hot runner
controller, then the machine technology factor is:
f machine = 1.1 + 0.05 + 0.05 = 1.2
To calculate the hourly rate of the molding machine, the clamp tonnage must first be
estimated:
Fclamp = 75 ⋅ 106 [Pa] ⋅ (1 ⋅ 0.24 m ⋅ 0.16 m [m 2 ]) ⋅

[mTon]
= 294 mTon
9800 [N]

It should be noted that the true required clamp tonnage is likely less than 294 metric tons
since the laptop bezel has a large window in it. The analysis, however, is conservative.
The molding machine rate is then estimated as:
Rmolding_machine = [47.0 + 0.073 ⋅ 294 − 4.7 ln(294)] ⋅ 1.2 = 50.1

$
h

The processing cost of the molded part can then be estimated by Eq. (3.22) as:
Cprocess/part =

3.4.4

13.5 s/cycle 50.1 $/h
$

= 0.19
1 part/cycle 3600 s/h
part

Defect Cost per Part

There are many reasons that molded parts are rejected. Some common defects include short
shot, flash, contamination, improper color match, surface striations due to splay or blush,
warpage and other dimensional issues, burn marks, poor gloss, and others. Since customers
demand high quality levels on the molded parts they purchase, molders often internally filters
out the defective parts that are molded before shipment to the customer. The cost of these
defects can be incorporated into the part cost by estimating the yield.
Typical yields vary from 50 to 60% at start-up for a difficult application with many quality
requirements to virtually 100% for a fully matured, commodity product. Table 3.14 provides
yield estimates according to the number of molding cycles and quality requirements.
Table 3.14:

Yield estimates

Total number of molding cycles

Low quality
requirements

High quality
requirements

~10,000

0.95

0.90

~100,000

0.98

0.95

~1,000,000

0.99

0.98

66

3 Mold Cost Estimation

Example: Estimate the yield for molding the laptop bezel.
Since the production quantity is on the order of one million pieces and the quality
requirements are assumed to be high, the yield factor is estimated as:
f yield = 0.98
To summarize the foregoing analysis, the total part cost is estimated as:
Cpart =

$0.21 + $0.06 + $0.19
= $0.47
0.98

The large cost of the mold relative to the material and processing costs indicates that the
mold may have been over designed. Further cost analyses should be performed to analyze
the effectiveness of a cold runner mold design with a lower initial mold cost but increased
material and processing costs.

3.5

Chapter Review

This chapter presented an overview of the mold quoting process, followed by a detailed
mold cost and part cost estimation methodology. The methodology was developed to utilize
minimal information and yet provide the causality relating critical mold design decisions to
the mold cost and part cost. It is recommended that multiple cost estimates be developed for
different mold designs until an effective mold specification is established.
After reading this chapter, you should understand:
• The primary cost drivers for injection molds,
• The primary cost drivers for molded parts,
• The mold quoting process, and the typical schedule of payments required to make and
operate a mold,
• How to estimate the cost of an injection mold,
• How to estimate the cost of molded parts,
• How to use the cost estimation methodology to improve the mold design by minimizing
the total cost of the mold, material, and process per part.
The burden to minimize the total part cost is shared between the mold designer, molder, and
end-user of the molded parts. The mold designer must contemplate trade-offs between the
mold costs, material costs, and processing costs. In the long run, significant inefficiencies in
the mold design brought about by poor design decisions will lead to lost profitability for all
parties.
In the next chapter, the specification resulting from the cost analyses will be used to design
the layout of the mold. Afterwards, the design and analysis of the underlying systems in
injection molds is conducted.

4

Mold Layout Design

During the mold layout stage, the mold designer commits to the type of mold and selects the
dimensions and materials for the cavity inserts, core inserts, and mold base. Mold bases are
only available in discrete sizes, so iteration between the inserts’ sizing and mold base selection
is normal. The goal of the mold layout design stage is to develop the physical dimensions of
the inserts and mold so as to enable procurement of these materials. Mold material selection
is also an important decision, since the material properties largely determine the mold making
time and cost as well as the mold’s structural and thermal performance.
The mold layout design assumes that the number of mold cavities and type of mold has been
determined. To develop the mold layout, the mold opening direction and the location of the
parting plane are first determined. Then, the length, width, and height of the core and cavity
inserts are chosen. Afterwards, a mold base is selected and the inserts are placed in as simple
and compact a layout as possible. It is important to develop a good mold layout design since
later analysis assumes this layout design and these dimensions are quite expensive to change
once the mold making process has begun.

4.1

Parting Plane Design

The parting plane is the contact surface between the stationary and moving sides of the mold.
The primary purpose of the parting plane is to tightly seal the cavity of the mold and prevent
melt leakage. This seal is maintained through the application of literally tons of force (hence
the term “clamp tonnage”) that are applied normal to the parting plane. While the term
“parting plane” implies a flat or planar surface, the parting plane may contain out-of-plane
features. The mold designer must first determine the mold opening direction to design the
parting plane.

4.1.1

Determine Mold Opening Direction

Examination of any of the previous mold designs (e.g., Figure 1.4 to Figure 1.8) indicates that
the mold opening direction is normal to the parting plane. In fact, the mold usually opens
in a direction normal to the parting plane since the moving platen of the molding machine
is guided by tie bars or rails to open in a direction normal to the platen. Accordingly, guide
bushings and/or mold interlocks are almost always located on the parting plane to guide the
mold opening in a direction normal to the parting plane.
It may appear that there is nothing about the mold opening direction to determine since
the mold opens normal to the parting plane. However, it is necessary to determine the mold

68

4 Mold Layout Design

opening direction relative to the mold cavity. There are two factors that govern the mold
opening direction:
1. First, the mold cavity should be positioned such that it does not exert undue stress on
the injection mold. The mold cavity is typically placed with its largest area parallel to the
parting plane. This arrangement allows the mold plates, already being held in compression
under the clamp tonnage, to resist the force exerted by the plastic on the surfaces of the
mold cavity.
2. Second, the mold cavity should be positioned such that the molded part can be ejected
from the mold. A typical molded part is shaped like a five-sided open box with the side
walls, ribs, bosses, and other features normal to its largest area. If so, then the part ejection
requirement again supports the mold opening direction to be normal to the part’s largest
projected area.
Consider the cup and lid shown in Figure 4.1. A section of the core and cavity inserts used
to mold these parts was previously shown in Figure 1.6. There are only two potential mold
opening directions relative to the part. One mold opening direction is in the axial direction
of the cup, while the second direction is in the radial direction of the cup.

Figure 4.1: Sectioned isometric view of cup assembly

4.1 Parting Plane Design

Figure 4.2: Axial mold opening direction
for cup

69

Figure 4.3: Radial mold opening direction
for cup

A section of a cavity block with an axial mold opening direction is shown in Figure 4.2. The
two bold horizontal lines indicates the location of the parting plane where the two halves of
the insert are split to form the cavity insert (top) and the core insert (bottom).
Consider next the same cavity block but with a radial mold opening direction for a portion
of the cavity insert as shown in Figure 4.3. For this design, four bold lines separate the sides
from the top and bottom. Since the metal core is located inside the molded part, there is no
way to remove the core other than in the part’s axial direction. The cavity insert, however,
can be separated into three pieces that move along two different axes in order to remove the
molded part.
Of these two designs, the axial mold opening direction shown in Figure 4.2 is the simplest
design and is usually preferred. However, the second design is sometimes used in practice
since it allows for a more complex part design as well as more options in locating the parting
line. For instance, the second design might be required if a handle were added to the cup, or
if it was necessary to move the parting line to a location away from the top lip. This second
design is known as a “split cavity mold” and is discussed in more detail in Section 13.9.1.
As another example, consider the laptop bezel shown in Figure 3.5. There are again two
potential mold opening directions. The first opening direction is in the screen’s viewing
direction, as indicated by the section view shown in Figure 4.4. In this case, the mold section
is split by two horizontal lines into a cavity insert forming the outside surface of the bezel
and a core insert that forms the inner surface and ribs of the bezel. When the core and cavity
inserts are separated as indicated by the arrows, the molded bezel can be readily removed.

Figure 4.4: Normal mold opening direction for bezel

70

4 Mold Layout Design

Figure 4.5: Complex mold opening directions for bezel

Alternatively, the cavity block for the PC bezel can be split as indicated with the three vertical
lines shown in Figure 4.5. In this case, the former cavity insert is split into two pieces, resulting
again in a split cavity mold design. The two halves of the former cavity insert must now
be removed in oblique directions in order to remove the molded part; the mold opening
direction is inclined in order to allow the mold surfaces to separate from the molded part
without excessive surface friction or shearing of features on the molded part. This movement
requires several additional mold components to control the moving cavity inserts, which add
significantly to the cost of mold design, manufacture, and operation.

4.1.2

Determine Parting Line

The term “parting line” refers to the location at which the cavity insert, the core insert, and
the plastic molding meet. Since the core and cavity insert meet at this location, any significant
deflection of the cavity insert away from the core insert will result in a gap into which the
plastic will flow and form a thin film of plastic known as “flash”. Imperfections in the core and
cavity inserts at this location, for instance due to wear or improper handling, will also create
gaps into which the plastic will flow. Even with new and well-crafted molds, the location of
the parting line usually results in a very slight “witness line” along its length.
For this reason, the parting line should be located along a bottom edge of the part, or some
other non-visual, non-functional edge. Consider the previous cup shown in Figure 4.1.
Placing the parting line very close to the lip as indicated by the dashed line in the left drawing
of Figure 4.6 would result in a witness line and possible flash that might make the molded
cup unusable. Alternatively, a better location for the parting line is at the bottom of the rim
as indicated in Figure 4.2, corresponding to the parting line shown in the right drawing of
Figure 4.6.

Figure 4.6: Two parting line locations for cup

4.1 Parting Plane Design

71

Figure 4.7: Parting line location for bezel

For the laptop bezel, the parting line will be located around the bottom edge of the part as
shown in Figure 4.7. It is observed that, unlike the cup, the parting line for the bezel is not in
a single plane. Rather, the parting line follows the profile of the features on the side walls. This
non-planar parting line is required to fit the core insert which hollows out the mold cavity
to form the holes required for the various connectors. As will be seen in the next section, this
complex parting line shape will cause a more complex parting plane.

4.1.3

Parting Plane

Once the parting line is identified, the parting plane is projected outwards from the part, so
as to separate the core insert from the cavity insert. The preferred parting plane for the cup is
shown in Figure 4.8. The cavity insert will form the outer and top surfaces of the part, while
the core insert will form the rim and inner surfaces.

Figure 4.8: Parting plane for cup

72

4 Mold Layout Design

Figure 4.9: Parting plane for bezel

For the laptop bezel, the parting line in Figure 4.7 can be radiated outward to form the parting
surface shown in Figure 4.9. It can be observed that all of the out of plane features along the
parting line now become complex surfaces on the parting plane. These surfaces pose two
significant issues during mold operation. First, any misalignment between the sharp features
on core and cavity inserts will cause wear between the sliding surfaces if not an outright impact
between the leading edge of the core and the mating cavity surface. Second, the clamp tonnage
exerted on the core and cavity inserts can cause the surfaces to lock together with extreme
force, causing excessive stress and potential mold deformation during mold operation.
To avoid excessive stress, interlocking features on the parting plane should be inclined at least
five degrees relative to the mold opening direction. The parting surface is now typically created
via three dimensional computer aided design (“3D CAD”) using lofted surfaces. Each lofted

Figure 4.10: Modified parting surface for bezel

4.1 Parting Plane Design

73

surface blends a curved feature along the parting line to a line of corresponding width on
the parting plane. The result is a surface with the needed profile at the parting line and the
necessary draft down to the parting plane. The lofted surfaces are then knit together with the
parting plane to provide a parting surface, as shown for the bezel in Figure 4.10.

4.1.4

Shut-Offs

Shut-offs are contact areas between the core insert and the cavity insert that separate portions
of the cavity formed between the core and cavity inserts. A shut-off will need to be defined
for each window or opening in the molded part. Conversely, if a part has no windows, like the
cup, then no shut-offs are defined. Each shut-off is defined by a parting line, which should
be located in a non-visual area where a witness line or slight flashing would not reduce the
value of the molded part.
For example, the laptop bezel has one large opening above the parting plane for the display.
A shut-off is necessary across the entire area of the opening. As indicated in Figure 4.11, there
are essentially two possible locations for the shut-off ’s parting line, corresponding to the top
and bottom of the shelf that supports the display.
Either location (or even any location in between) would likely be acceptable since the entire
shelf is hidden from view. If the parting line is placed at the top of the shelf as indicated at
the right of Figure 4.11, then a shut-off surface as shown in Figure 4.12 will result.

Figure 4.11: Shut-off surface for bezel

Figure 4.12: Shut-off surface for bezel

74

4 Mold Layout Design

4.2

Cavity and Core Insert Creation

With the definition of the parting plane and all necessary shut-offs, the core insert and the
cavity insert have been completely separated. To create the cavity and core inserts, the length,
width, and height of the inserts must be defined.
The length and width of the cavity and core inserts must be large enough to:
• enclose the cavity where the part is formed,
• withstand the forces resulting from the melt pressure exerted upon the area of the
cavity,
• contain the cooling lines for removing heat from the hot polymer melt, and
• contain other components such as retaining screws, ejector pins, and others.
All of these requirements suggest making the core and cavity inserts as large as possible. For
smaller molded parts, increasing the sizing the core and cavity inserts may have little added
cost. However, the cost of larger core and cavity inserts can become excessive with increases
in the number of cavities or molded part size.

4.2.1

Height Dimension

The height dimension is often determined by two requirements. First, the core and cavity insert
should have enough height above and below the molded part to safely pass a cooling line.
Cooling line diameters typically range from 4.76 mm (3/16″) for smaller molds to 15.88 mm
(5/8″) for large molds. Generally, large inserts with larger cooling lines will provide faster
and more uniform cooling as will be analyzed in Chapter 9. While cooling line design will
be later discussed, the minimum height dimension between the molded part and the top or

Figure 4.13: Insert height allowance

4.2 Cavity and Core Insert Creation

75

bottom surface of the insert is typically three times the diameter of the cooling line to avoid
excessive stress as analyzed in Chapter 12. The initial height dimensions for the core and
cavity inserts are shown in Figure 4.13.
Second, the core and cavity insert should have a height that is matched with the height
of available cavity and core insert retainer plates (the “A” and “B” plates). These plates are
commonly available in ½″ increments in English units, and in 10 mm increments in metric
units. As such, the insert heights should be adjusted up such that the faces of the cavity and
core inserts are flush or slightly proud with respect to the “A” and “B” plates on the parting
plane. It should be noted that the height of the core insert as indicated in Figure 4.13 is not
its total height but rather the height dimension from the rear surface to the parting plane.
For materials procurement and cost estimation, the total height of the core insert should also
include the height of the core above the parting plane.

4.2.2

Length and Width Dimensions

The length and width dimensions are similarly determined by two requirements. First, if a
cooling line is needed around the exterior of the mold cavity, then the inserts should be sized
large enough to accommodate such a cooling line. As for the height allowance, length and
width allowances of three cooling line diameters per side are typical. Second, the width and
length dimensions of the inserts should provide side walls, also known as “cheek”, that are
thick enough to withstand the lateral loading of the melt pressure exerted on the side walls
of the mold cavity. This requirement will become dominating for deep parts with large side
walls. While the structural design will be discussed in detail in Section 12.2.4, a safe guideline
is that the thickness of the side wall in the length and width dimension should equal the
depth of the mold cavity.
Figure 4.14 demonstrates an allowance that should be added to the length and width of the
mold cavity to derive the length and width of the core and cavity inserts. It can be observed
that for the laptop bezel, the requirement of fitting a cooling line will exceed the structural
requirement. For the molded cup, however, the insert length and width dimension are driven
by the structural requirement.

Figure 4.14: Insert length and width allowance

76

4 Mold Layout Design

4.2.3

Adjustments

The core and cavity inserts can now be created with the prescribed dimensions. However, it is
sometimes desirable to adjust the cavity insert dimensions to provide a more efficient mold
design. In general, the length and width dimensions of the inserts are more critical than the
height dimension, since these dimensions will



drive the size of the mold base in multi-cavity applications, and
contribute more to the material and machining costs.

As such, these dimensions may be decreased somewhat by effective cooling and structural
designs, which will be supported by later engineering analysis.

Figure 4.15: Core and cavity inserts for cup

Figure 4.16: Core and cavity inserts for bezel

4.3 Mold Base Selection

77

Figure 4.15 provides the core and cavity inserts for the cup. Since the molded part is round,
the design of the core and cavity insert may also be round. This shape provides a benefit with
respect to ease of manufacturing, since both the core and cavity inserts can be turned on
a lathe. While the allowances in the axial and radial dimensions are sufficient to fit cooling
lines, the allowance in the radial dimension may not be sufficient to withstand the pressures
exerted on the side wall by the melt.
There is no fundamental requirement on the external shape of the core and cavity inserts.
While the insert design in Figure 4.15 showed round inserts, the mold design for the cup
shown previously in Figure 1.4 used square inserts. Rectangular inserts with or without filleted
corners are also quite common. The design of the insert should be dictated by the shape of
the molded part, the efficiency of the mold design, and the ease of manufacture.
The core and cavity inserts for the laptop bezel are shown in Figure 4.16. In this case,
rectangular inserts are designed. The length and width dimensions of the inserts have
been designed quite aggressively. While the bezel is quite shallow and the inserts are
structurally adequate, the thickness of the surrounding cheek may not allow for sufficient
cooling around the periphery of the mold cavity while also providing space for other mold
components.

4.3

Mold Base Selection

After the core and cavity inserts have been initially sized, the mold layout can be further
developed and the mold base selected. It is critical to order a mold base with appropriately sized
plates and materials, since any mistakes in the mold base selection can consume significant
time and expense. To determine the appropriate size, the mold designer must first arrange
the mold cavities and provide allowances for the cooling and feed systems. Afterwards, the
mold designer should select a standard size from available suppliers and verify suitability
with the molder’s molding machine.

4.3.1

Cavity Layouts

The goal of cavity layout design is to produce a mold design that is compact, easy to
manufacture, and provides molding productivity. If a single cavity mold is being designed,
then the cavity is typically located in the center of the mold, though gating requirements may
necessitate placing the mold cavity off center. For multi-cavity molds, there are essentially
three fundamental cavity layouts:




cavities are placed along one line
cavities are placed in a grid, or
cavities are placed around a circle.

78

4 Mold Layout Design

Figure 4.17: Series layout of cavities

Figure 4.18: Grid layout of cavities

Placing all the cavities along a line, as shown in Figure 4.17, is a simple but poor design. Unless
the insert geometries are long and narrow, the resulting mold layout produces a mold that has
a high aspect ratio. In general, the width to length ratio of the bounding envelope around all
cavities should be kept less than 2 : 1. Higher aspect ratios will require the use of large molds
that are significantly under utilized while at the same time producing structural loadings
across the mold for which molding machine platens may not be designed. Furthermore, the
use of such a line layout requires an unbalanced feed system which can result in poor melt
control as discussed in Chapter 6.
As an alternative to a linear layout of all cavities, it is common to place cavities in a grid as
shown in Figure 4.18. This design is most common for applications requiring high production
volumes when the number of cavities is a multiple of 2, i.e., 4, 8, 16, 32, etc. There are two
primary benefits to a grid layout. First, the grid layout will result in a compact mold with an
acceptable aspect ratio. Second, the grid layout lends itself well to naturally balanced feed
system layouts as discussed in Chapter 6.
While the grid layout is compact and very common, it can result in a feed system design with
multiple branches. To reduce the feed system complexity and ensure more balanced melt
filling, a circular layout is sometimes used when the molded parts are relatively small or when
the number of mold cavities is relatively low, for example 8 or less. Figure 4.19 shows one
such layout in which all the cavities are provided at an equal distance from the center of the
mold. The primary disadvantage is that such a circular layout requires a larger mold surface
area than the previously discussed grid layout.
While the previously discussed layouts are the most common, there is nothing to prevent
a mold designer from utilizing other layout designs. Some applications may best utilize a
combination of the above layouts. For example, Figure 4.20 shows a combination of a line
layout plus a circular layout. The resulting layout is a very compact design for six cavities.
Again, the designer should develop the layout that is best for the application’s geometry and
requirements.

4.3 Mold Base Selection

79

Figure 4.19: Circular layout of cavities

Figure 4.20: Hybrid layout of cavities

4.3.2

Mold Base Sizing

The size of the mold base is determined primarily by the area required to accommodate the
designed cavity layout. A primary issue, however, is the potential for conflict between the
placements of the cavities and other mold components (such as leader pins, guide bushings,
and others). Furthermore, there is the potential for conflict between cavity support systems
(such as cooling lines, ejector pins, support pillars, etc.) and other mold components (such
as leader pins, guide bushings, and others.) Due to these conflicts, mold bases are often sized
larger than what would first be considered.
The shaded area in Figure 4.21 represents the usable area of the parting plane into which
the core and cavity inserts can be placed. Ejector return pins are located to the left and
right of this area, while guide pins and socket head cap screws are located above this area. A
dimensional allowance equal to at least one-half of each component’s diameters is provided
between the mold cavity and the surrounding components to avoid excessive stress during
the mold’s operation.

80

4 Mold Layout Design

Figure 4.21: Usable parting plane area

Given the cavity layout and its geometric envelope, a mold base with a feasible length and
width is selected. Standard mold bases are widely available from 200 mm up to 1000 mm on
a side. When specifying a mold base, it is also necessary to specify the height of the “A” plate,
the height of the “B” plate, the height of the support plate “S”, and the distance of the ejector
travel, “E”, as shown in Figure 4.22. The total stack height is defined as the distance from the
bottom of the rear clamp plate to the top of the top clamp plate.

Figure 4.22: Height dimensions to specify

4.3 Mold Base Selection

81

With respect to mold base selection, the height of the “A” and “B” plates are respectively
matched to the height of the cavity and core inserts as previously discussed. The height of the
support plate, “S”, is normally determined from the mold base supplier based on the height
of the “A” and “B” plates, though the height of the support plate can be special ordered to
varying dimensions. The travel of the ejector plate should be selected to eject the part from
the mold. Often, the ejector travel is set to be equal to the depth of the molded part. From
the ejector travel, the height of the ejector housing, dimension “C”, is assigned by the mold
base supplier.
When selecting a mold base, it is also necessary to specify an orifice diameter for the sprue,
which is not shown in Figure 4.22. This dimension is of lesser importance since the sprue
bushing may be replaced or machined, or the molding machine nozzle changed, to match
the sprue to the nozzle as later discussed in Chapter 6.

4.3.3

Molding Machine Compatibility

When selecting a mold base, the mold designer should verify that the mold will fit in the
available molding machine(s). There are many requirements that should be considered when
matching a mold to a molding machine. First, the mold must physically fit in the machine.
Perhaps the most common limitation is that the mold will not fit between the tie bars. The
tie bar spacing is easily measurable on an available molding machine, or can be checked in
a machine drawing for a potential molding machine. For instance, Figure 4.23 shows the tie
bar spacing and bolt pattern for a Battenfeld HM320 molding machine. It can be viewed that
the horizontal tie bar spacing is 800 mm, and that the vertical tie bar spacing is 630 mm. This

Figure 4.23: Typical tie bar and bolt pattern (dimensions in mm)

82

4 Mold Layout Design

Figure 4.24: Minimum and maximum daylight (dimensions in mm)

means that the maximum mold width, including cooling plugs, hot runner connectors, etc.,
is 800 mm (less some relatively small clearance between the mold and the tie bars to provide
for mold insertion).
A cross-section view of the same machine platens is shown in Figure 4.24 with the same
orientation as shown in Figure 1.1. In this view, the nozzle of the molding machine enters
the stationary platen on the right side of the drawing. The machine’s moving platen and the
ejector unit are on the left side of the drawing. For the mold to be operable in the machine, the
mold height must be greater than the indicated A dimension and smaller than the indicated B
dimension, or between 350 and 800 mm for this machine. If the mold is smaller than 350 mm,
then the molding machine platen can not fully close the mold and build clamp tonnage. If
the mold is larger than 800 mm, then the mold will not fit between the two platens when the
moving mold platen is fully open.
Even if the mold fits in the molding machine, the molding machine may still not be operable
with the mold. For instance, the injection unit of the molding machine must have sufficient
shot volume and provide enough melt pressure to fill the mold cavity with the polymer melt.
On the other hand, if the injection unit has too large a shot size, then the melt may degrade
in the barrel of the molding machine. For the Battenfeld HM320, the maximum shot volume
is 490 cc. To provide melt homogeneity without degradation, this machine is ideally suited
for molds requiring a shot volume between 120 cc and 250 cc.
The molding machine must also provide sufficient clamp tonnage to hold the two halves of
the mold together when pressurizing the polymer melt. For this machine, the clamp tonnage
is 3200 kN which is equal to 326 metric tons, 360 English tons, or 720,000 pounds. If the
molding machine does not provide sufficient clamp tonnage, then the mold will open during
operation and the melt will flow across the parting plane and shut-offs. If the molding machine
provides too much tonnage to a very undersized mold, however, the mold may be damaged
by the imposed compressive stresses.

4.3 Mold Base Selection

4.3.4

83

Mold Base Suppliers

The development of standardized mold base designs is considered a significant advance
in the history of the plastics molding industry. A majority of mold makers in the U.S. use
standard mold bases to reduce the time and expense of creating molds. Furthermore, mold
maintenance is simplified through the availability of standard mold components that are
replaceable at the molder’s facility.
It is noted that many mold makers do not use mold bases for various reasons. Mold bases for
very large parts, such as automobile body panels, may not be available as a standard product
and so may require custom design and manufacture. Some mold makers believe that standard
mold bases are inferior in quality, and strive to provide a better mold with higher quality or
lower lifetime cost through the development of custom designs with proprietary components.
At the other extreme, some mold makers can produce a simple but fully functional mold for
less cost than just the standard mold base could be purchased in the United States.
There are numerous mold base suppliers from which mold bases and mold components can
be purchased. When selecting a mold base, the mold designer should consider:


The range of mold base sizes and materials that are available. Not only should mold bases
of varying plate lengths, widths, and heights be available, but these mold bases should
also be available in different types of materials.



The portfolio of mold components that can also be purchased. The mold base supplier
should be able to provide insert materials, ejector pins, cooling accessories, etc.



The native system of units that in which the mold base was designed and the quality of
the associated drawings. If the mold designer prefers U.S. customary or metric units, the
mold base drawings should reflect a compatible same system of units through the use of
round numbers, fractions, etc. Drawings should fully detail the design of the various mold
components and, when appropriate, document their customization and operation.



The inventory availability and delivery terms. Standard “quick ship” mold components
should be in the supplier’s inventory. Customized mold bases with varying plate dimensions and material specifications should be custom manufactured and shipped within
one week. Orders that are placed before noon should be shipped the same day and no
later than the next day.



The quality of the supplied mold bases. All mold plates should be supplied finish ground,
heat treated, and ready for machining at the mold maker. Guide pins, ejector pins, and
other mold components should be finished, hardened, and/or coated as appropriate to
ensure low wear.



The previous experience with the mold base supplier. If a company or mold designer has
past favorable experiences with a supplier, then there may be risk or a significant learning
curve associated with switching suppliers.



The pricing should be competitive with commodity material prices. Clearly the mold
base supplier adds value to the raw materials included in the mold base, and is entitled
to recover their costs and reasonable profit. Still, the mold designer must compare the

84

4 Mold Layout Design

strengths and weaknesses of various mold base suppliers to determine whether to sole
source from one mold base supplier or choose from a few qualified suppliers.

4.4

Mold Material Selection

As part of the mold base and materials procurement process, the various types of metals must
also be selected. Just as there are many different plastics suitable for injection molding, there
are many ferrous and non-ferrous metals that are suitable for use in injection molds.
Some of the more common metals and their properties are provided in Appendix B. Of all
these metals, AISI P20 is the most common due to its favorable combination of properties.
However, P20 is sometimes improperly specified in many molding applications since other
metals would provide better performance, lower mold making cost, or lower injection
molding costs. In this section, important properties and trade-offs of mold materials will
be discussed.

4.4.1

Strength vs. Heat Transfer

Strength is typically characterized by the ultimate stress that a material can endure prior to
failure, or by the yield stress that can be applied to a material without causing permanent
deformation. For injection molds, however, neither of these properties should be utilized.
Instead, the fatigue limit stress (also known as the endurance limit) is the amount of stress
that can be applied and removed many times without causing material failure. This property
is provided in Appendix B for the various materials, and will be used later in the mold’s
structural engineering.
Heat transfer is often measured by the thermal conductivity, k, of the material. However, the
thermal diffusivity, defined as:
α=

k
ρ ⋅ CP

(4.1)

is a better measure of the ability of a material to transfer heat given a transient or cyclic
thermal load. This property is a ratio of the material’s ability to transfer heat divided by the
material’s ability to store heat. For fastest heat transfer, the material should have high thermal
conductivity as well as a low density, ρ, and a low heat capacity, CP. These material properties
are also provided in Appendix B for the various materials, and will be used later in the mold’s
thermal engineering.
The trade-off between the fatigue limit stress and the thermal diffusivity is shown in Figure 4.25 for various mold materials. In general, the materials that have the highest strength
(A6, D2, and H13) have the lowest heat transfer. Conversely, the materials with the highest

4.4 Mold Material Selection

85

-5

6

x 10

Al QC-7

Cu 940

5
Thermal Diffusivity (m*m/s)

Al 7075

DE

4

S

ED
R
I

3

2

1045

1
SS420
0
100

200

300

4140
P20

H13
D2

S7

400
500
600
Fatigue Limit Stress (MPa)

700

800

A6
900

Figure 4.25: Thermal diffusivity as a function of endurance limit

heat transfer (aluminum and copper alloys such as Cu 940) have the lowest strength. No
material exists that has a very high fatigue limit stress and a very high thermal diffusivity.
P20, the most common of all mold materials, has average fatigue limit stress and low thermal
diffusivity, suggesting that the mold’s performance may be improved by using other mold
materials in some molding applications.

4.4.2

Hardness vs. Machinability

To withstand wear and abrasion, it is desirable that the mold materials have very high hardness.
There are many ways to measure hardness, with one of the most common being the Brinell
Hardness test. In this test, a 10 mm diameter carbide ball is pushed into the mold material
with a force of 29,500 N (6,500 lbs). The diameter of the resulting indentation is measured
by a microscope after which the Brinell Hardness number is calculated. The hardness values
for various mold materials are provided in Appendix B. (Because of the variance of the
material properties, the Brinell hardness test may not be suitable for very soft or very hard
materials. For this reason, some of Brinell hardness values in Appendix B are derived from
other hardness tests as appropriate).
As the material hardness increases, the materials generally become more difficult to machine.
Harder cutting tools and lower cutting speeds and feed rates become necessary. The volumetric

86

4 Mold Layout Design

0.01
0.009

Al QC-7
Al 7075

Machining Rate (m3/Hr)

0.008

DE

0.007

D
RE
I
S

0.006
0.005
0.004
0.003
1045

0.002
0.001
0
100

Cu 940
4140
P20
SS420

S7

A6
D2

H13
200

300

400
Brinell Hardness

500

600

700

Figure 4.26: Machining rate as a function of Brinell hardness

machining rate can be computed from the recommended cutting speeds and feed rates for
various mold materials assuming a carbide cutter [22]. The resulting machining rate is plotted
as a function of Brinell hardness in Figure 4.26.
The data in Figure 4.26 indicate that the materials with high hardness have low machining
rates while materials with high machining rates have low hardness. For this reason, very hard
materials such as D2, A6, and H13 should only be used when required for molding abrasive
plastics that would quickly abrade the surfaces of softer mold materials. Due to their very
high machining speeds, aluminum alloys can be used to quickly and economically produce
molds but should be used carefully when molding at moderate melt pressures (100 MPa or
greater) or when molding even slightly abrasive plastics (such as carbon filled).

4.4.3

Mold-Maker’s Cost vs. Molder’s Cost

While there are many trade-offs that could be examined, perhaps the most important is
the trade-off between the cost to make the mold and the cost to use the mold. To minimize
the cost to make the mold, the material should provide a high machining rate, low material
purchase cost, and a low hardness. Accordingly, a mold making cost factor, fmold_making, can
be defined as:
f mold_making ∝

Material cost ⋅ Brinell hardness
Machining rate

(4.2)

4.4 Mold Material Selection

87

2
SS420

1.8

Mold Operating Cost Factor

1.6
1.4
1.2
P20
4140
1045
0.8
S7
1

D2

0.6

S
DE

0.4 Al 7075
Al QC-7
Cu 940
0.2
0

0

2

4

6

H13

ED
IR A6

8
10
12
14
Mold Making Cost Factor

16

18

20

Figure 4.27: Mold-operating vs. mold-making cost factors

The cost to use the mold can be minimized by having a material with a high thermal diffusivity
and a high hardness. Accordingly, a mold operating cost factor, fmold_operating, can be defined
as:
f mold_operating ∝

1
Thermal diffusivity ⋅ Brinell hardness

(4.3)

These two cost factors are plotted in Figure 4.27, where each of the factors has been normalized
relative to P20. It is desirable to use a mold material that has both low mold making and
mold operating cost factors. While the data in Figure 4.27 can not be interpreted as being
proportional to the actual mold making and mold operating cost (since these are dependent
on the application specifics), the data do provide some very useful insights.
It is observed that the aluminum alloys provide very low mold making costs and low operating
costs. For this reason, the aluminum alloys should be seriously considered when a molding
application does not require high strength or hardness. Copper alloys, such as Cu 940, provide
significantly lower mold operating costs but have higher mold making cost due to higher
materials cost coupled with moderate hardness and machining rates. Accordingly, copper
alloys are good candidates for molding applications with high production volumes that
require moderate strength and hardness.
If the relatively soft non-ferrous metals can not be used, then one of the many ferrous
materials in Figure 4.27 can be selected. Among the ferrous metals, lower mold operating
costs typically require higher mold-making costs. For instance, A6 is much harder than P20

88

4 Mold Layout Design

yet has a comparable thermal diffusivity. The higher hardness of A6 will tend to reduce the
mold maintenance cost in demanding molding applications, but also incurs added costs
during mold making associated with lower machining and finishing rates.
There are three outliers in Figure 4.27 that merit additional discussion. Stainless steel, SS420,
has a much higher mold operating cost than mold’s made of P20 due to SS420’s lower thermal
diffusivity, but should be used when corrosion resistance is needed. Unalloyed steel, 1045, has
a lower mold making cost than P20 due to a substantially greater machining rate. Interestingly,
the mold operating cost factor for 1045 is similar to that for P20 since 1045’s higher thermal
diffusivity (which means reduced cycle times) balances against its lower hardness (which
means more mold maintenance). Finally, H13 has a very high mold making cost factor due
to its very high hardness and very low machining speed but again is commonly used when
abrasion resistance is desired.

4.4.4

Material Summary

The data in Appendix B and the previous plots provide quantitative and qualitative comparisons of common mold materials. The mold designer must consider the requirements placed
on the mold in a given molding application and weigh the economic, structural, thermal, and
other requirements. While one material such as P20 may have always worked well for a given
mold designer, there is the possibility that significant improvements in mold performance
and profitability could be realized by utilizing other mold materials.
Table 4.1 recommends some of the commonly used mold materials according to the
application requirements. P20 is a fine material, and highly suitable for many molding
applications. However, other materials are better in diverse applications.
In Table 4.1, all the recommendations pertain specifically to materials for the core and
cavity inserts. Standard mold bases are not available in all these materials; mold bases are
typically available in 1045, 4140, or P20 (though aluminum and stainless steel mold bases

Table 4.1: Common mold materials by application

Low number
of cycles
(nCycles < 10,000)

Moderate
number of cycles

High number
of cycles
(nCycles > 1,000,000)

Non-abrasive melt with low
molding pressures

Al alloys

Al or Cu alloys

Cu alloys, P20,
SS420

Slightly abrasive melt or
moderate molding pressures

Al or Cu alloys
or 1045

Cu alloys, P20,
4140, S7

SS420, S7, D2, A6

Highly abrasive melt

P20, S7

D2, A6, H13

H13

High molding pressures

1045, 4140, P20

P20, S7

D2, A6

Highly corrosive melt

P20, SS420

SS420

SS420

4.5 Chapter Review

89

are respectively available for lower pressure and corrosive applications). Plain 1045 steel is
often chosen for molding applications with lower production volumes and moderate molding
pressures. For higher production volumes and molding pressures, the alloyed steels 4140 and
P20 are usually preferred.

4.5

Chapter Review

The mold layout design process includes the examination of the part geometry to be molded
to identify the parting line, parting plane, and shut-offs. The core and cavity inserts are then
sized and located relative to each other. Afterwards, a suitable mold base is chosen that can
efficiently hold and support the core and cavity inserts. The mold layout process finishes with
the selection of the materials used for the mold base as well as the core and cavity inserts. In
many mold making companies, these materials are immediately ordered concurrent with the
detailed analysis and design of the mold subsystems.
After reading this chapter, you should understand:
• How to identify the mold opening direction(s) and parting line(s) for a molded part,
• How to design a parting plane and shut-offs to separate the core insert from the cavity
insert,
• How to size the length, width, and height dimensions for the core and cavity inserts,
• The advantages and disadvantages of different cavity layouts,
• How to layout a given number of mold cavities,
• How to size a mold base for a given mold cavity layout,
• How to verify that a mold is appropriate for a molding machine, and
• The advantages and disadvantages of various mold materials.
The next chapter examines the mold cavity filling process, which is required to 1) verify
that the part design can be produced at available melt pressures, and 2) estimate the loading
that will be placed on the mold components. Afterwards, the analysis and design of the feed
system will be addressed.

5

Cavity Filling Analysis and Design

For a molded part to be produced, the polymer melt must be able to completely fill the mold
cavity. Accordingly, the wall thickness of the molded part and the gating locations must be
specified such that the melt is able to traverse from the gates to the edge of the cavity. Mold
filling analysis is used to ensure that the melt can not only fill the mold, but fills the mold in
a desired manner.

5.1

Overview

Cavity filling analysis may be performed for a variety of purposes. On the most basic level,
mold filling analysis is useful to ensure that the mold cavity can be filled with the plastic melt
given the melt pressure that can be delivered by the molding machine. Typically, the melt
pressure required to fill the cavity is less than 100 MPa (about 15,000 psi) even though most
modern machines can supply twice this amount. This safety margin between the required
and available melt pressures provides an allowance for the pressure drop in the feed system,
and also ensures that the mold can be filled given possible variances in the material properties
or molding process.
Cavity filling analysis is also performed to ensure that the filling pressures are not too low, since
very low melt pressures are indicative of a poor molded part design or improper processing
conditions. For instance, excessively thick wall sections will result in low pressures, excessive
material costs, and extended cycle times. In such cases, the nominal wall thickness should be
decreased and ribs utilized to provide the necessary stiffness. As another example, very low
melt pressures can indicate improper filling time, mold temperature, or melt temperature.
These processing conditions should be adjusted to reduce the processing time and cost at the
expense of higher melt pressures.
On a more advanced level, cavity filling analysis is useful to predict the melt front advancement
in the cavity and identify the location of knit-lines, end of fill, and other phenomena
before the mold is manufactured and tested. These results can be used to adjust the gating
location(s), type of gate, cavity thicknesses, ejector locations, vent locations, and other design
parameters.
While modern computer simulations can provide detailed results for very complex cavity
geometries, “lay flat” cavity filling analysis remains extremely useful. This manual analysis
provides a means by which the mold designer can understand the primary flow behavior
and develop useful estimations to affect the mold design, process conditions, or validate
computer simulation results. To perform analysis, the mold design engineer must understand
the fundamentals of melt rheology and the governing equations for flow. Afterwards, a
methodology for cavity filling analysis will be presented and validated.

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5 Cavity Filling Analysis and Design

5.2

Objectives in Cavity Filling

5.2.1

Complete Filling of Mold Cavities

The part and mold design must be developed such that the mold cavity can be completely
filled by the polymer melt at workable melt pressures. For this reason, filling analysis of the
mold cavity should be performed to verify the part wall thickness for a given material, and
assist in the gate selection and processing conditions.
Modern molding machines can typically deliver injection pressures of approximately 200 MPa
(30,000 psi). However, a lower melt pressure should be assumed for filling the cavity to allow
for:




a lower required clamp tonnage,
reasonable pressure drop in the feed system, and
a factor of safety for errors in assumptions.

Since it is easier to adjust the molding process for a mold with too low melt pressures than
it is to adjust a mold with too high pressures, mold designers should assume a conservative
cavity filling pressure. In practice, a melt pressure of 100 MPa is commonly specified as a
maximum limit for the cavity filling pressure. The maximum cavity pressure may be specified
higher if the molding machine is known to have a very high injection pressure, or if the
mold’s feed system is purposefully designed to incur a small pressure drop (via a hot runner
system for example).
In the event that a mold is very difficult to fill, molders will generally try to compensate by
increasing the mold and melt temperatures, enlarging the runner diameters, trying lower
viscosity plastics, and finally changing the wall thickness of the mold cavity. Conversely, if a
mold is very easy to fill, molders will generally reduce the mold and melt temperatures while
increasing the injection velocity to shorten the cycle time.

5.2.2

Avoid Uneven Filling or Over-Packing

During mold filling, the plastic will tend to flow radially throughout the cavity from the point
where it is injected. In general, the mold should be designed such that the polymer melt reaches
the edges of the mold cavity furthest from the gate at approximately the same time. Such even
filling allows for more uniform and lower melt pressures throughout the mold cavity.
If one portion of the mold fills substantially earlier than other portions of the mold, then
the melt in the filled portions will stagnate with potentially serious consequences. Figure 5.1
shows the filling contours from the analysis of the Laptop bezel in which the plastic melt is
injected at two locations. Each contour represents the location of the melt front at different
moments in time. As can be observed, the plastic melt flows radially out of the gate and is
then constrained by the side walls. The polymer melt then flows up and down the side walls,
then across the top and bottom walls of the bezel.

5.2 Objectives in Cavity Filling

7

6

8

9

Last area to fill

10

11

11

10

5

9

8

7
6

4

Gates (2)

5

3
1

4

2
3

2
2

3

1

4

5

93

2

End of flow
6

3
4

7

8

9

10

10

9

8

7

6

5

Figure 5.1: Melt front progression of laptop bezel

During the majority of the filling, the flow rates to the upper and lower halves of the part
are equal. However, the plastic was injected at gates located slightly toward the lower portion
of the part, such that the bottom portion of the part fills before the upper portion of the
part. When the two melt fronts meet at the bottom center, very little additional plastic melt
can be forced into the lower portion of the part. The flow to the bottom portion of the part
stagnates, causing a surge in the melt flow to the upper portion of the part. The resulting
defects can possibly include:





Excessive cavity filling pressures required to fill the mold, excessive clamp tonnage, and
flashing;
Inability to fill the mold cavity (short shot);
High residual stress and warpage; and
Melt fracture, jetting, hesitation or other aesthetic defects associated with changes in melt
velocity during mold filling.

To avoid or resolve these issues, the mold design should consider the type and location of gate,
the layout and sizing of the feed system, the nominal thickness of the mold cavities, and using
slight changes in the wall thicknesses to purposefully direct the flow in the mold cavity.

5.2.3

Control the Melt Flow

Even when the mold fills uniformly, cavity filling analysis may be used to maximize the quality
of the part. For instance, it is sometimes desirable to control the melt front advancement
such that knit-lines are placed in areas of the part that are less important with respect to
aesthetics or structural integrity. Similarly, cavity filling analysis may be performed to predict
the last area to fill so that vents and/or ejector pins are provided for the displaced gas to exit
the mold. For anisotropic plastics (such as glass filled materials), cavity filling analysis and
design can be performed to control the flow direction to effect the molded in orientation,
strength, or shrinkage.

94

5 Cavity Filling Analysis and Design

5.3

Viscous Flow

5.3.1

Shear Stress, Shear Rate, and Viscosity

To analyze the polymer flow, it is necessary to understand the relationship between the shear
stress, shear rate, and viscosity. The shear stress, τ, is a measure of how much force per unit
area is being exerted by the fluid as it flows. The shear rate, γ , is a measure of the rate at which
the melt velocity changes. The shear stress is related to the shear rate through the viscosity,
η, which is a measure of the fluid’s resistance to flow:
τ = η γ

(5.1)

Consider the flow between a moving plate and a stationary plate shown in Figure 5.2. Assuming
that the flow is fully developed and does not slip at the walls, then a linear velocity profile
may develop in the fluid with the velocity equal to zero at the stationary wall, and equal to
v at the moving plate.

Figure 5.2: Flow between two parallel plates

For such a flow between one stationary and one moving parallel plate, the shear rate is defined
as the change in the velocity through the thickness, or:
γ =

dv v
=
dz h

(5.2)

Example: Compute the shear rate of a polymer melt being pulled at 100 mm/s by a moving
plate 1.5 mm above a stationary plate. If the viscosity is 100 Pa s, estimate the resulting
shear stress. For a plate with a length of 200 mm and a width of 100 mm, compute the
lateral force required to continue moving the plate at 100 mm/s.
The shear rate is:
γ =

v 100 mm/s
=
= 67 1/s
h
1.5 mm

With a viscosity of 100 Pa, s, the shear stress in the melt is:
τ = η γ = 100 Pa s ⋅ 67 s −1 = 6,700 Pa

5.3 Viscous Flow

95

If the plate is 0.2 m in length by 0.1 m in width, the lateral force on the wall of the moving
plate is:
F = τ A = 6,700 Pa ⋅ (0.2 m ⋅ 0.1 m) = 135 N

5.3.2

Pressure Drop

The pressure drop caused by the flow of the polymer melt in a channel can be analyzed by considering the equation of motion. For steady flow, the sum of the forces must equal to zero:

∑F = 0

(5.3)

Consider the forces acting laterally on the flow in a rectangular channel as shown in Figure 5.3.
As the flow moves from left to right, there will be a pressure drop along the flow with P1 being
greater than P2. This pressure drop is being caused by the viscous flow in the channel that is
generating shear stresses, τ, against the side walls.
There are two forces on the polymer melt that must balance. First, there is the force due to
the pressure drop, FΔP, across the length of the melt flow:
FΔP = P2 (W H ) − P1 (W H ) = (P2 − P1 ) (W H )

(5.4)

Second, there is the force due to the shear stresses, Fτ, acting on the top and bottom surfaces
along the length:
Fτ = 2 τ (L2 − L1 ) W

(5.5)

Equating the force due to the pressure drop and the force due to the shear stresses provides:
(P2 − P1 ) (W H ) = 2 τ (L2 − L1 ) W

(5.6)

Let dP/dL be the pressure drop per unit length. Simplifying then provides the following
result:
dP 2 τ
=
dL
H

(5.7)
W


H

P1
L1

P2


L2

Figure 5.3: Pressures and shear stresses in channel

96

5 Cavity Filling Analysis and Design

Example: A polymer melt has a wall shear stress of 13,000 Pa in a mold cavity that is
1.5 mm thick. Estimate the pressure drop across a cavity that is 200 mm in length.
The pressure drop per unit length is:
dP 2 τ 2 ⋅ 13,000 Pa
MPa
=
=
= 17.3
dL
H
0.0015 m
m
For a cavity with a length of 200 mm, the pressure drop is:
ΔP =

dP
MPa
⋅ L = 17.3
⋅ 0.2 m = 3.5 MPa
dL
m

To compute pressure drop as a function of the viscosity, it is necessary to define the viscosity
as a function of the shear rate and temperature so that the shear stresses can be computed.

5.3.3

Rheological Behavior

The term“rheology”refers to the study of deformation and flow of matter. The term“viscosity”
refers to the resistance of a fluid as it deforms under shear stresses.
The viscosity behavior of polymer melts can be extremely complex, much more so than is
often appreciated when practitioners contemplate melt flow indices (MFI1). Indeed, the MFI
is a single point estimate of the viscosity, and may not be very representative of the behavior
of the material that experiences a broad range of shear rates, temperatures, and pressures
when it is being molded. For this reason, many viscosity models have been developed for
plastics injection molding.
The Cross-WLF model [26] is widely known as a capable model of the melt viscosity, η, as a
function of shear rate, γ , temperature, T, and pressure, P:
η( γ ,T , P ) =

η0 (T , P)

1− n

⎛ η γ ⎞
1+ ⎜ 0 ⎟
⎝ τ* ⎠

(5.8)

In this model, η0 is the “Newtonian limit” in which the viscosity approaches a constant at
very low shear rates, τ* is a critical stress level at which the viscosity transitions from the
Newtonian limit to the power law regime, and n is the power law index in the high shear rate
regime. The form of the Cross model is readily understandable since these three parameters,
η0, τ*, and n, can be estimated directly from a log-log plot of the viscosity as a function of
shear rate as shown in Figure 5.4.
1

The melt flow index, defined by ASTM D1238, measures how many grams of polymer flow through a
capillary of a specified length and diameter given a specified amount of pressure and time. A higher melt
flow index usually corresponds to a lower viscosity and improved ease of processing.

5.3 Viscous Flow

97

*

log 

0

n

log



Figure 5.4: Cross model terms

In the above equation, the zero shear viscosity, η0, is a function of temperature, T, and pressure,
P. The temperature dependence can take many forms, but one of the most common models
uses WLF temperature dependence which includes pressure dependence through the shifting
of the glass transition temperature, T*:
⎡ A (T − T * ) ⎤
η0 (T , p) = D1 exp ⎢ − 1
* ⎥
⎣ A2 + (T − T ) ⎦

T > T*

(5.9)

T *( p) = D2 + D3 p

(5.10)

A2 = A3 + D3 p

(5.11)

η0 (T , p) = ∞

T < T*

(5.12)

The model parameters (n, τ*, D1, D2, D3, A1, A3) are typically determined by curve fitting
experimental shear-viscosity data taken by a capillary rheometer at shear rates from 10
to 10,000 1/s. The material properties for many thousands of plastics resins have been
characterized, and the Cross-WLF model coefficients for some representative materials are
provided in Appendix A. The Cross-WLF viscosity model for a medium viscosity PC is plotted
as a function of shear rate for three different temperatures in Figure 5.5.
As shown in Figure 5.5, the viscosity exhibits a Newtonian plateau for shear rates up to 100 1/s,
then transitions into a power law regime. For a melt temperature of 280 °C, the viscosity
decreases from 350 Pa s at 100 1/s to 80 Pa s at 10,000 1/s. Since the viscosity is strongly
dependent on the shear rate, estimation of the filling time, melt velocity, and shear rate are
vital to the analysis predictions. The viscosity is also a strong function of temperature, with the
zero shear viscosity increasing from 250 Pa s at 290 °C to 660 Pa s at 270 °C. Thus, knowledge
of the processing temperature is also important to predicting the melt flow and pressure.
While the Cross-WLF model is a very adept model and commonly used in numerical
simulation, it is not as useful in manual filling analysis. The issue is that it is difficult to
operate and not amenable to analytical solution of the pressure as a function of the melt flow

98

5 Cavity Filling Analysis and Design

Viscosity (Pa s)

1000

100
270 C
280 C
290 C
10
1

10

100

1000

10000 100000

Shear rate (1/s)

Figure 5.5: Viscosity behavior for PC

rate. For this reason, several other viscosity models are commonly used that have relatively
simple analytical solutions.

5.3.4

Newtonian Model

Newton’s law of viscosity states that the shear stress, τ, between parallel layers of flow is
proportional to the velocity gradient, γ :
τ = μ γ

(5.13)

where the coefficient μ is the apparent viscosity and is assumed constant for “Newtonian”
fluids.
Figure 5.6 compares the Newtonian model against the non-Newtonian behavior provided by
the Cross-WLF model for a medium viscosity PC at 280 °C. As previously stated, the polymer
melt is known to be non-Newtonian. For this reason, the Newtonian model provides an
exact estimate for the viscosity only at a shear rate of 7,000 1/s. The Newtonian model over
estimates the viscosity at higher shear rates, and under estimates the viscosity at lower shear
rates. Even so, the Newtonian model is very simple to operate and can provide reasonable
engineering estimates when a representative shear rate is used.
For a Newtonian flow, the velocity profile is a parabolic function of the thickness, z:
2

⎛2 z ⎞ ⎤
v(z ) = v max ⎢1 − ⎜ ⎟ ⎥
⎝H⎠ ⎥
⎣⎢


(5.14)

where vmax is the velocity at the centerline and z varies from –1/2 to +1/2 of the thickness. The
volumetric flow rate is the integral of the velocity across the thickness times the width, W:

5.3 Viscous Flow

99

Viscosity (Pa s)

1000

100

Cross-WLF
Newtonian
10
1

10

100
1000
Shear rate (1/s)

10000 100000

Figure 5.6: Newtonian model of viscosity behavior

V = W

H /2

∫− H / 2

2

⎛2 z ⎞ ⎤ ⎛2⎞
v max ⎢1 − ⎜ ⎟ ⎥ = ⎜ ⎟ v max W H = v W H
⎝ H ⎠ ⎥ ⎝3⎠
⎣⎢


(5.15)

The apparent shear rate can be calculated from either the average linear flow velocity or the
volumetric flow rate as:
γ =

6v
6 V
=
H
W H2

(5.16)

Given this estimate of the shear rate, the apparent viscosity should be evaluated and used for
estimation of the pressure drop.
Equations (5.7), (5.13), and (5.16) can be combined to provide estimates of the pressure drop
as a function of either the linear flow velocity or the volumetric flow rate:
ΔP =

5.3.5

12 μ L v 12 μ L V
=
H2
W H3

(5.17)

Power Law Model

Newton’s law of viscosity assumed that the viscosity is not a function of shear rate. When a
material does not obey this law, it is said to be non-Newtonian. One of the simplest and most
common non-Newtonian models is the power law model, which states that the viscosity is
an exponential function of the shear rate:
η = k γ 1− n

(5.18)

where k is the value of viscosity evaluated at a shear rate of one reciprocal second and n is
the power law index.

100

5 Cavity Filling Analysis and Design

Viscosity (Pa s)

1000

100
Cross-WLF
Power law model
10
1

10

100

1000

10000 100000

Shear rate (1/s)

Figure 5.7: Power law model of viscosity behavior

Figure 5.7 compares the power law model against the non-Newtonian behavior provided by
the Cross-WLF model for a medium viscosity PC at 280 °C. It is observed that the power law
model provides excellent estimates of the viscosity at higher shear rates, but overestimates
the viscosity at lower shear rates. For this reason, it should be expected that the power law
model will provide more accurate estimates than the Newtonian model, yet overestimate
the pressure drop compared to the Cross-WLF model since it over predicts the viscosity at
lower shear rates.
It should be noted that some resins, such as some grades of polypropylene, transition to a power
law regime at very low shear rates. For these types of materials, there is no apparent Newtonian
plateau and the power law model can be expected to provide very good estimates. For other
materials exhibiting a significant Newtonian plateau, such as the above polycarbonate, the
power law model can purposefully fit to a smaller shear rate regime of interest to provide
more accurate results.
For a power-law flow, the velocity profile through the thickness is a function of the power
law index, n:
v(z ) = v max

1

1+ ⎤
⎢1 − ⎛ 2 z ⎞ n ⎥
⎜⎝ ⎟⎠ ⎥

H
⎢⎣
⎥⎦

(5.19)

The volumetric flow rate is the integral of the velocity across the thickness times the width,
W:

V = W

H /2

∫− H / 2 vmax

1⎞

1

1+ ⎤
1+
n⎟v
⎢1 − ⎛ 2 z ⎞ n ⎥ = ⎜
W H =vW H
⎜⎝ ⎟⎠ ⎥ ⎜
1 ⎟ max

H
+
2

⎢⎣
⎦⎥ ⎜⎝
n⎠

(5.20)

5.3 Viscous Flow

n=1.0
n=0.6
n=0.2

100%
90%
80%
Velocity (%)

101

70%
60%
50%
40%
30%
20%
10%
0%
-50%

-25%
0%
25%
Thickness location (%)

50%

Figure 5.8: Velocity dependence on the power law index

It should be noted that a power law index, n, equal to one reverts the power law model to the
Newtonian model. As the power law index decreases, the viscosity exhibits increased shear
thinning such that the polymer melt flows faster near the side wall. As the power law index
approaches zero, a plug flow develops in which the melt velocity is almost constant through
the thickness. These behaviors are graphically depicted in Figure 5.8. Note that that the melt
velocity at the center-line decreases to maintain a constant volumetric flow rate as the power
law index decreases.
With the power law model, the shear rate at the wall is not required to estimate the pressure
drop, but may be useful to calculate to avoid excessive shear rates or check the viscosity of
the melt. It can be calculated from either the average linear flow velocity or the volumetric
flow rate as:
1⎞
1⎞


2 ⎜2 + ⎟ v
2 ⎜ 2 + ⎟ V



n
n⎠
γ =
=
H
W H2

(5.21)

Equations (5.7), (5.18), and (5.21) can be combined to provide estimates of the pressure drop
as a function of either the linear flow velocity or the volumetric flow rate:
1⎞ ⎤
⎡ ⎛
2 ⎜1 + ⎟ v ⎥


2kL
n⎠


ΔP =
H ⎢
H

⎢⎣
⎥⎦

n

1⎞ ⎤
⎡ ⎛
2 ⎜ 2 + ⎟ V ⎥


2kL
n⎠


=
H ⎢ W H2 ⎥
⎢⎣
⎥⎦

n

(5.22)

102

5 Cavity Filling Analysis and Design

5.4

Validation

Validation is next provided for a multi-cavity ASTM test mold that has been instrumented
with multiple piezoelectric cavity pressure transducers and cavity thermocouples. To validate
the analyses, consider just the flow in a rectangular impact specimen being 125 mm in length,
12.6 mm in width, and 3.2 mm in thickness. During validation experiments, parts were molded
of ABS (GE Plastics Cycolac MG47) and PP (Dow Inspire 702).
The mold coolant temperatures were set to the middle of the range recommended by the
material supplier. Parts were molded near the upper and lower range of the recommended
melt temperatures, and at a range of velocities. For each molding trial, the time taken for the
melt to traverse from the pressure transducer near the gate to the thermocouple near the end
of flow was calculated from the acquired data and used to provide the average linear velocity
and volumetric flow rate of the melt. The cavity pressure at the time when the melt reached
the thermocouple was also acquired, and is an accurate estimate of the true melt pressure
required to fill the mold cavity.
For each material and run condition, mold filling analyses were performed using the Newtonian model, the power law model, and numerical simulation (Moldflow MPI 5.1). The results
for ABS are provided in Figure 5.9, and the results for PP are provided in Figure 5.10.
These validation results indicate that all the models overpredict the pressures required to fill
this mold cavity. There are many reasons that the observed filling pressures may vary from
the model predictions:


The temperature of the melt may have been drastically increased due to shear heating
through the runner system.



The cavity pressure transducer may have been improperly designed or installed, or its
signal was improperly acquired or conditioned.



The melt may have slipped along the mold walls while the models all assume a no-slip
condition.



There may have been a variation between the materials used in the molding trials for
validation and the materials used for rheological characterization;



The capillary rheometry and the Cross-WLF rheological models may not have been
suitable for characterization of the viscosity;



There may have been a combination of these and many other unknown sources of
error.

The magnitude of the error between the observed and predicted pressures may seem surprising. However, there are few good alternatives to such filling analysis. One alternative is to
perform no analysis, and rely on past experience for estimation of filling patterns and pressures.
While this option may work for a mold designer who routinely designs similar molds for the
same material, it quickly becomes inadequate for new designs or materials. Another option
is to develop prototype molds with the appropriate flow length and thickness, and test the

103

25

25

20

20

15

Observed
Newtonian
Power Law
Moldflow

10
5

Filling Pressure (MPa)

Filling Pressure (MPa)

5.4 Validation

0

15
Observed
Newtonian
Power Law
Moldflow

10
5
0

20

40
60
80
Volumetric Flow Rate (cc/s)

220

230
240
250
Melt Temperature (°C)

260

9

9

8

8

7

7

6
5
4
3
Observed
Newtonian
Power Law
Moldflow

2
1
0

Filling Pressure (MPa)

Filling Pressure (MPa)

Figure 5.9: Validation of models for ABS

6
5
4
3
Observed
Newtonian
Power Law
Moldflow

2
1
0

30

40
50
60
Volumetric Flow Rate (cc/s)

190

200 210 220 230
Melt Temperature (°C)

240

Figure 5.10: Validation of models for PP

materials to be used under the expected processing conditions. Development of such prototype
molds provides the most accurate results, but also requires significant investment and so is
not economical for many molding applications.
While there is significant error, the results are self-consistent and important. First, it is observed
that the power law model predicted higher pressures than the Newtonian model. This should
be expected since the Newtonian model assumes a constant viscosity through the thickness,
which was evaluated for a representative shear rate taken at the wall according to Eq. (5.16).

104

5 Cavity Filling Analysis and Design

By comparison, the power law model tends to over predict the viscosity at lower shear rates,
so will provide higher pressure estimates. The Moldflow results provided higher estimates
than either the Newtonian or the power law models, likely due to its consideration of heat
loss from the hot melt to the cold mold and the development of a solidified layer.
In general, all the models correctly predicted the qualitative dependence of the filling pressure
on the flow rate and temperature. Higher flow rates require higher pressure to force the melt
through the mold, and this is observed in all the results. High melt temperatures provide
for lower viscosity of the melt and lower filling pressures, which again is reflected by all the
results.
The mold designer may actually take some comfort from these validation results. First, all the
models always over predicted the filling pressures. These results mean that the analyses are
conservative and, if used for mold design, should provide a mold that can produce molded
parts. Unfortunately, the analysis will drive part designs that are somewhat thicker than may
actually be possible to mold. In this case, the designed mold will provide for low injection
pressures and so molders will reduce the melt temperature and fill time to reduce the cycle
time and improve molding productivity.

5.5

Cavity Filling Analyses and Designs

There are many applications for filling analysis, including cost reduction, process optimization,
and quality improvements. While the following examples provide a broad array of typical
applications, the mold designer should customize or further develop these analyses according
to the specific needs of the molding application.

5.5.1

Estimating the Processing Conditions

Mold designers should verify that the mold can be filled given the cavity geometry and the
material properties. However, the filling analyses require the processing conditions including
the melt temperature and either the linear velocity or volumetric flow rate of the melt. It
is recommended that mold designers assume a melt temperature in the middle of the melt
temperature range recommended by the material supplier since this provides the molder
with some freedom to adjust temperatures up or down to correct molding problems or
reduce cycle time.
The true melt flow rate is not known until after the mold is made and commissioned. The
maximum flow rate is typically bounded by the maximum ram velocity of the molding
machine, or molding defects caused by high flow rates such as flash, jetting, or burn marks.
The minimum flow rate is typically bounded by the premature solidification of the melt in
the mold cavity which results in a short shot. Typical linear velocities of the melt through the
mold range from 0.01 to 1 m/s depending on the specifics of the molding application.

5.5 Cavity Filling Analyses and Designs

105

Thin wall applications will generally have higher linear flow velocities since



they require a faster injection to avoid premature solidification, and
their thinness provides for faster linear velocities given the same volumetric flow rate
from a molding machine.

Melt flow rates may be estimated by computing the volume of the mold cavities and runners
and dividing by the estimated filling time. This approach works well for those practitioners
with experience, but may not work well for new molding applications having very different
geometries or material properties. Alternatively, additional analysis can lead to a recommended
flow rate that balances the amount of shear heating with the heat loss from the melt to the
mold. This result should provide not only a reasonable estimate of the melt flow rate, but
also a more accurate analysis since it will tend to produce a uniform melt temperature as the
melt fills the mold.
The derivation of the melt velocity is provided in Appendix F. For a Newtonian material, the
recommended velocity is:
v =

5 (Tmelt − Twall ) κ


(5.23)

where Tmelt and Twall are the melt and mold wall temperature, κ is the thermal conductivity
of the plastic melt, and μ is the Newtonian viscosity. Since the viscosity is a function of the
shear rate and velocity, it is necessary to recompute the shear rate and viscosity until the
velocity converges.
Example: This analysis will now be applied to the laptop bezel, which has a wall thickness
of 1.5 mm and is to be molded of ABS (Cycolac MG47) at a melt temperature of 239 °C
and a mold coolant temperature of 60 °C. For the purpose of the analysis, we will initially
assume that the linear velocity is 0.5 m/s. At this velocity, the shear rate is computed as:
γ =

6v
6 ⋅ 0.5 m/s
=
= 2000 s −1
H
0.0015 m

(5.24)

At this shear rate, the Cross-WLF model provides a melt viscosity of 120 Pa s. This value
can then be used to provide a new estimate of the recommended injection velocity:
v =

5 (239 °C − 60 °C) 0.19 W/m°C
= 0.69 m/s
3 ⋅ 120 Pa s

(5.25)

Additional iterations are useful to hone in on the recommended velocity. At a velocity of
0.69 m/s, the shear rate is 2,760 1/s. The viscosity at this shear rate is 95.4 Pa s, which in
turn suggests a linear melt velocity of 0.77 m/s. A further iteration would yield a shear
rate of 3,080 1/s, a viscosity of 88.1 Pa s, and a melt velocity of 0.80 m/s. With additional
iterations, the solution will converge to a final velocity of 0.82 m/s. Since the flow length is
approximately 0.2 m, the mold cavity for the laptop bezel will fill in approximately 0.25 s

106

5 Cavity Filling Analysis and Design

(not including the runner system). Since the cavity volume is 30 cc, this corresponds to
a volumetric flow rate at the nozzle of 125 cc/s.
As implied by the form of Eq. (5.23), the recommended velocity will vary with the melt
temperature, the mold temperature, the thermal conductivity of the melt, and the melt
viscosity. Higher temperature differences between the melt and wall temperatures, as well as
higher thermal conductivity of the polymer melt, require faster melt velocities to maintain a
uniform melt front temperature. Lower viscosity materials require a higher melt velocity to
generate the shear heating needed to avoid excessive heat loss to the melt.
While the melt velocity does not appear to vary with wall thickness, the effect of wall thickness
is considered through the inclusion of the viscosity which is a function of the shear rate. As
the wall thickness decreases, the increasing shear rate reduces the viscosity, which thereby
requires higher melt velocities to avoid cooling the melt. As expected, higher melt velocities are
required as the wall thickness decreases. Figure 5.11 plots the recommended melt velocity for
ABS as a function of melt temperature and wall thickness using the analysis. It is observed that
the melt velocity can vary from about 0.4 m/s for a molding application with a wall thickness
of 3 mm and a melt temperature of 218 °C to about 1.6 m/s for a molding application with
a wall thickness of 0.8 mm and a melt temperature of 260 °C.
While there is a significant range in the recommended melt velocity as a function of the
molding application, it is important to recognize that the exact melt velocity and flow rate
that will actually occur during the molding process is unknown. The objective should be
to provide a reasonable estimate of the melt velocity and filling time, and design the mold
to operate under a wide variety of conditions. While the foregoing analysis may seem
unnecessarily complex compared to simply assuming a filling time based on experience, the
analysis is objective and provides a quantitative result that provides insights to the design
and use of injection molds.
1.6
Tmelt = 260
Tmelt = 239
Tmelt = 218

Melt velocity (m/s)

1.4
1.2
1
0.8
0.6
0.4
0.2
0
0.5

1

1.5

2

2.5

3

3.5

Wall thickness (mm)

Figure 5.11: Recommended melt velocity for ABS as a function of wall thickness and temperature

5.5 Cavity Filling Analyses and Designs

5.5.2

107

Estimating the Filling Pressure and Minimum Wall Thickness

To estimate the pressure required to fill a mold, the mold designer must know the total distance
that the flow is required to travel to fill the mold. For this reason, the mold designer should
select the gating location(s) to balance the flow between the different portions of the mold.
Since this is a one-dimensional flow analysis, features such as ribs and bosses are neglected.
These features are very likely to fill if they are relatively small compared to the main flow
channel. Prediction of the filling pressure can be made once the linear velocity of the melt is
known by straightforward application of either Eq. (5.17) or (5.22).2
To predict the filling pressure in complex products, it is necessary to deconstruct the geometry
into a series of simple segments. The flow in each segment can then be separately analyzed
using the Newtonian or power law models relating pressure drop to flow rates in the segment.
Returning now to the laptop bezel shown in Figure 5.1, it may be assumed that the flows on the
left hand and right hand sides are symmetric. Accordingly, the analysis will consider just half
of the geometry. To do the analysis, any turns in the bezel will first be straightened as shown
in Figure 5.12. While this step is not necessary for the analysis, it emphasizes that the analysis
considers only the pressure drop along the length of the melt flow. Next, the edges are folded
out to reveal additional flow that is required to fill the vertical sides of the mold cavity.
As shown in Figure 5.12, the gate location has been selected near the center location. The lay
flat geometry for the laptop bezel is then split into two flow segments representing the flow
to the upper and lower portions of the mold. It should be noted that it is possible to include
changes in the channel width, such as narrower sections due to windows, as shown in the
middle lay flat on the right side of Figure 5.12. Sections of varying thickness should also be
broken out into different flow segments. By analyzing the flow in each of these segments, it is
possible to provide very good estimates of the melt front locations and melt pressures as the
melt fills the mold. Alternatively, sections of similar width may be lumped together to simplify
the computation of the flow rate and filling pressures as shown in the right most lay flat.
Example: Estimate the pressure drop for the laptop bezel assuming a constant melt
velocity of 0.82 m/s.
The left most lay flat of Figure 5.12 is used, modeling one-quarter of the mold cavity as
a rectangular strip with a length, width, and thickness of 200 mm, 20 mm, and 1.5 mm.
The viscosity is fit with the power law model. The coefficients for an ABS material at
239 °C are a reference viscosity, k, equal to 17,070 and a power law index, n, equal to 0.348.
According to Eq. (5.22), the pressure is then:
2

The primary assumption in the estimation of filling pressures is that the melt velocity will be maintained
at a constant value as the melt propagates from the gate to the end of the mold. In theory, such a uniform
melt velocity could be achieved by careful ram velocity profiling. In practice, complex mold geometries
preclude the realization of uniform melt velocities, and ram velocity profiling is seldom used towards
this purpose anyways. As such, the melt velocity will vary substantially from the gate (where the velocity
is initially very high due to the small cross-sectional area of the melt) to the point of end of fill. Even so,
the estimation of filling pressures is vital to ensuring that the moldings can be made with the mold design
and the plastic materials used.

C:W=12, L=80

5 Cavity Filling Analysis and Design

W=20, L=200

or

or

A: W=20, L=200

Gate

B: W=20, L=120

W=20, L=200

108

Figure 5.12: Lay-flat of Laptop bezel (dimensions in mm)

1 ⎞
⎡ ⎛

2 1+
⎟⎠ 0.82 m/s ⎥
2 ⋅ 17,070 Pa s ⋅ 0.2 m ⎢ ⎜⎝
0.348


ΔP =
0.0015 m
0.0015 m


⎢⎣
⎥⎦
= 83,200,000 Pa = 83.2 MPa = 12,060 psi

0.348

This pressure is a fairly significant amount relative to the capabilities of most injection
molding machines, especially when considering that the estimated filling pressure does
not include the pressure drop through the feed system.
The product designer and mold designer may wish to consider the pressure required to fill
for a variety of wall thicknesses, flow rates, and melt temperatures. Figure 5.13 provides
the estimated filling pressure required to fill the cavity for a range of wall thicknesses at the
material’s mid-range melt temperature.
The minimum wall thickness allowable for a given injection pressure can be derived as indicated in Figure 5.13. Specifically, a line indicating the maximum allowable pressure is placed
on the graph with the minimum wall thickness occurring at the intersection of the pressure
curve. The analysis in this instance indicates that the minimum wall thickness is 1.36 mm.

5.5 Cavity Filling Analyses and Designs

109

Pressure to fill cavity (MPa)

250
200

Tmelt = 239

150
100
50
0
0.5

1

1.5

2

2.5

3

3.5

Wall thickness (mm)

Figure 5.13: Filling pressure as a function of wall thickness

There are two important concepts that should be understood when minimizing the wall
thickness. First, the minimum wall thickness is a function of the melt temperature. It is
recommended that mold designers use the mid-range temperature for analysis since this
reserves the opportunity for the molder to increase melt temperature and thereby reduce the
filling pressures if needed. Second, the minimum wall thickness is also a function of the feed
system design since the pressure deliverable to the cavity from the machine is dependent on
the pressure drop through the feed system as later discussed in Chapter 6.

5.5.3

Estimating Clamp Tonnage

The clamp tonnage is defined as the amount of force, usually measured in units of English
or metric tons of kiloNewtons, which is required to hold the mold closed during operation.
The clamp tonnage, FClamp, can be calculated as the integral of the melt pressure acting on
the projected area of the mold cavities:
Fclamp =

∫A P(A) cos θ(A) dA

(5.26)

where P(A) is the melt pressure in the mold across the area of the cavity and θ(A) is the angle
between the direction normal to the mold cavity surface and the mold opening direction.
The projected area of the cavity is used rather than the total area of the mold cavity since the
melt pressure acting on inclined (or vertical) side walls contribute little (or no) force in the
direction of the mold opening.
The maximum clamp tonnage typically occurs at the end of the filling phase when the filling
pressure is at their peak value, or at the start of the packing phase when the entire mold
cavity becomes pressurized at the packing pressure. It can be difficult to discern during
actual molding whether the maximum clamp tonnage will be driven by the pressures during
filling or packing.

5 Cavity Filling Analysis and Design

75
50
25
0

Gate

100
75
50
0

End of filling

180

200

140

120

(m
m)

160

80

alo
ng
flow

200

160

Po
siti
on
180

120

140

on
alo
ng
flow
(m
m)

100

80
100

Po
siti

60

60

40

40

20

20

25
0

Melt pressure (MPa)

Gate

100

0

Melt pressure (MPa)

110

Start of packing

Figure 5.14: Cavity pressures during filling and packing

Consider the cavity pressure distributions along the lay flat model of the laptop bezel shown
in Figure 5.14.
The figure at left indicates that there will be a linear pressure drop along the flow in the cavity
from 100 MPa at the gate to 0 MPa the end of fill. The average pressure exerted in the cavity
is 50 MPa. While the width of the lay-flat was approximately 20 mm, the projected area of
the lay flat (refer to Figure 5.12) is approximately 12 mm. The clamp tonnage for this strip
required at the end of filling is:
Fclamp = 50 MPa ⋅ 0.2 m ⋅ 0.012 m = 120 kN = 12.2 mTon

(5.27)

During packing, a slightly lower pressure is applied but the pressure in the cavity is much
more uniform. Typically, the packing pressure is between 50 to 90% of the filling pressure. As
shown at right in Figure 5.14, the average cavity pressure may be 75 MPa, which corresponds
to a clamp tonnage required at the start of packing of:
Fclamp = 75 MPa ⋅ 0.2 m ⋅ 0.012 m = 180 kN = 18.3 mTon

(5.28)

The analysis indicates that the peak clamp tonnage in this case will occur at the start of
packing when the melt pressure in the cavity equilibrates. Since the packing pressure depends
on the molding process and desired shrinkage, the exact value of the packing pressure is not
known until the mold is made and operated. For this reason, a conservative approach is to
assume that the filling pressure will be exerted everywhere in the cavity. The clamp tonnage
can then be estimated as:
Fclamp = Pcavity ⋅ Acavity_projected

(5.29)

where Pcavity is the assumed average pressure in the cavity and Acavity_projected is the projected
area of the cavity. If the filling analysis suggests a reasonable filling pressure, then this value
may be used for estimation of the clamp tonnage. The filling pressure for some molding

5.5 Cavity Filling Analyses and Designs

111

applications, however, may be very low and give rise to excessive shrinkage. To avoid this issue,
molders will generally use packing pressures in the vicinity of 50 MPa. As such, the mold
designer should verify the expected cavity pressures with the molder or assume a minimum
cavity pressure of 50 MPa.
Example: Estimate the maximum clamp tonnage required to mold the laptop bezel.
For the laptop bezel with a 1.36 mm wall thickness, the melt pressure was designed to be
100 MPa. The projected area is 9,724 mm2. If this pressure is assumed throughout the
mold cavity, then the estimated clamp tonnage is:
Fclamp = (100 ⋅ 106 Pa) ⋅ (9724 ⋅ 10 −6 m 2 ) = 972,000 N = 99 metric tons
To validate the foregoing analyses of the previous three sections, a thickness of 1.36 mm was
implemented in the laptop bezel. Two gates were located at the center of the left and right
side walls. The simulation (Moldflow MPI 5.1) was performed for ABS (Cycolac MG47) with
a melt temperature of 239 °C, a mold temperature of 60 °C, and a filling time of 0.25 s to
correspond to a linear melt velocity of 0.8 m/s.
A comparison of the analytical results with those of the numerical simulation is provided
in Table 5.1. The simulation predicted a filling pressure of 110 MPa, which compares well to
the designed filling pressure of 100 MPa. The simulation would be expected to predict higher
pressures since it models the development of a solidified layer as well as the flow in ribs, bosses,
and other thin sections. The simulation predicted an increase in the average melt temperature
of 3.4 °C, which verifies that the analytically derived melt velocity is a very good estimate.
The clamp tonnages predicted by the described analysis and the commercial simulation during
filling are very close. The simulation predicted a 7% higher clamp tonnage during filling,
which corresponds closely to the 10% higher melt pressure that the simulation predicted
during filling. The clamp tonnages predicted during packing, however, vary substantially.
The presented analysis assumed that the injection pressure was exerted throughout the cavity.
This assumption is conservative, and predicted a high clamp tonnage. By comparison, the
simulation models the solidification of the melt throughout the cavity and the resulting decay
in the melt pressures. For this reason, the simulation predicted a much lower clamp tonnage
of 397 kN occurring at 1.2 s into the packing stage. While this clamp tonnage may occur at
this time, it does not represent the peak clamp tonnage that occurs at the very start of the
Table 5.1: Comparison of analytical and simulation results

Parameter

Analysis result

Filling pressure (MPa)
Change in bulk melt temperature (°C)
–1

Average shear rate (s )

100
0

Simulation result
110
+3.4

1760

1290

Clamp tonnage during filling (kN)

486

519

Clamp tonnage during packing (kN)

972

397

112

5 Cavity Filling Analysis and Design

packing stage, or the clamp tonnage that may be required if the molding machine controller
overshoots the velocity to packing changeover location.

5.5.4

Predicting Filling Patterns

Filling patterns can be readily predicted using the lay flat analysis technique, and are useful to
understand the behavior of the melt in filling the mold, locating gates, identifying knit-line
locations, and assisting in other aspects of mold design. Analysis will be performed for a five
sided container with a width, length, and height of 100 mm, 160 mm, and 60 mm respectively.
The container is shown in Figure 5.15 and has a 2° draft with 10 mm fillets. Assuming that a
two-plate mold will be used, the container will be gated at the edge of a side wall.
To predict the filling patterns, the sides of the container are “cut” at the corners and the side
walls folded down to make a lay flat. The gate location is next identified. The flow will emanate
from the gate producing a circular melt front. As such, an arc may be drawn from the gate
representing the position of the melt at a given point in time. Figure 5.16 provides the lay
flat and some early melt front locations.
Each arc in Figure 5.16 corresponds the location of the melt front at a different time step; the
distance between arc is equal to the linear melt velocity times the time step. While the melt
location at the first time step is correct, the melt will hit the adjacent side wall by the end of
the second time step. As such, it is necessary to draw additional arcs on these adjacent side
walls reflecting the position of the melt flow at various time steps. To correctly predict the
flow behavior, the analysis must maintain the same flow resistance between the melt flowing
in the various portions of the mold. This can be accomplished by creating a “phantom” gate
and maintaining the same flow lengths from this “phantom” gate as from the real gate. For
each time step, the length of flow is increased and an arc of corresponding radius is drawn.

Figure 5.15: Container for prediction of fill patterns

5.5 Cavity Filling Analyses and Designs

Gate

1

2

3

113

4

Figure 5.16: Lay flat and first melt front locations

Intersecting arcs corresponding to the same time step are then trimmed. The flow is advanced
with more phantom gates added as needed until the flow throughout the entire lay flat is
created.
Figure 5.17 demonstrates this melt front prediction process and the resulting melt front
locations for the container. It is observed that the flow races around the side walls and will
form a weld line and a gas trap on the side wall opposite the gate. This phenomenon, known
as “race-tracking”, is quite common in molded parts and can occur when the length of flow
around the perimeter of the molding is less than the length of flow across the center-line of
the part.
Weld line
Gas trap

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9
1

Phantom
gate

2

…

9

10

Gate

Phantom gate

Figure 5.17: Melt front locations for part of uniform thickness

114

5 Cavity Filling Analysis and Design

In this case, race-tracking occurred because the 60 mm depth of the container is more than
one-half the 100 mm width of the container. While the weld line is not desirable, a gas trap
on a side wall such as shown in Figure 5.17 is especially problematic since it is difficult to vent.
As such, the trapped air will likely combust, causing a burn mark to appear at this location.

5.5.5

Designing Flow Leaders

The gas trap in the previous example could have been avoided by moving the edge gate to the
center of the 160 mm long side wall, or by using a three-plate or hot runner mold to gate at
the center of the mold cavity. Sometimes, however, the mold layout precludes these designs. As
such, another alternative is to vary the thickness so that the melt purposefully flows faster in
some portions of the mold. Such thicker sections used to control the flow velocity are generally
known as “flow leaders”. It should be understood that thickness variations in molded parts
are generally undesirable as discussed in Section 2.3.1. For the reasons discussed therein, the
cavity thickness variation should be kept to a minimal amount.
Newtonian flow analysis will now be used to redesign the wall thickness of the container
to resolve the race-tracking issue. Equation (5.17) relates the pressure drop, velocity, and
thickness. To eliminate the race tracking, the pressure drop across the center-line should
equal the pressure drop around the perimeter:
ΔPcenterline = ΔPside_walls

(5.30)

This condition will ensure that the flow traverses across the center-line at the same time
that the flow reaches the far corners of the adjacent side walls to eliminate the race-tracking
phenomenon. The flow lengths are provided in Figure 5.18. From the geometry of the

Gate

1

2

Lcenterline = 280 mm

Lside walls = 210 mm
Figure 5.18: Lay flat showing flow lengths

5.5 Cavity Filling Analyses and Designs

115

container, the lengths of flow across the center-line and around the side walls are calculated
to be 280 mm and 210 mm, respectively.
From Eq. (5.17), the pressure drops across the center-line and around the side walls can be
evaluated and equated as:
12 μcenterline Lcenterline vcenterline 12 μside_walls Lside_walls vside_walls
=
2
2
H centerline
H side_walls

(5.31)

The melt velocities in sections of different sections will not be equal. In fact, it is desired that
the velocity of the perimeter be:
vside_walls = vcenterline

Lside_walls
Lcenterline

(5.32)

This condition will cause the melt to arrive at the far corner of the side wall at the same
time it reaches the opposite side of the cavity along the center-line. Substituting this relation
into Eq. (5.31) and solving for the thickness of the side walls, Hside_walls, as a function of the
nominal thickness, H:
H side_walls = H

Lside_walls
Lcenterline

μside_walls
μcenterline

(5.33)

The analysis indicates that the wall thickness will be largely proportional to the ratio of the
flow lengths with a lesser dependence on the melt viscosities. Assuming the same viscosity
throughout the cavity, the thickness of the side walls can be evaluated as:
H side_walls = 2 mm

210 mm
= 1.5 mm
280 mm

(5.34)

The lay flat analysis can also be used to predict the filling patterns for parts of varying
wall thickness. When the wall thickness varies, it is necessary to increase the radii of the
arcs to represent the distance that the melt traveled during the time step. For this case, the
thickness of the side walls has been chosen such that the velocity of the melt in the side
walls is:
vside_walls = vcenterline

Lside_walls
210 mm
= vcenterline
= 75% vcenterline
Lcenterline
280 mm

(5.35)

In the lay-flat analysis, the radius of each arc in the thinner section should be incremented by
75% of the arc in the thicker sections. Still using the same phantom gate, the resulting melt
front progression in the redesigned container is shown in Figure 5.19. The arrows along the
edge of the side wall show the incremental position of the melt front in this section at various
time steps. The analysis indicates that the melt does reach the end of the side walls before the
melt reaches side of the cavity opposite the gate.

116

5 Cavity Filling Analysis and Design

2 mm wall
thickness

1

2

3

4

5

6

7

8

9

10

11

11

Gate

1.5 mm wall
thickness
Phantom
gate
1

6

2

3

4

5

7

6

8

7

9

10

8

9

10

Figure 5.19: Melt front locations for part with flow leaders

Uniform thickness

Thinner side walls

Figure 5.20: Simulated melt front with and without flow leaders

To validate the lay flat approach, numerical simulations were performed for the container
having a uniform thickness of 2 mm, and a second container in which the thickness of the
side walls was decreased to 1.5 mm. The results are shown in Figure 5.20.
As in the lay flat analyses, the simulation indicated that the container without the flow leader
would exhibit race-tracking, a weld line, and a gas trap. Reducing the thickness of the side
walls to 1.5 mm eliminated the problem. For reference, the reduction in the thickness of the
side-wall from 2 mm to 1.5 mm did increase the injection pressure 10% to fill out the thinner
side walls but also decreased the part weight by a similar amount.

5.6 Chapter Review

5.6

117

Chapter Review

All mold engineering designs should consider the propagation of the viscous polymer melt
throughout the mold cavity. Numerical simulations are preferred due to their ability to quickly
and accurately consider non-Newtonian flows in complex geometries. However, analyses with
Newtonian and power law viscosity models are not difficult to use and have been shown to
provide accurate results when aptly used.
The single most important purpose of filling analysis is to ensure that the mold cavity can
be completely filled by the specific plastic material. If the wall thickness of the cavity is too
thin and the melt pressure required to fill the cavity exceed the capability of the machine,
then incomplete moldings (known as “short shots”) will be produced. The molder will try to
remedy the problem by attempting to increase the melt temperature or injection pressure, or
by using another resin. If these attempts are unsuccessful, then the mold will require design
changes including the addition of more gates, increasing the diameters of the feed system,
increasing the wall thickness of the mold cavity, or other changes. Such physical alterations
of the mold can be expensive and time consuming.
Filling analyses can also be used to estimate the clamp tonnage, optimize the wall thickness,
estimate the processing conditions, predict the advancement of the plastic melt throughout
the cavity, and remedy filling problems by locating gates or designing flow leaders. While the
governing equations for the Newtonian and power law provided in Eqs. (5.17) and (5.22)
seem simple, careful application is required to obtain useful solutions. It is recommended
that filling analyses utilize mid-range melt temperatures when evaluating the viscosity, and
the dependence of the viscosity on shear rate be verified when using the Newtonian model.
After reading this chapter, you should understand:
• The relationship between shear stress, shear rate, and viscosity;
• The relationship between cavity fill time, linear melt velocity, and volumetric flow rate;
• The assumptions made in development of the Newtonian and power law models, and
potential issues associated with their use;
• How to estimate the length of flow in a mold cavity from a gate to the end of flow;
• How to calculate the shear rate, viscosity, filling pressure, and clamp tonnage for melt flow
in a rectangular mold cavity using either the Newtonian or power law model;
• How to estimate the minimum wall thickness in a molding application given the material
properties and maximum filling pressure.
The next chapter examines the design of the feed system for two plate molds, three plate
molds, and hot runner molds. Flow analyses for the viscous melt in cylindrical and annular
members is presented and used for feed system design. Afterwards, the analysis and design of
gates will be presented before addressing cooling and other elements of mold design.

6

Feed System Design

6.1

Overview

The purpose of the feed system is to convey the plastic melt from the molding machine to
the mold cavities. The design of feed systems can range from very simple to very complex.
Increased investment in the feed system design will tend to provide for reduced cycle time
and less material waste when using the mold. However, it is possible to overdesign the feed
system and the “best” feed system design is a function of the production volume, availability
of molding pressure, and level of allowable investment.
The design of the feed system follows a three step process. First, the type of feed system (twoplate cold runner, three-plate cold runner, or hot runner) is selected if not already known.1
Second, the routing of the feed system through the mold is determined. Third, the diameters
of each segment of the feed system are specified to balance pressure drops, shear rates, and
material utilization. To assist the design process, a discussion of the objectives in feed system
design is next provided.

6.2

Objectives in Feed System Design

6.2.1

Conveying the Polymer Melt from Machine to Cavities

The primary function of the feed system is to convey the polymer melt from the nozzle of the
molding machine (where it is plasticized) to the mold cavities (where it will form a desired
product). In most molding applications, the polymer melt must traverse portions of both the
mold height and the mold width. The traversal of the height and width can be accomplished
by two different layouts designs for the feed systems as shown in Figure 6.1. The feed system
layout shown at left corresponds to a two-plate mold design. The sprue is used to guide the
polymer melt from the nozzle of the molding machine to the parting plane. Runners in the
parting plane are then used to guide the polymer melt across the parting plane to one or
more mold cavities.
The second layout design, shown at right of Figure 6.1, corresponds to a three-plate or hot
runner mold. In this second design, the polymer melt is guided across the width and length
dimensions of the mold by runners that are offset to the parting plane. Since the runners are
offset from the parting plane, there is significant design freedom with respect to their routing
and gating location. However, two sets of sprues are needed for the polymer melt to traverse
1

These three types of feed systems are the most common, though a few other feed system technologies are
discussed in Section 13.6.

120

6 Feed System Design

Down
ss
Acro

Down

Down

Down
ss
Acro

ss
Acro

ss
Acro

Figure 6.1: Two feed system layouts for melt conveyance

the height of the mold. First, a sprue is needed to guide the polymer melt from the nozzle
of the molding machine to the plane of the lateral runners. After the melt flows across the
runners, a second set of sprues is needed to guide the melt down through a portion of the
mold height to the mold cavities.

6.2.2

Impose Minimal Pressure Drop

As the melt propagates through the feed system and cavities, the melt pressure in the
injection molding machine will increase. The feed system must be designed so that there is
sufficient melt pressure to drive the polymer melt throughout the mold cavities. As shown
in Figure 6.2, a feed system with a large flow resistance will incur a substantial pressure drop
during the molding process. The flow rate of the polymer melt will begin to decay when
the molding machine reaches the maximum allowable injection pressure. If the flow rate
decreases substantially before the end of the mold filling process, then a short shot or other
defects are likely to occur.
The feed system must be designed to incur an acceptable pressure drop to avoid short shots,
extended cycle times, and other defects. The “acceptable” pressure drop through the feed
system will depend on the specifics of the molding application, especially the melt pressure
required to fill the cavity compared to the melt pressure available from the molding machine.

Pcavity
Pgate
Psprue & runners

Time

Figure 6.2: Pressure and flow rate coupling

Flow rate

Pressure

Pmax

Time

6.2 Objectives in Feed System Design

121

For example, a thin wall molding application may use a molding machine with 200 MPa of
available melt pressure. If 150 MPa is required to fill the cavity, then the pressure drop through
the feed system should not exceed 50 MPa. However, if the same machine was used to mold
a part requiring only 100 MPa of pressure, then the feed system could be designed to impose
a pressure drop of 100 MPa.
To accurately specify the acceptable pressure drop for the feed system design, the mold designer
should contact the molder to obtain the molding machine’s maximum injection pressure. The
mold designer should also obtain an estimate of the melt pressure required to fill the cavity
through analysis, simulation, prototype molding, or prior experience. If this information is
not known, then the mold designer can assume a maximum pressure drop through the feed
system of 50 MPa (7,200 psi). While this pressure drop is slightly higher than some industry
practices, this specification will result in a steel-safe design with smaller feed system diameters
and lower material utilization.

6.2.3

Consume Minimal Material

Pmax

Vfeed_system

Pfeed_system

To achieve the best feed system design, the mold designer should specify the diameters of the
feed system to jointly minimize the pressure drop and the feed system volume. These design
constraints are represented in Figure 6.3. As the diameters of the various segments of the
feed system increase, the pressure drop decreases below the specified maximum. However,
increasing the diameters of the feed system also results in an increase in the volume of the
feed system, which can be undesirable for both cold and hot runner feed systems.
In cold runner designs, the large size of the feed system can result in extended cycle times
as well as excessive waste associated with the molding of the feed system. Some molding
applications allow the use of regrind mixed with virgin material. A typical limit on regrind
may be 30%, which translates directly to a specification on the maximum volume of the feed
system. For example, if a molding application had two cavities totaling 50 cc, then a 30%
regrind specification would limit the volume of the feed system to 15 cc.
In hot runner designs, large feed systems reduce the turn-over of the material in the hot runner.
Low turn-over is undesirable for two reasons. First, long residence times of the polymer melt
in the hot runner can cause material degradation which frequently causes black spots and
reduced properties of the molded product. Second, large volumes of material in the hot runner

Vmax

Dmin
Diameter

Figure 6.3: Coupling between volume and pressure drop

Dmax
Diameter

122

6 Feed System Design

system can impede color changes during molding, not only due to the large volume of the
plastic melt that needs to be flushed, but also due to the low associated shear stresses along
the walls of the feed system. Low shear stresses during purging allow the material to stick to
the walls of the hot runner, reducing the removal of old material during color changes.
The maximum volume of polymer melt in a hot runner feed system can be difficult to specify
since it is related to the type of material being molded, the need to perform color changes, and
the desired pressure drop. Hot runners are being increasingly designed with smaller diameters,
such that the material turns over every molded cycle. For example, if a molding application had
two cavities totaling 50 cc, then a turn over of the melt with every molding cycle would specify
the volume of the feed system to be 50 cc. If a very low pressure drop is desired, then the volume
of the feed system may be specified as 100 cc or even 200 cc if degradation and color change
issues are not expected. It should be noted, however that unlike a steel-safe designed cold runner system, high costs may be incurred to reduce the diameters of a hot runner system.

6.2.4

Control Flow Rates

Since the primary function of the feed system is to convey the melt from the molding machine
to the mold cavities, it is desirable for the feed system to control the amount of polymer
melt to each mold cavity. The two most common applications pertain to multi-cavity and
multi-gated molds.




In a multi-cavity mold, as shown in Figure 6.1, the molding application may require different pressure drops in each leg of the feed system to cause the different mold cavities to fill at
the same time. In this example, if the cup required a higher pressure to fill than the lid, then
the mold designer could provide a lower pressure drop in the portion of the feed system
leading to the cavity for the cup. Such a mold design is known as “artificially balanced”.
In a multi-gated mold, a common objective in the feed system design is to control the
polymer melt flowing through the feed system to alter the melt front advancement in a
multi-gated mold. For instance, it may be desirable to drive more material through one gate
to move a knit-line to a different location. Other common uses include the altering of the
mold filling to eliminate a gas trap or avoid over-filling a portion of the mold cavity.

Using different diameters in the feed system can control the flow of the polymer melt, but
there are limits as what can be achieved. First, the pressure drop through each leg of the feed
system is dependent on the viscosity of the polymer melt. As such, an artificially balanced feed
system may not balance the mold filling for different materials and processing conditions.
Second, differently sized feed systems will solidify at different rates and thereby provide
different dynamics during the packing stage of the molding process; runner segments with
smaller diameters will tend to freeze quickly and reduce the amount of packing to downstream
cavities. For these reasons, the mold designer should strive to utilize mold cavities that have
similar filling requirements. If family molds or other needs dictate very different flow rates
through each gate, then the mold designer may wish to utilize a melt control technology such
as Dynamic FeedTM as discussed in Section 13.6.4.

6.3 Feed System Types

6.3

123

Feed System Types

The most common types of molds were first introduced in Chapter 1. In this section, the
layouts of the different types of feed systems and their accompanying components are
discussed in greater detail.

6.3.1

Two-Plate Mold

The two-plate mold is so named since it consists of two assembled sections that sandwich
the melt; each half of the mold can consist of one or more mold plates. A section of an
isometric mold is provided in Figure 6.4. During the molding process, the nozzle of the
molding machine mates with the radius of the sprue bushing. The polymer melt flows down
the sprue bushing, thereby traversing the thickness of the top clamp plate and A plate. The
material then flows across the parting plane through runners and gates into one or more
mold cavities.
After the plastic has solidified, the mold is opened at the parting plane, which is located
between the A and the B plates. Typically, the A-half of the mold remains stationary while
the B-half of the mold is pulled away with the moldings and runner system remaining on the
core. To facilitate ejection, a reverse taper is usually provided below the sprue to ensure that
the sprue and attached runner remains with the B half. After the mold has opened sufficiently
to remove the moldings, the ejector plate is pushed forward by the molding machine. The
sprue knock-out pin pushes on the sprue, breaking the small under-cut and ejecting the
sprue from the B-side of the mold. While not shown in Figure 6.4, additional ejector pins
and knock-out pins can be placed down the length of long runners to facilitate ejection of
the feed system.
Figure 6.5 shows the molding that would be produced from the mold design of Figure 6.4.
In the design of the feed system, the length of the sprue is determined by the combined
thicknesses of the top clamp plate and the A plate. The lengths of the runners are determined
by the position of the cavities and the layout of the associated runners. Given this layout, the
mold designer needs to specify the diameters of the feed system. In general, the diameters
of the upstream runners are larger than the diameters of the downstream runners, since the
flow of the polymer melt branches at runner junctions and there will be a lesser flow rate
through each of the downstream runners.
While a two cavity, two-plate mold is used to demonstrate mold design concepts, the provided
analysis can be applied to more complex feed system layouts. For example, Figure 6.6
provides a feed system design for an eight cavity family mold including two primary runners,
four secondary runners, and eight tertiary runners. If the flow rate through the sprue was
100 cc/s, then the flow rate through each of the primary, secondary, and tertiary runners
would respectively be 50 cc/s, 25 cc/s, and 12.5 cc/s. If the flow resistance in the cavities varied
substantially, however, then the flow rate in the tertiary runners could vary substantially
during the mold filling stage.

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6 Feed System Design

Figure 6.4: Isometric section of two-plate mold

Figure 6.5: Two-cavity molding with runners and sprue

6.3 Feed System Types

125

Figure 6.6: Eight-cavity molding with runners and sprue

As with the feed system design shown in Figure 6.5, the diameter of each downstream runner
is smaller than the upstream runner shown in Figure 6.6. There is one notable exception:
the diameter of the molding machine’s nozzle orifice is typically smaller than the diameter
of the sprue inlet. The smaller nozzle orifice provides a point for separation between the
molded sprue and the solidified plug in the nozzle of the molding machine. If the nozzle
orifice were larger than the sprue inlet, then the frozen section of plastic in the nozzle behind
the sprue bushing could cause the sprue to stick to the A-half of the mold. If such sticking
occurs frequently, then the molder may choose to perform a “sprue break” by retracting the
injection unit of the molding machine from the machine nozzle prior to mold opening and
part ejection. This action is undesirable since it adds complexity and variance to the molding
cycle, so the mold designer should verify and/or recommend the nozzle orifice diameter
appropriately.

6.3.2

Three-Plate Mold

A sectioned isometric view of a fully open three-plate mold design is provided in Figure 6.7; the
view provided in Figure 6.7 does not include the ejector housing and associated components
since these are not central to the operation of the three-plate mold. Three-plate molds are
comprised of three mold sections that move relative to each other, with each section consisting

126

6 Feed System Design

Figure 6.7: Isometric section of three-plate mold

of one or more plates. The addition of a second parting plane between the A plate and the top
clamp plate allows for runners to be located above the mold cavities, and to traverse across
the width and length of the parting plane without interfering with the mold cavities. For this
reason, the three-plate mold provides greater freedom with respect to gating locations and the
feed system layout. An added benefit is that three-plate molds provide automatic separation
of the molded parts from the feed system as shown in Figure 6.7.
Figure 6.8 provides a section through a fully closed three-plate mold. In this design, the
polymer melt flows down the sprue bushing across the thickness of the top clamp plate and
stripper (or “X”) plate. The polymer melt then flows along runners located in the parting
plane (referred to here as the “A-X” parting plane) between the A plate and the stripper plate.
Tapered sprues are then used to convey the melt through the thickness of the A plate and any
cavity insert support plate to the mold cavities.
Sprue pullers, also known as“sucker pins”, are used near the sprue locations and other portions
of the runner to ensure that the feed system remains with the stripper plate; the mold designer
should design the sucker pins such that they do not restrict flow. In the feed system design
of Figure 6.8, the pins have a small diameter and depth compared to the dimensions of the
primary runner. To further reduce the flow obstruction, they could be moved further away
from sprue bushing.

6.3 Feed System Types

127

Figure 6.8: Section of closed three-plate mold

Figure 6.9 provides a section through a partially opened three-plate mold. After molding, the B
side of the mold is pulled away from the A-side, forcing the mold to open at the parting plane
between the A and B plates; the ejector system, rear clamp plate, and associated components
have been omitted. A spring located between the A plate and the stripper plate may be used
to cause early separation of the A-X parting plane. The B-side continues to open, with the
distance between the A and the B plates controlled by the length of a stripper bolt connecting
the A plate to the B plate. The free length of the stripper bolt must be sufficient to allow for
the ejection of the molded parts. A typical mold open distance between the A and B plates
is equal to two to three times the height of the molded parts. As shown in Figure 6.9, this
distance can be quite large for even relatively short parts.
Once the length of the stripper bolt is traversed, the A plate will move away from the stationary
platen along with the B plate. The A-plate will traverse the free length of the stripper bolt for
the stripper plate. The free length of this stripper bolt determines the mold opening distance
between the A plate and the stripper plate. As with the A plate stripper bolt, the length of
the X plate stripper bolt must be sufficient to allow for the removal of the feed system. Once
the A plate traverses past the free length of the X plate stripper bolt, the stripper plate will
move away from the top clamp plate along with the A section, B section, and ejection system
of the mold.

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6 Feed System Design

Figure 6.9: Partial section of partially opened three-plate mold

Figure 6.10 provides a section through a fully opened three-plate mold without the ejector
system or rear clamp plate. During mold operation, the mold opening velocity and position
must be carefully determined and controlled to achieve an efficient and fully automatic
cycle. If the molding operation is not carefully set up, then the feed system may not be
reliably ejected or the mold can be damaged. To optimize the mold operation, the mold
opening distances in many three-plate molds can be adjusted by changing the position
of nuts on the stripper bolts or by adding washers between the plates and the ends of the
stripper bolts.
It should be noted that this three-plate design has been made as compact as possible with
respect to mold opening distances, selection of plate thicknesses, and stripper bolt lengths. As
such, it is insightful to compare the design of the three-plate mold with that of the two-plate
mold as done in Table 6.1. The additional plates and components in the three-plate mold
has increased the stack height by 44 mm (1 ¾ inches) and the mass by 30 kg, relatively small
increases (on the order of 20%). However, the three-plate mold has a mold opening distance
of 250 mm, much greater than the mold opening distance of 75 mm for the two-plate mold.
This larger mold opening distance is undesirable since it adds to the mold opening and closing
time, and may also prevent the mold from operating in some injection molding machines
with limited daylight.

6.3 Feed System Types

129

Figure 6.10: Partial section of a fully opened three-plate mold
Table 6.1: Two- and three-plate feed system comparison

2

Feed system type

Two-plate mold

Three-plate mold

Mold stack height
Mold opening distance
Total required daylight
Mold mass
Mold opening time2

264 mm
75 mm
339 mm
151 kg
0.36 s

308 mm
250 mm
558 mm
181 kg
1.2 s

Mold opening time was calculated as the mold opening distance divided by the mold opening velocity, where
the mold velocity was found by regression across multiple commercially available molding machines as:
v mold_opening = 184 + 13 ⋅ log(Fclamp [mTons]) [mm/s]
For a 100 ton mold, the typical maximum mold opening velocity is approximately 210 mm/s.

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6 Feed System Design

6.3.3

Hot Runner Molds

Hot runner molds should be considered whenever gating flexibility, cycle efficiency, and
material efficiency are important. In a hot runner system, the feed system is encased in a
heated channel so that the plastic remains molten during the molding process. Since the
plastic does not cool in a hot runner system, there is no need to:






plasticize the melt that would be required to fill the feed system,
inject the material that would fill the feed system,
wait for the material in the feed system to cool,
open the mold a substantial amount to remove the feed system, or
de-gate the feed system from the molded products.

For all these reasons, it is not uncommon for hot runner molds to operate with 20% faster
cycle times and 20% less material scrap than a conventional two-plate or three-plate cold
runner mold. However, hot runner molds do require a higher initial investment than either
two-plate or three-plate molds, and also require controllers and energy to maintain a uniform
melt temperature.
Figure 6.11 provides a section through an isometric view of a hot runner system. This hot
runner design includes a hot sprue bushing, manifold, two drops or “nozzles”, four heater
control zones, and other components. During operation, the material from the molding
machine’s nozzle will travel down the hot sprue bushing to the primary runner located in the
manifold. The melt then traverses down the length of one or more runners to downstream
hot runner nozzles. The length of the nozzle is determined by the distance from the manifold
to the gating location of the mold cavity.

Figure 6.11: Isometric section of hot runner system

6.3 Feed System Types

131

Compared to cold runner designs, the diameters of the runners and drops in a hot runner
system may be quite large since all the material in the hot runner will eventually be forced
into the mold cavities. Since the polymer melt is not wasted, hot runner systems can have
large runner diameters to provide for very low flow resistance and excellent transmission of
the injection pressure to the mold cavities. However, overly large diameters can permit the
material to degrade in the hot runner and prohibit rapid change-overs between different
plastic resins and colors.
A section through a hot runner mold assembly is provided in Figure 6.12. This mold design
provides for the injection of the plastic melt into the left and right sides of the laptop bezel
via a naturally balanced hot runner system with two drops. As can be observed, an air gap
surrounds the majority of the hot runner system to restrict the transfer of heat from the heated
manifold and nozzles to the colder mold steel. During molding, the melt pressure exerted
on the faces of the mold cavity and hot runner system will result in forces that would tend
to cause the cavity insert and the manifold to deflect. Thrust pads, typically machined from
titanium, are used to transfer these forces from the hot runner system to the top clamp plate
while transferring a minimal amount of heat. With hot runner molds, cooling lines and/or
insulating sheets should be used with the top clamp plate to prevent the transfer of significant
heat to the platens of the molding machine.
The hot runner system design provided in Figure 6.12 is a relatively simple design, which
utilizes thermal gates that will be specified in the next chapter. In this design, the hot runner
nozzles are concentric with the gate cut-out provided in the cavity insert. Since the manifold

Figure 6.12: Partial section of hot runner mold

132

6 Feed System Design

will expand with changes in the manifold temperature, the manifold is allowed to expand
and slide across the top surface of the nozzles. The manifold and drop are maintained in
compression in the height direction to prevent any significant amount of material from
escaping.
There are many different hot runner system designs, including drops which are threaded
and otherwise fit to the manifold. Different configurations of hot runner manifolds are
also common, including the straight-bar manifold (as shown in Figure 6.11), the “X”
manifold (in which all primary runners emanate directly from the center of the manifold
at the hot sprue bushing), the “H” manifold (in which multiple branches in the manifold
allow for flow to reach many gates as with the design of Figure 6.6), stack molds (in which
two or more hot runner systems are stacked in the mold height direction to allow for
multiplication of the mold cavities without an increase in clamp tonnage), and the “seven
leg special” (in which the lengths and branching of a hot runner are custom designed to
achieve special application requirements). The mold designer should consult with multiple
hot runner suppliers to understand the benefits and issues associated with available hot
runner systems.

6.4

Feed System Analysis

While the two-plate mold, three-plate mold, and hot runner mold designs differ significantly
in form and function, the design of the feed systems should adhere to basic guidelines as
previously discussed. To summarize, the feed system should:





impose a minimal pressure drop, typically no greater than 50% of the pressure required
to fill the mold cavities or 50 MPa;
consume a minimum amount of material, typically no greater than 30% of the volume
of the mold cavities for cold runner molds or 100% of the volume of the mold cavities
for hot runner molds; and
not extend the mold cooling time.

Historically, many feed systems have been designed with the intent to maintain the same
linear velocity as the melt flows through the sprue, primary runner, etc. The melt velocity
can be preserved in a branched runner systems by setting the diameter of the downstream
diameters, Ddownstream, equal to:
Ddownstream =

Dupstream
ndownstream

(6.1)

where Dupstream is the upstream runner diameter and ndownstream is the number of downstream
runners branching off the upstream segment.

6.4 Feed System Analysis

133

Example: Consider the feed system layout provided in Figure 6.5. If the diameter of the
base of the sprue is 6 mm, suggest the diameter of the primary runners to maintain a
uniform melt front velocity.
According to Eq. (6.1), the downstream diameter should be:
Ddownstream =

6 mm
= 4.24 mm
2

To validate this solution, the linear melt velocity can be computed in each branch.Assuming
a flow rate of 50 cc/s, the linear velocity in the sprue is:
vsprue =

50 ⋅ 10−6 m 3 /s
= 1.77 m/s
⎛ π (0.006 m)2 ⎞


4



Since the flow branches into two segments, the linear flow velocity in the primary runner
is computed as:
vrunner =

0.5 ⋅ 50 ⋅ 10−6 m 3 /s
= 1.77 m/s
⎛ π (0.00424 m)2 ⎞


4



While this design guideline is simple and seems intuitive, the resulting designs are inferior
with respect to the imposed pressure drops and the consumed plastic material. As such, an
engineering methodology for feed system design is next presented based on the analysis of
the above three objectives.

6.4.1

Determine Type of Feed System

The type of feed system is often specified as part of the mold quote by the mold designer
since it is either obvious or has been specified by the customer. However, if the type of
feed system is uncertain, then the mold designer should consider the requirements of the
molding application and the capabilities of the molder. Table 6.2 provides a comparison of
the properties for common feed system types.
Some discussion is warranted regarding Table 6.2. First, the upfront investment refers not
only to the cost of the mold design and associated components, but also the time required
to manufacture and test the finished mold. For instance, a two-plate mold with two cavities
may cost $20,000 and require a few weeks to complete. By comparison, a 64 cavity stack mold
may cost $1,000,000 and require several months to complete. For many accelerated product
development projects, the added time may be as significant an issue as the added cost. Supply
chain logistics can also be an issue. For example, a customer may prefer to construct twelve

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6 Feed System Design

Table 6.2: Feed system types and properties

Feed system type

Upfront
investment

Molder
capability

Material
efficiency

Cycle
efficiency

Two-plate cold runner

Lowest

Lowest

Low

Lowest

Three-plate cold runner

Low

Low

Low

Low

Insulated runner

Moderate

Moderate

Moderate

Moderate

Hot runner

High

Moderate

High

High

Stack mold

Highest

High

High

Highest

relatively simple molds, each having four cavities. A few molds can then be separately operated
in Europe, Asia, and America. While the cycle time and efficiency is not as high as a single hot
runner mold with high cavitation, this approach may reduce the initial mold development
time, provide redundancy to mold failure, and allow for reduced tact time in the supply chain
in response to fluctuations in consumer demand.
The capability of the molder is also an issue with respect to the selection of the type of feed
system. While all molders are expected to operate two-plate molds, some molders may not be
familiar with the proper setup, operation, and maintenance of three-plate molds, insulated
runner molds, or hot runner molds. The operation of stack molds, while not significantly more
complex than that of a conventional hot runner, may seem daunting to some molders and
require auxiliary controllers that are not available. For these reasons, the mold designer should
verify the capabilities of the molder if the type of feed system has not been specified.
The material and cycle efficiency may be the primary driver to use more sophisticated feed
systems. Since the economics are dependent upon the specifics of the molding applications,
cost estimation should be performed for each feed system type to determine the most
appropriate design. As previously discussed, it may be useful to perform a sensitivity analysis
to identify the risk of under or over designing the mold for a targeted production volume.

6.4.2

Determine Feed System Layout

Section 4.3.1 provided some common layouts for mold cavities. The feed system must be
designed to provide the needed amount of melt flow at the proper melt pressures to each of
the cavities. For this reason, a number of feed system layouts have become common including
series, branching, radial, hybrid, and custom. Each of these types of feed system layouts is
next discussed.
A series layout of cavities can most compactly deliver the polymer melt to many in-line
cavities through a single primary runner with many subsequent runners leading to individual
cavities. Such a scenario is shown in Figure 6.13. Unfortunately, since the secondary runners
branch off at different locations down the length of the primary runner, the pressure drop
along the length of the primary runner will cause lower flow rates to be delivered to cavities

6.4 Feed System Analysis

135

Figure 6.13: Series layout of runner system

further from the sprue. This non-uniform flow can be abated somewhat by reducing the
diameters of the secondary runners closer to the sprue as shown by the secondaries off the
right primary runner in Figure 6.13. However, such artificial balancing can be difficult to
achieve, and does not guarantee consistent part quality associated with different dynamics
during the post-filling stages of the injection molding process. For these reasons, the series
layout of runner systems is not frequently used in precision applications.
By branching the feed system multiple times, the melt flow to multiple cavities can be naturally
balanced as shown in Figure 6.14. Compared to the series layout, the branched layout consumes significantly more material while also imposing a high pressure drop from the sprue
to the cavities. Another problem with naturally balanced feed systems is the development of

Figure 6.14: Branched layout of runner system

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6 Feed System Design

melt temperature imbalances associated with the turning of the melt across multiple branches.
This effect has been well document [27, 28], and led to the development of a “Melt FlipperTM”
to assist in correcting flow imbalances in naturally balanced systems with multiple branches.
For all these reasons, molding applications with a high number cavities are increasing utilizing
hot runner feed systems to avoid excess material utilization and pressure drops.
Radial layouts of feed systems, in which multiple primary runners emanate from the sprue,
are also quite common. The primary benefit of a radial feed system layout is that the flow rates
and melt pressures are naturally balanced with only a moderate amount of runner volume.
The number of primary runners that can emanate from the single sprue is somewhat limited
due to the large size of the primary runners compared to the base of the sprue. To increase the
number of primary runners, a disk cavity, or “diaphragm”, may be located at the base of the
sprue. This diaphragm can be used to feed many primary runners as shown in Figure 6.15.
Compared to the branched layout of Figure 6.14, this radial layout has a lower feed system
volume and provides more balanced flow. However, longer primary runners and more waste
is necessary as the size of the cavities increases.
Mold designers are free to develop the feed system layout to best fit their molding application.
As previously discussed, the primary motivation is to provide balanced flow and minimal
pressure drops while consuming the least amount of material. As such, many feed systems
utilize a hybrid of branched and radial layouts. One such design is shown in Figure 6.16,
which consists of a branched feed system with primary and secondary runners which then
feeds four separate radial feed systems, each with four tertiary runners. Compared to the feed
system layouts shown in Figure 6.14 and Figure 6.15, the hybrid layout of the feed system
design utilizes less material while also providing naturally balanced flow.
Many molding application requirements are best fulfilled by custom feed systems that do
not comply with any of the previous feed system layouts. For example, many multi-gated
parts require the feed system to deliver melt to different locations across the mold cavity. In
such molding applications, there is no reason to adhere to either branched or radial or even
naturally balanced layouts. Indeed, the mold designer should purposefully choose a feed

Figure 6.15: Radial layout of runner system

6.4 Feed System Analysis

137

Figure 6.16: Hybrid (branched-radial) layout of runner system

system layout and specify dimensions that deliver the desired amount of polymer melt at the
desired melt pressures to different portions of the mold cavities.
One example of a custom layout is shown in Figure 6.17. This feed system consists of four
primary runners. The two longer primary runners feed the polymer melt via four secondary
runners to a relatively large part surrounding the feed system. The two small primary runners
closer to the sprue are used to feed smaller mold cavities that provide optional components
for assembly with the large molding. These secondary runners may be fitted with rotating
shut-offs that can be installed in the mold to change the connectivity of the feed system,
and thereby produce different combinations of moldings while the mold is in the molding
machine.

Figure 6.17: Custom layout of runner system

138

6 Feed System Design

The performance of the feed system is ultimately determined by the creativity and care of the
mold designer according to the requirements of the molding application. The mold designer
has significant freedom in the design of the feed system. However, some general guidelines
are as follows:









The total length of the feed system should be as short as possible to minimize material
consumption;
The total length of the feed system should be as short as possible to minimize pressure
drop through the feed system;
Naturally balanced feed systems provide greater cavity to cavity consistency with respect
to melt flow, melt pressure, and molded part quality than artificially balanced designs;
The total number of branches in a feed system should be minimized to avoid excessive
runner volume and potential melt temperature imbalances;
To minimize pressure drop for a given feed system volume, the diameters of the feed system
are generally largest with the sprue and subsequently become smaller with the primary,
secondary, and other runners with decreasing flow rates;
Economic analysis is vital to determine the correct number of mold cavities, the layout
of the mold cavities, and the type of feed system; and
Hot runner and three-plate molds should be considered when cavities in a two-plate mold
obstruct the desired layout of the feed system.

6.4.3

Estimate Pressure Drops

Once the layout and lengths of the feed system have been determined, the diameters of each
portion of the feed system should be determined according to analysis. The flow of polymer
melt through the feed system is in the laminar flow regime. To verify laminar flow, the Reynolds
number, Re, should be less than 2300:
Re =

4 ⋅ ρmelt ⋅ Vmelt
< 2300
π ⋅ μmelt ⋅ D

(6.2)

where Vmelt is the volumetric flow rate (typically on the order of 50 · 10–6 m3/s), ρmelt is
the density (typically on the order of 1000 kg/m3), μmelt is the apparent viscosity (typically
on the order of 100 Pa s), and D is the runner diameter (typically on the order of 0.01 m).
Substituting typical values for the variables in Eq. (6.2) indicates that the Reynold’s number
is on the order of 0.1. As such, the flow regime is far from turbulent, inertial effects are
negligible, and the pressure drop, ΔP, can be estimated using the well-known HagenPoiseuille law:
ΔP =

8 ⋅ μmelt ⋅ L ⋅ Vmelt
π ⋅ R4

(6.3)

6.4 Feed System Analysis

139

where L and R are the length and radius of a portion of the runner. To provide an accurate
estimate of the pressure drop using the Newtonian model, the apparent viscosity should be
evaluated for the polymer melt at an appropriate shear rate:
γ =

4 V
π R3

(6.4)

For a power law fluid, the pressure drop can be estimated directly without calculation of the
shear rate as:
1⎞
⎡⎛

3 + ⎟ Vmelt ⎥
2 k L ⎢ ⎜⎝
n⎠


ΔP =
R ⎢
π R3

⎣⎢
⎦⎥

n

(6.5)

where k and n are the reference viscosity and power law index of the polymer melt at the
melt temperature.
Example: Estimate the pressure drop through the hot runner system design shown in
Figure 6.18 during the molding of the laptop bezel.
The analysis assumes that ABS is molded with a volumetric flow rate at the inlet of 125 cc/s.
To avoid calculating the shear rate in each portion of the runner, the power law model is
used with k equal to 17,000 Pa sn and n equal to 0.35.
The bore of the hot sprue bushing is 90 mm in length and has a radius of 6 mm. The
volumetric flow rate through the hot sprue bushing is 125 cc/s, so the pressure drop
through the sprue is:

Figure 6.18: Dimensions of hot runner feed system

140

6 Feed System Design

1 ⎞
⎡⎛
−6 3 ⎤
3+
⎟ 125 ⋅ 10 m /s ⎥
2 ⋅ 17000 Pa sn ⋅ 0.09 m ⎢ ⎜⎝
0.35 ⎠


=
0.006 m
π (0.006 m)3


⎢⎣
⎥⎦

ΔPsprue

0.35

= 5.9 MPa

After the hot sprue bushing, the melt branches into two flow streams. Since the multi-gated
laptop bezel is nearly symmetric, the flow rate through each leg of the hot runner system is
assumed to be 50% of the inlet flow rate, or 62.5 cc/s. Each leg of the manifold is 118 mm
in length with a radius of 5 mm, so the pressure drop through the manifold is:

ΔPmanifold

1 ⎞
⎡⎛
−6 3 ⎤
3+
⎟⎠ 62.5 ⋅ 10 m /s ⎥
2 ⋅ 17000 Pa sn ⋅ 0.118 m ⎢ ⎜⎝
0.35


=
0.005 m
π (0.005 m)3


⎢⎣
⎥⎦

0.35

= 8.8 MPa

To calculate the pressure drop through the nozzle, the most accurate estimate may be
provided by analyzing each segment of the tapered bore. Given this particular nozzle
bore geometry, however, a reasonable estimate may be obtained by modeling the tapered
bore as a constant section with a radius of 3.5 mm and a length of 108 mm. The pressure
drop is then:

ΔPnozzle

1 ⎞
⎡⎛
−6 3 ⎤
3+
⎟⎠ 62.5 ⋅ 10 m /s ⎥
2 ⋅ 17000 Pa sn ⋅ 0.108 m ⎢ ⎜⎝
0.35


=
0.0035 m
π (0.0035 m)3


⎢⎣
⎥⎦

0.35

= 16.7 MPa

The total pressure drop through the hot runner system is the sum of the pressure drops
through each portion of the hot runner system:
ΔPtotal = ΔPsprue + ΔPmanifold + ΔPnozzle
= 5.9 MPa + 8.8 MPa + 16.7 MPa = 31.4 MPa ≈ 4,500 psi
This pressure drop is significant but reasonable compared to typical injection pressures
of 150 MPa.

6.4.4

Calculate Runner Volume

Given the number, lengths, and radii of the feed system, the total feed system volume, Vtotal,
can be computed as:
Vtotal =

m

m

j =1

j =1

∑ N j ⋅ V j =∑ N j ⋅ L j (π R2j )

(6.6)

6.4 Feed System Analysis

141

where m is the number of different types of segments in the feed system, j is an index referring
to a specific type of runner segment, Nj is the number of times that the runner segment j
occurs in the feed system, Lj is the length of segment j, and Rj is the radius of segment j. As
previously discussed, the mold designer should minimize the total volume of the feed system
to avoid the production of excess material waste or regrind in cold runner molds or long
residence times in hot runner molds.
Example: Calculate the volume of the hot runner system design shown in Figure 6.18.
In this hot runner design, there is one sprue with a radius of 6 mm and a length of
90 mm. The primary runner in the manifold consists of two segments each with radius
and length of 5 mm and 118 mm, respectively. There are two nozzles, each with a bore
length of 108 mm and an approximate radius of 3.5 mm. Accordingly, the total volume
is calculated as:
Vtotal =

m

∑ N j ⋅ Vj
j =1

= 1 ⋅ 9 cm ⋅ π ⋅ (0.6 cm)2
+ 2 ⋅ 11.8 cm ⋅ π ⋅ (0.5 cm)2
+ 2 ⋅ 10.8 cm ⋅ π ⋅ (0.35 cm)2
= 37 cc
The volume of 37 cc is slightly larger than the 27.5 cc of the part, and should not lead to
extended residence times or degradation. Indeed, it may be preferable in this thin wall
molding application to redesign the hot runner system with large diameters for a lower
pressure drop. While it may be unnecessary to reduce the volume of the feed system in
this hot runner application, the large runner diameters in this design would likely be
unacceptable if applied to a three-plate cold runner system.

6.4.5

Optimize Runner Diameters

Once the pressure drop through the feed system is analyzed, it is possible to adjust the feed
system design to improve the performance. Multiple iterations of design and analysis may
be conducted to obtain a design that provides a low pressure drop while consuming very
little material. Multivariate optimization is a numerical technique that could be employed to
simultaneously minimize the pressure drop while minimizing the runner volume. However,
this approach requires time to implement and validate while hiding the details of the analysis
from the designer.
The approach recommended here is to utilize constraint based method to directly solve the
minimum runner system diameters given a specified constraint on the pressure drop. If the
maximum pressure drop for a portion of the runner is specified as ΔPmax, then for a Newtonian
material the radius of the runner could be directly solved as:

142

6 Feed System Design

R=

4

8 ⋅ μmelt ⋅ L ⋅ Vmelt
π ⋅ ΔPmax

(6.7)

A difficulty with this approach, however, is that the apparent viscosity, μmelt, is a function of the
shear rate and the runner radius. To avoid iterative estimation of the shear rate and viscosity,
the power law model can be used to calculate the radius in a single step as:
1

1 ⎞  ⎤ 3+ 1

1 ⎛
⎢ ⎛ 2 k L ⎞ n ⎜⎝ 3 + n ⎟⎠ Vmelt ⎥ n

R = ⎢⎜

π
⎢ ⎝ ΔPmax ⎠

⎢⎣
⎥⎦

(6.8)

An issue remains, however, as to what the maximum pressure drop should be in each segment
of the feed system. Knowing the specification on the total pressure drop from the machine
nozzle to the cavity, various schemes can be developed to allocate the pressure drop across
each portion of the feed system. The simplest approach is to divide the maximum pressure
drop for the entire feed system by the number of segments between the nozzle and the
cavity. For instance, if the polymer melt flowed through a sprue, a primary runner, and a
secondary runner and the maximum pressure drop for the feed system was 30 MPa, then
the mold designer could choose to allocate a maximum pressure drop of 10 MPa for each of
the segments of the feed system.
The problem with this approach, however, is that it does not account for the length of each
portion of the feed system. A very short secondary runner, for instance, would be allocated
the same pressure drop as a long primary runner. The resulting design would be suboptimal
with the diameter being too small for the secondary runner and too large for the primary
runner.
Another simple approach is to distribute the pressure drop across the feed system in proportion
to the length of each runner segment:
ΔPi = ΔPmax ⋅

Li
L
= ΔPmax ⋅ m i
Ltotal
∑ Lj

(6.9)

j =1

where ΔPi is the maximum pressure drop allocated to runner segment i with length Li, and
m is the number of runner segments between the inlet and outlet of the feed system. As such,
longer runner segments will be allowed a proportionally greater portion of the pressure drop
through the feed system.
Example: Calculate the minimum diameters in the hot runner system design shown in
Figure 6.18 so that the pressure drop through the feed system does not exceed 30 MPa.
Assume ABS is molded with the molding machine providing a volumetric flow rate of
125 cc/s.

6.4 Feed System Analysis

143

The total length of the feed system from the inlet to the outlet is:
Ltotal =

3

∑ Lj

= 90 mm + 118 mm + 108 mm = 316 mm

j =1

The maximum pressure drop through the sprue is allocated as:
ΔPsprue = 30 MPa ⋅

90 mm
= 8.5 MPa
316 mm

Given this pressure drop for the sprue, the sprue diameter can be calculated from Eq. (6.8)
as:
1

1 ⎞


1
−6
3 ⎤ 3+ 1
⎢ ⎛ 2 ⋅ 17,000 Pa s ⋅ 0.09 m ⎞ 0.35 ⎜⎝ 3 + 0.35 ⎟⎠ 125 ⋅ 10 m /s ⎥ 0.35

R = ⎢⎜

π
8.5 ⋅ 106 Pa

⎢⎝

⎢⎣
⎥⎦
Rsprue = 0.005 m = 5 mm
Similarly, the maximum pressure drop through the manifold is allocated as:
ΔPmanifold = 30 MPa ⋅

118 mm
= 11.2 MPa
316 mm

Given this pressure drop for the manifold, the primary runner diameter in the manifold
can be calculated from Eq. (6.8) as:
1

1 ⎞


1
3 ⎤ 3+ 1
−6
⎢ ⎛ 2 ⋅ 17,000 Pa s ⋅ 0.1188 m ⎞ 0.35 ⎜⎝ 3 + 0.35 ⎟⎠ 62.5 ⋅ 10 m /s ⎥ 0.35

R = ⎢⎜

π
11.2 ⋅ 106 Pa

⎢⎝

⎢⎣
⎥⎦
Rmanifold = 0.0044 m = 4.4 mm

Similarly, the maximum pressure drop through the nozzle is allocated as:
ΔPnozzle = 30 MPa ⋅

108 mm
= 10.3 MPa
316 mm

Given this pressure drop for the nozzle, the nozzle bore diameter can be calculated from
Eq. (6.8) as:

144

6 Feed System Design

1

1 ⎞


1
3 ⎤ 3+ 1
−6
⎢ ⎛ 2 ⋅ 17,000 Pa s ⋅ 0.108 m ⎞ 0.35 ⎜⎝ 3 + 0.35 ⎟⎠ 62.5 ⋅ 10 m /s ⎥ 0.35

R = ⎢⎜

π
10.3 ⋅ 106 Pa

⎢⎝

⎢⎣
⎥⎦
Rnozzle = 0.0044 m = 4.4 mm

It should not be surprising that the diameter of the runner in the manifold and nozzle are
the same since 1) the two runners have the same melt flow rate and 2) were purposefully
assigned the same pressure drop per unit length according to Eq. (6.9). The resulting
hot runner system design has a volume of 35 cc and a pressure drop of 30 MPa, both of
which are about 5% less than the previous design (which had a volume of 37 cc and a
pressure drop of 31.4 MPa). Furthermore, by maintaining the same runner diameter in
the manifold and the nozzle, more uniform shear stresses are maintained with a lower
likelihood for dead spots.
To further reduce the runner system volume, it is necessary to specify smaller feed system
diameters. This action will result in a larger pressure drop through the feed system unless
a higher melt temperature, lower viscosity material, or lower flow rate is assumed. If a
50 MPa pressure drop through the feed system was specified, then the above analysis can
be applied to achieve the following results:
Rsprue = 4 mm
Rmanifold = Rnozzle = 3.5 mm
Vtotal = 21.3 cc
The mold designer may repeat the analysis to evaluate the volume of the feed system for
different pressure drops. Figure 6.19 provides a plot of the volume of the feed system as
a function of the maximum pressure drop. To achieve a low pressure drop, large runner
diameters are necessary which results in a very high volume for the feed system. As the
allowable pressure drop increases to 100 MPa, the volume of the feed system decreases
substantially, though a runner volume of 10 cc remains necessary to convey the melt at
a flow rate of 125 cc/s.
In optimizing the feed system design, the mold designer needs to know the flow rates during
the filling stage and the expected pressured drop. Figure 6.19 indicates how the feed system
designs will change with the volumetric flow rates during the filling stage. Lower flow rates
will result in lower pressure drops, which in turn allow for a reduction in the radii and volume
of the feed system. Since the actual flow rates are determined by the molder after the mold is
designed and built, the molder should verify the expected fill time of the cavity with the molder
and calculate the expected flow rates through the feed system. If the flow rates are uncertain,
then the mold designer can estimate the linear melt velocity in the cavity per Eq. (5.23) and
assume that the flow rate is constant throughout the filling stage.

6.4 Feed System Analysis

145

100
300 cc/s
125 cc/s
50 cc/s

90

Volume of feed system (cc)

80
70
60
50
40
30
20
10
0

0

10

20

30
40
50
60
70
80
Pressure drop through feed system (MPa)

90

100

Figure 6.19: Feed system volume as a function of pressure drop and flow rate

6.4.6

Balance Flow Rates

The previous analysis and examples implied a naturally balanced, branching feed system.
However, the analysis can also be applied to artificially balanced feed system designs for family
molds and multi-gated parts. In these applications, different flow rates and pressure drops
may be desired for each branch of the feed system.
To properly balance the flow rates and melt pressures in a mold with complex cavity geometries, it is necessary to ensure that the polymer melt completes the filling of each portion of
the mold at approximately the same time. As such, the first step of the analysis is to calculate
the desired volumetric flow rate to each cavity, or for a multi-gated part, in each portion of
the cavity. The filling pressure at each gate is then estimated assuming this flow rate. Once
the cavity pressures are known, then the pressure drops through each portion of the runner
system can be allocated and the previously described analysis applied to optimize the feed
system design and provide the desired cavity pressure and flow rate.
While this analysis approach is as simple as possible, it does not account for discrepancies in
the filling time of the feed system itself. This error is often negligible since the feed system
has a small volume compared to the mold cavities for cold runner molds, and is already filled
for hot runner molds. Even so, the total filling time and pressure of each branch of the feed
system and the mold cavities should be evaluated to ensure a truly balanced design; multiple
iterations may be needed to achieve an acceptable design.

146

6 Feed System Design

The mold designer should recognize that a truly optimal, balanced mold design is extremely
difficult to achieve. Since polymer melts are non-Newtonian and the shear rates vary with
runner diameter and flow rates, the imbalance across the feed system is a function of the
material properties and the processing conditions. Furthermore, there is no guarantee that
a feed system designed to balance the flow rates during the filling stage will also balance the
packing pressures during the post-filling stage. As such, the mold designer should strive to
reduce the amount of balancing required by the feed system by ensuring the uniformity of
the mold cavity designs, and realize that there will be limits to the performance of static feed
system geometries.
Example: Artificially balance the feed system in the two-plate, cup and lid family mold.
Assume ABS is molded at its mid-range melt temperature and the cavity filling time is
1 s.
First, the pressures required to fill the cup and lid cavities are estimated. For a fill time
of one second, the flow length from the gate of the cup cavity to the opposite side of the
cavity (refer to Figure 6.5) is approximately 175 mm (equal to the diameter of the base
plus twice the height of the side wall). The average linear melt velocity will be 175 mm/s
(equal to the flow length divided by the filling time) corresponding to a volumetric flow
rate of 44 cc/s (equal to the volume of the mold cavity divided by the filling time). Using
the power law model for ABS, the pressure required to fill the cup cavity is:

ΔPcup

1 ⎞
⎡ ⎛

2 1+
⎟ 0.09 m/s ⎥
2 ⋅ 17000 Pa sn ⋅ 0.09 m ⎢ ⎜⎝
0.35 ⎠


=
0.003 m
0.003


⎢⎣
⎥⎦

0.35

= 16.8 MPa

The lid is not as deep as the cup, so the flow length for the lid is approximately 109 mm.
Assuming the same time 1 s filling time, the linear melt velocity for the lid is 109 mm/s,
with a volumetric flow rate of 19 cc/s. The pressure required to fill the lid cavity is:

ΔPlid

1 ⎞
⎡ ⎛
2 ⎜1 +
⎟ 0.055 m/s
n


2 ⋅ 17000 Pa s ⋅ 0.055 m
0.35 ⎠

=
0.002 m
0.003

⎢⎣



2⎥

⎥⎦

0.35

= 15.4 MPa

These two filling pressures are quite similar. However, the flow rates are significantly
different. To achieve the different flow rates, the diameters of the primary runner must
be designed to restrict the melt flow to the lid cavity. A first design can be produced by
applying Eq. (6.7) using different pressure drops and flow rates for each branch of the feed
system. Since the filling pressures are low, a pressure drop of 30 MPa across the primary
runner to the cup cavity is assumed with a volumetric flow rate of 44 cc/s. With a length
of 38 mm, the resulting radius for the runner to the cup cavity is:

6.4 Feed System Analysis

147

1

1 ⎞


1
−6
3 ⎞ 3+ 1
+

3
44
10
m
/s ⎟ 0.35


⎜ ⎛ 2 ⋅ 17,000 Pa s ⋅ 0.038 m ⎞ 0.35 ⎝
0.35 ⎠
R = ⎜⎜


π
30 ⋅ 106 Pa

⎜⎝



Rrunner_to_cup = 0.0015 m = 1.5 mm
The radius of the primary to the lid cavity is similarly computed, but with a different
pressure drop and flow rate. For the branch to the cup, the total pressure drop from the
edge of the cup cavity to the bottom of the sprue bushing was 46.8 MPa. As such, the
pressure drop across the primary to the lid cavity will be designed to be 31.4 MPa to ensure
this same total pressure drop. The required volumetric flow rate is 19 cc/s. The radius of
the runner to the lid cavity is then:

1
⎢ ⎛ 2 ⋅ 17,000 Pa s ⋅ 0.038 m ⎞ 0.35
R = ⎢⎜

31.4 ⋅ 106 Pa

⎢⎝
⎢⎣
Rrunner_to_lid = 0.00126 m ≈ 1.25 mm

1

1 ⎞

−6
3 ⎤ 3+ 1
⎜⎝ 3 +
⎟⎠ 19 ⋅ 10 m /s ⎥ 0.35
0.35

π

⎥⎦

Next, it is necessary to check the fill times through both branches of the feed system.
The volumes of the primary runners to the cup and the lid cavities are on the order of
0.3 cc. Since this volume is very small, the filling times are on the order of 0.01 s. Any
discrepancies in the filling time of the runners will not significantly affect the filling of
the two mold cavities.
To complete the design, Eq. (6.7) can be used to specify the diameter of the sprue. A reasonable pressure drop across the sprue may be assessed at 20 MPa. For conservation of
mass, the flow rate through the sprue is required to be the sum of the flow rates through
the primary runners, which total to 63 cc/s. With a length of 76 mm, the radius of the
sprue can be computed as:
1

1 ⎞


1
−6
3 ⎤ 3+ 1
⎢ ⎛ 2 ⋅ 17,000 Pa s ⋅ 0.076 m ⎞ 0.35 ⎜⎝ 3 + 0.35 ⎟⎠ 63 ⋅ 10 m /s ⎥ 0.35

R = ⎢⎜

π
20 ⋅ 106 Pa

⎢⎝

⎢⎣
⎥⎦
Rsprue = 0.0027 m = 2.7 mm
Finally, the volume of the cold runner system can be compared to the volume of the
moldings:

148

6 Feed System Design

pregrind =
=

Vsprue + Vrunner_to_cup + Vrunner_to_lid
Vcup + Vlid
1.7 cc + 0.26 cc + 0.2 cc
= 3.5%
44 cc + 19 cc

which is a very low percentage. The cost of collection, regrind, and re-use of this material
may exceed the purchase cost of the resin. It should be noted, however, that for a threeplate mold (as pictured in Figure 6.7) or a two-plate mold with more cavities (as pictured
in Figure 6.6), the scrap associated with a cold runner system will tend to be substantially
greater. The mold designer may asses a higher pressure drop through the feed system to
reduce this percentage, and may wish to recommend a hot runner system to the end user
of the mold to reduce resin costs if high production quantities are needed.

6.4.7

Estimate Runner Cooling Times

For cold runner mold designs, the mold designer should estimate the time required to solidify
the cold runner as well as the time required to solidify the cavity. The solidification times
can be estimated through one dimensional heat transfer analysis as discussed in Chapter 9.
Table 6.2 provides the cooling time equations for strips and cylinder geometries, where h is
the wall thickness of the cavity, D is the diameter of a portion of the feed system, Teject is the
specified ejection temperature (usually taken as the deflection temperature under load, or
DTUL), Tcoolant is the coolant temperature, and Tmelt is the melt temperature.
During the molding process, the cooling time will be dominated by whatever portion of the
mold requires the longest time to cool. For this reason, it is not necessary to calculate the
cooling times for every portion of the feed system and every mold cavity thickness. Instead,
the mold designer can simply check the cooling time for the thickest mold cavity section
and the largest feed system diameter (usually the diameter at the base of the sprue). If the
cooling time of the feed system greatly exceeds the cooling time of the mold cavities, then
the mold designer should redesign the feed system to avoid extending the molding cycle
time.
Table 6.2: Equations for estimation of cooling times

Geometry

Cooling times

Strip

tc =

⎛ 4 Tmelt − Tcoolant ⎞
h2
ln ⎜

π ⋅ α ⎝ π Teject − Tcoolant ⎠

Cylinder

tc =


− Tcoolant ⎞
T
D2
ln ⎜ 0.692 melt

23.1 ⋅ α ⎝
Teject − Tcoolant ⎠

2

6.4 Feed System Analysis

149

Example: Verify that the feed system design of the cup and lid family mold will not
extend the cycle time. Assume that the material is ABS with melt, cooling, and ejection
temperatures of 239, 60, and 96.7 °C, respectively.
The cooling time for the molding cycle will be dominated by the time to cool either the
3 mm cup or the 5.4 mm diameter sprue. These times are estimated as:
t ccup =

(0.003 m)2
⎛ 4 239 − 60 ⎞
ln ⎜
⎟ = 18.9 s
2
2
−8
π ⋅ (8.69 ⋅ 10 m /s) ⎝ π 97.6 − 60 ⎠

t csprue =

(0.0054 m)2
239 − 60 ⎞

ln ⎜ 0.692
⎟ = 26.7 s
3
−8

97.6 − 60 ⎠
23.1 ⋅ (8.69 ⋅ 10 m /s)

This analysis indicates that the two cooling times are close, but that the cycle may be
extended due the solidification of the sprue. However, the feed system does not need
to be as rigid as the molded part for ejection. If the mold is opened before the sprue is
sufficiently solidified, the feed system may be difficult to eject either because the sprue has
stuck to the A-side of the mold or the feed system is overly flexible. To avoid this problem,
the diameter of the sprue can be reduced albeit with a higher pressure drop.

6.4.8

Estimate Residence Time

For hot runner mold designs, the mold designer should check the residence time of the
polymer melt in the hot runner to ensure that the plastic will not degrade. The residence
time is directly related to the number of turns required to turn over the polymer melt in the
hot runner system, defined as:
nturns =

Vhot_runner
Vcavities

(6.10)

If the volume of the hot runner is large compared to the volume of the mold cavities, then
many molding cycles may be required to force new material through the feed system. The
number of turns does not represent the actual number of molding cycles required to purge
the hot runner of the old resin, but rather the minimum number of molding cycles before a
substantial amount of the new resin is delivered to the mold cavities.
A high number of turns is undesirable for molding applications in which the color of the resin
is frequently changed. To facilitate frequent color changes, mold designers should optimize
the feed system diameters and keep the number of turns to a minimum. If the number of
turns is less than or close to one, then the use of the hot runner system is unlikely to impede
color changes relative to the color change issues associated with purging the injection unit
of the molding machine. If the number of turns is large, on the order of 10 or more, then
purging the hot runner may become a very significant issue with hundreds (or thousands)
of molding cycles required to completely purge low viscosity resins.

150

6 Feed System Design

A high number of turns is also undesirable for molding applications with resins that have
short allowable residence times. The residence time of material in the hot runner system is
approximately:
t residence = (1 + nturns ) ⋅ t cycle

(6.11)

This residence time is approximate since material flows through the hot runner system at
various rates; the polymer melt near the walls and in dead spots of the hot runner can have
much longer residence times than predicted by Eq. (6.11). Furthermore, the mold designer
should remember that the material flowing into the hot runner system has already resided in
the barrel of the molding machine for a significant amount of time. Accordingly, the mold
designer should strive to minimize the number of turns to reduce the residence time and
potential degradation of the polymer melt.
Example: Compute the number of turns and residence time of the hot runner designed
in Section 6.4.5.
The hot runner design resulting from an allowed 50 MPa pressure drop had a volume of
21.3 cc. Since the volume of the bezel cavity is 27.5 cc, the number of turns is:
nturns =

21.3 cc
= 0.77
27.5 cc

which is very low. New material will through the hot runner system and into the mold
cavity with every cycle. In Section 3.4.3, the cycle time was estimated as 13.5 s. The residence
time in the hot runner system is estimated as:
t residence = (1 + 0.77 cycles) ⋅ 13.5

s
= 24 s
cycle

This residence time is very low compared to the allowable residence time of most polymers,
which is typically greater than 15 minutes.

6.5

Practical Issues

While this chapter so far has discussed the purpose, types, and analysis of feed systems, there
are some practical issues that the mold designer should consider before completing the feed
system design.

6.5.1

Runner Cross-Sections

The provided analysis has been restricted to “full round” circular runners since these are
extremely common in mold designs and provide for simple analysis. However, other runner

6.5 Practical Issues

151

cross sections are also fairly common in practice since they may be easier to machine. In
particular, the trapezoidal, round-bottom trapezoid, and half-round runners are often
machined into only the moving side of the mold as shown in Figure 6.20. This mold design
strategy not only reduces the amount of machining, but also reduces the design time and
potential for machining or misalignment mistakes associated with matching the two sides
of a full round runner.
The primary drawback associated with these non-circular runners is that they give rise to
non-uniform shear rates and shear stresses around the perimeter of the cross-section. For
example, the trapezoidal runner is easy to machine, but the sections near the four corners
conduct very little flow down the length of the runner. The performance of the trapezoidal
runner can be improved by rounding the bottom surface to eliminate two of the corners.
However, all these non-circular types of runner will need to be slightly larger and consume
additional material to provide the same pressure drop as a full round runner.
The previously described analysis can be adapted for use with non-circular runner sections.
While the results will not be as precise as for a full-round runner, the hydraulic diameter, Dh,
for each runner type can be calculated as:
Dh =

4 ⋅ Asection
psection

(6.12)

where Asection is the cross-sectional area of the runner and psection is the perimeter of the
cross-section of the runner. For reference, Table 6.3 provides equations relating the specified
dimensions of the different sections in Figure 6.20 to the hydraulic diameter. It should be
noted that the equations in Table 6.3 have been derived assuming a 5 degree taper angle to
assist with the ejection of the runner from the mold. This assumption allows for a reduction
in the number of design variables. The efficiencies listed in Table 6.3 are defined as:
⎛ π Dh2 ⎞
⎜ 4 ⎟


Efficiency =
Asection

Figure 6.20: Common runner cross-sections

(6.13)

152

6 Feed System Design

Table 6.3: Hydraulic diameter for different runner sections

Runner section
(% efficiency)

Equation

Full round
(100%)

Dh =

Trapezoidal
(78.5%)

4 ⋅ W ⋅ H + 0.09 ⋅ H 2
2 ⋅ W + (2.01 ⋅ H )
If W = H , then Dh ≈ H

Round-bottom trapezoid
(87.9%)

4 ⋅ [1.57 (R1)2 + 2 ⋅ (R1) ⋅ (H1) + 0.09 ⋅ (H1)2 ]
5.14 (R1) + 2.087 (H1)
If R1 = H1, then Dh ≈ 2 (R1)

Half-round
(61.2%)

Dh =

4 ⋅ π D 2 /4
=D
πD

Dh =

Dh =

0.5 ⋅ π (R2)2
= 0.306 ⋅ (R2)
(2 + π) (R2)

The results indicate that the full round runner is the most efficient section design, followed
by the round bottom trapezoid, the trapezoid, and the half-round.
Example: The primary runner in the three-plate mold of Figure 6.7 has a trapezoidal
section. Calculate the pressure drop through a 120 mm length of primary with a width
of 6 mm, a depth of 8 mm, and a 5 degree taper angle. Assume the use of ABS with a
flow rate of 44 cc/s.
First, the hydraulic diameter is calculated as:
Dh =

4 ⋅ 6 mm ⋅ 8 mm + 0.09 ⋅ (8 mm)2
= 7.04 mm
2 ⋅ 6 mm + 2.01 ⋅ 8 mm

Then, the pressure drop is calculated using the power law model using the hydraulic
diameter as if the trapezoidal runner were circular:

ΔPrunner

1 ⎞
⎡⎛
−6
3 ⎤
3+
⎟ 44 ⋅ 10 m /s ⎥
2 ⋅ 17000 Pa sn ⋅ 0.12 m ⎢ ⎜⎝
0.35 ⎠


=
0.00704 m
π (0.00704 m)3


⎢⎣
⎥⎦

0.35

= 3.9 MPa

The dimensions of this trapezoidal design are too large, providing a low pressure drop
but consuming excess material and cycle time. The depth and width of the runner should
be reduced.

6.5 Practical Issues

153

Figure 6.21: Annular section in valve gated hot-runner

There is one other runner section that is quite common in hot runner systems: the annulus.
Specifically, many hot runner systems incorporate valve pins down the length of the nozzles
to physically shut-off the gate as discussed in Section 7.2.9. In this design, the polymer melt
flows between a cylindrical drop and the cylindrical valve pin, forming an annulus as shown
in Figure 6.21.
The polymer melt flow through an annular section may be closely approximated by adapting
the equation for viscous flow in the strip. Specifically, the width of the strip can be replaced
by the circumference of the mean diameter of the melt annulus while the thickness of the
strip is replaced by the distance between the valve pin and the nozzle bore. Making these
replacements in Eq. (5.17) results in the following relation between pressure drop and flow
rate in an annular section:
ΔP =

0.5 π (Dpin

12 μ L V
+ Dbore )[0.5 (Dbore − Dpin )]3

(6.14)

where DPin is the diameter of the valve pin and DBore is the diameter of the bore through the
nozzle. The power-law model for an annulus can be similarly derived as:
1⎞



2 ⎜ 2 + ⎟ V



2kL
n⎠


ΔP =
2
0.5 (Dbore − Dpin ) ⎢ 0.5 π (Dbore + Dpin )[0.5 (Dbore − Dpin )] ⎥
⎢⎣
⎥⎦

n

(6.15)

Example: Calculate the pressure drop through a valve gated nozzle having a length of
150 mm, a bore diameter of 10 mm, and a valve pin diameter of 5 mm. Assume a material
with a viscosity of 100 Pa s flowing at a rate of 50 cc/s.
Substituting these values into Eq. (6.14), the estimated pressure drop is:
ΔP =

12 ⋅ 100 Pa s ⋅ 0.15 m ⋅ 50 ⋅ 10−6 m 3 /s
= 24.5 MPa
0.5 π (0.005 m + 0.010 m)[0.5 (0.010 m − 0.005 m)]3

154

6 Feed System Design

6.5.2

Sucker Pins

Three-plate mold designs, as shown in Figure 6.8, often use sprue pullers or“sucker pins”, to adhere the cold runner system to the stripper plate upon the opening of the mold. In this instance,
the use of sucker pins is needed to provide sufficient tensile force along the sprue such that
excessive tensile stresses break the gate between the sprue and molding.Without the sucker pins,
the cold runner system would travel with the cavity plates and be difficult to remove since



the gates would still be attached, and
there is no mechanism provided on the A-plate to eject the runner system.3

Similarly, mold designers should consider the necessity of sucker pins during the design of
two-plate molds. The primary concern is that the cold runner system may adhere to the A-half
of the mold due to either vacuum suction to the A plate surface, or to the solidification of
the plastic melt to the machine nozzle at the top of the sprue. If the cold runner system stays
with the stationary side of the mold and all the ejection mechanisms are on the moving side
of the mold, then the runner system can not be automatically ejected. The molding machine
operator will likely need to delay the molding machine to manually remove the runner system.
Furthermore, if the machine is operating on an automatic cycle, then the molding machine
may try to close the mold with the runner system still in the mold.
To avoid these issues and improve the reliability of the molding operation, sucker pins may
be placed at multiple locations along the feed system. Perhaps the most important sucker pin
is the sprue puller, located at the bottom of the sprue as shown in Figure 6.4 and Figure 6.5,
which most effectively serves to detach the sprue from the machine nozzle and retain the
sprue with the moving side of the mold. In this design, the reverse taper at the bottom of the
sprue causes an undercut that retains the sprue. This undercut is later sheared off with the
forward actuation of the sprue knock-out pin.
Other suckers pin may be placed at various locations along the cold runner system and, if
necessary, in the mold cavities. As shown in Figure 6.22, the design is quite similar to that
of the sprue puller. With respect to the design, it is recommended that the diameter of the
sucker be slightly less than the diameter of the associated runner to avoid increased cooling
times. The height and taper angle of the sucker pin should be sufficient to pull the runner
off the stationary side of the mold without excessive material utilization or causing buckling
of the associated ejector pins upon forward actuation. Typical heights and taper angles are
one half the runner diameter and 5 degrees, respectively.
The implementation shown at the left of Figure 6.22 merits a brief discussion. In this implementation, an ejector pin has been placed below the runner, and slotted with a reverse taper
to retain the runner until ejection. Compared with the implementation provided at right, the
use of the slotted ejector is much simpler to machine and easier to maintain. There are two
common issues, however. First, the pin as shown protrudes slightly into the runner section.
3

It should be noted that a different three-plate mold design could utilize a stripper plate mounted on the A
plate assembly, with ejection of the cold runner system towards the top clamp plate. However, this would
require some significant changes from the design shown Figure 6.8.

6.5 Practical Issues

155

Figure 6.22: Two sucker pin designs for a cold runner

While this protrusion will not significantly alter the flow rates or pressure drop through the
runner, there is a slight chance that it may inadvertently cause an undesired disruption or
instability in the flow front. For this reason, it is preferred to align the top of the ejector pin
with the bottom of the runner. Second, if multiple slotted ejector pins are used to retain and
eject the runner system, then the mold designer should consider the relative alignment of
the undercutting slots as later discussed in Section 11.2.6. If the alignment of the slots are
not controlled and provided at random angles, then the runner system may inadvertently
bind to the sucker pins at ejection in a random fashion, hampering the adoption of a fully
automatic molding cycle.

6.5.3

Runner Shut-Offs

Mold designers should consider the use of runner shut-offs to provide molders with
manufacturing flexibility. Some of the common uses of runner shut-offs include




to temporarily shut-off the flow to damaged cavities until mold repair can be performed,
to select different combinations of mold cavities to run in a family mold pursuant to
production requirements, and
to alter the gating and flow in a multi-gated part.

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6 Feed System Design

As such, runner shut-offs can be used by the molder to avoid molding defective or undesired
parts as well as improve the quality of multi-gated parts without re-tooling.4
An isometric, exploded assembly view of a runner shut-off design is shown in Figure 6.23.
In this design, a rotating cylindrical insert, item 50, is held between an outer casing, 40, and a
retainer, 60, that abuts the back plane of a cylindrical pocket cut into the mold plate. The insert
may be readily rotated by the molder with the use of a brass tool. A spring-loaded ball is used
to engage grooves, 54, on the back of the insert to ensure that the insert does not inadvertently
rotate during subsequent molding cycles. While the design of Figure 6.23 provides a runner
with a “T” branch, the shut-off assembly comes unfinished and can be provided with various
runner configurations, the most common being “T”,“L”, and straight. Commercially available
shut-offs are available for approximately US$150 for use with runner diameters ranging from
2 mm to 9.5 mm.

Figure 6.23: Design of runner shut-off per U.S. Patent 5,208,053
4

The use of runner shut-offs to temporarily seal damaged cavities is somewhat controversial since it 1)
requires changes to the molding machine process conditions (especially shot size and injection velocity),
and 2) can unbalance or otherwise alter the flow and heat transfer between cavities. Unless the molder
re-qualifies the molding process for the new cavity configuration, cavity shut-offs should not be used in
commercial production for high precision molding applications.

6.5 Practical Issues

6.5.4

157

Standard Runner Sizes

When designing the feed system for cold runner molds, the mold designer should specify
runner diameters that are machined with readily available cutting tools. The most commonly
available sizes for tapered, square, and ball end mills are: 1/32″, 1/16″, 3/32″, 1/8″, 3/16″, 1/4″,
5/16″, 3/8″, 7/16″, 1/2″, 2 mm, 3 mm, 4 mm, 4.5 mm, 5 mm, 6 mm, 8 mm, 10 mm, and 12 mm.
To achieve the most easily produced cold runner design, it may be necessary to round the
diameters to standard sizes, and verify the performance of the design with analysis. However,
if non-standard runner sizes provide for less material utilization and more balanced melt
flow, then non-standard runner diameters can and should be specified.
Hot runner systems are similarly available with a range of standard bore sizes, typically stepped
in 2 mm increments. The standard diameters and designs will vary by hot runner supplier.
Some suppliers may provide bore diameters of 5, 7, and 9 mm while other suppliers may
provide diameters of 4, 6, 8, and 10 mm. Most competitive suppliers will perform flow analysis
of the feed system and provide recommendations as to the hot runner technology and sizing.
However, the mold designer should verify the appropriateness of the recommendations. As
with the specification of custom diameters for a cold runner, many hot runner suppliers will
provide custom sizing at an added cost.

6.5.5

Steel Safe Designs

Often, the design of the feed system is uncertain. One common issue is the capability of an
available molding machine to fill the mold with a material whose flow characteristics are
unknown. Alternatively, there may be uncertainty as to the exact melt flow rates and pressures
that are required to properly balance a family mold or complex multi-gated part.
In uncertain situations, the mold designer should specify feed system dimensions that are
“steel safe”, which means that the design should call for the removal of less mold steel than
may ultimately be required. As such, the mold designer may wish to round the feed system
dimensions down one or two standard sizes. By doing so, the mold designer will impose
a greater pressure drop and use less material than predicted by the analysis. In doing this,
there is still a reasonable chance that this smaller feed system design may function properly.
Furthermore, if the feed system requires one or more changes, then the “steel safe” design
may be easily machined to improve the mold performance.
Example: Suggest a “steel safe” runner design if the analysis indicated an optimal diameter
of 4.6 mm for a cold runner.
If the feed system analysis resulted in a runner diameter of 4.6 mm, then the mold designer
may specify a diameter of 4.5 mm or even 4mm for a “steel safe” design. By comparison,
if the mold designer had rounded up to 5 mm, the design would have provided a lower
pressure drop but consumed unnecessary material throughout the mold’s entire lifetime.
Furthermore, if the molder desired to reduce the 5 mm diameter, then the mold would

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6 Feed System Design

require more extensive rework including pocket milling of the old feed system, the
manufacture and fitting of an appropriately sized insert, welding and/or the addition of
fasteners, and finally the provision of the new, smaller feed system. While this example
focused on steel safe design of cold runners, the steel safe concept should also be applied
to hot runner designs.

6.6

Chapter Review

The selection of the type of feed system is one of the most critical decisions in a mold’s
design, since it determines the type of mold and largely impacts the mold’s purchase and
operating costs. Two-plate cold runner molds are the simplest design, are readily produced,
and can be quite effective for a small number of cavities. Three-plate and hot runner mold
designs provide for increased flexibility in the feed system design, and are more suitable for
a greater number of cavities and/or gates. Of all the designs, the hot runner mold provides
the least pressure drop, least material utilization, and fastest cycle times. However, the hot
runner system requires a significant up-front investment, greater molder capability, and can
impede production of small batches of moldings.
All feed systems should minimize the feed system length to reduce both material utilization
and pressure drops. The optimization of the diameters along the feed system requires a tradeoff between the pressure drop and volume of the feed system. Smaller diameters provide
for less material consumption but higher pressure drops. If the pressure drop through the
runner is too high, then the molding machine may not be able to complete the filling of all
the mold cavities with the available injection pressure. For this reason, the mold designer
should perform analysis appropriate to the molding application, and provide a “steel safe”
feed system design that may be readily altered if needed.
When possible, feed system designs should be naturally balanced by using radial, branching,
or hybrid layouts. The artificial balancing of melt flow rates, for example in a family mold or
complex multi-gated part, can be accomplished by using different diameters to purposefully
impose different pressure drops and flow rates through each branch of the feed system.
Depending on the molding application, shut-offs may be placed at multiple junctions in the
runner system to direct the flow to different combinations of runners and mold cavities.
After reading this chapter, you should understand:
• The objectives to be considered in feed system design including melt conveyance,
minimizing pressure drop, minimizing material consumption, and balancing melt flow
rates and/or pressures;
• The form, function, advantages and disadvantages of two-plate, three-plate, and hot
runner mold designs;
• The different layouts of feed system designs, including series, branching, radial, hybrid,
and custom designs;

6.6 Chapter Review











159

How to analyze pressure drop in a feed system using the Newtonian and power-law
model;
How to optimize the feed system diameters to reduce material consumption without
imposing excessive pressure drops;
How to artificially balance the melt flow rates in a multi-gated or multi-cavity mold;
How to estimate the cooling time of a cold runner;
How to estimate the residence time in a hot runner;
How to select the runner cross-section, calculate the hydraulic diameter, and estimate the
pressure drop in a feed system with a non-circular section;
How to use sucker pins in two-plate and three-plate mold designs;
When and how to use runner shut-offs;
How to adjust analysis results to provide standard and “steel safe” feed system designs.

Chapter 5 focused on the filling analysis and design of the mold cavity. This chapter focused
on the filling and design of the feed system. The next chapter connects the feed system to
the mold cavity through the design and analysis of gates. Afterwards, the book moves away
from the mold filling system to other mold subsystems such as venting, cooling, ejection,
and others.

7

Gating Design

Gates provide the important function of connecting the runner to the mold cavity, and
initiating the flow of the melt into the cavity. There are many different types of gates, with
the most common types of gates being the edge and pin-point gates. Referring back to the
cost estimation of Section 3.3, gating represents a small portion of the mold cost but has a
significant impact on the operation of the mold. Knowing when to use what type of gate, and
how to properly dimension the gate(s), can reduce the likelihood of mold re-work.

7.1

Objectives of Gating Design

7.1.1

Connecting the Runner to the Mold Cavity

The primary function of the gate is to connect the runner to the mold cavity, so that the
polymer melt can flow throughout the cavity to form the molding. While this is a simple
function, the design of the gate provides a means by which the flow of the melt can be fine
tuned through the adjustment of its location or dimensions.

7.1.2

Provide Automatic De-Gating

For the economical use of an injection mold, the gate and runners should be automatically
disconnected from the molding at the time of ejection. Otherwise, an operator may need to
handle the moldings to remove the gate and runner from the molded part with a gate cutter.
Such use of an operator clearly imposes a higher labor cost for the molder. Furthermore, the
handling and de-gating of moldings by the operator can also limit the cycle time and induce
defects into the moldings.
There are three common approaches to providing automatic de-gating. First, it is possible to
use the opening action of the mold to separate the moldings from the feed system. Such use
is common in two-plate molds with tunnel gates or three-plate molds with pin-point gates.
Second, it is possible to use a hot runner with either thermal or valve gates to completely
eliminate the need for de-gating. Third, it is possible to use robots equipped with cutters to
de-gate as an added step in the removal and placement of the moldings. If this third approach
is to be used, then the mold designer should discuss alternative gate types and locations with
the molder to provide access for pick-up of the molding and de-gating of the feed system.

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7 Gating Design

7.1.3

Provide Aesthetic De-Gating

Since gates are physically attached to the moldings, their removal will leave a witness mark
on the surface of the molding. One common approach is to use a very small gate (such as a
pin-point gate) in combination with a coarse texture such that the gate vestige is less apparent.
Another common approach to resolve this issue is to locate gates on non-visible surfaces such
as underneath a side wall instead of into the side wall. Figure 7.1 demonstrates the relocation
of a gate to a non-aesthetic surface. It should be noted, however, that careful gate removal
may be required since any significant gate vestige may interfere with mating surfaces in the
product assembly.

Gating on side wall

Gating below side wall

Figure 7.1: Re-locating gates for improved aesthetics

7.1.4

Avoid Excessive Shear or Pressure Drop

Both aesthetics and de-gating suggest gates with small dimensions. From a flow perspective,
however, small gates can provide excessive shear rates and pressure drops. Some of the resulting
defects may include:






material degradation,
non-laminar flow and jetting of the melt into the mold cavity,
splay and other visual defects,
extended mold filling times, and
short shots.

For these reason, the shear rate should be calculated and verified that it is below the maximum
permissible value. While Appendix A provides maximum shear rates for some materials, the
mold designer should consult with the material supplier for application-specific data. If the
shear rate is permissible, then the pressure drop is usually acceptable as well. However, the mold
designer should calculate the pressure drop to ensure that it is not excessive. A typical pressure

7.2 Common Gate Designs

163

drop through a gate is on the order of 2 MPa (300 psi), with 6 MPa (900 psi) potentially
excessive dependent on the availability of melt pressure to fill the mold cavity.

7.1.5

Control Pack Times

Another important function of the gate is to control the post-filling time (generally known
as the pack time) of the melt into mold cavity. After the mold is filled with the polymer melt,
the molding machine maintains a high melt pressure to force additional melt into the mold
cavity to compensate for volumetric shrinkage as the melt in the cavity cools. It is really the
gate, and not the molding machine, that determines the packing time of the cavity.
Consider gate designs that are either too small or too large. If the gate is too small, then the
melt in the gate will prematurely solidify and prevent the conveyance of additional melt into
the mold. As a result, the melt in the cavity may experience excessive volumetric shrinkage
resulting in poor dimensional and aesthetic properties. Conversely, if the gate is too large, then
the gate will not solidify in a timely manner. In this case, the molding machine is required to
maintain a very long pack time. If a shorter packing time is used, then the melt in the cavity
will flow out of the cavity and back into the runner system and the molding machine. As a
result, the melt in the cavity may again experience excessive volumetric shrinkage resulting
in poor dimensional and aesthetic properties. For these reasons, the theoretical minimum
packing time of the gate should be calculated and checked against the expected process parameters. If the packing time is unexpectedly short or long, then the dimensions should be
adjusted even if the shear rates and pressure drops were found acceptable.

7.2

Common Gate Designs

The most common types of gate designs are next discussed. It should be mentioned that
many additional kinds of gates exist, and the designs of these common gate types should be
customized to best meet each molding application’s requirements.

7.2.1

Sprue Gate

The sprue gate provides the flow of melt from a sprue directly into the mold cavity as shown
in Figure 7.2. The sprue gate is most commonly used in single cavity molds in which the
mold’s sprue bushing directly abuts the surface of the mold cavity. The sprue gate itself is the
interface between the bottom of the sprue and the top of the cavity. Since it has no length,
there is no pressure drop associated with the sprue gate. For the verification of the shear rate,
the smallest diameter of the sprue should be used. Given relatively large dimensions of most
sprue designs, the pressure drops and shear rates are relatively low such that high flow rates
into the cavity can be achieved.

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7 Gating Design

Figure 7.2: Sprue gate design

Figure 7.3: Recessed gate well around sprue gate

A significant disadvantage of the sprue gate is the difficulty of de-gating due to its large
diameter. While the operator may manually remove the sprue in many applications with a
gate cutter, powered cutters are necessary for many applications with large sprue diameters
or tough engineering materials. Furthermore, the removal of the sprue gate can leave a large
vestige that can interefere with the product usage. In the design provided in Figure 7.2, a small
rim has been provided around the perimeter of the base so the cup may sit flat after sprue
removal. If such a rim is not desired, then a recess around the sprue gate may be designed as
in Figure 7.3 to provide clearance for the gate vestige.

7.2.2

Pin-Point Gate

The pin-point gate is a common type of gate used to connect a sprue or runner to the mold
cavity via a small cylindrical opening as shown in Figure 7.4. The pin-point gate is frequently
used due to its small size which provides for ease of de-gating and minimal gate vestige.
Pin-point gates are often used with three-plate molds having sprues with reverse taper. Due
to the pin-point gate’s small size, the de-gating is readily accomplished upon the opening
of the mold as discussed in Section 6.3.2. Pin-point gates are also often used in two-plate

7.2 Common Gate Designs

165

Figure 7.4: Pin-point gate designed with inverted sprue

molds to connect the runner to the side walls of the mold cavity. Compared to other types
of gates, however, the flow of the melt through such a small orifice will incur high pressure
drops and shear rates.
The diameter of the pin-point gate should be specified so as to be large enough to avoid
excessive shear rates yet small enough to provide the desired de-gating and aesthetics. The
length of the pin-point gate is typically on the order of its diameter, and need only be long
enough to provide for the manufacturability of the mold. A properly designed pin-point
gate will have a reverse taper between the cavity surface and the gate breakpoint as shown
in Figure 7.4. A recess may be provided in a gate well as shown in Figure 7.3 to provide a
clearance for any gate vestige after de-gating. A smooth transition should also be designed
between the gate and the sprue or runner.

7.2.3

Edge Gate

The edge gate is a very common type of gate used to connect a cold runner to the edge of
a mold cavity. The design and re-design of an edge gate for the cup has been previously
discussed with reference to Figure 7.1. Another edge gate design is specified in Figure 7.5. In
this design, the edge gate connects to the inner periphery of the screen’s supporting frame.
Since this gate location is internal to the laptop assembly, any vestige remaining after the
gate removal will not be observed by the end-user of the molding. Therefore, the edge gate
can and should utilize the full thickness of the adjacent wall section, and need not be gated
underneath the lower surface of the frame.
Compared to the pin-point gate, the edge gate has greatly reduced shear rates and pressure
drops. The mold designer can select the thickness, length, and width values according to
the needs of the application. In general, the thickness of the edge gate should be less than
the wall thickness of the molding, but may approach the thickness of the molding if shear

166

7 Gating Design

Figure 7.5: Edge gate design

rates are a concern. The width of the gate should be less than the diameter of the runner but
wide enough to avoid excessive shear rates. The length of the edge gate should be kept to a
minimum, but long enough to provide the molding machine operator access for de-gating
with gate cutters.

7.2.4

Tab Gate

The tab gate can be considered a variant of the edge gate, in which a tab is permanently
added to the molding for the purpose of improved gating. For example, the edge gate design
of Figure 7.5 could be problematic since the melt flows from the runner into the thin inner
frame of the bezel, which can cause premature freeze-off of the flow and excessive volumetric
shrinkage in the surrounding thicker sections. To improve the flow, a tab, rib, or other feature
is added to the mold cavity for the sole purpose of gating as shown in Figure 7.6. In this
design, a rib with a thickness equal to the thickness of the nominal thickness of the part has
been provided that connects the runner to the thicker portion of the molding outside the
thin inner frame. Since the thickness of the tab gate is greater than the thickness of the thin
frame, sink will likely develop on the top surface. However, this issue is not significant since
this area is hidden by the screen assembly.
Tab gates can be extremely effective with respect to cost and molding performance. The key to
their effectiveness is to establish potential gating areas where their remnants will not affect the
aesthetics or functionality of the resulting moldings. Once such gating areas are established,
the mold designer should select whatever tab geometry and dimensions are appropriate for
the application.

7.2 Common Gate Designs

167

Figure 7.6: Tab gate design

7.2.5

Fan Gate

The fan gate can be considered as another variant of the edge gate, in which the width of the
fan gate at the molding exceeds the diameter of the runner. One fan gate design is shown in
Figure 7.7. In this case, the width of the fan gate has been selected to avoid excessive shear
rates when the melt flows into the cavity at a high volumetric flow rate. Given the large width
of most fan gates, the feed system is typically removed powered gate cutter, a reciprocating
saw, or a router.

Figure 7.7: Fan gate design

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7 Gating Design

Figure 7.8: Fan gate designed for linear flow

One common use of fan gates is to provide a linear melt flow from the gate instead of the
radial flow that will result with the previous gate designs. A simple molded plaque application
is shown in Figure 7.8. For this design to be effective, two criteria must be met. First, the fan
gate must span the width of the molding across which linear flow is desired. Second, the flow
resistance across the width of the fan gate must be negligible. Various fan gate geometries
have been developed to adjust the flow rates into the cavity across the width of the fan gate.
The design shown in Figure 7.8 is typical, and consists of a simple loft between the circular
section of the runner and the rectangular section of the mold cavity.

7.2.6

Flash/Diaphragm Gate

While fan gates are effective, another alternative is the flash gate. The word “flash” implies a
melt flow through a very thin section. Accordingly, the flash gate consists of a thick circular
section adjacent to a thin rectangular section as shown in Figure 7.9. During molding, the
melt will proceed from the runner into the thick circular section. The thin adjacent section
will cause the melt flow to slow, cool, and potentially freeze while the melt fills the thick
section. Once the melt hits the end of the thick section, the melt pressure will then increase
significantly and force the frozen material in the thin section to flow. Since the flow resistance
along the thick section is small compared to the flow resistance across the thin section, the
flash gate provides a nearly linear melt flow to the cavity across its width.

Figure 7.9: Flash gate design

7.2 Common Gate Designs

169

Figure 7.10: Diaphragm gate design

The concept of the flash gate can be extended to a cylindrical geometry to provide a linear
melt flow without knit-lines as shown in Figure 7.10. In this design, a solid thick “diaphragm”
is used to convey the melt from the sprue to the inner periphery of the mold cavity. A thinner
gate section is then used to ensure a uniform cavity filling and also assist in the removal of the
diaphragm from the molding. Even though the geometry of the diaphragm gate is cylindrical,
the analysis is correctly performed according to a strip geometry with a width equal to the
circumference of the diaphragm.
A flash gate can typically be removed by an operator without the need for power assisted
cutters. Due to the geometry of the diaphragm gate, however, power tools or a punch press are
typically required for de-gating. Both the flash and the diaphragm gates will leave a witness
line, so it is desired to minimize the thickness of the gate itself. The geometry and thinness
of these gates may seem to impose excessive shear rates and pressure drops upon the melt.
However, these gates’ large width will result in relatively low linear melt velocities even at high
volumetric flow rates. As a result, these gates can be effectively designed to provide moderate
shear rates and pressure drops.

7.2.7

Tunnel/Submarine Gate

With the exception of the pin-point gate used with a three-plate mold, all the preceding
gate designs require the removal of the feed system from the molding either by some postmolding system (usually the operator). The tunnel gate is a common type of gate that can
be considered a variant of the pin-point gate. Its primary advantage is that the tunnel gate
provides for automatic de-gating with the actuation of a simple two-plate mold. The design

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7 Gating Design

Figure 7.11: Tunnel gate design

of a tunnel gate for the lid molding is shown in Figure 7.11. Compared to the pin-point
gate, the changes appear to be cosmetic with the addition of some turns and tapers. These
differences are negligible with respect to the flow of the plastic melt, so the dimensions of
the tunnel gate should be determined as previously discussed to provide for reasonable shear
rates and pressure drops.
At first glance, the tunnel gate seems very similar to the pin-point gate. However, they differ
significantly in structure and function. The function of the tunnel gate can be understood
by examining the mold design. A cross section through the closed mold with the tunnel gate
is shown in Figure 7.12. The key to the function of the tunnel gate is that the tunnel gate
“tunnels” through the cavity insert. As shown in Figure 7.13, the molding will move away
from the cavity insert and stay on the core with the tunnel gate when the mold opens. At the
same time, the opening of the mold forces the tunnel portion of the runner to temporarily
remain with the cavity insert. The motion of the core insert away from the cavity insert causes
the tunnel gate to break at its junction with the molding. The molding and the feed system
can then be ejected as in a conventional injection molding process.
The diameter of the tunnel gate at the cavity should be designed to avoid excessive shear rates
and pressure drops. For the tunnel gate to operate reliably, there are two very important angles
that must be specified. First, a nominal 45 degree angle should be maintained between the
centerline of the tunnel gate and the parting plane to allow for the transmission of shearing
stresses to the gate. Second, the tunnel gate should have an included taper angle of at least 20
degrees to ensure that the tunnel gate does not stick in the mold and that the tunnel gate breaks
at the junction with the molding. To ensure adequate structural integrity of the cavity undercut,
the tunnel gate should be located at least three tunnel diameters off the parting plane.

7.2 Common Gate Designs

171

Figure 7.12: Section of closed mold with tunnel gate

Figure 7.13: Section of slightly opened mold with tunnel gate

The tunnel gate is a clever design since it provides for automatic de-gating without significant
investment. The primary risk in application is that the tunnel gate may be improperly designed
or wear such that the runner system does not reliably de-gate from the molding. To assist
the de-gating of the tunnel gate from the molded part, the runners should be designed with
nearby sucker pins as shown in Figure 6.1 to retain the runner system on the core side. If the
tunnel gates and the runner system remain on the cavity side, then they can not be removed
through actuation of the ejection system.
There are several variations of the tunnel gate. Just as the tunnel gate burrows up into the
cavity insert, the term “submarine” gate refers to a design variant in which the tunnel gate
descends into the core inserts. The actuation of the ejector system and the ejection of the
molding of the core then acts to break the gate and strip the feed system from the molding.

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7 Gating Design

Figure 7.14: Section of mold with extended submarine gate

With both tunnel and submarine gates, it is also possible to design extended gates that curve
around vertical side walls to gate onto the interior surfaces of the part. Such an extended
submarine gate design, also known as a “banana” or “cashew” gate, is shown in Figure 7.14,
though such designs pose additional risk with respect to reliable de-gating.

7.2.8

Thermal Gate

As discussed previously, the use of a hot runner feed system eliminates the need for the
molding and cooling of a cold runner. The design of gates for hot runners varies substantially
from those for cold runners. The primary objectives are generally the same regarding the
shear rate, pressure drop, and aesthetic requirements. However, thermal gates in hot runners
must also provide a solidified plug that prevents the liquefied plastic melt in the hot runner
from flowing out of the gate when the mold opens and the solidified plastic near the gate is
removed with the molding.
One of the most common types of gates used in hot runners is the pin-point thermal gate
formed with a torpedo. This design is shown in Figure 7.15. In this design, a highly conductive
torpedo is inserted into the nozzle near the gate. The purpose of the torpedo is to transmit
heat from the nozzle towards the gate and keep the plastic molten internally. Typically, three
or four orifices in the torpedo are used to connect the plastic melt in the feed system to the
cavity. A thin layer of residual plastic melt is used to insulate the hot torpedo from the cold
mold walls.
During the filling stage, the melt pressure from the molding machine increases until the
pressure within the torpedo orifices forces any solidified plastic between the torpedo orifices
and the gate into the mold cavity. The melt can then flow from the drop, through the orifices,
and into the mold cavity much like a conventional cold runner feed system. When the flow
ceases, the heat transfer to the mold will cause the insulating plastic to partially solidify,
with the plastic around the tip of the torpedo being fully solidified. When the mold opens,
an annulus of the solidified material will be broken around the torpedo tip. However, a thin
solidified layer will remain that prevents the leakage of the melt from the hot runner to the
environment.

7.2 Common Gate Designs

173

Figure 7.15: Section of mold with thermal pin-point gate

The thermal pin-point gate is a clever design with respect to its dual use of the plastic to reduce
heat transfer and form a solid seal. However, it does have two significant disadvantages. First,
pin-point gates typically have a small gate diameter. Just as with conventional pin-point gates
for cold runners, the diameter of the thermal gate and its associated orifices must be designed to
provide reasonable pressure drops and shear rates. Because of the small orifices, this gate design
may not be suitable for shear sensitive or heavily filled materials. The second disadvantage is
related to the residence of the insulating plastic. Over time, any stagnant material will degrade
with the potential to be pulled into the flow stream and contaminate the plastic melt, most
typically as black specks in the molded parts. The residence of the insulating plastic can also
cause significant issues when the molder performs a color change, since even small amounts
of residual material may cause color streaking on subsequently molded parts.1
Hot runner suppliers have worked to resolve these issues, but with limited success. For
molding applications involving frequent color changes or the use of shear sensitive or
heavily filled materials, it is desirable to open the flow bore in the gate and reduce the shear
rates. Accordingly, the thermal sprue gate design has been developed. This design is shown
in Figure 7.16. In this design, a nozzle tip is utilized that has a long contact length with the
surrounding mold. This allows the gate area at the cavity to cool significantly, such that no
insulating layer of plastic is required. An open flow bore within the nozzle and nozzle tip
can then guide the plastic melt directly to the cavity. After the melt fills the mold, the entire
sprue below the thermal gate solidifies. A set of converging-diverging tapers in the nozzle
tip dictates the break point of the sprue, leaving a thin layer of solidified plastic behind to
seal the plastic melt.
1

A third limitation of the thermal gate may also arise. Specifically, the solidified layer must be forced
from the gate by increased melt pressure at the start of the molding cycle. The magnitude and timing of
the melt pressure may vary slightly from gate to gate depending on gate tolerances, gate assembly, and
gate temperature distribution. While not an issue in most molding applications, these variances may be
problematic in precision molding applications.

174

7 Gating Design

Figure 7.16: Section of mold with thermal sprue gate

Compared to the thermal pin-point gate, the thermal sprue gate provides an open flow bore
with reduced shear rates and pressure drop. Since the shear rates are reduced, the thermal
sprue gate is better suited for use with shear sensitive and heavily filled materials. Due to its
open flow bore, moreover, the thermal sprue gate typically requires fewer molding cycles when
colors or materials are changed. One less apparent but important advantage is that the length
of the sprue can be designed to allow clearance for ribs or other cavity details that emanate
towards the feed system and may prevent direct gating with a thermal pin-point gate. There
is one significant disadvantage of the thermal sprue gate, however. Since a sprue is molded
with the part, it must remain with the part as vestige or otherwise be later detached by the
operator or another post-molding system.

7.2.9

Valve Gate

Thermal gates are economical and generally suitable for a wide range of molding applications
and materials. However, both the pin-point and sprue thermal gates have two potential
limitations. First, they rely on a solidified layer of plastic to prevent leakage, and this solidified
layer may not be sufficient in a variety of circumstances. Second, thermal gates provide
significant gate vestige that may not be acceptable in many applications. To resolve the
limitations of the thermal gate, mechanically actuated valve gates have been developed. One
such design is shown in Figure 7.17. During operation, the valve pin is retracted to provide
access to the mold cavity. After the cavity is filled and packed, the valve pin is advanced to
seal the gate.
Valves gates have two primary advantages over thermal gates. First, valve gates provide a
mechanical seal (steel on steel) and so are more robust with respect to preventing melt
leakage. Second, the face of the valve pin presents a mold shut-off surface to the mold cavity
when closed and thereby significantly reduces the gate vestige. Unfortunately, the mechanical
actuation system used by the valve gates increases the cost and complexity of the mold. The
cost is increased due to the addition of the valve pins, actuators, much larger top clamp

7.3 The Gating Design Process

175

Figure 7.17: Section of mold with valve gate

plate to house the actuators, hoses, fittings, and the control system. As such, the cost of a hot
runner system with valve gates may be twice the cost of a hot runner system with thermal
gates. Complexity of use is also increased, as the operator must correctly connect the hoses
and specify timings to coincide with the process settings on the molding machine.

7.3

The Gating Design Process

7.3.1

Determine Type of Gate

To design a gate, the mold designer must first determine the type of gate to be designed. Often,
the selection of a type of gate is obvious. The primary factors that should be considered include
the type of runner system, the desired method of de-gating, the allowable level of shear rates
through the gate, and the resulting flow that is desired. To facilitate gate selection, Table 7.1
provides a summary of the types and properties of common gates.
The following comments apply to the columns of Table 7.1. First, it is common in multicavity molds to use a hot runner system in which each drop feeds a plurality cold “subrunners” and associated gates to locally traverse the parting plane. For example, a four drop
hot runner can be used with four could runners emanating from each drop to economically
and reliably fill sixteen mold cavities. Second, the de-gating method refers to the use of
the mold action to de-gate the parts, and does not consider automated de-gating through
the use of robotics. Third, shear rate regimes are approximate since they are a function of
the gate dimensions and process conditions; the levels of low, moderate, and high roughly
correspond to shear rates on the order of ten, forty, and a hundred thousand reciprocal
seconds. Finally, most gates result in a radial flow pattern out of the gate with only the fan,
flash, and diaphragm gates purposefully designed to provide linear melt flow into the mold
cavity.

176

7 Gating Design

Table 7.1: Gate types and properties

Gate type

Runner type

De-gating method

Shear rates

Resulting flow

Sprue

Cold

Manual

Moderate

Radial

Pin-point

Cold

Automatic

High

Radial

Edge

Cold

Manual

Moderate

Radial

Tab

Cold

Manual

Moderate

Radial

Flash/diaphragm

Cold

Manual

Moderate

Linear

Fan

Cold

Manual

Low

Linear

Tunnel/submarine

Cold

Automatic

High

Radial

Thermal pin-point

Hot

Automatic

High

Radial

Thermal sprue

Hot

Automatic

Moderate

Radial

Valve

Hot

Automatic

Moderate

Radial

7.3.2

Calculate Shear Rates

The shear rates are calculated according to the previously provided equations for flow in strips
and cylinders. For reference, the formulae for Newtonian and power-law flows are provided
in Table 7.2. These formulas are based on the volumetric flow rate rather than the linear melt
velocity. The reason is that molding machines can only provide limited control of the melt
flow, and so the volumetric flow rate through the gate should be considered similar to that
through the runner system and the mold cavity.
Appendix A provides the material properties and recommended maximum shear rates for
some materials. The maximum shear rates should be considered approximate at best, since in
most cases these values are taken from general guidelines for various materials. In reality, the
maximum shear rates are dependent not just on the maximum shear rate, but also the entire
thermal and mechanical history of the polymer melt. In many if not most cases, much higher
Table 7.2: Shear rate equations

Geometry

Newtonian

Power-law

Strip

γ =

6 V
W h2

1⎞

2 ⎜ 2 + ⎟ V

n⎠
γ =
W h2

Cylinder

γ =

4 V
π R3

1⎞

⎜⎝ 3 + ⎟⎠ V
n
γ =
π R3

7.3 The Gating Design Process

177

shear rates may be possible than the maximum shear rates listed in Appendix A. Given this
dilemma and the ease of increasing the size of gates, it may be desirable for the mold designer
to be “steel safe” and specify a smaller gate with the intent that the mold will be tested and the
gate sizes increased as necessary to avoid excessive shear rates and fine tune the flow.
To calculate the shear rates, the mold designer must specify some initial gate dimensions.
For thicker gates having low and moderate shear rates (including the sprue, edge, tab, fan,
and valve gates), the initial thickness may be set equal to the wall thickness of the molding at
the location of the gate. For thinner gates having moderate and high shear rates (including
the pin-point, flash, diaphragm, tunnel, submarine, and thermal gates), the initial thickness
may be set equal to one-half the wall thickness of the molding. Strip-type gates also require
the specification of the width. For flash and diaphragm gates, the width should be set to the
edge length along which linear flow is desired. For other strip-type gates, the initial width
may be set to twice the gate thickness; this width can be increased or decreased to adjust the
shear rates as necessary.
Example: Calculate the shear rate through the two edge gates into the cavity of the bezel
mold as shown in Figure 7.5 assuming a volumetric flow rate for ABS at the nozzle of
125 cc/s.
Since two edge gates are specified, the volumetric flow rate through each gate will be
62.5 cc/s. Assigning the thickness and width of the edge gate to be 0.75 mm and 6.0 mm,
respectively, the shear rate is evaluated as:
γ =

6 ⋅ 12 ⋅ 125 ⋅ 10−6 m 3 /s
0.006 m ⋅ (0.00075 m)2

= 111,000 s −1

This shear rate is significantly above the maximum shear rate of 50,000 1/s. An increase
in the gate width to 14 mm would bring the shear rate within the specified maximum,
but require a change in the gate type to a fan gate. Alternatively, the flow rate can be
reduced from 125 cc/s at the nozzle to 60 cc/s, which would require a doubling of the
filling time.
Example: Calculate the shear rate through the pin-point gate in the molding of the cup
as shown in Figure 7.4.
Assuming a 1 s fill time and a 44 cc cavity volume, a volumetric flow rate of 44 cc/s is
used for analysis. The initial diameter of the pin-point gate is 1.5 mm (one half the wall
thickness of the cup). The shear rate is then:
γ =

4 ⋅ 44 ⋅ 10−6 m 3 /s
= 132,000 s −1
π (0.0015 m)3

As in the previous example, the shear rates are again excessive. To achieve a specific
maximum shear rate at the gate, the gate radius could be solved directly:

178

7 Gating Design

R=

3

4 V
=
π γ max

4

4 ⋅ 44 ⋅ 10−6 m 3 /s
= 1.03 mm
π ⋅ 50,000 s −1

which corresponds to a diameter of approximately 2 mm. This larger diameter would
leave a larger gate vestige and require greater forces for de-gating. It may be reasonable
to initially specify the lesser diameter of 1.5 mm, and then increase the diameter if issues
with excessive shear rates are encountered.

7.3.3

Calculate Pressure Drop

If the shear rates are within the allowable limits, then the pressure drops are likely acceptable
as well. However, the pressure drop through the gate should be calculated to ensure that
adequate injection pressure is available to fill the mold cavity. The pressure drops are calculated
according to the previously provided equations for viscous flow in strips and cylinders. For
reference, the formulae for Newtonian and power-law flows are provided in Table 7.3.
Table 7.3: Pressure drop equations

Geometry

Strip

Cylinder

Newtonian

ΔP =

ΔP =

Power-law

12 μ L V
W h3

1⎞ ⎤
⎡ ⎛
2 2 + ⎟ V ⎥
2 k L ⎢ ⎜⎝
n⎠


ΔP =
H ⎢ W h2

⎢⎣
⎥⎦

8 μ L V
π R4

1⎞ ⎤
⎡⎛
3 + ⎟ V ⎥
2 k L ⎢ ⎜⎝
n⎠


ΔP =
R ⎢ π R3 ⎥
⎢⎣
⎥⎦

n

n

In estimating the pressure drop through gates, it is important to calculate the viscosity at the
appropriate shear rate when using the Newtonian model, or alternatively use the equations
for the power law model. The pressure drop through the gates may vary from almost zero
to several MPa. Pressure drops above 10 MPa are usually indicative of improperly designed
gates that are either too thin or too long.
Example: Calculate the pressure drop across the fan gates in the bezel mold shown
in Figure 7.7, assuming ABS is molded at mid-range processing temperatures with a
volumetric flow rate at the sprue of 125 cc/s. The fan gate has an initial round section
with diameter of 6.35 mm and ends at the cavity as a rectangular section with a width of
14 mm and a height of 0.75 mm.

7.3 The Gating Design Process

179

The analysis of fan gates is complicated since the size and shape of its cross-section varies
down its length. The fan gate could be broken into a number of small segments each with
a different section to accurately calculate the pressure drop. For an approximation, this
analysis will assume a rectangular profile with a width of 10 mm (half way between the
starting diameter of 6.35 mm and the ending width of 14 mm), a thickness of 3.5 mm
(half way between the starting diameter of 6.35 mm and ending thickness of 0.75 mm),
and a length of 10 mm. Using the power law model for ABS, the pressure drop through
the fan gate can be calculated as:
1 ⎞
⎡ ⎛
−6
3 ⎤
2 2+
⎟ 62.5 ⋅ 10 m /s ⎥
2 ⋅ 17,000 Pa sn ⋅ 0.01 m ⎢ ⎜⎝
0.35 ⎠


ΔP =
0.0035 m
0.01 m ⋅ (0.0035 m)2


⎢⎣
⎥⎦
= 1.9 MPa = 280 psi

0.35

This pressure drop is negligible and requires no change to the gate design.
Example: Calculate the pressure drop through the pin-point gate in the molding of the cup
as shown in Figure 7.4 assuming ABS is molded at mid-range processing temperatures.
The previous analysis for the 1.5 mm diameter pin-point gate indicated a shear rate of
132,000 1/s for a volumetric flow rate of 44 cc/s. The viscosity at this shear rate can be
calculated from the Cross-WLF model as 5.4 Pa s. The pressure drop is then:
ΔP =

8 ⋅ 5.4 Pa s ⋅ 0.001 m ⋅ 44 ⋅ 10−6 m 3 /s
= 1.9 MPa
π (0.00075 m)4

Even though the shear rate through the pin-point gate was extremely high, the shear
thinning of the melt produced a low melt viscosity and an acceptable pressure drop.
For the 2 mm diameter pin-point gate, the shear rate of 50,000 1/s yields a viscosity of
11.2 Pa s. The pressure drop through the larger gate is approximately:
ΔP =

8 ⋅ 11.2 Pa s ⋅ 0.001 m ⋅ 44 ⋅ 10−6 m 3 /s
= 1.3 MPa
π (0.001 m)4

which again is normally acceptable.

7.3.4

Calculate Gate Freeze Time

After the mold cavity is filled with the plastic melt, additional material must be forced into
the cavity to compensate for volumetric shrinkage as the melt cools. As the melt in the cavity
cools, the melt in the gate will also tend to cool. The frozen skin will propagate from the mold
wall to the centerline of the gate. Since no additional melt flow can be supplied to the cavity

300

Melt temperature
120000
Viscosity

250

100000

200

80000

150

60000

100

40000

50

20000

0

Viscosity (Pa s)

7 Gating Design

Bulk melt temperature (°C)

180

0
0

1

2

3

Time (s)

Figure 7.18: Gate temperature and viscosity history

once the gate freezes, the molder should set up the molding machine to end the packing stage
at gate freeze-off and begin the plastication stage.
The cooling of the melt in the cavity and the use of the associated heat equation will be
discussed in the Chapter 9. Using the provided analysis, the bulk melt temperature is plotted
as a function of time in Figure 7.18 for a 2 mm diameter cylindrical gate for ABS at mid-range
melt and coolant temperatures. The temperature of the plastic melt in the gate will initially
be close to the set melt temperature, and then decrease in the post-filling stage as the heat
transfers to the colder mold walls.
Using the Cross-WLF viscosity model, the apparent viscosity of the plastic melt in the gate at a
shear rate of 10 1/s is also plotted in Figure 7.18. It is observed that the viscosity of the plastic
melt is initially low, and then begins to increase exponentially as the temperature decreases.
Eventually, the viscosity will increase such that no flow is effectively transmitted through the
gate and the packing stage should end. In this case, a viscosity of 100,000 Pa s has been arbitrarily selected as a no-flow condition, corresponding to a final pack time of 2.2 s. Appendix A
provides the “no flow temperature” for various materials estimated in this manner.
For reference, the equations to calculate the minimum packing time are provided in Table 7.4
for rectilinear and strip geometries. It should be mentioned that these equations will provide
the minimum pack times since they assume perfect heat conduction between the melt and
the mold wall. Furthermore, these equations do not consider the melt flow through the gate
into the cavity and the associated convection of heat that will tend to prevent the freezing of
the gate. For these reasons, gate pack times should be expected to be significantly longer than
those predicted with the equations of Table 7.4. Even so, the equations are useful to provide
an estimate of the order of magnitude of the gate solidification time.

7.3 The Gating Design Process

181

Table 7.4: Gate freeze time equations

Geometry

Packing time

Strip

ts =

⎛ 8 T
− Tcoolant ⎞
h2
ln ⎜ 2 melt

π ⋅ α ⎝ π Tno_flow − Tcoolant ⎠

Cylinder

ts =


T
− Tcoolant ⎞
D2
ln ⎜ 0.692 melt
Tno_flow − Tcoolant ⎟⎠
23.1 ⋅ α ⎝

2

Example: Estimate the solidification time of the fan gates in the bezel mold shown in
Figure 7.7 assuming ABS is molded at mid-range processing temperatures. The fan gate has
an initial round section with diameter of 6.35 mm and ends at the cavity as a rectangular
section with a width of 14 mm and a height of 0.75 mm.
The 0.75 mm thick rectangular section at the end of the fan gate will be first to solidify
and determine the solidification time, so:
ts =

(0.00075 m)2
⎛ 4 240 − 60 ⎞
ln ⎜
⎟ = 1.5 s
2
2
−8
π ⋅ 8.69 ⋅ 10 m /s ⎝ π 132 − 60 ⎠

Since the thickness of the molding is the same as the gate thickness, increasing the gate
thickness will have no effect on the packing of the material in the mold cavity away from
the gate. It is noted that this edge gate design does gate into a thinner section of the mold
cavity, which is not recommended. For this reason, a three-plate mold or hot runner
mold should be considered to provide gating into the thicker 1.5 mm section with a
longer packing time.
Example: Calculate the solidification time for 2 mm diameter pin-point gate in the
molding of the cup as shown in Figure 7.4.
The solidification time can be estimated as:
ts =

(0.002 m)2
240 − 60 ⎞

ln ⎜ 0.692
⎟ = 1.1 s
132 − 60 ⎠
23.1 ⋅ 8.69 ⋅ 10−8 m 2 /s ⎝

This gate freeze time may be compared to the solidification time of the cup with a nominal
wall thickness of 3 mm:
ts =

(0.003 m)2
⎛ 4 240 − 60 ⎞
ln ⎜
⎟ = 24 s
2
2
−8
π ⋅ 8.69 ⋅ 10 m /s ⎝ π 132 − 60 ⎠

It is likely that the gate will freeze prematurely and the cup may not be adequately
packed.

182

7 Gating Design

7.3.5

Adjust Dimensions

After the shear rate, pressure drop, and gate freeze time have been calculated for an initial
design, the type and dimensions of the gate can be modified to improve the design. For
aesthetic and de-gating purposes, smaller gate sizes are desired. As the previous examples
have shown, however, excessive shear rates may dictate the use of larger gate sizes. These
shear rate calculations are dependent upon an assumed flow rate, and this flow rate will not
be known until after the molder has optimized the process with the implemented mold. For
this reason, the mold designer should assume a reasonable flow rate for analysis, select a type
of gate that can be enlarged, and specify dimensions that are “steel safe”. In this way, the size
of the gates can be readily increased to reduce shear rates as needed.
Gate dimensions are may also be adjusted to tweak the pressure drops and flow rates at
different gates. Such fine-tuning may help to balance the melt flow between multiple cavities,
or to adjust the flow rates and knit-line locations within a multi-gated cavity. The extent of
the balancing that can be achieved through gate design is extremely limited due to the small
size of the gate. To bring about large changes in flow, the gate dimensions must vary by such
significant amounts that the shear rates and gate freeze times will vary substantially between
gates, causing unintended consequences. For this reason, it may be preferred to change the
dimensions of the runners or to use a dynamic flow control technology as later discussed for
melt control in Section 13.6.4.
Gate dimensions are often adjusted to improve the dimensional control of moldings. When
the gate solidification time is significantly less than the packing time required by the melt in
the cavity, then excessive volumetric shrinkage may occur. There are two common approaches
that are used to reduce the volumetric shrinkage. The most common approach used by the
molder is to impose a very high packing pressure before the gate freezes, such that the residual
melt pressure in the cavity will be relieved as the melt shrinks. Unfortunately, this approach
can lead to excessive flashing and/or residual stresses. For this reason, a second common
approach is to increase the diameter or thickness of the gate to increase the solidification time
and provide packing at more moderate melt pressures. A third and seldom used approach is
to rework the mold to reduce the nominal thickness of the molding.

7.4

Chapter Review

The gate design process includes the selection of the type of gate and the careful specification
of the gate dimensions to balance aesthetics, shear rates, pressure drops, and packing times.
The selection of the gate type will primarily be determined by the previous specification of
the mold type (two-plate, three-plate, or hot runner), the need to bring about a certain type of
flow in the gate and/or cavity, and finally by the desire to provide a robust and fully automatic
molding cycle. The optimization of gate dimensions is driven by the trade-off between small
gate sizes (that provide for improved aesthetics and ease of de-gating) and large gate sizes (that
provide for lower shear rates and pressure drops). If the specification of the gate dimensions

7.4 Chapter Review

183

is uncertain, then the mold designer should utilize smaller gate dimensions since they can
be more readily increased if required after molding trials.
After reading this chapter, you should understand:
• The various types and functions of gates, including sprue gates, pin-point gates, edge gates,
tab gates, fan gates, flash gates, diaphragm gates, tunnel gates, submarine gates, thermal
pin-point gates, thermal sprue gates, and valve gates,
• The various requirements and trade-offs associated with gate designs,
• How to select a type of gate for a given molding application,
• How to calculate the shear rate for a given gate design,
• How to calculate the pressure drop for a given gate design,
• How to calculate the minimum gate freeze time for a given gate design, and
• How to adjust the gate dimensions to optimize the gate performance.
Now that the gates, feed system, and cavity have been analyzed and designed, the next chapter
discusses the need for venting the air displaced by the advancing melt during the filling of
the mold cavity. Afterwards, the mold cooling system is developed.

8

Venting

Venting is normally a minor aspect of mold design, which is frequently neglected until molding
trials indicate mold inadequacies related to venting. An understanding of the purpose and
function of vents can assist the mold designer to design vents where clearly needed and ensure
that the mold may accommodate additional vents when required.

8.1

Venting Design Objectives

8.1.1

Release Compressed Air

The primary function of the vent is to release the air in the mold that is being displaced by
the highly pressurized plastic melt. If all the air in the cavity is not removed during the filling
stage, then several defects can result.





First, the trapped air can form a highly pressurized pocket in the mold cavity through
which the melt can not flow, forming a short shot in the molded product.
Second, the highly compressed, high temperature gas can combust in the presence of the
plastic melt, causing a phenomenon known as “dieseling” and a defect known as “burn
marks”. If the burn marks appear on an aesthetic surface, the molder should reject the
molded part.
Third, the presence of gas between two converging melt fronts can reduce the part strength
due to interference of the air with the two welding melts while also forming v-notches
on the surface of the molded part that act as a stress concentration during the part’s
end-use.

8.1.2

Contain Plastic Melt

Since a lack of venting is associated with several significant defects, many large vents are
desirable at different locations. However, if a vent is too thick, then the polymer melt can seep
out of the vent, causing a thin but sharp line of plastic flash to form at the vent locations. In
many molding applications, this flash needs to be trimmed by the machine operator using a
deburring tool. Such deflashing is undesirable since the operator incurs labor cost yet does
not provide 100% consistency. Furthermore, if a molder continues operation with excessive
flashing, then the mold’s parting plane can wear and require resurfacing. For these reasons,
fewer and smaller vents are preferred.

186

8 Venting

8.1.3

Minimize Maintenance

The use of vents also provides more features on the mold that can require maintenance.
Many polymers will off-gas in the molten state, releasing particles that can build up and clog
the venting system. Such clogged vents can occur especially quickly with the use of mold
release. As a result, the molding process may intermittently develop defects related to a lack of
venting. Many molders resolve this issue by incorporating vent cleaning as part of a preventive
maintenance program. In any case, the mold designer should strive to design venting systems
that require minimal maintenance, and are easy to maintain when required.

8.2

Venting Analysis

A three step analysis process is recommended for the analysis and design of vents. First, the
air displacement rate should be estimated relative to the melt flow rate. Second, the number,
type, and location of vents must be assessed. Third, the width, length, and thickness of each
vent must be specified. With respect to the thickness selection, the thickness must be greater
than some minimum value to ensure adequate venting while also smaller than some maximum
amount to avoid excessive flashing.

8.2.1

Estimate Air Displacement and Rate

The amount of air displaced will be approximately equal to the volume of the injected
plastic. The term “approximately” is used here to imply that the air will expand somewhat
when contacted by the hot plastic melt. However, the heated air will also cool somewhat as
it flows past the surface of the mold. For these reasons, the analysis here will assume that the
volumetric flow rate of the air will equal the volumetric flow rate of the melt.
Example: The volumetric flow rate of the melt for the bezel was 125 cc/s. This will be
assumed for the air flow rate.

8.2.2

Identify Number and Location of Vents

Next, it is necessary to identify the locations where the venting is needed. These locations may
seem obvious, but on closer consideration these locations may not be so trivial to identify.
There are generally three different types of locations where venting is necessary as shown in
Figure 8.1. The first type of vent is required where the melt converges at an edge of the mold’s
parting plane or other shut-off surface. The second type of vent is required where two melts
converge to form a knit or weld line. The third type of vent is required where the melt converges
at a dead pocket in the mold. Each of these scenarios will next be briefly discussed.

8.2 Venting Analysis

187

Figure 8.1: Vent locations by type

Figure 8.1 suggests twelve potential vent locations around the bezel’s parting plane and shutoff surfaces. Some of these vents, including the four locations near the gates and the four
locations at the corners may not be necessary since the melt flow is predominantly radial.
Since the flow is radial, the melt should reach the edges of the mold without trapping any air,
and thus there is no need for a vent at those locations. However, the exact melt front behavior
may change slightly and it is not uncommon for the melt to trap gas at these locations as
shown in Figure 8.2. While the vents in the corner and near the gate may be considered as
optional, the mold designer may choose to specify vent locations at these locations to avoid
mold changes later. The other four vent locations at the end of flow indicated in Figure 8.2
should be included since a significant fraction of the displaced air from the cavity will likely
exit here.




Figure 8.2: Vent locations on shut-off surface



188

8 Venting



Figure 8.3: Vent locations on part interior

The second type of vent is required where two melt fronts converge as shown in Figure 8.3.
In this case, two concave melt fronts can come together and form an entrapment from which
the air can not escape. As indicated in Figure 8.3, a vent is therefore required on an internal
surface of the mold cavity. Usually, ejector pins are designed to provide such venting functions
on the surface of the mold cavity.
The third type of vent occurs at dead pockets in the mold. The exact locations are not always
obvious, so three examples are provided in Figure 8.4. In the left detail, the melt flows from
the cavity surface along the length of the boss, and eventually trapping the air at the top of
the boss. In the center detail, two melt fronts come together at a rib, pushing the air to the
top dead center of the rib. In the right detail, the melt front flows diagonally across a rib.
Due to a cutout in the rib, the air can be trapped in this corner of the mold cavity. There are
approximately twenty such dead pockets in the bezel design that may require venting.

Figure 8.4: Vent locations in dead pockets

8.2 Venting Analysis

189

The above discussion indicates that there are about three dozen vent locations that the mold
designer may wish to consider. It is unlikely that all of these vent locations are necessary.
Furthermore, the addition of vents is usually a relatively simple operation that can be
accomplished after the mold is built and tested. For this reason, it is fairly common for the
mold designer to initially specify vents at only the most critical vent locations.
Example: For the bezel mold, the mold design will initially specify eight vent locations
as indicated in Figure 8.5.

Figure 8.5: Initial vent locations

8.2.3

Specify Vent Dimensions

Once the number of vents is specified, the rate of air flow through each vent can be calculated.
It may seem reasonable to estimate the air flow through each vent as the total volumetric
air flow divided by the number of vents. However, this approach would not be conservative.
The reason is that the exact location of the end of fill is not known. As such, it is possible
that much of the air flow can disproportionately favor any one of the four locations on each
side of the part. A more conservative approach is to assume that all the local air flow exits
through each available vent.
Example: The assumed flow rate of the air for the bezel was 125 cc/s. This total flow rate
will certainly be split into two air flows, each with a flow rate of 62.5 cc/s, towards the top
and bottom sets of vents. Since the exact flow rate to each vent is unknown, the analysis
will assume that each vent be designed for a volumetric flow rate of 62.5 cc/s.
In general, the length and width of the vent are determined by the application geometry.
The minimum vent thickness is related to the pressure drop across the vent necessary to

190

8 Venting

release the displaced air. The minimum thickness can be derived using analysis of the air as
a laminar, viscous flow according to the Newtonian model previously presented. While air
flowing through vents may be better modeled as a compressible, turbulent flow, the following
analysis is extremely conservative. The pressure drop of a Newtonian fluid in a rectangular
channel is:
ΔPair =

12 μair Vair L
3
W hvent

(8.1)

The minimum thickness of a vent can then be evaluated from the width and length of the
vent as:
min
hvent
=

3

12 μair Vair L
ΔPair W

(8.2)

where μair is the apparent viscosity of the air, V is the volumetric flow rate of air through
the vent, ΔPair is the specified pressure drop of air across the vent, and the other variables
are the vent dimensions.
Example: Evaluate the minimum thickness of a typical vent required to vent the displaced
air at low air pressures.
A conservative analysis assumes air flow at 100 cc/s through a single vent with a width of
10 mm and length equal to 10 mm. To avoid compressing the gas and increasing increased
pressure on the plastic melt, the allowable pressure drop across the vent is one atmosphere
(14.7 psi or 0.1 MPa). The viscosity of air at room temperature is 1.8 · 10–5 Pa s. Then,
the minimum thickness is:
min
hvent
=

3

12 ⋅ 1.8 ⋅ 10−5 Pa s ⋅ 100 ⋅ 10−6 m 3 /s ⋅ 0.1 m
= 6 ⋅ 10−5 m = 0.06 mm
0.1 ⋅ 106 Pa ⋅ 0.1 m

The analysis indicates that a vent thickness of 0.06 mm is sufficient for this case, and
could be further decreased if the vent were wider or shorter, or if there was less air flow
or a higher pressure drop was tolerable.
It is again emphasized that the previous analysis and example are conservative since
• an analysis with laminar flow would suggest higher pressure drops and the need for thicker
vents than a turbulent flow,
• the geometry and process conditions apply to a single, small vent with relatively high air
flow, and
• the assumed viscosity of air at room temperature is higher than would occur if the air were
heated by the polymer melt or compression. For these reasons, the minimum thickness
of the vent will not generally be a limiting design constraint.

8.2 Venting Analysis

191

The maximum size of the vent is related to the maximum amount of flashing that is tolerable
at the vent locations. The formation of flashing in extremely thin channels such as vents is
an advanced research topic, requiring transient simulation with small time steps. No simple
analytical solution exists. However, for the purpose of discussion only, consider the application
of laminar viscous flow. The average volumetric flow rate of the melt during the flashing is:
W Lflash hvent
Vflash =
t flashing
Substituting this relation into the Newtonian flow model of Eq. (8.1) and solving for the
thickness provides the upper constraint on the thickness of the vent:
max
hvent
=

12 μ
Lflash
Pmelt t flashing

(8.3)

where Pmelt is the melt pressure at the vent inlet. When the melt first reaches the vent, the melt
pressure is zero. For the purpose of analysis, the melt pressure can be conservatively assumed
as the melt pressure ramp rate times the time for the flashing to solidify:
Pmelt =

dPmelt
⋅ t flashing
dt

(8.4)

For most injection molding processes, the melt pressure ramp rate is less than 100 MPa/s. The
flashing time is related to the solidification time of the polymer melt in the vent.
Example: Evaluate the maximum thickness of a typical vent using Eq. (8.3).
Assuming a vent thickness on the order of 0.06 mm, the gate freeze time equations provided
in Table 7.4 can be used to estimate that the approximate time for the melt to solidify
while flashing is 0.003 s. Given this solidification time, the flashing should solidify by the
time the melt pressure reaches:
Pmelt = 100

MPa
⋅ 0.003 s = 300,000 Pa
s

Since the vent is thin, there will be significant shear thinning so a low viscosity of 10 Pa s
is assumed. Substituting these values, the maximum thickness of the vent is:
H max =

12 ⋅ 10 Pa s
Lflash = 0.4 ⋅ Lflash
300,000 Pa ⋅ 0.003 s

For example, if a flash length of 0.2 mm is allowed, then the maximum thickness of the
vent is 0.08 mm. For comparison, the minimum thickness for the vent required to provide
adequate air flow is 0.06 mm. If less flashing was desired, then more and wider vents could
be used to reduce the required air flow, after which the vent thickness could be reduced
to reduce flashing while providing adequate air flow.

192

8 Venting

Table 8.1: Recommended vent thicknesses (mm)

Plastic

Glanvill (1965)

Rosato (1986)

Menges (2000)

Low viscosity materials:
PP, PA, POM, PE

0.08

0.1

0.015

Medium viscosity materials:
PS, ABS, PC, PMMA

0.2

0.3

0.03

Since the above analysis may be difficult to apply given the requisite assumptions, several
recommendations for vent thickness are listed in Table 8.1 from various handbooks. The
differences in the recommendations are interesting and explainable in part. The majority of
the variance likely stems from the fact that there has been a long term trend in the plastics
industry to move to thinner walls, faster injection rates, and higher injection pressures; the
maximum thickness of the vent decreases with increasing melt pressure. At the same time,
material manufacturers have sought to reduce the viscosity of plastic resins while improving
structural properties. Accordingly, it should not be surprising that the technical standards
for vents changes, with thinner vents being recently recommended.

8.3

Venting Designs

8.3.1

Vents on Parting Plane

The first type of vent to be considered is the vent on the parting plane. These vents are
commonly provided as very thin channels directly at the end of flow. Many molds are
produced with vents on the parting plane that emanate from the edge of the parting line
outwards to a thicker vent “relief ” or vent “channel”. Figure 8.6 provides a venting system
design for the bezel, in which two vents have been provided on the inside and outside surfaces
of the cavity insert. The width of the vent, W, has been made purposefully high to provide
for uncertainty in the last area of the melt to fill the cavity. The thickness of the vent, hvent,
has been specified as 0.06 mm. The length of the vent, L, is 2 mm, after which the air flows
through a 2 mm thick channel to a 3 mm diameter outlet located at the center and top of
the insert.
While vents should be provided on the parting plane at the end of fill, it is not uncommon for
vents to be placed periodically around the periphery of the cavity. For the molding of centergated cylindrical parts, vents can be placed around the periphery of the entire mold cavity
as shown in Figure 8.7. In this design, the cavity for a lid is center gated as in a three-plate or
hot runner mold. A vent is placed around the entire periphery of the mold cavity. Given the
ample vent width, the vent is specified with a thickness of 0.015 mm and a length of 1 mm.
A vent channel connects the vent ring to the side of the insert and subsequent outlets.

8.3 Venting Designs

193

Figure 8.6: Vent design on parting plane

While the above designs are certainly effective with respect to venting the displaced air, it
should be mentioned that they are susceptible to flashing with bending of the mold plates. As
will later be discussed in Chapter 12, the melt pressure exerts significant forces on the mold
cavity and core. Any significant deflection will tend to increase the thickness of the vents and
thereby increase the likelihood and amount of flashing. Indeed, the design of Figure 8.7 may
be especially problematic since the outside, bottom surface of the lid is an area observed and
handled by the end-user. The use of an internal vent around the periphery of a stripper plate
will resolve this issue as later designed in Section 11.3.4.
To avoid excessive flashing and associated maintenance, it is recommended that vents on
the parting plane be used sparingly with a thickness on the order of 0.02 mm. If venting is
subsequently found to be inadequate, then additional vents can be added or the thickness of
existing vents increased.

194

8 Venting

Figure 8.7: Vent design around cylindrical part

8.3.2

Vents around Ejector Pins

A very common practice is to use the clearance around ejector pins for venting purposes.
There are many advantages to this vent design. First, the actuation of the ejector serves to at
least partially clear the venting channel between the pin and the core. Second, ejector pins are
commonly used and well understood. Since a clearance needs to be specified around the pin
to provide a sliding fit anyways, it is economical to specify a clearance suitable for venting.
Holes for ejector pins are normally drilled and subsequently reamed. In mold manufacturing,
the diametral clearance between the ejector pin and ejector hole is typically 0.13 mm (0.005 in),
which leaves 0.065 mm (0.0025 in) thickness for venting. While this is somewhat larger
than previously suggested vent thicknesses, this thicker clearance around the ejector pins
is recommended for several reasons. First, the clearance is useful to avoid increased sliding
friction and ejector pin buckling. Second, ejector pins are usually machined through solid
steel, so increased flashing due to parting plane deflection are unlikely. Third, any witness lines
associated with flashing at the ejector pins are usually located on non-aesthetic surfaces.

8.3 Venting Designs

195

Figure 8.8: Vent design around ejector pin and blade

Figure 8.8 provides some typical venting design details using ejector pins. Detail B shows an
ejector blade and an ejector pin that have been assigned clearance for venting. For both these
ejectors, a venting channel has been provided up to 3 mm away from the mold cavity surface,
after which the channel tapers down to the nominal bore of the ejector hole. Both of these
elements should be present in a good vent design. The larger channel serves to reduce the
flow resistance of the air while also assisting in the assembly of the ejector pins to the mold.
The taper is useful to guide the head of the pin during mold assembly.
The vent length, L, of 3 mm has been chosen for illustrative purposes and is certainly not
mandatory. The previous air flow analysis with Eq. (8.2) implies that the standard 0.06 mm
vent thickness between an ejector pin and its hole will provide significant air flow. For this
reason, it is possible to extend the length of the vent to a location that is convenient. For
instance, it may be desirable to avoid a large vent channel near cooling lines. As another
example, a mold may be more economically produced with the same vent section through
the majority of the core insert, tapering to a larger size only where the core insert faces the
support plate.

196

8 Venting

8.3.3

Vents in Dead Pockets

For venting dead pockets, one approach is to use a mold insert for the purpose of venting.
Figure 8.9 shows a design in which a rectangular pocket has been machined in the core insert,
into which a vented insert has been placed. As shown in Detail A, the vent only spans the
width of the rib where the trapped air is expected. As shown in Details B and C, the vent has
thickness, H, of 0.2 mm and a length, L, of 2 mm. Afterwards, a wider vent channel has been
placed behind the vent. Since there is no ejector pin, there is no need for a smooth transition
between the vent and the vent channel.
It should be noted that the venting function of the insert provided in Figure 8.9 could have
also been provided by using an ejector blade at the same location. The ejector blade like
could have been provided at lower cost while also facilitating the ejection of the part. As such,
venting inserts are not especially common.
Another design alternative is the incorporation of a sintered vent, pictured in Figure 8.10, which
is a type of mold insert that can be used for releasing gas in dead pockets. These devices are
relatively small in size, typically ranging from 2 mm to 12 mm in diameter, and contain many
small vent holes in sizes ranging from 0.03 to 0.1 mm in diameter. Given their small size and
non-machinable top surface, sintered vents are best placed with their venting surface flush with
flat mold cavity surfaces. Furthermore, sintered vents can require intermittent replacement or
maintenance as the micro-channels may clog without any easy method for in-mold cleaning.

Figure 8.9: Vent design in core insert

8.4 Chapter Review

197

Figure 8.10: Vent design in core insert

8.4

Chapter Review

Venting design and analysis is often neglected during mold design, with venting channels
placed after the mold is trialed and issues are identified. This approach has some merit since all
of the required venting locations may not be known until the mold filling patterns are verified.
However, a complete lack of analysis and foresight regarding venting can lead to significant
mold defects, time consuming mold changes, and costly product development delays.
After reading this chapter, you should understand:
• The three different types of venting required: 1) around the periphery of the part on the
parting plane, 2) internal to the cavity where two or more melt fronts can form a gas trap,
and 3) in dead spots where the air can not escape.
• The different types of vents that can be designed including those on the parting plane,
around ejector pins, and alongside core inserts;
• How to calculate the thickness of a vent given the required air flow without causing
flash.
The next chapter examines the mold cooling system, whose purpose is to provide maximum
and uniform heat transfer from the hot polymer melt to the mold coolant. Afterwards, the
mold’s ejector and structural systems will be designed and analyzed.

9

Cooling System Design

The cooling system is extremely important to the economics and operation of the designed
mold, and yet remains one of the most under engineered systems in injection molds. Perhaps
the reason for the lack of engineering is that the temperature distribution is not obvious when
molding compared to defects related to flow.
Improperly designed cooling systems often result in two undesirable outcomes. First, cooling
and cycle times are much longer than what could have been achieved. Second, significant
temperature gradients arise across the mold, causing differential shrinkage and warpage of
the moldings. To operate effectively, cooling systems must be carefully designed to manage
the heat flow throughout the mold without incurring undue cost or complexity.

9.1

Objectives in Cooling System Design

9.1.1

Maximize Heat Transfer Rates

In steady state heat conduction, the heat transfer rate, Q conduction , is proportional to the
thermal conductivity, k, and temperature gradient of the mold, dT/dz:
dT
Q conduction = k
dz

(9.1)

There are two implications of this equation. First, heat transfer rates are proportional to
the thermal conductivity. A highly conductive material like Cu 940 or QC7 has a thermal
conductivity several times higher than all of the steels, and should be able to operate at much
faster cycle times. The second implication is that a temperature gradient is required to transfer
heat, which means that heat transfer rates can be increased by moving the cooling lines closer
to the surface of the mold cavity.

9.1.2

Maintain Uniform Wall Temperature

The temperature of the molded parts at the time of ejection is a complex function of the
molded part design, cooling line design, material properties, and processing conditions.
While high heat transfer rates are desired, an overly aggressive cooling system design can
actually cause quality problems. As the cooling lines approach the mold cavity surface, the
heat transfer path between the surface and the cooling line becomes more direct. As a result,
there can be a great variation in the temperature across the cavity surface unless the cooling
lines are also placed very close together.

200

9 Cooling System Design

When differential shrinkage and warpage occurs in the molded parts due to variations in the
temperature of the moldings, the molder often has no choice but to run longer cycle times
and use the mold as a cooling fixture. By running longer cycle times, often with higher mold
coolant temperatures, the molder is reducing the heat transfer rate (and its variation), and
then allowing the temperature of the molded plastic to fully equilibrate across the mold.
The result is a cycle much longer than might have been planned, and which could have been
prevented with a better cooling system design without any additional cost.

9.1.3

Minimize Mold Cost

Equation (9.1) implies that infinitely high heat transfer rates can be achieved by moving to
higher conductivity materials and using many cooling lines very close to the surface. However,
there is a point at which further investment in the cooling system reaps no rewards. The reason
is that the heat transfer rate becomes not limited by the heat conduction through the mold,
but rather by the heat conduction through the plastic as well as the heat convection to the
mold coolant. For these reasons, molds made out of highly conductive materials may have
a 30% reduction in the cycle time by improving heat conduction through the mold, but not
anything near the eight-fold improvement that might be anticipated from these material’s
high thermal conductivity values.
The key to designing a cost effective mold is to know where to invest. Highly conductive
materials are extremely effective in some applications and are usually easier to machine, but
are not universally best. Similarly, cooling line layouts can range from the very simple to the
very complex. Complex cooling line designs often require substantial machining, plugging,
sealing, fitting, and maintenance. It is important for the mold designer to know when the
added cost of a complex cooling system design is justified.

9.1.4

Minimize Volume and Complexity

A very significant issue in the design of cooling systems is that they often conflict with the
placement of other components. While placing many, tightly spaced cooling lines provides for
fast and uniform cooling, this design will also result in very little space in the mold to place
the ejector systems, runners, bolts, and other mold components. For this reason, the mold
designer should strive to route cooling lines that parallel the geometry of the mold cavities.
A smaller cooling line diameter, while more difficult to machine and transferring less heat,
may have a lesser impact on nearby components and allow for the use of multiple lines to
achieve more uniform cooling.

9.1.5

Minimize Stress and Corrosion

The melt will exert significant pressures on the surfaces of the mold cavities. These forces
translate directly into significant stresses within the mold plates and inserts. The mold’s

9.2 The Cooling System Design Process

201

structural integrity is weakened by every cooling line, each of which requires the removal of
supporting mold material and also provides a stress concentration.
While the impact of the cooling lines on the structure of the mold can be especially acute
in molding applications with high melt pressures, the potential impact remains significant
in most applications since the cyclic loading and unloading of the melt pressure gives rise
to failure due to fatigue. Worse, corrosion of the metal by the circulating coolant tends to
exacerbate the stress concentrations. Cracks form, corrode, and propagate through the mold
to the cavity and subsequently require repair.

9.1.6

Facilitate Mold Usage

Molding machine operators should be able to operate the injection mold with minimal
information. The number of external connections should be kept to a minimum, and
preferably two (one inlet and one outlet) per mold half. If more than two connections are
required, then the connections should be labeled “in” and “out” to help the operator avoid
forming a dead circuit. To avoid damage to the cooling system, all external components should
be recessed to avoid direct contact with tie bars, work tables, or other items.

9.2

The Cooling System Design Process

Given that there are multiple objectives in the design of the cooling system, it is not likely that
every objective will be simultaneously optimized. The goal is for the mold designer to reach a
good compromise, such that fast and uniform cooling is achieved in a cost effective manner.
The following seven step analysis is provided to support the mold design decisions that have
to be made. Afterwards, some common cooling issues and designs are developed.

9.2.1

Calculate the Required Cooling Time

The cooling time is defined as the amount of time required after the mold is filled for the
plastic to become sufficiently rigid to eject. The following theory is provided to support the
estimation of the theoretical minimum cooling time.1 Since there is very little flow of the
melt (and very little convection of heat) after the mold is full, the transfer of heat between
the plastic and the mold is governed by the transient heat conduction equation:
1

In practice, cooling times can be substantially longer than those predicted by analysis for two reasons. First,
the following analysis assumes perfect heat conduction between the plastic and the mold, while there is
known to be a substantial thermal contact resistance between two dissimilar materials. The cooling time
can be futher increased by thin gaps which open up between the shrunken molding and the mold walls.
Second, the cooling time is often not driven by the rigidity of the part, but rather by quality requirements
that may necessitate the molder to extend the cooling time to achieve the specifications.

202

9 Cooling System Design

∂T
∂2T
=α 2
∂t
∂z

(9.2)

where α is the thermal diffusivity defined as:
α=

k
ρ ⋅ CP

(9.3)

where T is the temperature, t is the time, z is the dimension in the thickness direction, k is
the thermal conductivity, ρ is the density, and CP is the specific heat. The thermal diffusivity
is essentially a measure of a material’s ability to transmit heat relative to its ability to store
heat. For more rapid heat transfer, mold materials with higher thermal diffusivity are desired
though these materials (e.g., aluminum) tend to have lower structural properties than steel
as plotted in Figure 4.25.
The transient heat conduction Eq. (9.2) is a second-order, parabolic, partial-differential
equation. Analytical solutions for transient heat transfer have been developed for simple
geometries such as plates and rods. The temperature of the melt at the centerline of the mold
cavity can be evaluated from a series expansion:
Tz = 0 (t ) = Tcoolant + (Tmelt − Tcoolant )





m=0

(−1)m
2 m +1



e

π2 (2 m +1)2 α
h2

t

(9.4)

Taking the first six terms in the series, a plot of the plastic’s temperature at the center-line
is shown as a function of the cooling time in Figure 9.1. The temperature of the plastic at
3000

Temperature
Modulus

250

2500

200

2000

150

1500

100

1000

HDT/DTUL

50

500

0

0
0

5

10
Time (s)

Figure 9.1: History of melt temperature at centerline

15

20

Modulus (MPa)

Melt temperature at centerline (°C)

300

9.2 The Cooling System Design Process

203

the center of the molding is equal to the initial melt temperature at the start of the cooling
process. After a delay of two seconds, the melt at the center of the molding begins to cool.
Eventually, the plastic will approach the temperature of the mold coolant.
To determine the cooling time, it is necessary to provide some criterion that indicates when the
molding is rigid enough to be ejected from the mold. One reasonable approach is to consider
the modulus of the material, which is a measure of the material to resist deflection. The effective
modulus of the material as it cools is shown on the right hand axis of Figure 9.1. It can be
observed that as the plastic melt approaches the mold coolant temperature, the modulus also
approaches a steady state value. The temperature at which the material has significant rigidity
is known as the heat distortion temperature (HDT) or the deflection temperature under load
(DTUL) as characterized by standard tests such as ASTM D648.
Equation (9.4) can be solved to provide the cooling time as a function of the melt, coolant,
and ejection temperatures. For plates, the theoretical minimum cooling time is:
tc =

⎛ 4 Tmelt − Tcoolant ⎞
h2
ln ⎜

2
π ⋅ α ⎝ π Teject − Tcoolant ⎠

(9.5)

where h is the wall thickness, Teject is the specified ejection temperature (usually taken as the
DTUL), Tcoolant is the coolant temperature, and Tmelt is the melt temperature. For rods, the
theoretical minimum cooling time is:
tc =


T
− Tcoolant ⎞
D2
ln ⎜1.60 melt

23.1 ⋅ α ⎝
Teject − Tcoolant ⎠

(9.6)

When computing the cooling time, the mold designer should consider the thickest section
that is likely to require the longest time to solidify.
Example: Estimate the cooling time for the two cavity family mold used to produce the
cup and the lid.
The nominal thickness of the lid is 2 mm, the nominal thickness of the cup is 3 mm, and
the diameter of the primary runner is 6.25 mm. Assuming that the material is ABS with
melt, cooling, and ejection temperatures of 239, 60, and 96.7 °C, then the cooling times
for each of the various portions of the mold are:
t clid =

(0.002 m)2
⎛ 4 239 − 60 ⎞
ln ⎜
⎟ = 8.4 s
2
−8
π ⋅ (8.69 ⋅ 10 m /s) ⎝ π 97.6 − 60 ⎠

t ccup =

(0.003 m)2
⎛ 4 239 − 60 ⎞
ln ⎜
⎟ = 18.9 s
2
−8
π ⋅ (8.69 ⋅ 10 m /s) ⎝ π 97.6 − 60 ⎠

2

t crunner =

2

(0.00476 m)2
⎛ 239 − 60 ⎞
ln ⎜1.6
⎟ = 22.9 s
2
−8
23.1 ⋅ (8.69 ⋅ 10 m /s) ⎝ 97.6 − 60 ⎠

204

9 Cooling System Design

These results provide some important insights. First, since the cup and the lid are different
thickness, the family mold will be forced to operate at the much longer cycle time of the
cup. If high production quantities are desired with parts of different wall thicknesses,
then it may be more economical to use two different molds operating at different cycle
times for separately producing the different designs. However, such a mold design strategy
gives up color matching and at-press assembly which are very significant benefits for
family molds.
Second, the cooling time of the runner is larger than that for the cup. In practice, the
runner need not be as rigid as the part being de-molded so the required cooling time of
the runner may be less than the 22.9 s calculated above. However, the results do indicate
that the cycle time can be dominated by the cooling of the cold runners, so it is important
to minimize the runner diameters not just for material savings but also to maintain a
productive molding process.
To validate the above cooling analysis, the transient heat conduction is numerically simulated
for a molding with a wall thickness of 3 mm. The simulation assumes that the plastic is
initially at the melt temperature, and that the temperature of the plastic:steel interface at
the mold wall is always at the coolant temperature. As before, the simulation assumes that
the material is ABS with melt, cooling, and ejection temperatures of 239, 60, and 96.7 °C,
respectively. The temperature of the plastic through the wall thickness of the molding is
shown in Figure 9.2 for various time steps. At the start of cooling, the temperature of the
plastic is at the melt temperature. According to this analysis, the temperature of the plastic
at the mold wall immediately drops to the mold coolant temperature. As heat is transferred
from the plastic to the mold, the temperatures at the outside decrease until finally the core
approaches the mold coolant temperature.
260
240

0

0

0

0
0.4

220
0.4

Temperature (°C)

200

1

180

0 0
0
0
0
0
0
0.4 0
0.4 0.4
1 0.4
1 0.4
0.4 0
1
1 0.4
0.4 0.4 1 1 2 2 2 2 1
1
2
2
2
1
4 4 4 4
2
4
4
4
2
4

2

1

160

0.4

140
120

1

100
80
60

16
12
8
4
2
28
1
20
24
0.4

2
4
8
12
16
20
24
28

2

4

4

8

4

8
8

8

8
12
16
20
24
28

12
16
20
24
28

8

12

12

16
16
20
20 24
24
28 28

8

8

0

4
8

8

4

8
8

12 12 12 12

12
12
16
16
16
16 16
16
16
16
20 20 20 20 20
20 20
20
24
24
24
24
24 24
24 24
28 28 28 28 28 28 28 28
12

12

8

0
0.4 0 0 0 0 0
1 0.4 0.4
1
0.4
2
1
2
0.4
1
4
2
2

1

4

2

8

4

1

8
12
16
20
24
28

2
4
8
12
16
20
24
28

0.4

8
12
16
20
24
28

12
16
20
24
28

12
16
20
24
28

28
0.4
12
24
16
20
8
4
2
1

40
0

0.5

1

1.5
Thickness (mm)

Figure 9.2: Cooling of plastic, isothermal boundary

2

2.5

3

9.2 The Cooling System Design Process

205

During cooling, the plastic molding must become sufficiently rigid to withstand ejection
forces. As such, the cooling time can be estimated from Figure 9.2 as the time at which
the temperature at the center-line drops below the specified deflection temperature.2 The
simulation results shown in Figure 9.2 confirm the previous analytical results that the cooling
time will be approximately 19 s for a centerline ejection temperature of 97 °C.
These results are for an isothermal boundary condition at the mold wall, meaning that plastic
at the mold wall immediately drops to the mold coolant temperature. In reality, the mold steel
can’t withdraw heat so quickly. As a result, the adjacent mold steel will increase in temperature.
This behavior can be modeled using a convective boundary condition:
hc [Tcoolant − Tmelt ] = k

∂T
∂z

(9.7)

where hc is the representative heat transfer coefficient from the melt at the polymer:mold
interface to the coolant. Previous research [29] has indicated that the convective heat transfer
coefficient in molding is on the order of 1000 W/°C. The simulated temperature history with
a convective boundary condition is shown in Figure 9.3.
260
240

0

0

200
Temperature (°C)

0
0.4

220

0.4 1

180
160
0.4

140
120

1

100

2
4
8
12
16
20
24
28

80
60

1

2

2

4

4

8

8
12
16
20
24
28

12
16
20
24
28

0 0
0
1
0.4 0
0.4
0.4
0.4
1 0
0.4 0
1 0
0.4 0.4 1 1 2 2 2
2
1
4
2
4
1
4
2
4
4
2
8 8
4
8
8
4
8
12
8
12 12
12
12
8
16 16
12
16 16
16
12
20
20
16
20 20
16 20 20
24 24 24
24
20 24 24
28 28
28 28 28
24
28 28

0
0
0 0
1 0
0.4
0.4
1 0.4
0.4
1 0.4
2
2
2 1 1
2
4 4
2
4
4
4
8 8
8
8
8
12 12
12
12
12
16 16 16
16
16
20 20 20
20
20
24 24 24
24 24
28 28 28 28
28

0
0 0 0
0.4 0
0.4
1
0.4
1
2
0.4
2 1
4
2 1
4
8
12
16
20
24
28

8

4

12 8
12
16
20
24
28

16
20
24
28

0.4

2
4

1

8
12
16
20
24
28

2
4
8
12
16
20
24
28

40
0

0.5

1

1.5

2

2.5

3

Thickness (mm)

Figure 9.3: Cooling of plastic, convective boundary
2

There are different forms of the cooling time equation. The two most frequently used assume either the
centerline temperature or the average temperature through the thickness reach the ejection temperature.
This book recommends analysis using the centerline criterion for two reasons. First, it is conservative and
will yield mold designs that should outperform the analysis in the case of error. Second, this approach
is supported by bending theory. Specifically, consider a part that is rigid at the walls but semi-molten at
the centerline. Since the plastic at the centerline is not able to transmit the shear stresses from one wall
to the opposing wall under ejection loads, the deformation of the molded part will be much higher than
if the plastic at the centerline were solidified and able to transmit stress.

206

9 Cooling System Design

With a convective boundary condition, the plastic at the mold wall requires additional time
to approach the mold coolant temperature. This slower rate of heat transfer also limits the
cooling at the center of the molding. If the core must reach a specified temperature of 97 °C,
then the cooling time should be closer to 24 s rather than the 19 s predicted with an assumed
mold wall temperature.
On a side note, there is a common rule in the plastics industry that the cooling time can be
roughly calculated as:
⎡ s ⎤
tc = 2 ⎢
(h [mm])2
⎣ mm 2 ⎥⎦

(9.8)

where the wall thickness, h, is evaluated in units of mm.
Example: Use Eq. (9.8) to estimate the cooling time for a molding that is 3 mm in
thickness.
⎡ s ⎤
tc = 2 ⎢
(3 mm)2 = 18 s
⎣ mm 2 ⎥⎦
This result compares very well to the previous analysis results of 19.2 s (assuming perfect
conduction) and 24 s (assuming convection of 1000 W/m°C).
The reason that Eq. (9.8) provides a good approximation is that most thermoplastics
have a thermal diffusivity on the order of 9 · 10–5 m2/s, and processing temperatures such
that (Tmelt − Tcoolant )/(Tcoolant − Teject ) is around 5. Substituting these values into Eq. (9.5)
provides:
tc =

h2
⎛4 ⎞
⎡ s ⎤
ln ⎜ 5 ⎟ = 2.08 ⎢
(h [mm])2
2
2


π
π ⋅ 0.09 [mm /s]
⎣ mm 2 ⎥⎦

(9.9)

The rule of thumb provided in Eq. (9.8) closely matches the typical heat conduction analysis
provided in Eq. (9.9). While Eq. (9.8) is an excellent guideline, it is a good idea to use Eqs. (9.5)
and (9.6) to evaluate the cooling time for the specific application’s design, material properties,
and processing conditions. Also, it should be noted that Eq. (9.9) provides an estimate of the
cooling time, which is roughly half of the cycle time previous estimated by Eq. (3.23).

9.2.2

Evaluate Required Heat Transfer Rate

Once the cooling time is known, the heat transfer rate or “cooling power” required of the
feed system can be calculated. The total amount of heat to be removed by the cooling system,
Qmoldings, is:
Qmoldings = mmoldings ⋅ CP ⋅ (Tmelt − Teject )

(9.10)

9.2 The Cooling System Design Process

207

where mmoldings is the combined mass of the molded parts and any associated cold runners,
which can be estimated as the volume of these moldings times their density at room
temperature.
The cooling power is the defined as the amount of energy that the must be removed per
second of cooling time:
Q cooling =

Qmoldings
tc

(9.11)

Typically, an injection mold has multiple cooling lines. Assuming that the mold is well
designed and each cooling line removes the same amount of heat, then the heat transfer rate
per cooling line may be evaluated as:
Q line =

Q cooling
nlines

(9.12)

where nlines is the total number of cooling lines in the mold. At this point, the mold designer
should recognize that multiple design iterations may be necessary to perform the cooling
analysis for different cooling line layouts with varying number of cooling lines.
Example: Analyze the power required to cool the cup and lid family mold.
The mass of the two moldings totals 62.6 g. If an ABS material is processed at mid-range
temperature, then the heat to be removed is:
⎡ J ⎤
Qmoldings = 0.0626 [kg] ⋅ 2340 ⎢
⎥ ⋅ (239 °C − 96.7 °C) = 20,900 J
⎣ kg ⋅ °C ⎦

For the cup and lid family mold designed for a cooling time of 20 s, the total cooling
power is:
20,900 J
= 1,050 W
Q cooling =
20 s
Assuming for now that the cup and lid mold has 4 cooling lines (2 lines per side), then:
1,050 W
Q line =
= 260 W
4
So, each side of the mold with two cooling lines will require an average cooling power
of 500 W.

208

9 Cooling System Design

9.2.3

Assess Coolant Flow Rate

Any heat removed from the polymer melt in the mold cavity must be carried away by the
coolant. As such, the coolant will increase in temperature as it travels through the mold.
This temperature increase is not desirable, since the coolant will provide less cooling to the
last portion of the mold through which it flows. If the coolant temperature increase is too
great, then thermal gradients will arise across the molded part which may lead to differential
shrinkage and warpage.
Given a volumetric flow rate of the coolant, Vcoolant , the increase in the coolant temperature
along one cooling line is:
ΔTcoolant =

Q line

Vcoolant ⋅ ρcoolant ⋅ CP, coolant

(9.13)

The thermal properties of some coolants are provided in Appendix C. The required coolant
flow rate can be calculated given the allowable increase in the coolant temperature. A typical
allowable increase in the coolant temperature is 1 °C. For a precision part, the allowable
increase in the coolant temperature may be 0.1 °C. Much tighter control of the coolant
temperature requires much higher flow rates, and yet provides little added benefit given that
the mold cavity surface temperatures will tend to vary more significantly between the cooling
lines as later discussed.
Example: Calculate the required volumetric flow rate for the mold coolant, assuming an
allowable increase in the coolant temperature for the cup/lid family mold of 1 °C.
If water is used as the coolant, then the required volumetric flow rate is:
Vcoolant =

260 W
m3
= 6.2 ⋅ 10−5
3
s
1 °C ⋅ 1000 kg/m ⋅ 4200 J/kg V

which is equal to about 1 gallon per minute per line. It should be noted that if two cooling
lines were connected in series, then the cooling power would also be doubled such that
twice the flow rate would be needed to maintain the same temperature distribution.
Table 9.1: Specifications of two mold temperature controllers

Model

Vactherm coolant controller

IMSelect oil controller

Minimum temperature (°C)

10

32

Maximum temperature (°C)

99

304

Heating capacity (kW)

9

16

Cooling capacity (kW)

14.6

3

Coolant flow rate [m /s (GPM)]
Coolant pressure [Kpa (psi)]

16
–3

1 · 10
200

(15)
(29)

3 · 10–3
30

(45)
(4.3)

9.2 The Cooling System Design Process

209

After estimating the required coolant flow rate, the feasibility of this value should be checked
against the capabilities of commercial mold temperature controllers. The specification for
a typical coolant temperature controller and an oil temperature controller are listed in
Table 9.1.
Example: Assess the capability of the VacTherm controller specified in Table 9.1 for the
two cavity, cup/lid family mold.
For the cup/lid family mold, the required volumetric flow rate of 1 gallon per minute is
well within the capabilities of commercial controllers. In fact, a single mold temperature
controller will be able to supply the needed flow to all four cooling lines:
m3
m3
total
= 4 ⋅ 6.2 ⋅ 10−5
= 2.5 ⋅ 10−4
Vcoolant
s
s
Note, however, that multiple mold temperature controllers would be needed if the
allowable temperature increase were set to 0.1 °C, or if the number of cavities in the mold
was increased from 2 to 8.

9.2.4

Assess Cooling Line Diameter

The allowable range of cooling line diameters can now be determined based on the heat
transfer and fluid flow constraints. To ensure adequate heat transfer from the mold steel to
the coolant, turbulent flow in the coolant is desired. If the cooling line diameter is too large,
then the linear velocity of the water may not be sufficient to ensure turbulent flow. To ensure
turbulent flow, the Reynolds number, Re, should be greater than 4000:
Re =

4 ⋅ ρcoolant ⋅ Vcoolant
> 4000
π ⋅ μcoolant ⋅ D

(9.14)

where D is the cooling line diameter and μcoolant is the viscosity of the coolant. This turbulence
requirement implies a maximum diameter, Dmax, for the cooling line of:
Dmax =

4 ⋅ ρcoolant ⋅ Vcoolant
π ⋅ μcoolant ⋅ 4000

(9.15)

Example: For the cup/lid mold, determine the upper limit on the diameter of the cooling
line to ensure turbulent flow.
Given a flow rate of 1 GPM and a viscosity of 0.001 Pa s, then Eq. (9.15) provides a
maximum diameter of:
Dmax =

4 ⋅ 1000 kg/m 3 ⋅ 6.2 ⋅ 10−5 m 3 /s
= 20 mm
π ⋅ 0.001 Pa s ⋅ 4000

210

9 Cooling System Design

As this example indicates, the requirement of turbulent flow is not very constraining since
any diameter less than 20 mm would ensure turbulent flow in the cup/lid family mold.
Most molding applications require a high rate of heat transfer and an associated high
volumetric flow rate such that turbulent flow is almost given.
A more binding constraint governs the minimum cooling line diameter, which is related
to the pressure drop required to force the coolant through the cooling lines at the required
volumetric flow rate. The pressure drop for water through a cooling line can be estimated
from pipe flow [30] as:
2
ρcoolant ⋅ Lline ⋅ Vcoolant
10 π ⋅ D 5

ΔPline =

(9.16)

where the cooling line has length, Lline. This pressure drop requirement implies a minimum
diameter of:
Dmin =

5

2
ρcoolant ⋅ Lline ⋅ Vcoolant
10 π ⋅ ΔPline

(9.17)

To calculate the minimum cooling line diameter, the line length and allowable pressure drop
across the cooling line must be known. This information can actually be a bit uncertain, since
it depends not only upon the configuration of the cooling lines in the mold, but also whether
the cooling lines are piped in series or parallel.
Example: For the cup/lid mold, determine the lower limit on the diameter of the cooling
line to avoid an excessive pressure drop in the coolant temperature controller.
The analysis will assume that the cooling lines traverse the width of the mold, and each
has a length of 302 mm. The analysis further assumes that the two cooling lines on each
side of the mold will be connected in series. The allowable pressure drop is set to 100
kPa, which is ½ of the maximum supply pressure from the VacTherm controller. This
last assumption is made to ensure that some supply pressure is reserved for flow through
the cooling hoses from the controller to the mold, as well as for pressure drops associated
with turns, plugs, etc.
The minimum cooling line diameter may then be estimated as:
Dmin =

5

1000 kg/m 3 ⋅ 0.6 m ⋅ (6.2 ⋅ 10−5 m 3 /s)2
= 3.7 mm
10 π ⋅ 100 ⋅ 103 Pa

Combining the turbulence and pressure drop requirement, the allowable range of cooling
line diameters for the cup/lid mold is:
3.7 mm < D < 20 mm
While this is quite a broad range, the allowable range may be much smaller depending
on the molding application and manufacturing requirements.

9.2 The Cooling System Design Process

211

Table 9.2: Specifications of typical cooling plugs

DME plug

Normal pipe thread

Cooling line diameter

JP-250

1/16

4.76 mm (3/16″)

JP-251

1/8

6.35 mm (1/4″)

JP-352

1/4

9.53 mm (3/8″)

JP-553

3/8

11.1 mm (7/16″)

JP-554

1/2

15.9 mm (5/8″)

In selecting the final cooling line diameter, the mold designer should consider the manufacturability of the cooling lines and the molder’s standards regarding cooling plugs, connectors,
and hoses. Table 9.2 provides some specifications for typical cooling plugs provided by a mold
component supplier (DME). As observed in the table, the commercial plugs range from 4.76
to 15.9 mm. The mold designer should select a cooling line diameter that satisfies the above
analysis and is a standard size.
Example: Specify an appropriate cooling line diameter for the cup/lid mold.
The analysis of the previous example indicates that any standard diameter between 3.7 mm
and 20 mm is feasible, which means that any of the cooling plugs listed in Table 9.2 would
be fine. For this reason, the mold designer should choose a cooling line diameter that is
readily machinable and also compatible with the cooling plug standards at the molder. A
reasonable cooling line diameter is 6.35 mm.
It should be noted that the above analysis is most appropriate for water as the coolant. Ethylene
glycol and oil are not as common in practice due to environmental and cost concerns. These
non-water coolants are also substantially more viscous than water, such that turbulent flow is
not likely to be achieved. For laminar, viscous flow, the pressure drop can be estimated using
the previously developed Hagen-Poiseuille law with the coolant properties of Appendix C:
ΔPline =

128 ⋅ μcoolant ⋅ Lline ⋅ Vcoolant
π ⋅ D4

(9.18)

The mold designer should then select an appropriate cooling diameter to ensure that the
maximum pressure drop across the cooling lines does not exceed the capability of the coolant
temperature controller.

9.2.5

Select Cooling Line Depth

After the cooling line diameter has been determined, the depth of the cooling lines must be
selected. From a structural point of view, it is desirable to place the cooling lines far from the
surface of the mold cavity. Deep placement avoids the stress concentrations associated with

212

9 Cooling System Design

Hline = 1 D

Hline = 4 D

σ = 3.3 · Pmelt

σ = 2.6 · Pmelt

Figure 9.4: Stress distributions around cooling line

the removal of material close to the surface. For example, Figure 9.4 plots the stress contours
for mold designs with cooling line depths, Hline, equal to one –four times the cooling line
diameter. It is observed that there are stress concentrations around the cooling line, and the
magnitude of the stress increases as the cooling line approaches the mold wall.
Many mold inserts are made of P20 which has an endurance stress (to avoid fatigue) of
456 MPa. Even when the cooling lines are placed at a distance of four diameters, the mold
can only be designed for a maximum melt pressure of:
max
Pmelt
=

σ endurance
= 175 MPa
2.6

(9.19)

Fortunately, this melt pressure is at the limit of the injection pressures for most molding
machines, and is unlikely to be fully transmitted to the mold cavity.
The stress concentration associated with cooling lines is very significant, since this constraint
requires the cooling line to be placed far away from the mold surface. Even when the cooling
lines are placed far from the cavity surface, the stress concentrations still potentially limit
the melt pressures with which the mold may be operated. Consider, for example, the desire
to produce a mold from aluminum with a cooling line depth equal to one diameter. In this
case, the fatigue limit stress for is 166 MPa. When this stress limit is divided by the stress
concentration factor of 3.3, the maximum allowable melt pressure is just 50 MPa. This analysis
does not prevent a mold designer or a molder from operating at higher melt pressures, but
simply indicates that the mold will likely not operate for a long life without developing cracks
emanating from the cooling lines. Stress concentrations in molds are discussed in more detail
in Section 12.2.6.
While the structural considerations suggest that cooling lines should be placed far from the
mold surface, the rate of heat transfer is maximized by placing the cooling lines as close to

9.2 The Cooling System Design Process

213

the surface as possible. The heat conduction equation states that the thermal resistance is
linear with the distance between the cooling line and the mold surface. The effective heat
conduction coefficient is:
hconduction =

kmold
H line

(9.20)

As previously discussed with the heat transfer analysis of Eq. (9.7), a typical convective heat
transfer rate in molding is 1000 W/°C. To ensure that the cooling line depth does not add
unnecessarily to the cooling time, the maximum cooling line depth may be estimated as:
H line <

kmold
1000 W/°C

(9.21)

A commonly used steel, P20, has a thermal conductivity of 32 W/m°C, which suggests a
maximum cooling line depth of 32 mm for effective cooling. Combining the structural and
heat transfer requirements for a typical 6.35 mm diameter cooling line, the recommended
range for the cooling line depth is:
2 D < H line < 5 D

(9.22)

which is a commonly used range in mold design. While a mold designer may choose an
arbitrary cooling line depth from this range, the provided analysis should be used for special
applications with diverse structural or heat transfer requirements.
Example: Specify the cooling line depth and maximum melt pressure for the cup/lid mold
if P20 is to be used as the mold material.
The cooling line diameter is 6.35 mm. Let us assume that the depth will be set to four
cooling line diameters, so the cooling line depth is set to 25.4 mm. This depth still imposes
a stress concentration of 2.6. If the endurance limit for P20 is 456 MPa, then the maximum
melt pressure for infinite life is:
max
=
Pmelt

456 MPa
= 175 MPa
2.6

which is close to the maximum injection pressures available from most molding machines.

9.2.6

Select Cooling Line Pitch

Once the cooling line depth is selected, the distance between the cooling lines (known as the
“pitch”) is assigned. A tighter pitch, Wline, between cooling lines provides for faster and more
uniform cooling. However, a tighter pitch also means more cooling lines and the likelihood of

214

9 Cooling System Design

40

Variance in Heat Flux (%)

35
Steel

30

Aluminum

25
20
15
10
5
0
0.5

1

1.5

2

2.5

3

Cooling Line Pitch : Depth Ratio
Figure 9.5: Effect of pitch on variation in heat flux

conflicts arising between the cooling lines and other mold components. The mold designer
should select a cooling line pitch that is appropriate for the specific molding application
using analysis.
The temperature prediction of the melt during cooling involves the solution of a system of
parabolic differential equations. While this is readily solved using the finite element method
as above, no suitable analytical treatment has yet been developed. Menges [31] provides an
estimate of the percentage variation in the heat flux across the mold between cooling lines:
⎛W ⎞
ΔQ [%] ∝ ⎜ line ⎟
⎝H ⎠

⎛W

2.8 ln ⎜ line ⎟
⎝ H line ⎠

(9.23)

line

This function is plotted in Figure 9.5 for steel and an aluminum mold materials. The analysis
indicates that the variation in the heat flux is less than 5% up to a cooling line pitch equal
to twice the cooling line depth. Afterwards, the variation in heat flux increases dramatically
and is indicative of slower rates of mold cooling and high temperature gradients within the
molded part.
To avoid a significant temperature gradient between cooling lines, it is recommended that
mold designers use a cooling line pitch in the range of:
H line < Wline < 2 H line

(9.24)

9.2 The Cooling System Design Process

215

depending on the requirements of the application. A commodity product with loose tolerances
would likely be fine with a cooling line pitch equal to two or three times the cooling line
depth. For tighter tolerance applications or for applications requiring faster cycle times or
more uniform cooling, a closer spacing equal to the cooling line depth is desirable.
Figure 9.5 indicates that the use of highly conductive materials (such as aluminum or copper)
actually increases the variation in heat flux by improving the heat conduction between the
cooling line and the cavity surface. As such, the use of highly conductive materials does not
directly allow for a wider pitch and a reduced number of cooling lines. If fewer cooling lines
are desired, then this may best be accomplished by selecting a large cooling line depth and
still setting the pitch to twice this amount. Highly conductive mold materials can then be
utilized to accomplish high rates of heat transfer with uniform cooling.
Example: Transient thermal simulation was performed for the cup/lid family mold for
two mold designs having different pitch to cooling line depth ratios. Figure 9.6 plots the
heat flow from the center-line of the molding in the cavity to the cooling. In the figure, the
lengths of the arrows represent the relative amount of heat flowing out of the mold cavity
at that location. As the cooling lines are moved further apart two adverse conditions arise.
First, the effective heat transfer rate at the mold wall is reduced given the finite capacity
of the cooling lines to remove heat. Second, a significant variation in the heat transfer
rate arises across the cavity surface.
This variation in the heat transfer rate across the cavity surface will give rise to a gradient
in the temperature of the moldings at the time of ejection as plotted in Figure 9.7. With a
tight cooling line pitch, the moldings are ejected not only with a lesser temperature gradient
across the molding, but also at a significantly lower temperature. With a wide pitch, the
moldings exhibit a much higher temperature gradient and a much higher temperature.
Interestingly, extending the cycle time for the mold with the wider pitch does not reduce
the temperature gradients across the part until the entire molded part approaches the
coolant temperature.

Wline = Hline

Wline = 4 Hline

Figure 9.6: Heat flow from cavity center-line to cooling line

216

9 Cooling System Design

Wline = Hline

Wline = 4 Hline

Figure 9.7: Temperature distribution in plastic and mold

9.2.7

Cooling Line Routing

Once the cooling line diameter, depth, and pitch have been determined, the cooling lines can
be routed through the mold. This routing is of critical importance since it not only impacts
the cost and quality of the moldings, but also limits the placement of other mold components
such as ejector pins and bolts. In general, the mold design should provide at least half a cooling
diameter between the surface of the cooling line and the surface of any other mold component.
This requirement maintains the structural integrity of the mold while also minimizing cooling
leaks during mold operation due to corrosion. The shaded area in Figure 9.8 represents the
possible locations in the mold where cooling lines may be placed.

Figure 9.8: Potential mold areas for cooling lines

9.2 The Cooling System Design Process

217

While the shaded area of Figure 9.8 represents a large portion of the mold, the placement of
cooling lines is further constrained by potential interference with the mold cavity, cavity inserts,
core inserts, ejector return pins, guide pins, sprue bushing, and other mold components. The
previous analysis for the cup/lid mold suggested that the cooling system design use:




a cooling line diameter of 6.35 mm,
a cooling line depth of 12.7 mm, and
a cooling line pitch of 25.4 mm.

The design exactly implemented according to these recommendations is shown in Figure 9.9.
This initial design is infeasible for many reasons. Perhaps the most significant shortcoming in
the design is that many of the cooling lines intersect critical mold features such as the sprue
bushing or the interface between the cavity inserts and the mold plates. There are two different
strategies to resolve this issue. One approach is to enlarge the cavity insert, core insert, and
associated mold plates to fit all the cooling lines within the envelope of the core and cavity
inserts. This option is costly since it requires redesign of the mold, procurement of a larger
mold base, and more machining. However, such a design may be economically justified given
the more rapid and uniform cooling.
An alternative approach is to move the cooling lines further from the mold cavity while
maintaining the same pitch to depth ratio for the cooling lines. The resulting design is shown
in Figure 9.10. This design requires fewer cooling lines, all of which avoid the intersection
with other mold components. While this design provides poor cooling performance, it is
quite common. A primary advantage is that all of the cooling lines are not only straight, but
each cooling line also passes through a single mold plate as well. As such, the cooling lines
can be machined in a single setup without any need for seals or gaskets. Unfortunately, the
placement of the cooling lines far from the mold cavity will reduce the rate of heat transfer
and necessitate longer cycle times.

Figure 9.9: Infeasible initial cooling line layout

218

9 Cooling System Design

Figure 9.10: Feasible but poor cooling line layout

Figure 9.11: Temperature gradient from poor design

There is a second significant shortcoming in this cooling line layout, which stems from the
use of a straight cooling line with a core of significant height. The source of cooling is at the
base of the core, and heat originates from the plastic all along the height of the core. As such,
significant temperature variations will develop throughout the molded part during cooling.
The predicted temperature distributions at the end of the molding cycle for the cup are
provided in Figure 9.11, in which each contour line represents a 2 °C change in temperature.

9.3 Cooling System Designs

219

Due to the relatively deep core, a gradient of 6 °C exists from the base of the core to the top
of the core. The temperature gradient in Figure 9.11 will drive differential shrinkage along
the axis of the cup as well as differential shrinkage through the wall thickness of the molding.
The reason is that the temperature at the top of the core is not only 6 °C hotter than the
temperature at the base of the core, but is also roughly 6 °C hotter than the temperature at
the opposing surface on the cavity insert. Three options for rectifying the situation include
using a highly conductive core insert, implementing a baffle or bubbler, or designing a cooling
insert. These different cooling designs are next discussed.

9.3

Cooling System Designs

There are many different cooling system designs that are used in practice. While many molds
use straight lines, such designs are often not optimal. Instead, the mold designer should strive
to achieve uniform and high rates of cooling across the entire cavity surface. Creativity is
often required to provide effective cooling system designs at reasonable costs. Next, some of
the most common designs and components are analyzed.

9.3.1

Cooling Line Networks

When molds have more than one cooling line, an issue will arise as to how the molding
machine operator will connect the mold to the mold temperature controller. Consider the
computer bezel, overlaid with cooling lines as shown in Figure 9.12. The mold has been
provided with eight cooling lines traversing across the width of the mold cavity. Faced with
eight cooling line connections, the machine operator may use short hoses to loop the cooling
lines as shown. Such a setup has two compounding issues. First, the flow resistance through
the combined length of all the cooling lines can be extremely high, reducing the coolant
flow rates per Eq. (9.16). Second, the mold coolant temperature can increase along the
length of the cooling circuit at reduced coolant flow rates. As such, a significant temperature
differential can arise from where the coolant enters the mold to where the coolant exits the
mold.
Aware of this problem, many if not most molders have coolant manifolds installed on the
molding machine between the mold temperature controller and the mold. The operator can
then use longer cooling hoses to individually connect two sets of cooling lines with a short
return loop on the opposite side of the mold. Such a setup is shown in Figure 9.13. This
configuration is extremely common since it is simple and provides effective cooling. However,
the installation and removal of the mold from the machine is complicated by the number
of lines that must be connected and disconnected. The high number of components and
operator steps also increases the likelihood that the cooling system may be setup incorrectly
or fail, for instance, due to a loosely connected hose.

220

9 Cooling System Design

Figure 9.12: Bezel cooling line layout in series

Figure 9.13: Bezel cooling line layout with four parallel cooling circuits

There is currently a great deal of interest in the plastics industry in lean manufacturing, which
places significant emphasis on reduced process complexity and setup times. By investing slightly
more in the injection mold, it is possible to reduce the mold setup time, reduce potential failure
modes, and improve the mold performance. Figure 9.14 shows the addition of two vertical
cooling lines connecting all eight horizontal lines within the injection mold; twenty pressure
plugs have been installed to block the coolant flow at selected locations. The result is that a
cooling manifold has been designed internal to the mold, such that only two connections are
required. At the same time, the cooling uniformity is increased. This internal manifold design
has very little added cost while delivering both increased performance and ease of use.
Once plugging is considered an option in the routing of cooling lines, many more complex
cooling line layout become available. In the former cooling system designs for the bezel, the
portion of the cooling lines located inside the screen area of the bezel is not removing any
significant heat. (If a two-plate mold with a cold runner is used as shown in Figure 7.7, then
these cooling lines would cool the sprue and runners. For a three-plate or hot runner mold,
however, there is no heat being generated in the central area of the mold cavity.)

9.3 Cooling System Designs

221

Figure 9.14: Bezel with internal, parallel cooling line layout

Figure 9.15: Bezel with drilled peripheral cooling line layout

Given that there is no need for cooling in the center of the mold, it is possible to route the
cooling lines around the periphery of the part to improve the cooling of the mold cavity
while reducing the mold making cost and providing a mold that is even easier to operate.
Figure 9.15 shows another cooling system design using blind drilled holes and plugs that can
be produced for a cost similar to that shown in Figure 9.14. This design provides extreme ease
of use, moderate flow resistance, and uniform cooling about the entire molding.

222

9 Cooling System Design

9.3.2

Cooling Inserts

As an alternative to drilling cooling lines, cooling lines that conform to the shape of the mold
cavity can be milled into the rear faces of the cavity or core inserts as shown in Figure 9.16.
In this case, a ball end mill is routed around the bottom of the core insert, after which
connecting lines are drilled to one side of the mold. The cooling lines can thereby closely
follow the contours of the molded part, even for curved surfaces. The location of the coolant
entrance and exits has been selected to balance the pressure drop between the internal and
external circuits.
Gasket

Figure 9.16: Bezel core insert with milled cooling

Even though the cooling insert design shown in Figure 9.16 provides exceptional cooling, it
presents potential leakage issues. In this design, a groove has been provided and fitted with
a gasket. When fastened tightly to the support plate, the gasket will prevent leakage outside
the mold. However, leakage should be expected at any ejector pins located internal to the
area surrounded by gasket. In this application, a stripper plate could be successfully used as
discussed in Section 11.3.4.

9.3.3

Conformal Cooling

Manufacturing technology is continuing to advance, and one relatively new mold making
technology is selective laser sintering (SLS). One of SLS’ benefits is the ability to directly place
cooling lines at any location as the core and cavity inserts are being selectively laser sintered.
Returning now to the core insert for the cup, a conformal cooling line design is provided in
Figure 9.17. Since nearly any geometry can be made with SLS, helical cooling lines can be
made to conform to the cavity surfaces to improve heat transfer rates and uniformity, thereby
eliminating the temperature gradients shown in Figure 9.7.

9.3 Cooling System Designs

223

Figure 9.17: Core insert for cup with conformal cooling lines

9.3.4

Highly Conductive Inserts

Another approach to reducing temperature gradients is to utilize highly conductive insert
materials, such as Cu 940 or Al QC7, for portions or the entire core insert. Since these
materials have much higher thermal conductivity than steel, their use in certain situations
will tend to reduce the variation along cores. The predicted temperature distributions at the
end of the molding cycle for the cup using a Cu 940 core insert are provided in Figure 9.18.
As before, each contour line represent a 2 °C change in temperature. The results indicate that
the temperature gradient has been reduced by approximately 60% compared to temperature
gradients shown in Figure 9.11.

Figure 9.18: Temperatures in deep conductive core

224

9 Cooling System Design

(a) P20 cavity and core

(b) P20 cavity and Cu 940 core

Figure 9.19: Temperature distribution in corner

Conductive inserts can also provide improved cooling in the internal corners of moldings.
Because of the heat transfer in three dimensions and limitations regarding the proximity
of the cooling line to the mold wall, the cavity insert will conduct approximately twice
the amount of heat away from the molding compared to the core insert. The temperature
distribution for a typical design using a single material for both the core and the cavity is
shown in Figure 9.19(a). When the core and cavity inserts both consist of P20, there is a 5 °C
gradient across the wall thickness of the molding. However, only a 1 °C differential across the
wall thickness of the molding occurs when the core insert is specified with Cu 940 as shown
in Figure 9.19(b).
The primary advantage of highly conductive core inserts is the ability to strategically control
the heat flow. While these materials increase the rate of heat transfer, their properties are not
appropriate for use throughout the mold. There are two primary reasons. First, it should be
noted that the improved temperature distributions achieved in Figure 9.19(b) were the result
of using different materials for the core and cavity inserts. These temperature distributions
would not have been as uniform if both the core and cavity inserts were made from Cu 940.
Second, these highly conductive materials tend to have lower hardness and are more susceptible
to wear. As such, highly conductive inserts may be best when used in applications with high
production volumes, low to moderate injection pressures, and non-abrasive materials.

9.3.5

Cooling of Slender Cores

Mold cores with a high length to diameter ratio prevent effective heat transfer along the length
of the core, even with the use of highly conductive materials. For this reason, it is desired to

9.3 Cooling System Designs

225

Table 9.3: Slender core cooling options

Core diameter

Hole diameter

Cooling rate

Cooling insert

> 50 mm

> 25 mm

Very high

Baffle

12–75 mm

6–25 mm

Very high

Bubbler

6–30 mm

3–12 mm

High

Heat pipe

5–20 mm

3–12 mm

Medium

Conductive pin

<5 mm

N/A

Low

provide a cooling channel along the axis of the core to conduct heat from the surface of the
core and then convect the heat down the center of the core. Larger cooling channels in the
center of the core generally allow for higher coolant flow rates and higher rates of heat transfer.
Larger cooling channels, however, require the removal of more volume inside the core and
a lessening of the core’s structural integrity. To balance these two issues, different cooling
components have been developed for use in different ranges of core diameters. Table 9.3 lists
some of the various options, which will next be discussed.
9.3.5.1 Cooling Insert
Deep cores with medium and large diameters, more than 50 mm, may be most effectively
cooled through the use of a custom cooling insert. In this design, a significant portion of the
inside of the core is removed. An insert is then designed to provide multiple cooling channels
around the periphery and down the length of the core. The coolant is returned via a cooling
line provided down the axis of the cooling insert, which connects back to the primary cooling
line. One possible design is shown in Figure 9.20. Even though the cooling insert design appears
extremely complex, it is readily produced on a four axis milling machine or on a lathe.

Figure 9.20: Core cooling insert

226

9 Cooling System Design

This particular design may favor cooling at too great an expense of core strength. Depending
on the melt pressures, it may be warranted to move the cooling channels further from the
cavity surface while reducing their width. A more significant issue may be the management of
stress in the vertical direction arising from the application of melt pressure on the top surface
of the core. For this reason, the cooling insert can be provided with a tight fit to the back
surface of the core so that forces resulting from the melt pressure are transmitted directly to
the support plate. Structural issues related to cores are analyzed in Section 12.3.
9.3.5.2 Baffles
Baffles are used to cool deep cores by circulating coolant along the axis of the core. Baffles
are normally inserted into a drilled hole on the inside of the core. Because these devices must
convey the coolant fluid up and down the length of the core, these devices have a minimum
size corresponding to holes with a diameter greater than 6.35 mm (1/4 inch). A design with a
spiral baffle is shown in Figure 9.21. In this case, the coolant flows down the primary cooling
channel, up the straight portion of the baffle, spirals around the helical grooves, then reverses
direction at the top of the baffle. This particular design uses a baffle with a 12 mm diameter
in a core with a diameter of 60 mm. While this design is likely sufficient, a larger baffle could
have been used to reduce the distance between the cooling channel and the cavity surface.
Compare the design and function of the baffle, shown in Figure 9.21, with the cooling insert,
previously shown in Figure 9.20. The two designs function in essentially the same manner with
a few important differences. Baffles are not designed to carry any load in the axial direction
and have limited load carrying capability in the radial direction (especially straight baffles).
For this reason, the wall thickness of the core should be designed appropriately according
to the analysis in Chapter 12. In terms of availability, baffles are standard components
readily available from a number of suppliers, whereas cooling inserts must be designed and
manufactured. Given the complexity, expense, and risk associated with a custom cooling
insert, the baffle is clearly preferred whenever the molding application allows.

Figure 9.21: Spiral baffle

9.3 Cooling System Designs

227

9.3.5.3 Bubblers
Bubblers are a slightly smaller alternative to baffles with very similar cooling performance.
In this design, shown in Figure 9.22, the coolant circulates around the outside of the bubbler,
and returns down the inside of the bubbler. The bubbler does not contact the core and so
carries no load from the core compression. Because of this, the bubbler is designed with very
thin wall thickness and compact dimensions. Bubblers with a diameter of less than 2 mm can
be used in drilled holes less than 3 mm in diameter. The primary disadvantage of bubblers is
that they require two cooling channels – one to provide flow around the bubbler and a second
to return the flow from inside the bubbler. As such, the benefit of the smaller hole diameter
associated with the bubbler comes as greater expense with regard to its installation.

Figure 9.22: Bubbler

9.3.5.4 Heat Pipes
A heat pipe is a closed device with an inner cavity that contains a fluid which boils at a
temperature between the melt temperature and the coolant temperature. Capillary action
causes the cooled internal fluid to climb the outer walls of the heat pipe. When placed inside
the core as shown in Figure 9.23, the increased temperature along the length of the heat pipe
causes the fluid to evaporate and return to the base of the heat pipe where the gas cools and
condenses. Because of this continual cycle of condensation and evaporation of the liquid
within the heat pipe, relatively high cooling rates can be achieved without requiring the flow
of mold coolant along the axis of the mold core.
The heat pipe has become a standard mold component available from a number of suppliers.
Their primary advantages include small size, good heat transfer rates, and ease of installation.
However, their cooling effectiveness is not as high as that as bubblers or baffles. The reason
is that the bulk conveyance of the mold coolant, which has a high specific heat and a much
lower temperature than the melt temperature, provides a much higher rate of heat transfer

228

9 Cooling System Design

Figure 9.23: Heat pipe

Figure 9.24: Conductive pin

9.3 Cooling System Designs

229

than that provided by heat pipes. Heat pipes also have potential issues related to their
initial response (since they require a significant temperature gradient to initiate an effective
condensation-evaporation cycle) as well as their effectiveness under a variety of coolant and
melt temperatures (related to the geometry and material properties).
9.3.5.5 Conductive Pin
For cores with very small diameters, less than 5 mm, it may not be possible to convect heat
along the axis of the core using any of the previously mentioned designs. As such, the only
option may be to utilize a conductive pin to facilitate heat transfer as shown in Figure 9.24.
Mold coolant flows around the back of the pin to transfer as much heat as possible from the
pin. With high length to diameter ratios, however, the heat transfer is not very effective. In
such cases, the core pins prevent the flow of heat down the length of the core pins and act
primarily as insulators.
9.3.5.6 Interlocking Core with Air Channel
When the part geometry allows, slender cores with very small diameters can be interlocked
with the opposing mold cavity as shown in Figure 9.25. Such a design has two advantages.

Figure 9.25: Conductive pin

230

9 Cooling System Design

First, the interlocking of the core with the cavity provides support for the core and will tend
to reduce the core flexure as analyzed in Section 12.3.3. Second, the interlocking provides
a means by which to convey coolant from the moving side of the mold, through the core,
and to the stationary side of the mold. Air is typically used as the coolant in such a design
since this coolant will be exposed to the molded part and the environment when the mold is
opened. While air has a very low density which reduces its cooling effectiveness, this design
will provide much more heat transfer than a solid core pin.

9.3.6

One-Sided Heat Flow

There are two common molding situations in which there is negligible heat flow from one
side of the molding. The first is the long slender core shown earlier in Figure 9.24 which relies
solely on conduction down the axis of the slender pin to transfer heat from the inside of the
molding. Since the pin is so slender, there will be very little heat transfer down the length of
the pin. As a result, the majority of the heat must be transferred to the cooling lines in the
cavity insert.
Figure 9.26 plots the heat flux in a mold having a slender core pin. The flux vectors indicate
that there is some significant heat transfer around the centerline of the pin towards the coolant

Figure 9.26: Heat flux in slender pin

9.3 Cooling System Designs

H

Q  0

HH

Mold

Core

231

Mold
Mold

Q

Q

Q

Figure 9.27: Worst case heat flux scenario

at its base. However, the pin’s cross-sectional area is so small that there is a dominating radial
heat flux at the surface of the pin. In other words, the hot plastic melt that is touching the core
must transfer a majority of its heat all the way through the plastic to the metal and cooling
lines of the cavity inserts.
With regard to the cooling of such slender cores, the mold designer should understand that
the cooling time must be extended due to the limited heat transfer to the coolant. A worst case
scenario can be easily analyzed by assuming that there is no heat transfer to the core. The heat
flux in this scenario is shown in Figure 9.27. Since all the heat must transfer through one side
of the molding, the thermal behavior is essentially the same as if two layers of the plastic melt
were on top of each other. This double thickness representation is valid since the temperature
distribution is symmetric across the centerline so there is no associated heat flux.
To calculate the cooling lines for one sided heat flows, then, Eqs. (9.5), (9.6), and (9.8) may
be used by substituting twice the thickness of the molding for the variable, h. The result is
that any molding application with a one sided heat flow will have a four fold increase in the
cooling time over a molding cooled from two sides.
Example: Estimate the cooling time for an application using a process called two-shot
molding, which will mold a 3 mm thick layer of ABS over a 2 mm thick layer of PC.
Given that the layer of PC will act as an insulator, the ABS will have a one sided heat flow.
The cooling time can be estimated as:
t cABS =

(2 ⋅ 0.003 m)2
⎛ 4 239 − 60 ⎞
ln ⎜
⎟ = 75.6 s
−8
2
2
π ⋅ (8.69 ⋅ 10 m /s) ⎝ π 97.6 − 60 ⎠

Such an extended cooling time is uneconomical since the cycle time will typically apply
to the molding of both the ABS and the thinner PC layer. To be more economical, it is
preferable to mold the thinner layer second. Then the cooling time for molding the second
PC layer would be approximately:

232

9 Cooling System Design

t cPC =

(2 ⋅ 0.002 m)2
⎛ 4 300 − 80 ⎞
ln ⎜
⎟ = 13.5 s
2
2
−7
π ⋅ (1.89 ⋅ 10 m /s) ⎝ π 138 − 80 ⎠

which is less than the cooling time of 18.9 s for a single layer ABS with a thickness of
3 mm. As such, molding the thinner layer of PC over the ABS would not require additional
cooling time in a two shot molding process.

9.4

Chapter Review

Cooling system design is often not leveraged in injection mold design even though relatively
little additional investment can reap significant increases in molder productivity. The cooling
system design process includes the estimation of the cooling time, required heat transfer rate,
and coolant flow rate to subsequently determine the cooling line diameter, depth, and pitch.
Once these specifications are determined, a suitable cooling line layout can be developed
that provides high and uniform rates of heat transfer while not interfering with other mold
components. The cooling system design must also specify the flow of the coolant through
the cooling line network as well as the design of conductive inserts and other mold elements
for achieving uniform temperatures across the molded parts.
After reading this chapter, you should understand:
• The cooling system design process, and the flow of decisions needed to rationally engineer
a cooling system;
• How to estimate the cooling time and potential errors in this estimation;
• How to estimate the required rate of heat transfer and check this value with the
specifications of mold temperature controllers;
• How to calculate the required coolant flow rate and check this value with the specifications
of mold temperature controllers;
• How to estimate the minimum and maximum size of a cooling line, and select a final
cooling line diameter;
• How to estimate the depth and pitch of the cooling lines for a specific molding application;
• How to layout an effective cooling line design that does not interfere with other mold
components, or redesign the mold to provide for more effective cooling;
• How to identify and remedy cooling-related issues in molding applications, such as sharp
corners and deep cores.
In the next chapter, the shrinkage and warpage behavior of the solidified molding is examined.
Afterwards, an ejection system design process is presented. As will be made clear, the shrinkage
and ejection of the molded parts are closely linked to the cooling process.

10

Shrinkage and Warpage

Plastic part designers often use design for manufacturing and assembly (DFMA) guidelines
to reduce the number of parts in an assembly. For this reason, plastic part designs can be
extremely complex with many features and tight tolerances. The delivery of plastic moldings
that satisfy the dimensional requirements is a joint responsibility of the mold designer, molder,
material supplier, and part designer. The part designer should provide a design with uniform
thicknesses and achievable specifications. The material supplier should provide consistent
polymer resin and useful guidance regarding material properties. The molder should select
suitable and consistent processing conditions for operation of the mold. The mold designer
should provide a mold with balanced melt filling and cooling, and for which the mold cavity
dimensions were engineered for an appropriate shrinkage.
The shrinkage of molded plastic parts is governed primarily by the thermal contraction of the
plastic, the compressibility of the plastic at packing pressures, and to a very small extent by the
thermal expansion of the mold metal. The sequence of effects that determines the final part
dimensions is shown in Figure 10.1. Prior to molding, the mold cavity dimensions may change
slightly from the machined dimensions given that the mold may be at a coolant temperature
above the room temperature. The thermal expansion of the mold cavity, indicated by the
dashed lines, can be computed as the mold metal’s coefficient of thermal expansion multiplied
by the temperature difference between the mold coolant and room temperature. For a P20

Mold thermal
expansion
L = 0.0005 m/m
Packing
L = 0.0005 m/m
0
In-mold cooling
L = 0.0005 m/m
<0
Ejection
L = −0.003 m/m
0
Post-mold cooling
L = −0.005 m/m
 0

Figure 10.1: Mold and molding shrinkage behavior

234

10 Shrinkage and Warpage

mold insert, the coefficient of thermal expansion is 12.8 · 10–6 m/m°C. If molding ABS, the
mold operating temperatures might be 60 °C, which is 40 °C above room temperature. As
such, thermal expansion of the mold cavity might be 0.0005 m/m or 0.05% (12.8 · 10–6 m/m°C
times 40 °C). While this change in mold dimensions is small compared to the magnitude of
shrinkage of the plastic, it is readily predicted and should be considered when specifying the
final mold cavity dimensions for tight tolerance applications.
During the filling and packing stages of the molding process, the melt in the mold cavity
is constrained by the surfaces of the mold cavity and compressed at high pressures. This
compression drives expansive stresses, which means that the melt in the mold cavity would
expand if not contained by the mold cavity. During in-mold cooling, the temperature of the
melt drops. In most molding processes, the thermal contraction of the melt causes the decay
of the melt pressure and release of associated compressive stresses. Subsequent cooling of the
melt causes significant thermal contraction. The molding will physically shrink in the mold
through the thickness and along any unconstrained surfaces such as ribs and side walls. In
some areas of the part, however, the shrinkage of the plastic is constrained by side walls. In
these areas, the plastic does not shrink so instead develops internal tensile stresses.
Upon ejection, most of the developed stresses in the plastic are released, and the plastic
molding instantaneously shrinks. Further post-mold cooling allows the molding to equilibrate
at room temperature and additional relaxation of any residual stress. In the example shown
in Figure 10.1, the total change in length, ΔL, was –0.005 m/m. This relative reduction of the
part length from the designed mold dimension is referred to as the shrinkage, s:
s =1−

Lmolding
Lcavity

(10.1)

Example: Calculate the nominal shrinkage if a mold cavity 20 mm in length produced a
molding with a length of 19.85 mm.
s =1−

19.85 mm
= 0.0075 = 0.75%
20.00 mm

Example: Calculate the length of a molding if a mold cavity 300 mm in length was used
with a material that shrank 0.8%.
Lmolding = (1 − s) Lcavity = (1 − 0.008) 300 mm = 297.6 mm
The change in length of the molding due to shrinkage may or may not be significant depending
upon the requirements of the molding application. Tolerances on plastic part dimensions
are typically specified as a percentage of their nominal length. For instance, the Society of
the Plastics Industry provides guidelines about standard and tight tolerances in commercial
production. A typical standard tolerance may be specified as ± 0.4% while a typical tight
tolerance might be ± 0.1%. In either case, a 0.5% shrinkage rate will cause the molding to

10.1 The Shrinkage Analysis Process

235

be out of tolerance. As such, the mold designer must take the plastic shrinkage into account
when specifying the mold cavity dimensions. If the mold designer knew that the net shrinkage
was 0.5%, then the mold cavity dimension would be set to 100.5 mm to produce a molding
100 mm in length.

10.1 The Shrinkage Analysis Process
The primary goal of shrinkage analysis is to understand the shrinkage behavior of the plastic
and its dependence upon the processing conditions. By understanding the shrinkage of the
plastic, rational recommendations can be made regarding the shrinkage rates to be used for
mold design. This same understanding can provide assistance to the molder regarding the
selection of processing conditions to deliver the specified tolerances.

10.1.1 Estimate Process Conditions
The first step in predicting the shrinkage is to estimate the pressure and temperature of the
polymer melt from the mold geometry and expected machine set-points. Since the exact
pressure and temperature are not known beforehand, the mold designer may assume that
the melt temperature is equal to the mid-range temperature recommended from the material
supplier. The melt pressure is more difficult to predict since the molder will adjust the filling
and packing pressures to address a variety of needs (including shrinkage). However, a common
molding practice is that the packing pressure is initially set to 80% of the pressure required
to fill the mold.
Example: For the Tablet PC Bezel molded of ABS (Cycolac MG47), the melt temperature
is assumed to be 239 °C. The filling pressure was previously analyzed in Section 5.5.2 and
found to be 83 MPa for two gates feeding into the cavity with a 1.5 mm nominal wall
thickness. Accordingly, the melt pressure during packing is assumed to be 66 MPa. The
mold temperature is also assumed to be at the middle of the recommended range for the
coolant temperature, which equals 60 °C.

10.1.2 Model Compressibility Behavior
The compressibility (or PvT) behavior of the polymer melt can be modeled by the double
domain Tait equation, which specifies the specific volume, v, as a function of the melt’s
pressure and temperature. The term “double domain” implies that the specific volume is
modeled separately in the solid and melt states. The transition temperature between the solid
and melt states is modeled as a function of pressure as:

236

10 Shrinkage and Warpage

Tt (P) = b5 + b6 P

(10.2)

where b5 is the transition temperature at zero pressure, and b6 is the rate of change of the
transition temperature with respect to pressure. For temperatures below the transition
temperature, the reference specific volume, v0(T), and compressibility, β, are modeled as:
v0 = b1,s + b2,s (T − b5 )
B(T ) = b3,s exp [−b4,s (T − b5 )]

(10.3)

where b1…4,s are material coefficients related to the material properties in the solid state.
For temperatures above the transition temperature, the reference specific volume and
compressibility are modeled as:
v0 = b1,m + b2,m (T − b5 )
B(T ) = b3,m exp[−b4,m (T − b5 )]

(10.4)

where b1…4,m are material coefficients related to the material properties in the melt state. The
specific volume is then modeled as a function of pressure and temperature as:

P ⎤⎫

v(T , P) = v0 (T ) ⎨1 − 0.0894 ln ⎢1 +
⎬ + vT (T , P)
(
B
T ) ⎥⎦ ⎭



(10.5)

The term vT represents the additional specific volume associated with the transition of semicrystalline polymers from their closely packed semi-crystalline state to a more loosely packed
amorphous state. This transition volume is modeled as:
vT (T , P) = b7 exp{b8 [T − Tt (P)] − b9 P}

(10.6)

Coefficients for the double domain Tait equation are available for many polymers. Appendix A
provides model coefficients for a variety of different materials. The specific volume for an
ABS (Cycolac MG47) is plotted in Figure 10.2 as a function of temperature for three different
pressures. Figure 10.2 shows that as the melt temperature increases, the polymer melt expands
and the specific volume increases. When pressure is applied, the polymer melt is compressed
so the specific volume decreases. Many useful items can be extracted from a PvT graph. First,
the specific volume at room temperature and zero pressure is approximately 0.955. This
implies a density, ρ, of:
ρ=

1000 kg/m 3
= 1047 kg/m 3
0.955

(10.7)

This value compares well with the density of 1044 kg/m3 stated by the material supplier.
The coefficient of volumetric thermal expansion, CVTE, is the change in the specific volume
with respect to temperature. From the graph, the CVTE may be calculated as:

10.1 The Shrinkage Analysis Process

237

1.15
P= 0 MPa
P=100 MPa
P=200 MPa

Specific Volume (cc/g)

1.1

1.05

1

CVTE 
0.95

0.9


0

v
T

v
P

50

100
150
200
Melt Temperature (°C)

250

300

Figure 10.2: PvT behavior for an ABS

CVTE =

v(T = 100 °C) − v(T = 20 °C) 0.98 − 0.955
1
=
= 3.1 ⋅ 10−4
100 °C − 20 °C
80 °C
°C

(10.8)

As will be subsequently discussed, the CVTE is directly related to the coefficient of linear
thermal expansion and the shrinkage.
The compressibility of the material, β, can also be evaluated from the PvT graph as the rate
of change of the specific volume with respect to the melt pressure:
β=

v(P = 200) − v(P = 0) 0.905 − 0.955
1
=
= −2.5 ⋅ 10−4
200 MPa − 0 MPa
200 MPa
MPa

(10.9)

It can be observed in Figure 10.2 that the coefficients related to thermal expansion and
compressibility of the polymer are larger in the melt state than the solid state. The reason is
that the polymer at an elevated temperature in the melt state has more atomic energy than
the polymer in the solid state. This increased energy provides more “free volume” around
the molecules and a significant increase in the thermal expansion and compressibility of the
polymer.

10.1.3 Assess Volumetric Shrinkage
As the polymer melt fills, packs, and cools in the mold cavity, it will be subjected to a range of
melt pressures and temperatures. At the same time, the specific volume of the polymer melt

10 Shrinkage and Warpage

0

Melt
temperature
(°C)

300
200

1.05

s
Pla
1

&
tion
Ejec kage
shrin

v

100
0

1.1
Specific Volume (cc/g)

100

P= 0 MPa
P=100 MPa
P=200 MPa

on
a ti
tic

Filling

Ejection &
shrinkage

Cooling

Filling

1.15

Packing

Melt
pressure
(MPa)

200

Plastication

238

g
kin
Pac

Cooling

0.95

0

10
Time

20

0.9

0

50

100
150
200
Melt Temperature (°C)

250

300

Figure 10.3: PvT cycle during molding of an ABS

in the cavity will change accordingly. Figure 10.3 provides the melt’s pressure, temperature,
and specific volume history during a molding cycle.
Figure 10.3 indicates that during plastication, the melt’s temperature and specific volume
increases. During filling, the melt temperature is nearly constant, but an increased melt
pressure causes a reduction in the specific volume. During packing, the material cools with
a reduction in pressure and temperature, causing a further reduction in the specific volume.
After the end of the packing stage, no additional material is forced into the mold cavity so
the melt pressure decays as the melt cools, which thereby causes an increase in the specific
volume. At the end of the cooling stage, the mold opens and any residual melt pressure is
released. The part is then ejected and allowed to cool to room temperature.
The specific volume of the plastic after each of the various molding stages is represented in
Figure 10.4 with a scale four times the values graphed in Figure 10.3. Each cube contains the
melt temperature and pressure at the end of different molding stages, while the size of each
cube represents the specific volume of the melt.
Figure 10.3 and Figure 10.4 indicate that the specific volume after cooling is 0.97, and the
specific volume after ejection (when the part has cooled to room temperature) is 0.955. As
such, the change in the specific volume of the plastic is –0.015. This change in the specific
volume will lead directly to the linear shrinkage of the molded plastic part. The estimation
of the volumetric shrinkage at the end of the packing stage is crucial to the calculation of the
volumetric and linear shrinkage.
A reasonably accurate estimate of the volumetric shrinkage can be calculated if the melt
pressure and temperature at the end of the packing stage are known. As previously discussed,
the melt pressure in the cavity during packing was estimated as 66 MPa. The temperature of
the plastic in the cavity is a function of the material properties, mold geometry, and processing
conditions. If the packing time is known, then the average melt temperature can be estimated

10.1 The Shrinkage Analysis Process

After
drying
T = 120 °C
P = 0 MPa
v = 0.98

After
plasticating
T = 260 °C
P = 0 MPa
v = 1.08

After
filling
T = 250 °C
P = 100 MPa
v = 0.99

After
ejection
T = 20 °C
P = 0 MPa
v = 0.955

After
cooling
T = 70 °C
P = 0 MPa
v = 0.97

After
packing
T = 130 °C
P = 80 MPa
v = 0.96

239

Figure 10.4: Changes in specific volume of ABS during molding cycle

as discussed in Chapter 9. However, a more simple approach is to assume that the melt
temperature at the end of the packing stage is equal to the no-flow melt temperature, which
is the temperature at which the polymer has a very high viscosity. The no flow temperatures
for a variety of materials are provided in Appendix A.
The change in the specific volume can be calculated as the change in the specific volume of
the plastic at the end of the packing stage and the specific volume of the plastic during end
use of the molded part:
Δv = v (Tno_flow , Ppack ) − v (Tend_use , Pend_use )

(10.10)

The ratio of the specific volumes, rv, is also useful to calculate:
rv =

v (Tno_flow , Ppack )

(10.11)

v (Tend_use , Pend_use )

Example: Calculate the absolute and relative change in the specific volume for the bezel
molded of ABS.
The packing pressure is assumed to be 66 MPa. The melt temperature at the end of the
packing stage is assumed to be equal to the transition temperature, which equals 132 °C
or 405 K.
The transition temperature of ABS at the packing pressure is:
Tt (P) = 370.6 K + 2.3 ⋅ 10−7

K
⋅ 66 ⋅ 106 Pa = 386 K = 113 °C
Pa

240

10 Shrinkage and Warpage

Since the no flow temperature of 405 K is above the transition temperature of 386 K,
the coefficients for the melt state should be used. The specific volume at the end of the
packing stage (66 MPa and 405 K) can be calculated as:
v0 = 9.83 ⋅ 10−4

m3
m3
m3
+ 6.51 ⋅ 10−7
(405 K − 370.6 K) = 1.01 ⋅ 10−3
kg
kg
kg

1


B = 1.33 ⋅ 108 Pa ⋅ exp ⎢ −4.38 ⋅ 10−3 (405 K − 370.6 K)⎥ = 1.16 ⋅ 108 Pa
K


v (132 °C, 66 MPa) = 1.01 ⋅ 10−3
= 9.65 ⋅ 10−4


m3 ⎡
66 ⋅ 106 Pa ⎞ ⎤
⎢1 − 0.0894 ln ⎜1 +
⎥+0
kg ⎣⎢
1.15 ⋅ 108 Pa ⎟⎠ ⎦⎥

m3
kg

After molding, the plastic is assumed to be used at a room temperature of 20 °C. Using
the PvT model coefficients for the solid state, the specific volume at 293 K and 0 MPa
pressure is:
v0 = 9.83 ⋅ 10−4

m3
m3
m3
+ 3.47 ⋅ 10−7
(293 K − 370.6 K) = 9.56 ⋅ 10−4
kg
kg
kg

v (20 °C, 0 MPa) = 9.56 ⋅ 10−4
= 9.56 ⋅ 10−4


m3 ⎡
0 ⎞⎤
⎢1 − 0.0894 ln ⎜1 + ⎟ ⎥ + 0
kg ⎣
β ⎠⎦

m3
kg

The absolute change in the specific volume is then:
Δv = 9.65 ⋅ 10−4

kg
kg
kg
− 9.56 ⋅ 10−4 3 = 0.09 ⋅ 10−4 3
3
m
m
m

Finally, the ratio of the specific volume is:

rv =

9.56 ⋅ 10−4
9.65 ⋅ 10−4

kg
m 3 = 0.9907
kg
m3

The relative change in the volumetric shrinkage is about 1%. As will next be shown, the
linear shrinkage will be significantly less.

10.1 The Shrinkage Analysis Process

241

10.1.4 Evaluate Isotropic Linear Shrinkage
The volumetric shrinkage corresponds to shrinkage in all three spatial dimensions of the
molded part. If a material exhibits the same properties in every direction, it is said to be
“isotropic”. Most unfilled plastics exhibit isotropic behavior, such that the properties of the
molded part are similar in directions parallel to the direction of flow, perpendicular to the
direction of flow, and across the thickness.
If a material is isotropic, then it should exhibit the same linear shrinkage, s, in all directions.
Consider a unit cube and a shrunken cube as shown in Figure 10.5, in which the shrunken
cube has a relative change in the volumetric shrinkage of rv. Each side of the shrunken cube
has been reduced from L to L (1 – s), where s is the linear shrinkage.
L

L

L(1−s)

Unit
cube

L(1−s) Shrunken
cube
L

L(1−s)

Figure 10.5: Volumetric and linear shrinkage

The volume of the unit cube is L3. The volume of the shrunken cube is L3 · rv, which to maintain
conservation of mass must also equal (L(1-s))3 after shrinking. This leads to the equation:
L3 ⋅ rv = [L (1 − s)]3

(10.12)

Solving for s provides an equation for the linear shrinkage:
s =1−

3

rv

(10.13)

Example: Compute the linear shrinkage for the bezel molded in ABS.
Assuming the previous conditions, the relative change in the volumetric shrinkage was
0.991%. This leads to the isotropic shrinkage of:
s =1−

3

0.9907 = 1 − 0.9968 = 0.0031 = 0.31%

This shrinkage estimate is below the recommended shrinkage rate of 0.6% provided by
the material supplier. The difference, which is not necessarily an error, is likely due to the
relatively high packing pressure of 66 MPa (9,600 psi) that was assumed for this thin-wall
application.

242

10 Shrinkage and Warpage

10.1.5 Evaluate Anisotropic Shrinkage
Some materials, such as liquid crystal polymers and glass filled polymers, exhibit material
properties that are a dependent on the flow direction. For these anisotropic materials, the
molecules and/or fibers can become highly aligned in the flow field during the filling and
packing stages as shown in Figure 10.6. As shown by the aspect ratio and direction of the
ellipses, the orientation through the thickness can be quite complex. The shear flow during the
filling and packing stages will tend to orient the plastic melt in the direction of flow through
a substantial portion of the thickness.
Anisotropic materials exhibit different properties in their principle directions. For example, a
glass filled material will be stronger and exhibit less shrinkage in the principle flow direction
compared to the other directions. This increase in strength is due to the higher strength glass
fibers that are aligned in the flow direction. Since glass has a lower coefficient of thermal
expansion, the material will also tend to have lower shrinkage in the flow direction than in
other directions. The relationship between volumetric and anisotropic linear shrinkage is
shown in Figure 10.7, where the variable a represents the fraction of anisotropy in the flow
direction related to the other two directions.
Following the previous derivation for shrinkage in an isotropic material, the volume of a
shrunken cube with the anisotropic shrinkage is:
L3 ⋅ rv = L3 (1 − s)2 (1 − a s)

(10.14)

Flow

Figure 10.6: Orientation leading to anisotropy
L

L

L(1−as)

Unit
cube

L(1−s)
L

Figure 10.7: Volumetric and anisotropic shrinkage

Flow
Flow

L(1−s)

10.1 The Shrinkage Analysis Process

243

which yields the cubic equation:
a s 3 − (2 + a) s 2 + (2 + a) s − (rv − 1) = 0

(10.15)

While this cubic equation can be solved analytically, the solution may be more readily achieved
through iteration of the equation:
s=−

(rv − 1) + (2 + a) s 2 − a s 3
(2 + a)

(10.16)

Example: Assume that an ABS is used to mold the bezel with 15% glass fiber by weight.
(Such a material does exist for this application, known as Cycolac CRT3370.) Estimate
the anisotropic shrinkage if the plastic material is known to shrink half as much in the
flow direction compared to the other directions.
First, the addition of 15% glass fiber will reduce the volumetric shrinkage since the glass
has very little thermal expansion compared to the plastic. Since glass has a density of
2600 kg/m3, and the unfilled or “neat” ABS has a density of 1040 kg/m3, the volume of
the glass fiber in the ABS is:
kg

1044 3

m
p = 15% ⋅ ⎜
kg
⎜ 2600 3

m



⎟ ≈ 6%



which means that 94% of the filled plastic will shrink as the unfilled ABS while 6% of the
plastic will not shrink significantly. This reduced compressibility implies a reduction in
the volumetric shrinkage:
Δv = 94% ⋅ 0.09 ⋅ 10−4

kg
kg
= 0.085 ⋅ 10−4 3
m3
m

So the relative change in the volumetric shrinkage is:

rv =

9.56 ⋅ 10−4

kg
m3

(9.56 + 0.085) ⋅ 10−4

kg
m3

= 0.9912

The amount of anisotropy, a, is 0.5. To iteratively solve the anisotropic shrinkage, an initial
guess for the shrinkage is required. Since the shrinkage is small and Eq. (10.16) is highly
stable, an initial guess of zero shrinkage should suffice. The first iteration yields:
s=−

(0.9912 − 1) + (2 + 0.5) 02 − 0.5 ⋅ 03
= 0.00352 = 0.352%
(2 + 0.5)

244

10 Shrinkage and Warpage

Using the shrinkage of 0.00352 for another iteration yields:
s=−

(0.987 − 1) + (2 + 0.5) (0.00352)2 − 0.5 ⋅ (0.00352)3
= 0.00351 = 0.351%
(2 + 0.5)

The solution has converged after two iterations. The shrinkage, s, equals 0.35% in the cross
flow and thickness directions, and the shrinkage in the flow direction, a · s, is 0.18%.

10.1.6 Assess Shrinkage Range
Prior to making any recommendations, it is useful to assess the potential error on the shrinkage
estimate. The most significant errors in the shrinkage predictions will likely stem from the
assumed melt pressures and temperatures. For this reason, it is useful to estimate the most
extreme but realistic limits for the pressure and temperature to provide a lower and upper
limit for the shrinkage:




The lower limit for shrinkage will correspond to a packing stage with a long duration
and high melt pressure. The maximum duration corresponds to the time at which the
plastic melt ceases to flow once it cools to the no-flow temperature. The estimate for the
high packing pressure is difficult to predict, since it is governed by the molder’s process
settings, specifications of the molding machine, etc. A practical upper limit for the packing
pressure may be the greater of 120% of the injection pressure or 100 MPa.
The upper limit for shrinkage will correspond to a packing stage with a short duration
and low melt pressures. The reduced duration will cause the pressure in the cavity to fully
decay before the plastic melt has sufficiently cooled, thereby causing excessive volumetric
shrinkage. As such, the maximum shrinkage may be estimated by evaluating the volumetric
shrinkage at a low packing pressure (equal to the lesser of 40% of the injection pressure
or 30 MPa) and a high melt temperature (equal, perhaps, to the temperature half-way
between the no-flow temperature and the melt temperature).
Example: Estimate the minimum and maximum shrinkage for the laptop bezel.
To calculate the minimum shrinkage, assume that the melt temperature and pressure at
the end of packing are 132 °C and 100 MPa, respectively. The specific volume at the end
of packing is 9.50 · 10–4 kg/m3, which results in an increase in the relative volumetric
shrinkage to 1.007. The linear shrinkage is estimated to be –0.2%. In other words, so
much material has been packed into the cavity that the material will expand rather than
contract once the part is ejected from the mold! While this is an interesting finding and
a possible event, molds are not usually designed or operated with the intent of obtaining
zero or negative shrinkage. The reason is that some shrinkage is desirable so that the plastic
molding will shrink away from the walls of the cavity and onto the core so the molding
can be ejected. Negative shrinkage corresponds to “over packing” of the plastic in the mold
cavity. In an over pack situation, the material remains compressed, such that it may not
be possible to release the part from cavity details such as ribs and bosses.

10.1 The Shrinkage Analysis Process

245

To calculate the maximum shrinkage, assume that the melt temperature and pressure at
the end of packing are 185 °C and 30 MPa, respectively. The specific volume at the end
of packing is 10.14 · 10–3 kg/m3, which results in a decrease in the relative volumetric
shrinkage to 0.943. The linear shrinkage is estimated to be 1.9%, which is significantly
higher than the previously estimated shrinkage of 0.3%. In this case, the packing stage has
provided insufficient material to compensate for the volumetric shrinkage in the mold
cavity. The mold designer should suggest an extended packing stage with higher packing
pressures to avoid excess shrinkage.

10.1.7 Establishing Final Shrinkage Recommendations
The unfortunate reality is that the exact shrinkage will not be known before the mold is
designed, built, and tested. The goal in the establishing the final shrinkage recommendation
is




to provide a shrinkage value that is close to the actual shrinkage of the material,
to provide a mold machined with a shrinkage value that may be operated under a range
of process conditions to bring the part dimensions within specification, and
to provide a mold that is machined “steel safe” such that the mold can be readily altered
if necessary to bring the part within specifications.

The presented shrinkage analysis should provide reasonable shrinkage estimates given valid
melt temperatures and melt pressures. However, the estimated shrinkage can vary widely
based on the material properties and processing conditions that are assumed. For this reason,
the shrinkage analysis should be considered as complementing other sources of information
about shrinkage. The shrinkage analysis should not be used in isolation given the potential
for error. However, the shrinkage analysis should be used to verify the shrinkage estimates
coming from other sources.
There are several common sources of shrinkage data that may be used (in addition to
analysis) to assist in establishing the final shrinkage recommendation. Most commonly,
a material supplier or other testing laboratory may mold parts in a standard test mold to
estimate the shrinkage. Typically, the test mold consists of a 2 or 3 mm thick plaque that is
molded at mid-range melt temperatures and pressures. The molded parts are then allowed
to equilibrate for some time before their dimensions are measured and the linear shrinkage
calculated. This shrinkage information, when available, is roughly accurate since the testing
was conducted for the exact material of interest at conditions close to most molding
applications. However, the provided shrinkage data may not be very accurate if the wall
thickness or processing conditions of the molding application vary significantly from that
of the test mold.
One significant issue with shrinkage data from a material supplier is that the shrinkage data
may not be based on testing of the actual material, but rather assumptions that the material
will behave as supposedly similar materials that have been previously tested. A more expensive

246

10 Shrinkage and Warpage

but more accurate alternative is to design, build, and test a prototype mold that has a flow
length, wall thickness, and cooling system similar to the specific molding application. Such
prototype molding provides melt pressures and temperatures that should be very similar
to those of the final production mold, so the shrinkage observed with the prototype mold
should be very close to the final production mold. While the development of a prototype
mold can be expensive, the accuracy of the shrinkage measurements can be very useful in
tight tolerance applications.
Another option is to rely on shrinkage data from previous mold designs and molder experience. In many cases, molds may already have been designed and operated for production of
moldings that are very similar to the current mold design application. In such cases, the mold
designer may obtain the best estimates by comparing the measurements of the moldings with
those of the mold steel dimensions. Prior to making final recommendations, however, the
mold designer should inquire with the molder to check if the molder would have preferred to
operate the molding machine at different melt temperatures and/or pressures. If so, the mold
designer should ask the molder to produce moldings at the preferred conditions (even if the
moldings fall outside of specification), and then calculate the shrinkage of these moldings
for use in mold design applications.
A fourth option is to perform sophisticated computer simulation of the mold filling, packing,
and cooling stages to predict the linear shrinkage in the molding application. While computer
simulation utilizes more advanced physics and provides more detailed results than the
shrinkage analysis presented here, the computer simulation is still subject to the same errors
regarding the assumed material behavior and processing conditions. However, the numerical
simulation can be valuable to validate the manual shrinkage analysis while providing nonuniform shrinkage estimates across the mold cavity.
In establishing the final shrinkage recommendation, the mold designer should perform the
presented shrinkage analysis and confirm the results with data from the material supplier and
previous experience, if available. If the shrinkage rate is uncertain, then the mold designer
should communicate the potential error with the molder, material supplier, and end-user to
reduce the uncertainty and assess liability should the utilized shrinkage rates be so erroneous
to incur costly mold changes. In some contracts, the final shrinkage recommendation is the
responsibility of the mold’s customer who ultimately pays for the cost of the mold design
and any mistakes. In other cases, no party is willing to accept responsibility for an uncertain
shrinkage rate, so the parties agree that a prototype molding project is necessary to characterize
the shrinkage and reduce risk.

10.2 Shrinkage Analysis and Validation

247

10.2 Shrinkage Analysis and Validation
10.2.1 Numerical Simulation
To validate the described shrinkage analysis, a numerical simulation was conducted for the
laptop bezel using a commercial injection molding simulation (Moldflow MPI 5.1). To perform the analysis, this simulation uses the PvT material model as well as a proprietary shrinkage model based on shrinkage observations from molding experiments. Since the required
shrinkage experiments were not available for Cycolac MG47, the numerical simulation was
conducted using Cycolac 570 instead.
The shrinkage rates predicted by the simulation are provided in Figure 10.8 assuming a
mid-range melt temperature, mid-range coolant temperature, a constant packing pressure
of 66 MPa, and a cooling time of 20 s. The results indicate that the shrinkage varies widely
across the mold cavity. Low shrinkage rates (on the order of 0.3%) are predicted in thin areas
which freeze at high melt pressures. Moderate shrinkage rates (around 0.6%) are predicted
in the bulk of the part, which is more than the 0.31% shrinkage previously predicted by the
manual analysis.
High shrinkage rates (above 1%) are predicted near the end of fill. The high shrinkage rate
at the end of fill is due to the fact that the material near the gate is freezing and preventing
the polymer melt from reaching the end of flow. The results indicate a significant quandary
for the mold designer and the end-user: what shrinkage value should be used? If an average
shrinkage of 0.6% is used, then the part width may be out of specification due to the excessive
unaccounted shrinkage along the top and bottom edges.

Figure 10.8: Shrinkage rate for bezel molded of an ABS

248

10 Shrinkage and Warpage

There are several different strategies that can be employed by the mold designer if non-uniform
shrinkage occurs. One increasingly common method, which is supported by the joint use of
computer simulation and CNC machining, is for the mold designer to use different shrinkage
values in different portions of the mold. For the laptop bezel shown in Figure 10.8, the molder
may choose a shrinkage value of 0.6% for the left and right sides and a shrinkage value of 1%
for the top and bottom sides. In this example, this strategy is relatively easy to employ and
would likely be successful since the geometry is relatively simple. For more complex product
geometry with a tightly interconnected surface, however, the application of non-uniform
shrinkage values can become a complex and risky endeavor.
A more common approach to obtaining tight tolerances is to ensure more uniform shrinkage
across the mold cavity through the addition of multiple gates. By increasing the number of
gates for the laptop bezel from two to four as shown in Figure 10.9, the packing pressure and
shrinkage rate are made more uniform across the mold cavity. In this example, the additional
two gates have decreased the maximum shrinkage from 1.1% at the center of the top edge to
0.9% at the corners. Furthermore, the average shrinkage in the cavity has been reduced from
0.6% for the two-gated mold design to 0.5% for the four-gated mold design.
In many cases, unacceptable non-uniform shrinkage is not recognized until after the mold is
designed, built, and tested. In some cases, the addition of runners and gates may be a relatively
simple and inexpensive activity. In other cases, however, the addition of two gates may prove
to be expensive. For example, the modification from a two-drop “straight bar” manifold to
a four-drop “H” or “X” style manifold may require the purchasing of a new manifold, the
addition of bores to the A-side of the mold, and the re-routing of cooling lines. In such cases,
the mold designer and molder may try to correct the shrinkage behavior through processing
or material changes.

Figure 10.9: Shrinkage rate for bezel molded of an ABS

10.2 Shrinkage Analysis and Validation

249

10.2.2 “Steel Safe” Mold Design
Because the exact shrinkage rate is unknown, a common practice for mold designers is to
design and build the mold so that it is “steel safe”. In this context, “steel safe” means that the
core and cavity inserts are purposefully designed so that they can be enlarged by removing
existing mold metal if the product dimensions are found to be undersized. For example, the
expected shrinkage rate in a molding application may be 0.5%. A “steel safe” design might
utilize a shrinkage rate of 0.4% on the cavity insert, and a 0.6% shrinkage rate on the core insert.
Such a mold design strategy is shown in Figure 10.10. By designing the cavity smaller and the
core larger than required by the expected shrinkage behavior, the mold designer is providing
reserve metal that may readily be machined to fine tune the dimensions of the mold.
Cavity insert, s = 0.4%
Expected, s = 0.5%

Core insert, s = 0.6%

Figure 10.10: PvT behavior for an acetal

One drawback to a“steel safe”mold design is that machining will be necessary in some molding
applications regardless of the shrinkage behavior that is encountered. The reason is that by
utilizing different shrinkage estimates for the core and cavity, the nominal dimensions of
the plastic moldings will be out of tolerance. For this reason, many mold designers prefer to
use a constant but mid-range estimate of the shrinkage for the design of the core and cavity
inserts, and hope that the molder can adjust the molding process to meet quality specifications.
Another common “steel safe” practice is to avoid finishing critical cavity details until after
the mold is constructed and tested. By leaving features such as bosses, snap fits, and other
mold cavity surfaces in a semi-finished state, the mold designer can finalize the design and
implementation of these features after the shrinkage has been characterized. While such staged
deployment of features in the mold design does lengthen the mold build time, the risk during
mold development is reduced and the tolerances of the final moldings can be increased.

10.2.3 Processing Dependence
As the analysis has shown, the volumetric and linear shrinkage are dependent upon the melt
temperature and pressure. As such, molders frequently rely on adjustment of the molding
conditions to control the shrinkage and optimize the part dimensions. The effect of several
critical processing conditions on shrinkage is shown in Figure 10.11. The primary variables,

10 Shrinkage and Warpage

Shrinkage (%)

250

Packing
time

Packing
pressure

Barrel
temperature

Coolant
temperature

Cooling
time

Figure 10.11: Effect of processing conditions on shrinkage

as expected, are related to the pressure and temperature of the melt in the cavity. Both packing
time and cooling time are significant but have a small effect on shrinkage when sufficient
packing and cooling times are used. The coolant temperature has a slightly greater effect than
the barrel temperature, because it more directly controls the temperature of the molding
upon ejection.
Adjustment of the molding process provides significant freedom to modify the nominal
shrinkage rate in the mold cavity. To influence the distribution of the shrinkage as a function
of position in the mold cavity, it is possible to profile the packing pressure to control the melt
pressure in the cavity as the melt solidifies at different locations and times. Specifically, a
higher packing pressure may be initially used at the start of packing to reduce the shrinkage
rate at distances far from the gate. The packing pressure may then be reduced as the material
closer to the gate freezes so as to avoid over-packing. To demonstrate this approach, a packing
pressure profile was used in the numerical simulation with the two-gated mold design. The
results of Figure 10.12 show that the linear shrinkage has approached that of the four-gated

Figure 10.12: Effect of packing pressure profiling on shrinkage

251

10.2 Shrinkage Analysis and Validation

mold design without added expense. Unfortunately, few molders leverage the capabilities of
pack pressure profiling to maximize part quality.

10.2.4 Semi-Crystalline Plastics

0

Melt
Temperature
(°C)

0.85
Specific Volume (cc/g)

100

300
200
100
0

P= 0 MPa
P=100 MPa
P=200 MPa

10
Time

20

tion
ica

ing
Pack
0.8

Cooling
v

0.75

n&
Ejectio e
g
shrinka

0.7

0

st
Pla

0.65

Filling

Ejection &
shrinkage

Cooling

Filling

0.9

Packing

Melt
Pressure
(MPa)

200

Plastication

Many amorphous plastics have shrinkage rates on the order of 0.5%. However, semi-crystalline
polymers can exhibit significantly higher shrinkage rates. For example, the specific volume
for an acetal (Delrin 500) is plotted in Figure 10.13. Since acetal is a semi-crystalline polymer,
there is a significant change in the specific volume when the polymer transitions from a
closely packed semi-crystalline solid to a loosely packed amorphous melt. This increase in
the specific volume can give rise to significant volumetric shrinkage and high shrinkage rates
compared to amorphous materials.

0

50

100
150
Melt Temperature (°C)

200

250

Figure 10.13: PvT behavior for an acetal

Figure 10.13 indicates that the specific volume at the end of packing is 0.77. The material then
cools and transitions to a semi-crystalline solid with a specific volume at room temperature
equal to 0.69. The relative change in the volumetric shrinkage is 0.90. This corresponds to
a linear shrinkage of 3.5%. Molding applications with such high shrinkage rates tend to
be more difficult to control to tight tolerances due to their increased sensitivity to process
conditions.

10.2.5 Effect of Fillers
To a significant extent, fillers can be used to influence the amount of shrinkage that a
material exhibits. The most common fillers are mica, glass bead, glass fiber, carbon black,
and rubber. The density and coefficient of thermal expansion for these materials are provided
in Table 10.1.

252

10 Shrinkage and Warpage

Table 10.1: Density and CTE for common fillers

Filler

Density
(kg/m3)

Carbon black

2000

0.5

No

Glass bead

2600

3

No

Glass fiber

2600

3

Yes

Mica powder

2800

10

No

Rubber particles

1500

80

No

CTE
(μm/m°C)

Significant
anisotropy?

It can be observed from Table 10.1 that with the exception of rubber (which is typically added
as an impact modifier), all the fillers have a very low coefficient of thermal expansion (on
the order of 5 · 10–6 m/m°C) compared to that of plastic (on the order of 100 · 10–6 m/m°C).
For this reason, the addition of one or more fillers to a neat resin can be used to reduce the
polymer’s volumetric shrinkage and increase the molded part dimensions. The analysis of
filled resins for which the PvT behavior is not available can be conducted with the PvT model
for the unfilled resin according to the analysis example provided in Section 10.1.5.

10.3 Warpage
The above analysis regarding shrinkage pertains to in-plane dimensional changes in the plastic
moldings. When moldings distort or bend out of plane, then warpage is occurring. In some
applications, the dimensional changes due to warpage can far exceed the shrinkage. Worse,
warpage can be more difficult to predict and correct. While an exhaustive analysis is outside
the scope of this book, some practical guidance is provided for mold design.

10.3.1 Sources of Warpage
While all warpage is due to differential shrinkage, the sources of the differential shrinkage
vary. The simplest cause of differential shrinkage may be a temperature gradient through
the wall thickness of the molding. This phenomenon is shown in Figure 10.14. In this mold
design, the cooling system design is providing non-uniform cooling. The temperature of the
molded part will be higher near the core insert than the cavity insert. The previous cooling
analysis of Figure 9.11, for example, has shown that a temperature difference of 5 °C between
surfaces of the core and the cavity inserts is not uncommon.
Any temperature difference through the thickness of the moldings translates directly to
different shrinkage rates through the thickness as well. The difference between the shrinkage
rate on the core surface and the shrinkage rate on the cavity surface will cause a resulting strain

10.3 Warpage

253

Non-uniform
cooling system
design

Non-uniform
temperature
and shrinkage


RW

Warpage with
radius of curvature

Figure 10.14: Warpage due to differential shrinkage across thickness

in the part as it cools. For the example of Figure 10.14, the core surface is hotter so this side
of the plastic molding will experience greater shrinkage. From statics, the radius of curvature,
Rwarpage, of the molding caused by warpage can be calculated according to the equation:
Rwarpage =

2⋅h
(score − scavity )

(10.17)

where h is the wall thickness of the molding, and score and scavity are the shrinkage rates of the
molding adjacent to the core and cavity inserts according to Eqs. (10.2) to (10.13). Given the
radius of curvature, the maximum out of plane deflection at the edges of the molding, δ, can
be estimated as approximately:
⎛ W ⎞
δ = W ⋅ sin ⎜

⎝ Rwarpage ⎠

(10.18)

where W is the distance from the center to the edge of the molding.
Example: Calculate the out of plane distortion for the laptop bezel if the cavity is 2 °C
cooler than the core.
Using the PvT model for ABS, the analysis will assume that the temperatures of the
molding on the cavity and core surface are 132 and 134 °C, respectively, at the end of
packing with a pressure of 66 MPa. The specific volume and linear shrinkage on the cavity
are 9.65 · 10–4 kg/m3 and 0.31%; the specific volume and linear shrinkage on the core are
9.66 · 10–4 kg/m3 and 0.34%. While the difference in the shrinkage rates between the core
and cavity do not seem significant, the warpage may be significant.
The resulting radius of curvature is:
Rwarpage =

2 ⋅ 1.5 mm
= 9050 mm
(0.34% − 0.31%)

254

10 Shrinkage and Warpage

Since the part is 240 mm wide, the effective width from the center of the part, W, is
120 mm. The out of plane warpage from the center to the edge is then:
⎛ 120 mm ⎞
δ = 120 mm ⋅ sin ⎜
= 1.6 mm
⎝ 1050 mm ⎟⎠

There are two items of potential interest. First, this warpage of 1.6 mm is somewhat greater
than the absolute edge to edge shrinkage, which is 0.8 mm (evaluated as 0.31% · 240 mm).
Second, this warpage estimate is not sensitive to the overall temperature of the molding, but
only to the temperature gradient through the thickness. For example, if the shrinkages were
evaluated at a pressure of 0 MPa, a cavity temperature of 100 °C, and a core temperature of
102 °C, then the resulting warpage would be 2.1 mm, which is fairly close to the previous
estimate. As such, the analysis is useful for predicting warpage due to temperature gradients
through the thickness of the molding.
Temperature gradients through the wall thickness of the molding are one common cause of
warpage. Another significant cause of warpage is differential shrinkage due to temperature
and/or pressure gradients across the area of the part. One typical example is shown in
Figure 10.15. In this case, the melt pressure in the cavity can be much higher near the gate
than at the extremities of the mold cavity. As such, the volumetric and linear shrinkage in the
center will be less than the shrinkage around the outside of the molding. If the difference in
the shrinkage is large enough, then the center of the part will warp out of the plane.
The differential shrinkage shown in Figure 10.15 is similar to the differential shrinkage for the
laptop bezel shown in Figure 10.8. However, Figure 10.15 will tend to warp due to differential
shrinkage while the bezel shown in Figure 10.8 will not. The reason is that the window in the
laptop bezel mechanically decouples the various sides from each other, such that each side is
free to shrink independently. Warpage would likely only occur due to differential shrinkage
across the part if the shrinkage rate on the left side was very different from the shrinkage
rate on the right side, and similarly for differential shrinkage on the top side compared to
the bottom side.

Center-gated
mold cavity

Non-uniform
pressure
and shrinkage



Warpage with
radius of curvature

Figure 10.15: Warpage due to differential shrinkage across area

10.3 Warpage

255

When the molding consists of a single closed area, the material within the molding is in
continuous contact such that any non-uniform shrinkage and stresses across the part may
only be resolved through out of plane distortion of the part. Such warpage requires buckling
of the plane of the part, which can occur when:1
⎛h ⎞
(sedge − scenter ) > 0.44 ⋅ ⎜ ⎟
⎝W ⎠

2

(10.19)

where h is the wall thickness of the molding, and scenter and sedge are the shrinkage rates at the
center and edge of the part, and W is the distance from the center to the edge of the molding.
If a molded part buckles, then the out of plane warpage can be conservatively estimated as:
δ=

W 2 − {W [1 − (sedge − scenter )]}2

(10.20)

Example: Analyze warpage assuming that the cup lid is center gated and molded with ABS
at a packing pressure of 66 MPa at the center of the part and 0 MPa at the outer rim.
To evaluate the warpage, it is first necessary to calculate the shrinkage rates and check
the buckling criterion. Given the 66 MPa packing pressure and a temperature of 132 °C,
the linear shrinkage at the center will be 0.31% at the center. At the edge, the pressure of
0 MPa and temperature of 132 °C provides a linear shrinkage of 1.66%. Given that the
cup is 2 mm in thickness and 81 mm in diameter, the buckling criterion is stated as:
⎛ 2 mm ⎞
(1.66% − 0.31%) > 0.44 ⋅ ⎜
⎝ 0.5 ⋅ 81 mm ⎟⎠
?

2

0.0135 > 0.0011
This criterion indicates that the central portion of the lid will buckle. The estimated
warpage is:
δ=

(40.5 mm)2 − {40.5 mm [1 − (1.66% − 0.31%)]}2 = 6.6 mm

In the actual molding of the lid, it is somewhat unlikely that the lid would warp and very
unlikely that the lid would warp to this extent. The reason for the warpage in the analysis
is that the analysis assumed that the pressure at the edge of the lid was 0 MPa and did
not pack out at all. As such, the material around the edge was predicted to shrink at a rate
much higher than would be encountered in practice.
1

This buckling analysis assumes a isotropic circular plate under uniform radial edge compression with a
buckling stress threshold of
σ Buckling = K

⎛h⎞
⋅⎜ ⎟
1 − ν ⎝R⎠
E

2

2

where K is a constant dependent upon the Poisson’s ratio, v, E is the modulus of the material, H is the
thickness of the plate, and R is the plate radius. Equation (10.19) assumes a material with a Poisson ratio
of 0.4 (valid for most plastics).

256

10 Shrinkage and Warpage

As the previous warpage analyses have shown, warpage is caused by non-uniform shrinkage
due to temperature gradients through the wall thickness of the molded part, pressure
gradients across the area of the molded part, or temperature gradients across the area of the
molded part. These are the most common causes of warpage, and have been treated with
the simplest possible analysis. However, there are other causes of non-uniform shrinkage
including orientation and residual stress. For further information, the interested mold designer
is referred to the research literature [32–39]. Reasonably accurate warpage predictions may
also be obtained with computer simulation as previously discussed.

10.3.2 Warpage Avoidance Strategies
There are several common strategies that should be used to avoid and address warpage
issues. By far, the most important strategy is to design a mold that will provide uniform melt
temperatures and pressures throughout the cavity, so that the shrinkage of the molded part(s)
will be highly uniform. To maximize the shrinkage uniformity in tight tolerance molding
applications, the mold designer should:





Avoid high flow length to wall thickness ratios by utilizing multiple gates;
Maintain uniform cavity pressures by designing a balanced feed system with low flow
resistance;
Maximize the mold surface temperature uniformity with a tight cooling line pitch and
highly conductive mold inserts where needed; and
Facilitate melt pressure and temperature uniformity in the molding by requiring uniform
part thickness and generous fillets.

If the mold is well designed, then warpage is less likely to occur. In the event that warpage is
encountered, a molder may try to reduce or eliminate the warpage by:








Filling the mold cavity as fast as possible to reduce cooling in the solidified skin;
Increasing the pack time until the part weight no longer increases;
Increasing the packing pressure to reduce the amount of material shrinkage;
Utilizing a profiled packing pressure as discussed with respect to Figure 10.12 to increase
melt pressure and shrinkage uniformity across the part; and
Utilizing different coolant temperatures on different sides of the mold or in different
portions of the mold to purposefully control the temperature and shrinkage distribution;
and
Trying different types of materials and filler systems with varying shrinkage behaviors to
find satisfactory performance.

Even with the all these mold design and molding actions, warpage issues may require mold
design changes. There are several mold design changes that are commonly used to reduce
the magnitude of the warpage. The most common approach might be the addition of one or

10.4 Chapter Review

257

more gates to improve the uniformity of the shrinkage across the cavity. Another common
approach to reduce the likelihood of buckling is to increase the stiffness of the molding through
the addition of shallow ribs. A less common approach of increasing interest is to contour
the mold cavity surfaces such that upon warping the molded part straightens to the desired
shape. This last approach places a significant burden on the mold designer and mold maker,
since it involves a very high level of predictive capability and very fine surface machining.
Since the dimensional shifts of the part due to warpage may exceed steel safe limits, errors in
this approach can incur very high costs.

10.4 Chapter Review
In this chapter, shrinkage and warpage analyses were provided to predict changes in the
molded part dimensions based on the pressure-volume-temperature (PvT) behavior of the
polymer together with the melt pressures and temperatures. These analyses provide insight
into the shrinkage and warpage phenomenon, but are highly dependent upon the assumed
pressures and temperatures. For this reason, many mold designers use a mid-range shrinkage
value recommended by a material supplier or other source. In tight tolerance applications,
prototype molding and/or steel safe mold design strategies are frequently used to converge
to the optimal dimensions of the mold cavity to deliver the desired part dimensions.
After reading this chapter, you should understand:
• The relationship between shrinkage, mold dimensions, and part dimensions;
• The PvT behavior of amorphous and semi-crystalline polymers;
• The qualitative relationship between melt pressure, melt temperature, and shrinkage;
• How to calculate volumetric shrinkage from the PvT model;
• How to calculate linear shrinkage from volumetric shrinkage;
• The causes of differential shrinkage;
• How to calculate warpage from differential shrinkage;
• The effect of processing conditions and fillers on shrinkage and warpage; and
• Mold design strategies for managing shrinkage and warpage.
The analysis of shrinkage is useful for specifying the mold dimensions. However, the shrinkage
of the plastic onto the mold core(s) also determines the forces required to eject the molded
part. The estimation of these ejection forces will guide the design of the ejection system so as
to avoid deforming the molded part(s) upon ejection. After the ejection system is designed,
the mold’s structural systems are analyzed and designed.

11

Ejection System Design

The ejection system is responsible for removing the molded part(s) from the mold after the
mold opens. While this may seem a simple function, the complexity of the ejection system
can vary widely depending on the requirements of the molding application. Many issues
must be considered including the need for multiple axes of actuation, the magnitude and
distribution of the ejection forces, and others. Before beginning the analysis and design of
the ejection system, an overview of its function is first provided.
Figure 11.1 provides a side view of a mold opening for the subsequent ejection of the laptop
bezel. The ejector assembly (consisting of the ejector plate, ejector retainer plate, return
pins, ejector pins, stop pins, and other components) is housed between the rear clamp plate,
support plate, and rails.
At this time in the molding cycle, the molded part has shrunk onto the core side of the mold
and has been pulled from the mold cavity as the moving side of the mold is retracted from
the stationary side of the mold. In a few moments, the molding machine will push the ejector
knock-out rod against the ejector plate to actuate the ejector assembly and strip the molded
parts off the core. At this time, however, a clearance exists between the ejector knock-out rod
and the ejector plate.
Figure 11.2 provides a side view of the mold during the actuation of the ejection system. Prior
to ejection, the opening of the molding machine platens separated the two mold halves to
allow clearance for the ejection of the part. The machine then drives the ejector-knock out
rod forward to make contact with the rear surface of the ejector plate. Since the machine can

Figure 11.1: Side view of opening mold

260

11 Ejection System Design

Figure 11.2: Side view of mold with actuated ejectors

Figure 11.3: Side view of mold with reset knock-out rod

provide a force to the knock-out rod much greater than the force with which the moldings
have shrunk onto the core, the entire ejector assembly is forced forward. The ejector pins in
contact with the molded part are displaced and push the molding off the core.
After the moldings are ejected, the molding machine then retracts the ejector knock-out rod
as shown in Figure 11.3. A clearance is then made between the front of the knock-out rod
and the back of the ejector plate, which allows the ejector assembly to be reset to its original
position for the next molding cycle.

11.1 Objectives in Ejection System Design

261

Figure 11.4: Side view of closing mold

There are several ways of resetting the ejector system which will be discussed later. However,
one common method for returning the ejector assembly is to simply close the mold as shown
in Figure 11.4. The front surface of the return pins will then contact the opposing face of the
A plate. The back surface of the return pins will then drive the ejector plate and ejector plate
backwards as the mold closes.

11.1 Objectives in Ejection System Design
The plastic moldings will tend to shrink during cooling and will usually remain on the mold
cores upon the opening of the mold. As such, mechanisms are required to push the parts off
the mold during the ejection stage. While this primary function is easily understood, there
are several related design objectives that should be satisfied in the design of the ejection
system.

11.1.1 Allow Mold to Open
The first step in the ejection of the moldings from the mold is to open the mold at one or
more parting planes. The mold designer should work with the product designer and molder
to ensure that the mold design is suitable and robust. In general, the number of moving cores
should be minimized by simplifying the product design and developing a suitable mold design.

262

11 Ejection System Design

When moving cores are used, they should be designed, when possible, to work with the opening
action of the mold rather than relying on additional actuators and control systems.
Sometimes the molded part necessitates a moving core design that can not be actuated by
the mold opening movement. Most modern molding machines support such “core pull”
sequences through the use of digital signals. After the cooling and plastication stages, when
the mold is ready to open, the molding machine can be programmed to provide one or
more core pull signals to the required actuators (typically pneumatic valves, hydraulic valves,
electric solenoids, or electric motors). The actuators can then retract the connected mold
components, which should be designed to contact a limit switch when fully retracted. The
molding machine will typically be programmed to delay the mold opening until all limit
switches from all core pull circuits are energized.

11.1.2 Transmit Ejection Forces to Moldings
To remove the moldings from the mold, ejection forces must be applied to strip the moldings
off the core surfaces. These ejection forces can be applied by many different mold components
including ejector pins, sleeves, blades, lifters, air poppets, stripper plates, and other devices.
The number, location, and design of these components must be developed to reliably transmit
the forces from the molding machine’s knock-out rod(s) through the ejection system to
the plastic moldings. With every ejection cycle, significant shear and compressive forces are
applied to the ejection system components. If the components are poorly designed, these
ejection forces may result in excessive shear stress, compressive stress, deflection, fatigue,
buckling, and mold failure.

11.1.3 Minimize Distortion of Moldings
Just as the ejection forces can cause stress and deflection in the ejection system components,
the ejection forces can also cause stress and deflection in the plastic moldings. To avoid
permanent distortion of the plastic moldings, the number, location, and design of the ejector
components must be developed to apply a low and uniform state of stress across the moldings.
If the ejector force is uniformly distributed across many points in the mold cavity, then the
molding will be uniformly ejected from the mold without any permanent distortion.

11.1.4 Actuate Quickly and Reliably
The ejection stage consumes precious seconds of the molding process, without providing much
value to the moldings. As such, the ejection system should be designed to remove the moldings
as quickly and reliably as possible, and then reset so that the mold may be closed and the next
cycle initiated. To increase the speed of the ejection system, some molders may specify the use
of air poppets and/or air jets to improve ejection velocities and reduce the cycle time.

11.1 Objectives in Ejection System Design

263

To increase the reliability of the ejection system, the mold designer should develop the mold
to tightly interface with the molder’s preferred part removal system. While many molds rely
on gravity drop of the moldings and the feed system to a moving conveyor, molders are
increasing using sprue pickers and gantry robots for part removal. In general, these systems
do not greatly reduce the molding cycle time but rather provide increased control of molding’s
removal and subsequent placement while protecting the aesthetic areas. If sprue pickers or
robots will be used, then the mold designer must appropriately customize the ejection system.
Typically, the moldings must be stripped off the core but retained at a controlled position by
some of the ejection system components. Furthermore, mold designers should confirm and
design interface geometry in the cavity and/or feed system that is easily identified and highly
repeatable for interfacing with the part removal system.

11.1.5 Minimize Cooling Interference
There can be many components in an ejection system and, unfortunately, most of these
components are not actively cooled. As such, the ejection system components can significantly
interfere with the heat transfer path from the molding to the coolant. There are two issues
that commonly arise. First, the ejection system components can be made of a metal that is less
thermally conductive than the core inserts. If the ejection system components are large, then
the cooling effectiveness will be greatly reduced. Second, the ejection system components are
assembled into the mold and provided with sliding fits. The result is that there is a thermal
contact resistance across every boundary between the ejection system components and the
adjacent mold. This thermal contact resistance results in lower rates of heat transfer through
and around components in the ejection system.
The effect of cooling interference by the ejection system can be very significant. Consider,
for example, an ejector pin with a diameter greater than the nominal wall thickness of the
molding. In this example, the ejector pin will not transfer significant heat from the adjoining
surface of the molding since


the ejector pin has a thermal contact resistance between it and the mold, and



the ejector pin is relatively large.

As a result, the plastic in the mold cavity above the ejector pin will have to cool via heat
transfer to the mold steel around the periphery of the ejector pin as well as heat transfer to
the opposite side of the mold. While the local cooling of this exact area of the molding may
not be the significant constraint on the cycle time, the result is that this large ejector pin will
cause a hot spot in the mold and less consistent properties upon ejection.
For this reason, the use of overly large ejector pins should be avoided in favor of multiple,
smaller ejector pins placed so as to not interfere with the mold cooling. Sometimes, large
ejection system components including stripper plates, lifters, core pulls, and others are
required. Such large components should be fitted with cooling channels and actively cooled
to provide consistent ejection temperatures.

264

11 Ejection System Design

11.1.6 Minimize Impact on Part Surfaces
The ejection system is usually located on the moving side of the mold along with the mold
cores. Since ejector pins and other components contact the molding, they leave witness marks
on the adjacent surfaces, which can




reduce the visual quality of the molding’s surface,
interfere with mating assembly surfaces, and
reduce strength in structural applications.

As such, ejector pins and other components should be located and designed to have a minimal
impact on the molding’s surfaces.
The most common approach is to locate ejector pins on non-visible surfaces and in low
stress areas of the molding. Alternatively, larger components such as sleeves, slides, lifters, and
stripper plates may be strategically used such that their witness lines coincide with features of
the molding. These carefully designed components can leave no apparent witness line while
providing very effective ejection across large areas of the part surface.
Some applications require one side of the molding to be completely free of all witness marks. In
these applications, one strategy in mold design is to locate the entire system on the stationary
side of the mold along with the feed system. This “reverse ejection” design allows the surface
of the moldings facing the moving side of the mold to be completely free of witness marks
due to both the feed system and the ejection system. This design will be discussed in more
detail in Section 13.9.4.

11.1.7 Minimize Complexity and Cost
The cost of the ejection system can be either a negligible or a significant portion of the total
mold cost. The simplest molds use an interchangeable set of ejector pins with a constant
diameter and length. However, most molds use a number of different ejector pins with varying
diameter, section, and length. While the cost of additional cost of the pins is small compared
to the cost of the mold, the mold designer and mold maker should be sure to key and label
each ejector pin so that they can be readily maintained by the molder.
The cost of the ejector system can increase dramatically with the use of slides, lifters, and
other ejection sub-assemblies. Again, the goal of the mold designer is to provide a simple,
cost-effective, and reliable design that satisfies the previously described objectives. The mold
designer should not just consider the initial design and tooling costs, but the operational,
maintenance, and failure costs as well.

11.2 The Ejector System Design Process

265

11.2 The Ejector System Design Process
The ejector system design is determined first by the required layout of the mold’s parting
surfaces, and subsequently by the detailed design of the various components required to
eject the molding(s).

11.2.1 Identify Mold Parting Surfaces
As described in Section 4.1, the product geometry and orientation in the mold determines
the number and location of the mold’s parting surfaces. If the mold has no under-cuts or
special requirements, then only one parting surface may be necessary. However, if the mold
has internal or external under-cuts, then additional parting surfaces may be necessary along
with the associated ejection components to actuate the sliding cavity and/or core inserts to
release the trapped areas of the moldings so that they may be ejected. Such “split cavity molds”
are discussed in Section 13.9.1.

11.2.2 Estimate Ejection Forces
The ejection force, Feject, required to remove a molding from a mold core is a function of
the normal force between the surface of the molding and the surface of the mold, Fnormal,
together with the associated draft angle, φ, and the coefficient of static friction, μs, between
the molded part and the core insert. To estimate the ejection force, the friction force, Ffriction,
is first computed as:
Ffriction = μs ⋅ Fnormal

(11.1)

The ejection force is then calculated as the component of the friction force that is normal to
the parting surface:
Feject = cos(φ) ⋅ Ffriction = μs ⋅ cos(φ) ⋅ Fnormal

(11.2)

The relationships between these forces are represented in Figure 11.5. Approximate values
for the coefficient of friction vary from 0.5 for highly polished surfaces (with low surface
roughness) to more than 1.0 for rough and/or textured surfaces [40]. As the draft angle
decreases from zero, the ejection forces decrease with the cosine of the draft angle.
The normal force acting between the molded part and the core is driven by the internal tensile
stresses in the plastic, which will cause the plastic molding to hug the core like an elastic band.
The normal force is estimated as the integral of the residual tensile stresses, σ, in the molded
part taken across the effective area of the molded part:
Fnormal =

∫ A

eff

σ(x , y , z ) dAeff

(11.3)

266

11 Ejection System Design

FFfriction
friction
Fnormal
normal
Feject

Figure 11.5: Ejection force vectors

Unfortunately, the estimation of the residual tensile stresses is a complex function of the
processing conditions, mold geometry, and material properties. A detailed treatment is well
beyond the scope of this book. For this reason, conservative simplifying assumptions are
applied to provide an estimate of the ejection force.
The analysis assumes that the tensile stresses in the molding are the result of the thermal
contraction of the mold. This assumption will cause the analysis to over predict the ejection
forces since in practice the polymer



may be in a compressive state before the application of thermal shrinkage, and
may tend to relax.

Since the polymer melt can not support tensile stress in a fluid state, the thermal strain, ε,
is estimated for the solidified plastic as the coefficient of thermal expansion of the plastic
material, CTE, multiplied by the difference between the solidification temperature, Tsolidification,
and the ejection temperature, Tejection:
ε = CTE ⋅ (Tsolidification − Tejection )

(11.4)

While there will be stress relaxation as the polymer melt becomes rigid, a conservative
assumption is that the strain develops with the material at its room temperature modulus, E.
The resulting tensile stress internal to the part can then be computed as a constant throughout
the entire molding as:
σ = E ε = E ⋅ CTE ⋅ (Tsolidification − Tejection )

(11.5)

To estimate the normal and ejection forces, the cross-section area upon which the stress effectively acts must be calculated. This effective area is not the projected area of the molding, but
rather the cross-sectional area of the molding in different directions. Figure 11.6 demonstrates
the governing concept by sectioning the molding into two halves. As previously suggested,
the molding is similar to an elastic band wrapped around the mold core. When the molding
is sectioned, the normal forces between the two halves are relieved. As such, the normal force
can be well estimated as the tensile stress multiplied by the cross-sectional area:
Fnormal = σ ⋅ Aeff

(11.6)

267

11.2 The Ejector System Design Process

Figure 11.6: Tensile stresses pulling across effective area

Combining all the previous terms provides the following estimate of the ejection force:
Feject = μs ⋅ cos(φ) ⋅ E ⋅ CTE ⋅ (Tsolidification − Tejection ) ⋅ Aeff

(11.7)

Example: Estimate the ejection force required to strip a cup molded from ABS off the
mold core.
From CAD, the area of the hatched cross-section of the cup in Figure 11.6 is 526 mm2.
A smooth core surface is used with a coefficient of friction of 0.5, and a draft angle of 1°.
The modulus, coefficient of thermal expansion, solidification temperature, and ejection
temperature are taken from Appendix A. The ejection force is then estimated as:
Feject = 0.5 ⋅ cos(10°) ⋅ 2.28 GPa ⋅

8.83 ⋅ 10−5
⋅ (132 °C − 97 °C) ⋅ 526 ⋅ 10−6 m 2
°C

≈ 1,800 N ≈ 400 lb
The analysis indicates that approximately 1,800 N (400 lb) of force is required to push
the molded cup off the mold core.
Example: Estimate the ejection force required to strip the laptop bezel molded from ABS
off the mold core.
The laptop bezel is more geometrically complex than the molded cup, and so involves
greater effort to estimate the effective area for the calculation of the ejection force. Some
different cross-sections of the laptop bezel are shown in Figure 11.7.
At first, the mold designer may first consider using the area of only section A-A or
section B-B as the effective area. However, if the molding was cut along only one of these
sections, then the resulting halves of the moldings would still remain on the core due to
the shrinkage along the other sections. As such, the mold designer might consider adding
the areas of section A-A to that of section B-B to estimate the effective area. However, this
area would still be insufficient.

268

11 Ejection System Design

Figure 11.7: Different cross sections of laptop bezel

If the molding were cut along these two sections, then the resulting pieces would still
remain on the core due to the tensile forces between the ribs. For example, the normal
force between the indicated ribs in section B-B is driven the tensile stresses across the
area of section C-C, which is dominated by the cross-section area of the top surface if
the molding. For these reasons, the effective area of a complex molding with ribs may
be estimated as:
Aeff = h (2 Lpart + 2 Wpart ) + nwall ⋅ h ⋅ H part + nrib ⋅ hrib ⋅ H rib

(11.8)

where h is the wall thickness of the molding, Lpart is the length of the part, Wpart is the
width of the part, nrib is the number of ribs, hRib is the average thickness of the ribs, Hrib
is the average height of the ribs, nwall is the number of side walls, and Hpart is the average
height of the side walls. For the laptop bezel, the effective area is:
Aeff = 0.0015 m (2 ⋅ 0.24 m + 2 ⋅ 0.16 m) + 4 ⋅ 0.0015 m ⋅ 0.01 m
+ 7 ⋅ 0.001 m ⋅ 0.01 m = 1.3 ⋅ 10−3 m 2
This effective area can be substituted into Eq. (11.7) along with a 1 degree draft angle to
estimate an ejection force of:
Feject = 0.5 ⋅ cos(1°) ⋅ 2.28 GPa ⋅
≈ 4,700 N ≈ 1,100 lb

8.83 ⋅ 10−5
⋅ (132 °C − 97 °C) ⋅ 1.3 ⋅ 10−3 m 2
°C

11.2 The Ejector System Design Process

269

Some discussion regarding the above examples is warranted. First, the analysis is conservative
in that assumptions have been made regarding the solidification temperatures and material
properties to provide estimates of ejection force that are higher than should be encountered.
Since the analysis is conservative, the use of this analysis for the ejection force should result
in effective ejection system designs without the use of safety factors. One potential issue may
arise, however, when a molder allows the molded part to remain in the mold and cool to low
temperatures. In this case, the final temperature of the molding should be used as the ejection
temperature which will result in significant increases in the predicted ejection force.
To validate the analysis, it is useful to compare the predicted ejection forces with the typical
ejection forces provided by commercially available molding machines. A survey of several
different sized machines available from different machine suppliers indicates that the ejection
force provided by the machine is typically 2% of the clamp tonnage of the machine. This
percentage means that if a molding machine provides 1000 kN of clamp force, then the
machine may provide 20 kN of ejection force. For comparison, the molded cup had an
expected clamp tonnage of 400 kN and an expected ejection force of 1.8 kN while the molded
bezel had an expected clamp force of 1400 kN and an expected ejection force of 4.7 kN. In
both examples, the analysis predicted an ejection force on the order of 0.5% of the clamping
force. Since molding machines would be expected to be designed to provide a higher ejection
force than what would normally be needed, the analysis results are believed to be on the right
order of magnitude and appropriate for ejection system design.

11.2.3 Determine Ejector Push Area and Perimeter
Once the ejection forces on the molding have been estimated, the next step is to determine the
total “push area” of the ejectors onto the molded part. Specifically, there is a minimum push
area that is required to avoid excessive compressive stress on the ejection system components
as well as excessive shear stress on the plastic moldings. These two phenomena are illustrated
in Figure 11.8 for a single pin ejecting a portion of the laptop bezel.

Figure 11.8: Compressive and shear stresses at ejection pin

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11 Ejection System Design

When the pin is actuated with the ejection system, a reaction force, Fpin, will develop between
the pin and the molded part before the part is ejected. The magnitude of this force is related to
the total ejection force required to eject the part as well as the number, location, and geometry
of the ejectors. The compressive stress on the pin, σpin, is the force on the pin divided by the
area of the pin, or:
σ pin =

Fpin
Acompression

=

4 Fpin

(11.9)

2
π Dpin

To avoid fatigue and/or buckling of the ejection system components, compressive stress levels
must be maintained below a critical threshold. This critical stress, σfatigue_limit, is dependent
upon the material and treatment of the ejectors. Most ejector pins and sleeves are made of
hardened materials, with fatigue limit stresses on the order of 800 MPa. A conservative mold
design, however, may assume a lower fatigue limit stress of 450 MPa for P20. In either case,
the total push area of all ejectors, Aejectors, to avoid excessive compressive stresses must meet
the requirement:
Aejectors >

Feject

(11.10)

σ fatigue_limit

Example: Calculate the combined push area of all ejectors required for the bezel mold
to avoid excessive compressive stresses in the ejector pins. Also, calculate the required
diameter if 20 ejector pins of the same diameter are to be used.
Assuming a fatigue limit stress of 450 MPa, the required push area is calculated as:
Aejectors >

4700 N
= 1.04 ⋅ 10−5 m 2 = 10.4 mm 2
450 MPa

If 20 pins are to be used, then each pin should have a cross section area of at least 0.5 mm2.
The minimum diameter is then:
min
>
Dpin

4 ⋅ 10.4 mm 2 /20 pins
= 0.8 mm
π

The required push area to avoid excess compressive stresses in the ejection system is very
small in most molding applications given the relatively high strength of steel. However, the
ejector system must also have enough push area to avoid developing excessive shear stresses
in the molded parts upon ejection. For the example of Figure 11.8, the shear stress exerted
on the molded part is the force on the pin divided by the area of the molded part directly
above the circumference of the pin, or:
τ part =

Fpin
Ashear

=

Fpin
π Dpin h

=

Fpin
Ωpin h

<

σ plastic_material
2

(11.11)

11.2 The Ejector System Design Process

271

where Ωpin is the perimeter of the pin. If the shear stress in the molded part is too high, then
the part can permanently distort near the pin (an effect known as “push pin”), permantenly
warp, or even fracture. To avoid these defects, the mold should be designed such that the
perimeter around all the ejectors provides a shear stress less than one-half the yield stress
of the material, σplastic_yield. This requirement leads to the following relationship for the total
perimeter of the ejector system, Ωejectors:
Ωejectors >

2 Feject
σ plastic_yield h

(11.12)

Example: Calculate the combined perimeter of all ejectors for the bezel mold. Also,
calculate the minimum required diameter to avoid excessive shear stresses in the ABS
molding if 20 ejector pins of the same diameter are to be used.
Assuming a yield stress of 44 MPa for ABS, the required combined perimeter of all
ejectors is:
Ωejectors >

2 ⋅ 4700 N
= 0.14 m
44 ⋅ 106 Pa ⋅ 0.0015 m

If 20 pins are to be used, then each pin should have a perimeter of 0.007 m. The minimum
diameter is then:
min
Dpin
>

Ωejectors
π

=

0.14 m /20 pins
= 2.23 mm
π

The analysis and examples indicate that for most molding applications, the design of the
ejector system is driven more by the yield stresses exerted on the plastic molding rather than
by the compressive stresses on the pin. However, compressive stress can cause buckling in
long, slender members such as ejector pins. For this reason, further analysis of the compressive
stresses is important, and will be subsequently used to avoid pin buckling.

11.2.4 Specify Type, Number, and Size of Ejectors
Once the required push area and perimeter of the ejectors is known, different ejector systems
designs can be developed. The mold designer should consider different designs with a
varying number and sizes of ejectors. There are advantages and disadvantages to having a
large quantity of small ejector pins compared to having fewer but larger ejector pins. With
respect to tooling and operation costs, a smaller number of large ejector pins are preferred.
There are two primary reasons. First, a smaller number of ejectors requires a lower number
of mold components and features to be machined. For this reason, the mold is less expensive
to manufacture and maintain. Meanwhile, the larger size of the ejectors will tend to have very
low compressive stresses and thus be less susceptible to buckling.

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11 Ejection System Design

With respect to design flexibility and mold operation, however, a larger number of small
ejector pins are preferred. There are several reasons. First, the greater number of ejector pins
allows for more frequent placement of the ejectors across the cavity. This higher density of
ejectors will tend to provide for more uniform venting and ejection. At the same time, smaller
sized ejectors allow greater design flexibility with respect to the placement of the ejectors.
As previously discussed, molds contain many tightly spaced and complex features so small
ejector sizes allows pins to be effectively placed between cooling lines, down narrow cores,
on side walls or ribs, etc.
The mold designer should remember that the above analysis only provides a lower limit for
the number and size of the ejectors. The mold designer can always add ejectors or increase
the ejector size to improve the uniformity of ejection or reduce stress in the molded part. The
mold designer must also determine the type of ejector to be used at various locations. Typical
components include ejector pins, ejector blades, ejector sleeves, stripper plates, slides, lifters,
angle pins, core pulls, collapsible cores, expandable cavities, split cavity molds, and others.
The selection of the most appropriate components is heavily dependent on the requirements
and geometry of the application. For this reason, the use of each of these components will
be subsequently discussed.
Example: Analyze and discuss the design of the ejector system for the laptop bezel
consisting of 10 and 40 ejector pins of the same diameter.
The minimum pin diameters are calculated according to the previous example for the
various number of ejector pins. Both designs provide the same total perimeter around
the ejectors and so also provide the same shear stress on the molded part. If only 10 pins
are used, then the minimum pin diameter would be approximately 4.5 mm. Assuming
uniformly distributed ejection forces, the compressive stresses in each of the 10 pins
would be 30 MPa. By comparison, if 40 pins are used, then the minimum diameter
would be approximately 1.125 mm. The compressive stress in each of the 40 pins would
be approximately 100 MPa.

Figure 11.9: Candidate ejector pin layout for laptop bezel

11.2 The Ejector System Design Process

273

The design for 10 evenly spaced, 4.5 mm ejector pins is shown in Figure 11.9. Since the
gates are located on the left and right side walls, the ejector pins located at the center of
the top and bottom walls would provide needed venting at the end of flow.
This design, however, may be unsuitable for two reasons. First, there may not be enough
ejectors at locations near where the molding will stick in the mold. In particular, the ribs
and bosses will tend to shrink onto the core and so require nearby ejector pins. Second,
the ejector pin diameter is slightly large given the close proximity of the nearby ribs. In
this design, only 1 mm of steel separates the ejector hole from the surface of the mold
cavity. With high melt pressures, stresses will develop in the steel, deforming the ejector
holes to be non-round, causing the ejector pins to bind. Eventually, cracks will propagate
between the ejector hole and the mold cavity. For these reasons, the ejector pins should
be made smaller and more strategically located.

11.2.5 Layout Ejectors
The previous example implied that the effectiveness of an ejector is not simply a function
of its size but also its location. In general, ejectors will be more effective when placed near
the locations where the ejection forces are generated. Furthermore, the ejectors will be more
effective when pushing on rigid areas of the molded part. A common but ineffective layout
arises when ejector pins are uniformly distributed across the mold cavity. Such an approach
can give rise to the layout design shown in Figure 11.10 with an ejector pin located relatively
far from the ribs and side walls of the molding. Since the molding has shrunk onto the core,
the ejection force is being generated by the friction between the molding and the mold core at
the rib and side wall. By placing the ejector pin far from these two sticking points, a significant
moment and deflection will be applied before the molding is stripped off the core.
The design can be improved by adding ejector pins closer to the rib and side wall as shown
in Figure 11.11. In this case, three additional pins are added to provide ejection forces close
to the molding. To avoid excessive stress in the core insert due to the provision of the ejector
hole, an allowance of at least one ejector pin diameter should be specified between the surface
of the mold cavity and the surface of the ejector hole. However, this ejector pin layout may
lead to a potential cooling issue since there may not be enough clearance to provide a cooling
line in the core insert between the rib and the side wall. As such, the diameter of the ejector
pins may be reduced slightly to allow the addition of a cooling line if desired.
Another alternative layout is to provide an ejector pin underneath the rib or side wall as shown
in Figure 11.12. This design has the direct benefit that the friction force and the ejection force
are in-line, such that very little deformation of the molding will occur. One common problem
arises due to the thinness of the rib and side wall compared to the larger ejector pin diameter.
To avoid very small ejectors that may buckle during operation, a solid boss or “ejector pad”
may be provided on the rib. When the ejector pin is actuated forward, the force is transmitted
from this pad down the length of the rib and to the surrounding areas of the part. Since the
ejector pin pushes directly on the ejector pad, no draft angle is required so the ejector pad
diameter can be maximized.

274

11 Ejection System Design

Figure 11.10: Ejector pin located away from sides of core

Figure 11.11: Ejector pins located near core side walls

Figure 11.12: Ejector pins located under rib with ejector pad

11.2 The Ejector System Design Process

275

Figure 11.13: Contoured ejector pins located on side walls

One issue with the use of the ejector pad, however, is the high volumetric shrinkage that can
lead to sink on the aesthetic surface of the part. For this reason, a cored out boss ejected with
an ejector sleeve (subsequently discussed) can provide for higher quality ejection albeit with
a higher mold manufacturing cost.
The need for ejector pads can be eliminated through the use of contoured ejector pins as
shown in Figure 11.13. In this case, the ejector pin is aligned with one side of the rib or wall,
and then contoured to push on the top surface of the feature. The pin is then contoured and
extended down along the side of the feature so as to also push on the parting plane of the
molding. Compared to the previous designs, this layout allows for effective transmission of
the ejection forces and compact ejector pin spacing without any changes to the molded part
design.
This last approach requires careful ejector pin design as well as careful alignment of the ejector
pin to the part features. Furthermore, there is a possible problem that can arise with the use
of contoured ejectors extending outside the parting line of the mold cavity as indicated in
Figure 11.13. Specifically, if the ejector pin is too short, then a gap will form between the top
of the ejector pin and the opposite surface of the cavity insert. If this gap is larger than the
thickness of a vent, then flash is likely to occur. Meanwhile, if the ejector pin is too long, then
the pin will be compressed on mold closure. With repeated ejection cycles, the pin can fatigue
and buckle. Given that the required length of the ejector pin is difficult to precisely determine
due to the stack-up in tolerances across the mold assembly, the mold designer may wish to
use a “steel-safe” approach with multiple length adjustments. Alternatively, the mold designer
may choose to place the ejector pin within the mold cavity and contour the pin as for the rib
in Figure 11.13. In these cases, slight errors in the contour of the pin will be on non-aesthetic
surfaces and so be less significant with respect to the quality of the molding.

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11 Ejection System Design

11.2.6 Detail Ejectors and Related Components
After the number, layout, and geometry of the ejectors have been determined, the detailing
of the design should be completed to ensure robust mold assembly and operation. There are
several very specific issues that need to be addressed. First, the mold designer should recognize
that the mold assembly is complicated by the large number of ejector system components
that must be simultaneously mated to the core inserts. This issue is compounded by tolerance
stack-up across multiple plates in the mold assembly. Taken together, the mold assembly can
consume a fair amount of time and result in damage of valuable mold components.
To facilitate the mold assembly, careful detailing is needed wherever the ejector system components interface with other components in the mold. Figure 11.14 provides a top and section
view of a round ejector pin (left) and a contoured ejector pin (right). Detail B of Figure 11.14
indicates that a clearance can be provided between the pin and the bore of the ejector hole for
the purpose of venting displaced air during the molding process. The analysis of the vent’s
clearance was provided in Chapter 8, indicating that typically a clearance of 0.02 mm (0.001 in)
is provided for a length of the order of two to three diameters of the ejector pin. Afterwards, the
ejector hole should step to a larger size so as to not restrict the sliding of the pin. The size of the
clearance is not critical but rather only limited by the interference with other nearby components. A chamfer should be provided from the larger diameter to the venting diameter. Otherwise, the ejector pin would tend to hang up on the sharp corner during mold assembly.
The larger clearance between the ejector pin and the ejector hole not only serves to eliminate
the sliding friction between the pin and the plate, but also provides needed slop to allow for
misalignment between the axes of the ejector holes in various plates. The specified clearance
should exceed the total stack-up of the holes’ positional tolerances across the mold plates.

Figure 11.14: Clearances around ejector pin

11.2 The Ejector System Design Process

277

Since typical drilling tolerances are on the order of 0.25 mm, a clearance of 0.5 mm should be
sufficient in most molding applications. Furthermore, a generous chamfer should be provided
at the interface between the core insert and the support plate. As indicated in Detail C of
Figure 11.14, this chamfer assists the guiding of the ejector pin from the support plate into
the core insert during mold assembly.
The detailed design of the ejector retainer plate is shown in Figure 11.15. As shown in Detail D,
a counterbore is provided in the ejector retainer plate to pull the head of the ejector pin(s) away
from the parting plane of the mold when the ejector system is reversed. To provide clearance
for misalignment of the positions of the ejector holes, the counterbore is provided a generous
tolerance so that the axes of the ejector pins are governed by the mating of the pin with the
reamed ejector hole in the core inserts. If a contoured pin is used, the head of the pin is typically
provided with a flat as shown in Detail E. A parallel slot and locating dowel are provided in
the ejector retainer to maintain the correct orientation of the contoured ejector pin.
Whenever possible, the mold designer should specify the same length and diameter of ejector
pins to facilitate mold assembly and maintenance. If different ejector pins are used in the mold
design, the mold designer and mold maker should be sure to key and label each ejector pin
and matching location on the ejector retainer plate so that the mold can be readily maintained
by the molder. The mold designer should always avoid designing ejector pins that vary only
slightly in their design, since similar pins may accidentally be considered interchangeable by
the molder. The incorrect assembly of ejector pins may cause damage to the pins as well as
the opposing mold cavity surfaces.

Figure 11.15: Retention and alignment of contoured ejector pin

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11 Ejection System Design

11.3 Ejector System Analyses and Designs
There are many different components that can be used for ejection system design. The most
common components and their usage are next discussed.

11.3.1 Ejector Pins
Ejector pins are typically hot forged and cylindrically ground from hard steels (such as H13).
Subsequently, the pins are nitrided and polished to provide a very hard and smooth surface for
low wear and friction. Ejector pins are available from several suppliers in standard diameters
(ranging from 1 mm to 25 mm) and lengths (from 150 mm to 500 mm). Typically, mold
makers cut and grind standard ejector pins to the finished length and contour specified in the
mold design. However, ejector pins may be custom ordered with varying options including
different materials or surface treatments, precise diameters or lengths, threads for mating
with the ejector plate, flats, grooves, etc.
While ejector pins are available in a range of diameters and lengths, especially long pins
with small diameters should be avoided. The reason is that such slender pins tend to buckle
under load. As shown in Figure 11.16, the loading of an ejector pin corresponds to a column
with the top end supported by the bore of the ejector hole, and the bottom end pinned by
the ejector retainer plate. If the compressive load become too large, then the pin may bow or
buckle in an unknown direction.
F

Figure 11.16: Buckling model of ejector pin

11.3 Ejector System Analyses and Designs

279

For this load case, Euler theory indicates that the critical load, Fbuckling, is [41]:
Fbuckling =

π2 E I
(0.7 L)2

(11.13)

where E is the modulus of the material, I is the moment of inertia, and L is the length of the
ejector pin. For a circular ejector pin of radius R, the moment of inertia is π R4. Since stress
is defined as force per unit area, the critical buckling stress, σbuckling, may be derived as:
σ buckling =

π2 E
(0.7 L / R)2

(11.14)

To avoid buckling, the ejector pin design must satisfy the constraint:
σ pin =

Fpin
Acompression

< σ buckling =

π2 E
(0.7 L / R)2

(11.15)

which when solved for the pin radius R provides the following result:
1

⎛ Fpin L2 ⎞ 4
R>⎜

⎝ 63.2 E ⎠

(11.16)

Example: Calculate the minimum diameter of the ejector pins for the bezel molded of
ABS and ejected with 20 ejector pins.
An ejection force of 4700 N was estimated in a previous example, so the force on each pin
is approximately 235 N. The modulus for steel is 200 GPa. The approximate length of the
ejector pin is 0.2 m. Then, the minimum ejector pin radius to avoid buckling is:
1

⎡ 235 N ⋅ (0.2 m)2 ⎤ 4
R>⎢
⎥ = 0.93 mm
9
⎣ 63.2 ⋅ 200 ⋅ 10 Pa ⎦
Given this radius, ejector pins with a diameter of 1.86 mm would theoretically be sufficient.
A standard pin size of 2 mm or 3/32″ could be selected.
The result from this example indicated that the minimum diameter required to avoid buckling
is on the same order of magnitude as the minimum diameter required to avoid excessive
compressive stress in the pin or excessive shear stress in the molding as calculated in previous
examples. The results from the above buckling analysis and example are strongly dependent
upon the length of the ejector pin; if the pin length was longer, then the buckling constraint
would be dominant. The mold designer should perform analysis for their molding application
to confirm the driving constraint and ensure an adequate ejector design.

280

11 Ejection System Design

A small ejector pin diameter might be desired in some molding applications for aesthetic or
pin positioning requirements. If the minimum pin diameter required to avoid buckling is
greater than the desired pin diameter, then a stepped pin with a larger diameter shoulder can
be investigated. Step pins typically have a shoulder approximately 1 mm larger in diameter
than the head of the ejector pin, and a typical shoulder length of 50 mm. When necessary,
the mold designer can custom order ejector pins with multiple steps and tapers for a given
application. If a stepped ejector pin is used, however, the mold designer should ensure that a
suitable hole and clearance is specified in the support plate and core insert.

11.3.2 Ejector Blades
Ejector blades are typically large diameter ejector pins that are contoured to present a
rectangular cross section to the core insert. As shown in Figure 11.17, the ejector blade’s large
width and small thickness allow for the blade to be positioned directly below ribs. This position
is very effective since the blade applies the ejection force at the location where the friction
forces between the molding and the mold core are generated. Furthermore, the rib is stiff and
so will effectively eject nearby portions of the rib and part. Finally, the rib is not an aesthetic
surface and so should not be adversely affected by the witness mark left by the ejector blade,
though this is a potential area of stress concentration during the molding’s end-use.
The detailing of the ejector blade, shown in Figure 11.17, is very similar to that previously
discussed for ejector pins. Clearances should be provided in the support and core inserts to

Figure 11.17: Ejector blade design

11.3 Ejector System Analyses and Designs

281

allow for free actuation of the ejector blade, with the mating being provided between the
rectangular section of the ejector blade and the tightly mating surfaces in the core insert.
To provide the rectangular hole in the core insert, wire or plunge EDM is necessary. The
amount of EDM can be minimized by specifying the clearance hole close to the surface of
the mold cavity, with a typical land length equal to twice the width of the ejector blade. The
mold designer should also ensure that the length of travel between the ejector blade’s tapered
shoulder and the narrowed hole in the mold insert exceed the maximum stroke of the ejector
system. Otherwise, the molder may inadvertently seize and damage the ejector blades.
The compressive stress in ejector blades and the imposed shear stress on the molding by the
ejector blades do not usually constrain the design of the ejector blades. Due to their small
thickness, however, buckling can be a concern. For this reason, the thickness of the ejector
blade should be set to the full thickness of the rib. The buckling is governed by Eq. (11.13),
with the moment of inertia is defined as:
I =

1
W H3
12

(11.17)

where W and H are the width and thickness of the ejector blade. The governing relationship
between the stress in the blade and the buckling stress is:
Fblade < Fbuckling =

1 π2 E ⋅ W H 3
12 (0.7 L)2

(11.18)

The thickness of the ejector blade is usually set to the thickness of the opposing rib or wall.
The maximum length of the blade section can then be verified as:
1

⎛ 1.7 ⋅ E ⋅ W H 3 ⎞ 2
L<⎜

Fblade



(11.19)

Example: Calculate the maximum length of the ejector blade for the bezel molded of ABS
and ejected with 20 ejector blades.
An ejection force of 4700 N was estimated in a previous example, so the force on each
blade is approximately 235 N. The modulus for steel is 200 GPa. The thickness and width
of the candidate ejector blade are preliminarily designed as 1 mm and 6 mm, respectively.
Then, the maximum length of the ejector blade to avoid buckling is:
1

⎡1.7 ⋅ 200 ⋅ 109 Pa ⋅ 0.006 m ⋅ (0.001 m)3 ⎤ 2
L<⎢
⎥ = 93 mm
235 N


In this molding application, the maximum blade length is computed as 93 mm. In the
mold design of Figure 11.17, the actual blade length (from the cavity surface to the taper)
is 93.8 mm. As such, this blade design is marginal. The mold designer could choose to
add additional blades to reduce the ejection force per blade, use a wider or thicker blade
if available, or use a push pad with a constant rectangular section through the rib to allow
for the use of a thicker ejector blade.

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11 Ejection System Design

11.3.3 Ejector Sleeves
The function of an ejector sleeve is similar to that of an ejector blade, in that both are typically
used to push on a vertical section of the molded part. The design of the ejector sleeve varies
significantly, however, since it is a hollow cylinder that slides along a fixed core pin to provide
an ejection force at the bottom surface of a molded boss. Ejector sleeves are very effective
components for part ejection, since they push on a stiff portion of the part at a location where
friction forces between the molding and the core occur.
A typical ejector sleeve assembly design is provided in Figure 11.18. In this design, a highly
conductive core pin is seated in the rear clamp plate and secured with a socket head set screw.
The core pin passes through the rear clamp plate, ejector plate, ejector retainer plate, support
plate, and core insert to hollow out the desired portion of the mold cavity. The ejector sleeve
is held by the ejector retainer plate and passes through the support plate and core insert. In
the design of detail A, the end of the ejector sleeve is coplanar with the top of the boss and
the adjacent rib. During the ejection cycle, the ejector plate is moved forward, causing the
ejector sleeve to slide along the core pin and push the boss off the core pin. Just like the ejector
pins and blades, the reverse actuation of the ejector retainer plate causes the ejector sleeve to
retract into the core insert for the next molding cycle.
Given the geometry of the ejector sleeve, there are typically no issues related to stress or
buckling. However, the detailed design of the ejector sleeve is especially critical since it slides
along between a stationary core pin and the stationary core insert. The axial location of the

Figure 11.18: Ejector sleeve design

11.3 Ejector System Analyses and Designs

283

ejector sleeve is governed by the concentric mating of the ejector sleeve with the ejector hole in
the core insert. Since the core pin is internal to the sleeve, the wall thickness and concentricity
of the molding around the core pin is governed by the tolerance stack-up of the ejector hole,
ejector sleeve, and core pin. To reduce dimensional variations in the molded part, clearances
for venting should be minimized. Details B to F Figure 11.18 provide examples of clearances
in the various mold plates. The mold designer should ensure that the core pin has a suitable
clearance through the ejector plate and ejector retainer plate, otherwise a slight lack of
concentricity between the ejector sleeve and core pin may cause the sleeve to bind.

11.3.4 Stripper Plates
The function of a stripper plate is similar to that of an ejector sleeve, in that both are typically
used to push on a periphery of the molded part. The design of the stripper plate varies
significantly, however, since it normally pushes on most or all of the entire periphery of the
molded part(s). For this reason, the stripper plate has a significantly larger area than a single
ejector sleeve and a completely different construction.
The design of a mold with a stripper plate is shown in Figure 11.19. In this design, the stripper
plate replaces the B plate and is made to float between the A plate and the support plate. To
locate the core inserts, a locating dowel has been placed to mate the center of the core inserts
with the support plate. Socket head cap screws (not shown) are used to securely fasten the

Figure 11.19: Stripper mold design

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11 Ejection System Design

Figure 11.20: Stripper plate actuation

core inserts to the support plate. Portions of the stripper plate are designed to extend beneath
the bottom surface of the molding, but not to interfere with the outer surfaces of the core
inserts.
As shown in Figure 11.20, the moldings are ejected by the opening of the mold when the
stripper bolt engages the stripper plate and pulls the moldings off the cores. Since the stripper
plate fully engages the bottom of the part, the ejection forces are uniformly distributed across
the moldings resulting in low imposed stress, little deformation, and reliable ejection. One
interesting aspect of this stripper plate design is that the ejector retainer plate, ejector plate,
and leader pins serve no purpose and can be eliminated from the mold, such that the support
plate may be used as the rear clamp plate. More conventional designs, however, use the forward
actuation of the ejector plate to engage the stripper plate to eject the molded parts.
There are some important items to note with regard to design details A and B, which are
identified in Figure 11.20 and magnified in Figure 11.21. One significant issue with respect
to this specific molding application is the location of the parting line along the top of the
cup. From the viewpoint of mold design, the center of the rounded top would be the best
location to mate the stripper plate with the core insert since it would provide a reliable sliding
surface. However, this mating location would result in an undesirable and possibly sharp
witness line. As such, the mating location has been moved towards the interior of the core
insert. While this provides an improved witness line location and a significant push area for
the stripper plate to push on the molded cup, it also results in a sharp edge at the parting
line of the stripper plate. This sharp edge can damage the vertical surface of the core insert,
and will likely quickly wear. For this reason, the mold designer may wish to avoid the use of
a stripper plate or request the redesign of this section of the cup to provide a flat push area
to mate with the stripper plate.

11.3 Ejector System Analyses and Designs

285

Figure 11.21: Potential stripper plate detailed design issues

11.3.5 Elastic Deformation around Undercuts
The molding of the lid shown in detail B of Figure 11.21 presents an entirely separate problem
related to the ejection of the molded undercut from the core insert. As shown in this detail,
the side wall of the molded lid must deform so that the lip of the lid can escape the undercut
on the core insert. If the amount of strain caused by ejection is within the elastic limit of the
material, then such undercuts can be reliably molded and ejected from the mold without
special concerns. In fact, stripper plates are ideal for such ejection since they provide very
uniform ejection forces that are nearly in-line with the friction force between the molding
and the core.
The strain, ε, caused by an undercut during ejection can be readily estimated as the amount
of deflection, δ, that the part is required to undergo divided by the distance, L, across which
the deflection is applied, or:
ε=

δ
L

(11.20)

Appendix A provides some material properties for various plastics, including the strain to
yield. It is observed that most plastics have a strain to yield above 2%, which is a reasonable
mold design guideline. The exception is heavily filled materials, which have a lower elastic
limit and tend to fail in a brittle manner.
The ejection force for a part that is elastically deformed during ejection can also be estimated.
First, the stress in the deformed section of the part can be calculated as the imposed strain
multiplied by the modulus of the material, E:
σ =Eε

(11.21)

This stress acts as a hoop stress around the perimeter of the part, similar to the previous
analysis, the normal force is estimated as:

286

11 Ejection System Design

Fnormal = σ Aeff

(11.22)

The ejection force may be estimated as a function of the normal force, the coefficient of
friction, μs, and the draft angle, φ. Combining the above terms provides:
Feject = μs ⋅ cos(φ) ⋅ E

δ
⋅ Aeff
L

(11.23)

Example: Verify that the lid may be elastically ejected off the core with the undercut.
Estimate the ejection force and stress exerted on the part during ejection.
The relevant dimensions of the part geometry are provided in Figure 11.22.
The strain in the part is:
ε=

δ
1 mm
=
= 1.3%
L 77 mm

which is significant but not excessive. The height of the undercut section of the lid is
approximately 3 mm, with an effective area under stress of 80 mm2. Assuming a coefficient
of friction of 0.5 and a draft angle of 0, then the ejection force is estimated as:
Feject = 0.5 ⋅ cos(0) ⋅ 2.3 ⋅ 109 Pa ⋅

1 mm
⋅ 725 ⋅ 10−6 m 2 = 1,200 N
77 mm

Fortunately, this force is approximately the same as the ejection force required to eject the
cup on the opposite side of the mold, since unbalanced ejection forces can lead to uneven
wear in the mold. To minimize this wear, the thickness of the stripper plate and the size of
the guide bushings can be increased. Additionally, the stripper plate should be actuated
at two locations that are in-line with the axis of the cavities instead of one central point
as indicated in Figure 11.20.

Figure 11.22:

Elastic ejection of undercut

11.3 Ejector System Analyses and Designs

287

The shear stress on the undercut portion will be approximately:
τ=

Feject
π φh

=

1,200 N
= 1.7 MPa
π ⋅ 0.077 m ⋅ 0.003 m

which is significantly less than the 44 MPa yield stress of the ABS. Accordingly, the ejection
of this lid with this undercut by a stripper plate should be acceptable.

11.3.6 Core Pulls
The term “core pull” or “side action” generally refers to a device that retracts a core in a
direction that is not parallel to the opening direction of the mold. Core pulls allow the molding
of parts with relatively large, complex undercuts that might otherwise not be economically
feasible to produce.
For example, the product design of the bezel may require the molding of lateral bosses and
a window as shown in Figure 11.23. To mold these features, an extra mold insert is required
to provide the steel around these features. This mold insert must be removed prior to the
opening of the mold and the actuation of the ejection system.

Figure 11.23: Undercut features in bezel

288

11 Ejection System Design

Figure 11.24: Layout of moving core

Figure 11.25: Moving core mold design layout

11.3 Ejector System Analyses and Designs

289

To design the core pull, it is necessary to first layout the moving mold insert. One design for
the moving core for the bezel is shown in Figure 11.24. In this design, cavity and core features
are provided to form the bosses, ribs, and window. A key is profiled along the bottom of the
core insert to provide a sliding fit with a matched keyway in the B plate and core insert. This
keyway will vertically retain the moving core in the mold and also guide the moving core
during actuation. A chamfer is provided on the leading edges of the moving core to avoid
damaging the mating surfaces of the mold.
The preliminary mold assembly with the moving core is shown in Figure 11.25. The A plate,
cavity insert, B plate, and core insert all required modifications to accommodate the moving
core. Any significant vertical displacement would cause flashing along top of the molding
or the bottom of the rib. For this reason, an interlock has been provided between the front
of the moving core and the core insert to prevent the moving core from shifting due to the
pressures imposed by the melt on the core. The sides of the moving core will prevent lateral
displacement and flashing along the sides of the core. Also, a clearance has been provided
between the front surface of the moving core and the core and cavity inserts. This clearance
ensures that entire clamping force of the actuation cylinder is applied to the window core to
prevent flashing of the window.
To complete the design of the core pull, the actuation mechanism must be designed. The first
step is to estimate the required actuation force, Fcore_pull, which is directly related to the melt
pressure, Pmelt, exerted on the projected area of the moving core, Acore_projected.
Fcore_pull = Pmelt ⋅ Acore_projected

(11.24)

Example: Calculate the maximum force required to maintain the core pull in the forward
position during the molding process.
The core pull is approximately 22 mm wide by 10 mm in height. While portions of
the front face of the core pull are not subjected to the melt pressure, the analysis will
make conservatively assume that the projected area is 220 mm2. Also, the analysis will
conservatively assume a melt pressure of 200 MPa. Using these assumptions, the maximum
expected force is:
Fcore_pull = 200 ⋅ 106 Pa ⋅ 220 ⋅ 10−6 m 2 = 44,000 N
which is approximately 4 tons of force! This result may be initially surprising, but the mold
designer should remember that the moving core must provide a closing force equivalent to
the clamp force required for the production of a similarly sized molding. Larger moving
cores will require proportionally larger actuation forces.
Once the actuation force is determined, the mold designer must select the type of actuator.
There are three common types: hydraulic, electric, or pneumatic. While an exhaustive
discussion is beyond the scope of this text, the reason for the predominance of hydraulic
actuators will be briefly discussed. First, hydraulic actuators have a power density an order
of magnitude above that of pneumatic or electric actuators. This increased power density
means that hydraulic actuators are much more compact and common than the other types.

290

11 Ejection System Design

As a result, hydraulic cylinders are widely available at low cost with an extremely broad range
of bore diameters and travel lengths. Furthermore, hydraulic actuators are easily integrated
with the hydraulic and electric systems on many molding machines. Accordingly, molders can
often utilize molds with hydraulically actuated moving cores without any need for auxiliary
equipment.
The mold designer must select an actuator that provides the appropriate actuation force and
travel. The travel must be sufficient for the moving core to clear the envelope of the features
of the molded part. If a hydraulic actuator is used, then the diameter of the bore can be
calculated as:
Dhydraulic_bore =

4 Fcore_pull
π Phydraulic_fluid

(11.25)

where Phydraulic_fluid is the available pressure of the hydraulic fluid or compressed air.
Example: Calculate the travel and bore diameter of the hydraulic cylinder to actuate the
moving core for the bezel.
To calculate the bore diameter, it is necessary to know the available hydraulic pressure.
While most hydraulic systems are designed for a pressure of 20.7 MPa (3,000 psi), many
molding machines and auxiliary systems are operated at 10 MPa. Assuming the actuation
force of 44 kN, the bore diameter can be calculated as:

Figure 11.26:

Mold design with actuated ejectors

11.3 Ejector System Analyses and Designs

Dhydraulic_bore =

291

4 ⋅ 44,000 N
= 75 mm
π ⋅ 10 ⋅ 106 Pa

Inspection of the layout provided in Figure 11.25 indicates that the required travel is
15 mm. A standard cylinder with a bore of 82.55 mm (3.25 in) and a stroke of 25.4 mm
(1 in) is selected.
The finished mold design with the retracted core is shown in Figure 11.26. The design
requires risers to be inserted between the hydraulic cylinder and the mold to allow for the
piston rod to be actuated with the moving core; the risers must be of sufficient strength
to avoid flexure under load when the cylinder pushes the moving insert against the mold
core. The height of the risers could have been reduced or eliminated by reducing the length
of the moving core and allowing the piston rod to travel within the keyed profile of the
mold. This height reduction is desirable since it reduces interference with the actuator,
molding machine, and operator. It should also be noted that the cylinder attachments
must be located on only one side of the mold.
To provide as safe and efficient a mold as possible, the mold designer should specify the use
of limit switches to confirm that the moving core is in its forward or retracted position. These
position signals can be used by the molding machine to ensure that the moving cores are
properly positioned so as to not damage the molded parts or the injection mold during mold
opening or part ejection. Furthermore, the mold designer should strive to design the moving
core such that the mold opening or part ejection does not damage the mold if the moving
core is improperly positioned. Consider, for example, the design shown in Figure 11.25. If
the mold is opened and the part ejected with the moving core in its forward position, it is
most likely that the plastic part will be sheared off at the primary rib by the actuation of the
nearby ejector sleeve and ejector blade. Obviously, this event is undesired and should not
occur for a properly set molding process. However, such events do occur and molders greatly
appreciate a robust mold design that can withstand intermittent abuse without reworking
the ejector pins, blades, sleeves, or moving cores.

11.3.7 Slides
Core pulls are quite common since they allow moving inserts to be actuated in different
directions, strokes, and times. However, core pulls require actuators, auxiliary control, and
significant space. For this reason, mold designers often prefer to use sliding cores that are
actuated by inclined angle pins.
One such mold design is shown in Figure 11.27. In this design, a bronze gib is located in the B
plate to provide a lubricated sliding surface for the moving insert. The core insert is provided
with an inclined can surface that mates with the angle pin. As the mold opens and closes,
the angle pin engages the sliding core, causing the core to move in and out. A retainer plate
secured to the B plate prevents the sliding core from falling out of the gib.

292

11 Ejection System Design

Figure 11.27: Moving slide layout view

Figure 11.28: Moving slide detail view

11.3 Ejector System Analyses and Designs

293

The detailed design is shown in Figure 11.28 and warrants further discussion. The angle pin
is located through the use of an angle pin insert, which has a flat surface to orient the angle
pin in the direction of the sliding action. While there are many ways to design a slide for side
action, the angle pin insert is retained between the core insert and a heel block by socket head
cap screws in this design. On the moving side of the mold, the bronze gib is located with
dowels and fastened with cap screws to a pocket cut in the B plate and core insert. The gib
provides a key way into which guides the sliding core. The sliding core itself is very similar
to that previously shown in Figure 11.24.
In operation, the clamping of the mold causes two forces to be imposed on the sliding core.
First, the angled surface on the heel block contacts the angled surface on the slide to force
the slide laterally against the core insert; this lateral force withstands the melt pressure and
prevents flashing of the ribs, bosses, and window. Second, the cavity insert contacts the top
surface of the slide, which provides a downward clamping force to prevent deflection and
flashing around the parting line of the molding. It should be noted that the angle pin does not
provide the lateral force and is not subjected to significant stress in this design. Well designed
clearances, tolerances, and fits are crucial to the function and longevity of the sliding core.
The application of core slides for side action is limited with respect to the slide direction
and stroke. To avoid excessive friction, the bronze gib may be drilled and filled with graphite
lubricant. However, any friction can cause sticking of the core slide during actuation so the
inclined angle, φangle_pin, between the axis of the angle pin and the mold opening direction
is limited to about 20 degrees. The stroke of the slide, Sslide, is then a function of the contact
length of the angle pin, Langle_pin, as:
Sslide = Langle_pin ⋅ sin(φangle_pin )

(11.26)

Example: Calculate the required length of the angle pin for the bezel mold.
The mold design uses an angle pin insert with a 20 degree incline. The required travel is
12 mm. Then, the contact length of the angle pin is:
Langle_pin =

Sslide
12 mm
=
= 35 mm
sin(φangle_pin ) sin(20°)

An additional 25 mm of length is required to mate the angle pin with the angle pin insert.
The length of the angle pin will be approximately 60 mm, which will be cut to length and
finished during mold assembly. This length was used in the design of Figure 11.24.
Just as with actuation of core pulls, improper actuation of slides is a significant issue. For
example, a curious operator or visitor may be intrigued with a mold in a molding machine,
and naively move the sliding core. If the mold closes with the core not in its outwards position,
then the angle pin will improperly contact the top surface of the slide rather than the inclined
bore, and cause the angle pin to bend under even a relatively low mold closing force. To
prevent this issue, the mold designer may place a compression spring between the front of
the sliding core and the core insert to maintain the core slide in its outward position when

294

11 Ejection System Design

the mold is not closed. In addition, the retainer plate can be designed with a limit switch to
provide a signal that the core is in its outward position. If multiple sliding cores are used,
then the multiple switches can be wired in series to indicate that all cores are in the proper
position and the mold is ready to be closed.

11.3.8 Early Ejector Return Systems
This chapter began with an overview of a basic ejector system that used the mold’s return pins
to retract the ejector assembly upon mold closure. While this design is simple and reliable,
some molders prefer the ejector assembly to be returned prior to the closing of the mold. There
are many ways to provide for early ejector return, but the two most common means are



positive return with a threaded ejector knock-out rod, and
the use of compression springs.

Each of these will be briefly discussed. It should be noted that there are many other ways
to provide early ejector return, including pneumatic cylinders, hydraulic cylinders, electric
motors or solenoids, mechanical cams, and others. However, these systems are less common
and so are not detailed.
The term “positive return” refers to the confirmed resetting of the ejector system. As shown
in Figure 11.29, one design threads the molding machine’s ejector knock-out rod(s) into the
ejector plate. After the molding machine pushes the knock-out rods forward to actuate the
ejector assembly and eject the moldings, the molding machine can then pull the knock-out
rods back. Since the knock-out rods are threaded into the ejector plate, the entire ejector

Figure 11.29: Positive ejector return with threaded knock-out rods

11.3 Ejector System Analyses and Designs

295

assembly is returned prior to the closure of the mold. As an added benefit, the molding
machine’s ejector knock-out system are typically instrumented with position transducers,
so positive return provides feedback as to the actual position of the ejection system prior to
mold closure. To properly interface the ejection system with the molding machine, the mold
designer should confirm the location(s), diameter, and thread of the knock-out rods with
the molder.
While threaded knock-out rods are relatively simple to design and operate, some mold makers
and molders use compression springs to return the ejector assembly prior to mold closure.
One design is shown in Figure 11.30, which uses several compression springs located between
the support plate and the ejector retainer plate. When the knock-out rod actuates the ejector
assembly, the springs are placed in compression. When the molding machine retracts the
knock-out rod(s), the compression springs will tend to reset the ejector assembly. A few notes
on the design of compression springs are warranted. First, a support pin should be used in
the center of the compression spring to avoid spring buckling when the free length of the
spring exceeds four times the diameter of the spring; the support pin should be threaded
into the support plate or rear clamp plate to locate the spring. Second, the range of spring
compression should be limited to about 40% of the free length of the spring. The diameter
and gauge of the spring should be selected to provide a return force that is a fraction (for
example, one-fourth) of the required ejection force.
Both these early return systems are very common, but the positive return with threaded
knock-out rods provides several advantages. First, positive return provides feedback to the
molding machine about the position of the ejector system. Second the positive return system
requires fewer changes to the mold design. Third, the compression springs limit the range of
ejector travel and can be damaged or cause damage if the molding machine forces the ejector
assembly beyond the compression spring’s range of free travel. Fourth, compression springs
and ejector systems tend to wear such that molds with compression springs frequently fail to
completely return the ejector system after an indefinite number of molding cycles. In either
case, if early return of the ejectors needs to be guaranteed prior to mold closure, then the mold
designer should include a limit switch that is active when the ejector system is fully reset.

Figure 11.30: Early ejector return with compression springs

296

11 Ejection System Design

11.3.9 Advanced Ejection Systems
This chapter has provided analysis and design of the most common ejection system components and systems. There are many different and more advanced designs used in practice.
While an exhaustive analysis if outside the scope of this book, some of the more common
but advanced ejector system designs are discussed in Section 13.9. For further information,
the mold designer is referred to the suppliers of ejection system components.

11.4 Chapter Review
The most typical ejector system designs consist of the ejector plate, leader pins, ejector pins,
and the ejector retainer plate. In operation, the molding machine’s ejector knock-out rod forces
the ejector plate forward, which in turn drives the ejector pins forward to strip the molded
parts off the core. The knock-out rod is then retracted so that the closing motion of the mold
can force the leader pins to retract with the entirety of the ejector assembly. While this ejector
system design is used in a predominance of molds, molding applications place many diverse
requirements on the ejection system. As a result, mold designers can be expected to utilize other
components including contoured ejector pins, ejector blades, ejector sleeves, stripper plates,
core pulls, angle pins, slides, and springs. When necessary, more advanced ejection systems
may be provided by third party suppliers or custom designed by the mold designer.
The design of the ejection system is governed first by the parting surfaces of the mold and the
required ejection directions. If more than one ejection direction is needed, then core pulls,
slides, or other components must be planned prior to the detailed design. Next, the ejection
forces should be estimated as a function of the geometry and thickness of the part, the draft
angle, the coefficient of friction, the material properties, and the processing conditions. Given
the ejection force, the mold designer determines the number, size, and location of the ejectors
to prevent excessive stress and buckling of the ejection system components as well as excessive
shear stress exerted on the molding(s). In general, mold designs using many small ejectors
are more expensive to make and maintain but provide greater flexibility and more uniform
ejection than a mold design using fewer, larger ejectors.
After reading this chapter, you should:
• Understand the design and function of basic ejection systems;
• Understand the different objectives that must be satisfied in good ejection system
designs;
• Be able to identify the mold parting surfaces and ejection directions for a given molded
part geometry;
• Know how to estimate the ejection forces for a given molding application;
• Know how to estimate the required push area and perimeter of all ejectors to avoid excessive
compressive stresses in the ejectors and excessive shear stresses in the molded parts;

11.4 Chapter Review






297

Know how to specify the type, number, size, and location of different ejectors such as
straight pins, contoured pins, stepped pins, blades, and sleeves;
Know how to detail the design of various ejection system components to avoid interferences and facilitate mold assembly;
Know how to design ejector pins and blades to avoid buckling;
Understand the function of stripper plates, core pulls, slides, and other more advanced
ejection system components.

With the ejector system design completed, the mold design is nearly completed. However,
structural analysis and design is required to ensure that the mold can withstand the melt
pressures that will be applied for many cycles.

12

Structural System Design

Injection molds are subjected to high levels of pressure from the heated polymer melt. When
this pressure is integrated across the surfaces of the mold cavities, forces result that typically
range from tens to thousands of tons. The structural design of the mold must be robust
enough to not only withstand these forces, but also to do so while producing high quality
molded products.
To develop a robust structural design, the mold designer should understand the relationships
between the pressures, forces, and stresses in an injection mold. Figure 12.1 shows the typical
flow of stresses through the mold, platens, and tie-bars. During molding, the melt pressure is
exerted against all surfaces of the mold cavities. This pressure results in both compressive and
shear stresses in the cavity inserts, core inserts, and support plates. This mixed state of stress is
indicated by the diagonal arrows in Figure 12.1. The molding machine’s platens are also under
a significant state of bending to transfer the forces to the tie bars, which are in tension.

Figure 12.1: Flow of stresses during molding

300

12 Structural System Design

12.1 Objectives in Structural System Design
In general, the mold designer wishes to provide a structural design for the mold that will not
break due to fatigue across many molding cycles, excessively deflect under load, and will not
be overly bulky or expensive. These objectives can be explicitly stated as:




Minimize the stress,
Minimize deflection, and
Minimize cost.

Each of these objectives will be briefly discussed after which the detailed analysis and design
of molds are presented.

12.1.1 Minimize Stress
The state of stress varies significantly between the moving and the stationary sides of the
mold. For most molds, the cavity inserts are directly supported by the top clamp plate and
the stationary platen. As such, the cavity inserts are generally in a state of pure compression
so very little out of plane bending occurs. On the moving side, however, the pocket required
to house the ejector assembly provides no support for the core inserts. As a result, the core
inserts and support plates must transmit the load via both compressive and shear stresses,
which will tend to result in significant plate bending.
Figure 12.2 plots the predicted von Mises stress in a hot runner mold for the laptop bezel
when the surfaces of the mold cavity are subjected to 150 MPa of melt pressure. The von Mises
stress, σMises, is a commonly used criterion to predict failure, which is defined as:
σ Mises =

σ12 − σ1 σ 2 + σ 22 < σ limit

(12.1)

where σ1 and σ2 are the first and second principle stresses. To avoid failure, the von Mises
stress should be less than some specified stress limit, σlimit.
The limit stress is usually determined by two primary concerns. The first concern is that the
stress should not be so high so as to plastically deform the mold. When a material is subjected to
stress, it will deform, or strain. For most materials, the amount of deformation is proportional
to the applied stress. The ratio of stress to strain is related to the elastic modulus, E, as:
ε=

σ
E

(12.2)

where ε is the strain that results from an applied stress, σ. A material with a higher elastic
modulus will tend to deform less given an applied stress.
The stress-strain behavior of two common mold metals, P20 and aluminum QC7, are
plotted in Figure 12.3. P20 has a much higher modulus than QC7, meaning that it will

12.1 Objectives in Structural System Design

Figure 12.2: Von Mises stresses during molding

1000
900
QC7
P20

800

Stress (MPa)

700

 Yield = 830 MPa
E P20 = 205 GPa

600
500
400

 Yield = 420 MPa

300

E QC7 = 71 GPa

200
100
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Strain (%)

Figure 12.3: Stress-strain behavior of P20 and Al 7076

0.8

0.9

1

1.1

1.2

1.3

301

302

12 Structural System Design

exhibit less strain and deformation given an applied load or stress. The yield stress is the
point at which the material departs from its linear behavior. The yield stress is also the stress
at which the material plastically deforms, meaning that the components with a higher stress
will not return to its original shape after the load is removed. Once the material exceeds
the yield stress, it can continue to carry load up to the ultimate stress, after which it fails
completely.
All mold designs should be engineered to operate at stresses lower than the yield stress. With
respect to relating the yield stress to the limit stress, there are two common approaches. One
approach is to simply set the limit stress equal to the yield stress, but then assume a worst
case scenario with respect to the load condition. For example, a mold designer working with
P20 could assume a limit stress equal to the yield stress of 830 MPa. To ensure the mold does
not yield under load, the mold designer should then perform analysis assuming the highest
melt pressures that the mold would ever be expected to see, perhaps 200 MPa.
Another approach is to set the limit stress equal to the yield stress divided by a factor of
safety:
σ limit =

σ yield
f

(12.3)

where f is the factor of safety, whose value is related to the level of uncertainty and the cost
of a potential failure. Typical values range from 1.5 for non-critical mold components to 6.0
for hoist rings. When a factor of safety is used, the mold designer should apply the expected
melt pressure for the mold, perhaps 100 MPa. To avoid over-designing the mold, the mold
designer should not jointly apply a factor of safety with the worst case scenario.
While the mold designer might expect that a design based on the yield stress with a conservative
factor of safety would be robust, this approach may result in molds that fail after a significant
number of molding cycles. The reason is that the continued cycling of clamping loads and
melt pressure in the mold cavity causes cyclic stresses as shown in Figure 12.4. Each stress
cycle allows small cracks in the mold to open and close, causing a few more crystals at the
crack tip to fail. Over the course of thousands of molding cycles, these cracks will grow and
propagate through the mold like a wedge driven by a hammer. Once the crack reaches a
critical size, the stress concentrations around the crack will cause the mold to fail even when
the mold was properly designed with a limit stress specified well below the yield stress. This
failure mode is generally referred to as fatigue.
Fatigue is a well understood mechanism, and the behavior of various materials has been
characterized through cyclic stress testing to a million cycles or more. In general, the number
of cycles that a mold can withstand will decrease with the applied stress. Figure 12.5 plots
the expected number of cycles before failure due to fatigue as a function of the imposed
stress; this data is generally referred to as “s-n” curves where the “s” implies stress and the
“n” implies number of cycles. The “endurance stress” is defined as the stress at which a
theoretically infinite number of stress cycles can be applied without failure. For most steels,
the endurance stress is approximately one-half the yield stress. For P20, the endurance stress
is approximately 450 MPa.

12.1 Objectives in Structural System Design

303

500
450
400

Stress (MPa)

350
300
250
200
150
100
50
0
0

20

40

60

80

100

120

Time (s)

Figure 12.4: Cyclic stresses in molds

The data in Figure 12.5 indicate that QC7 has a much lower endurance stress than P20. There
are two very important differences in the behaviors of QC7 and P20. First, the s-n curve for
QC7 has a greater slope than that for P20. Second, QC7 (and all known aluminums) do
not exhibit an endurance stress limit. In other words, the continued cycling of any stress on
aluminum will eventually cause failure due to fatigue. For this reason, the mold designer
working with aluminum should carefully select the limit stress according to the desired
number of molding cycles. If the mold is to be used for less than 1000 molding cycles, then the
mold designer may select a limit stress equal to the yield stress of 545 MPa. If approximately
10,000 molding cycles are expected, then the allowable limit stress drops to 370 MPa. If the
mold is to be operated for up to a million molding cycles, then the limit stress should be set
to 170 MPa.
To summarize, the limit stress is specified according to whether issues related to yielding or
fatigue will dominate during the mold’s operation:
⎛ σ yield

, σ endurance ⎟
σ limit = min ⎜
f



(12.4)

If the mold is to be designed for a low number of molding cycles, then the limit stress can be
set to the yield stress and designed using a safety factor or a worst case scenario. If the mold
is to be operated for a large number of molding cycles, then the endurance stress should
be used as the limit stress. These data are provided for some common mold materials in
Appendix B.

304

12 Structural System Design

1000

Stress (MPa)

 Yield = 830 MPa

QC7
P20

 Endurance = 456 MPa
 Yield = 545 MPa

100
1.0E+02

1.0E+03

1.0E+04

1.0E+05

1.0E+06

1.0E+07

Number of Cycles

Figure 12.5: Stress-failure curves for QC7 and P20

12.1.2 Minimize Mold Deflection
While excessive stresses in the mold components can cause damage to the mold, excessive
mold deflection is an even greater concern in many molding applications. The primary
reason is that excessive mold deflection can cause flashing at the parting lines between the
core and cavity inserts. In tight tolerance applications, mold deflection can also cause part
dimensions to be out of specification. As such, the mold design may be driven more by the
need to minimize deflection rather than minimizing stress.
Figure 12.6 plots the deflection of the mold and platens for the stress distribution shown in
Figure 12.2. It is observed that the maximum mold deflection occurs at the center of the mold
cavity, with the core surface deflecting 0.24 mm to the left and the cavity surface deflecting
0.12 mm to the right. As a result, the melt pressure in the mold cavity causes the surfaces
to separate by a total of 0.36 mm (0.014 in). This deflection will cause any nearby parting
lines to open a similar amount. Since this amount is much greater than the vent thickness
(typically on the order of 0.02 mm), a significant amount of flashing is expected. The mold
design must be improved to reduce this deflection.1
1

The contours of Figure 12.6 indicate that there is platen deflection as well. Mold designers and molders
usually assume platens to be flat and infinitely rigid. While outside the scope of this book, platen deflection
can be a significant issue. In Figure 12.6, the deflection of the stationary platen is approximately 0.04 mm,
roughly twice that of the moving platen. The reason is that the mold’s ejector housing tends to transfer
forces closer to the sides of the moving platen so there is less applied load and deflection in the center of
this platen compared to the deflection of the stationary platen.

12.1 Objectives in Structural System Design

305

Figure 12.6: Deflection during molding

12.1.3 Minimize Mold Size
The mold designer can investigate different mold materials and sizes to reduce the mold
stress and deflection. A review of the material properties in Appendix B will reveal that harder
materials (such as H13) can withstand much higher stresses than softer materials (such as
1045 or QC7). However, the mold designer should be aware that all steels have nearly the same
elastic modulus, around 200 GPa. As a result, the mold designer can not change the deflection
by steel selection, but rather must resort to changing the geometry of the mold.
The simplest method to reduce deflection is to increase the thickness of plates. As later
analysis will show, this approach is effective since the stiffness of the mold plates is related to
the cube of the plate thickness. Even so, the repeated use of very large and thick plates can
result in an overly heavy and expensive mold with a stack height that limits the availability
of molding machines. For this reason, the mold designer should seek to minimize the size
of the mold through appropriate analysis and careful specification of plate thicknesses and
support structures such as pillars and interlocks.

306

12 Structural System Design

12.2 Analysis and Design of Plates
In mold design, the term “plate” refers to a prismatic or rectangular structural member with
a length and width typically greater than the thickness. The “face” of the plate generally refers
to the top and bottom surfaces of the plate that span the width and length directions. The
“sides” of the plate refer to the four sides of the plate that traverse the thickness direction.
Mold plates are widely available from a number of suppliers in a variety of sizes and materials.
Plates can be provided oversized with a slight (1 mm) stock allowance, or finish ground to
tolerances on the order of ±0.02 mm.
The majority of the mold consists of plates, including the top clamp plate, A plate, cavity
inserts, core inserts, B plate, support plate, ejector plate, ejector retainer plate, and the rear
clamp plate.2 Each of these plates is typically subjected to a load on one face of the plate. While
the sides of the plate may be constrained by surrounding plates, the majority of the applied
load is carried by compressive and shear stresses and thus transmitted through the thickness
and across the plate. Plate compression and bending are next separately analyzed.

12.2.1 Plate Compression
If the plate is fully supported by subsequent mold plates and the mold platen (as typical on
the stationary side of the mold), then all plates are in compression and there is negligible
plate bending. It should be noted that compressive forces due to mold clamping will tend
to cause uniform compressive stresses through the mold plates. The compressive stress, σ, is
defined as the force, F, per unit of compressed area, Acompression:
σ =

F
Acompression

(12.5)

The strain, ε, that develops is the stress divided by the elastic modulus, E:
ε=

σ
E

(12.6)

The amount of deflection, δcompression, is equal to the strain multiplied by the length across
which the strain exists:
δcompression = ε L

(12.7)

Deflection due to compression is not usually an issue since 1) it is relatively small and 2) it
is uniform across the mold. As such, it does not cause flashing or significant dimensional
2

One notable exception is the design of molds with deep cores, in which the core insert is not constructed
from a plate but rather from a rod. This type of mold design has a separate set of issues that are subsequently
discussed in Section 12.3.

12.2 Analysis and Design of Plates

307

change in the molded part. As the following example will show, however, the mold designer
should slightly increase the depth of the mold cavity to compensate for plate compression if
a tight tolerance is specified on the thickness of a part with a deep cavity.
Example: Estimate the change in the stack height of the bezel mold when clamped with
200 metric tons of force.
To provide an accurate estimate of the mold deflection, the compressive stress and strain
in each plate and rail could be calculated. Each component’s deflection in the height
direction would then be computed and summed to provide the total mold compression.
However, a faster but approximate estimate can be readily provided by assuming the mold
is a monolithic block in a uniform state of compression. Figure 12.7 provides the outside
mold dimensions along with a few other critical dimensions later discussed.
The compressive stress in the mold is approximately:
σ =

F
Acompression

=

200 tons ⋅ 9807 N/ton
= 17 MPa
0.381 m ⋅ 0.302 m

This stress level corresponds to a strain of:
ε=

σ
17 MPa
=
= 8.3 ⋅ 10−5
E 205 GPa

The deflection across the entire mold during clamping is then:
δmold = ε L = 8.3 ⋅ 10−5 ⋅ 403 mm = 0.03 mm
In actual molding, the total mold deflection may be twice this amount since the rails on
the sides of the ejector housing will exhibit a significantly higher state of stress. However,
the above analysis provides a quick estimate on the correct order of magnitude.

Figure 12.7: Bezel mold dimensions for compressive stress analysis

308

12 Structural System Design

Example: Estimate the change in the height of the mold cavity due to the clamping of the
surrounding A plate with 200 tons of force.
The change in the height of the mold cavity is due to the compression of the plate
surrounding the mold cavity. To provide an accurate analysis, the compressive stress in the
plate surrounding the mold cavity is based on the area of the supporting material shown
in Figure 12.8. This area does not include the mold cavity, leader pins, and guide bushings
since these components do not transmit any of the clamping force from the stationary
to the moving side of the mold. As a result, the compressive stress in the surrounding B
plate will be somewhat higher than the 17 MPa previously calculated.
The projected area of the cavity retainer plate is approximately:
Acompression = 0.381 m ⋅ 0.302 m − 0.248 m ⋅ 0.168 m
⎡ π (0.032 m)2 π (0.020 m)2 ⎤
2
−4⎢
+
⎥ = 0.069 m
4
4



Given 200 metric tons of clamping force, this projected area leads to a compressive stress
in the plates surrounding the cavity of:
σ plate =

F
200 tons ⋅ 9807 N/ton
=
= 28.5 MPa
A
0.069 m 2

This stress level corresponds to a strain of:
ε=

σ 28.5 MPa
=
= 1.4 ⋅ 10−4
E
205 GPa

Figure 12.8: Support area around cavity

12.2 Analysis and Design of Plates

309

Given a height of 12 mm, the deflection across the height of the mold cavity during
clamping is then:
δmold = ε L = 1.4 ⋅ 10−4 ⋅ 12 mm = 0.002 mm
The change in the cavity height due to the mold clamping is very small. Furthermore, the
melt pressure will be exerted on the surfaces of the mold cavity during molding, which
will tend to counteract the mold clamping force. As such, the change in the cavity height
during molding does not need further consideration.

12.2.2 Plate Bending
If the back face of the plate is not fully supported, then shear stresses will develop and cause
the plate to bend. Plate bending is a typical issue for the plates located between the ejector
housing and the mold cavity on the moving side of the mold. The shear stress, τ, is defined
as the force, F, per unit of area in shear, Ashear:
τ=

F
Ashear

(12.8)

Figure 12.9 provides an example of a static force analysis of a portion of the bezel mold that is in
shear. While the actual shear stresses will vary with the distribution of the melt pressure across
the mold cavity, a reasonable estimate can be achieved by assuming a uniform distribution
around the perimeter of the mold cavity. As such, the area in shear is:

Figure 12.9: Shear stresses around perimeter

310

12 Structural System Design

Ashear = perimeter ⋅ height
= (2 Wcavity + 2 Lcavity ) (H b_plate + H support_plate )

(12.9)

Example: Calculate the shear stresses in the core insert and support plates if the melt
pressure exerts a total force of 200 metric tons across the mold cavity.
The dimensions from the mold design are provided in Figure 12.10.

Figure 12.10: Bezel mold dimensions for shear stress analysis

The area in shear is:
Ashear = (2 ⋅ 0.248 m + 2 ⋅ 0.168 m) (0.12 m − 0.012 m) = 0.090 m 2
The shear stress is:
τ=

F
Ashear

=

200 tons ⋅ 9807 N/ton
= 21.8 MPa
0.090 m 2

This shear stress is very low relative to the limit stress of either aluminum or steel.
The fundamental issue with plate bending in mold design is not the existence of shear stresses
in the plates, but rather the development of large deflections across any long unsupported
spans of the mold plates. Most molds utilize a moving ejector assembly, and so do not fully
support the support plate between rails of the ejector housing. Accordingly, the mold plates
behave like a beam in bending. The idealized case is represented in Figure 12.11 in which the
entire load, F, is assumed to be applied to the center of the mold section. This assumption is
made to provide a conservative estimate of the maximum deflection.
The deflection of the plate is conservatively estimated assuming the beam bending equation
with a central load as:
δbending =

F L3
48 E I

(12.10)

12.2 Analysis and Design of Plates

Fully
supported

311

F

Figure 12.11: Plate bending modeled as a beam

where L is the length of the span and I is the moment of inertia. For a rectangular section,
the moment of inertia is:
I =

1
W H3
12

(12.11)

where W is the width of the mold section in bending (in the direction normal to the section
of Figure 12.11) and H is the combined thickness of the core insert and the support plate.
Example: Compute the deflection due to plate bending in the bezel mold assuming a
loading of 200 metric tons from the melt pressure.
The width of the mold that is in bending is conservatively assumed to be equal to the width
of the mold cavity, which is shown as 248 mm in Figure 12.10. The combined height of
the core insert and support plate is 120 mm. Then, the moment of inertia is:
I =

1
0.248 m (0.120 m)3 = 3.6 ⋅ 10−5 m 4
12

The free span in bending is taken as the distance between the inside surfaces of the ejector
housing, shown as 215.9 mm in Figure 12.11. The deflection due to bending can then be
estimated as:
δbending =

200 tons ⋅ 9807 N/ton ⋅ (0.2159 m)3
= 0.056 mm
48 ⋅ 205 GPa ⋅ 3.6 ⋅ 10−5 m 4

This deflection is roughly twice the 0.024 mm deflection presented in Figure 12.6 from the
finite element analysis. The reason is that the finite element analysis assumed a uniformly
distributed load, which reduces the predicted deflection by 60% compared to the single,
centrally located load used above. The presented analysis will tend to over predict the
mold deflection due to bending, but is on the correct order of magnitude and should
lead to robust mold designs.

312

12 Structural System Design

H
W

L

F

Figure 12.12: Decomposition of separate bending areas

With respect to multiple cavity molds, the analysis should be applied to separate portions of
the mold cavity as appropriate. Figure 12.12 provides a top and side view of a layout design
for a six cavity mold. One analysis approach is to lump the melt pressure across three cavities
together to compute the applied force, F, which acts primarily on the effective width, W. It
should also be noted that the effective plate thickness, H, should not include the thickness of the
cores when the cores do not contribute significantly to the stiffness of the mold assembly.

12.2.3 Support Pillars
Plate deflection can be reduced significantly through the use of support pillars located
between the rear clamp plate and the support plate. In general, support pillars are best placed
directly under the portions of the mold cavity that generate significant force. By providing
direct support of the mold plates, shear stresses and bending close to the support pillar are
significantly reduced.
A typical design is provided in Figure 12.13. In this design, a clearance is provided through
the ejector plate and the ejector retainer plate. The support pillar is then located using a
dowel that mates the center of the support pillar to a hole is in the rear clamp plate. Since
the support plate is secured to the rear clamp plate with socket head cap screws, the support
pillar is fully secured upon mold assembly.
Unfortunately, the location of support pillars can conflict with other components including
the ejector pins and the ejector knock-out rod(s). For this reason, different layouts and sizes
of support pillars should be analyzed. If mold deflection is a critical issue, then the ejector
layout can be adjusted to provide space for several large support pillars at ideal locations. Three
potential support pillar locations are provided in Figure 12.14. At left, two smaller support
pillars are located outside the ejector blades; the support pillars are fairly evenly spaced with
regard to the span of the bezel. However, the support pillars can not be placed directly under
the bezel face without rearranging the ejector layout.

12.2 Analysis and Design of Plates

313

Figure 12.13: Typical mold design with support pillar

Another design may call for one very large support pillar at the center of the mold so as to avoid
interference with the ejector pin layout. However, this support pillar will not greatly reduce
the deflection of the mold plates since the majority of the plate bending will occur due to the
loading on the left and right sides of the molding. Furthermore, this design could conflict with
the use of a centrally located ejector rod from the molding machine, which is quite common.
As another alternative, the layout at right uses a single support pillar of intermediate size. This
design requires fewer support pillars than the first design, but has a larger span between the
support pillar and the ejector rail and so will likely provide more deflection.
The number, location, and size of the support pillars should be analyzed. One of the
complexities of the analysis is that the support pillars are structural members of finite diameter
and stiffness. This means that the support pillars will deflect under the compressive load.
The core insert and support plate will deflect with the support pillar. Furthermore, the core
insert and the support plate will exhibit bending between the support pillar and the ejector
rail. To estimate the total plate deflection, superposition must be used to add the deflection
due to compression and bending. This concept is shown in Figure 12.15.

314

12 Structural System Design

Figure 12.14: Different support pillar placements

Compression

Bending

Total

compression
bending

total

Figure 12.15: Superposition of compression and bending

To perform the analysis, the forces across the mold must be converted to a set of load cases
that is suitable for manual analysis.3 Figure 12.16 provides the conversion from the melt
pressure imposed on the surface of the mold cavity to compression and bending load cases.
The total force, F, is the integral of the melt pressure across the length and width of the cavity.
To estimate the bending, this force is broken into two equal parts applied at the center of the
span between the support pillar and the ejector rail. A force balance can then be applied to
determine the forces that must be carried by the support pillar(s) and the ejector rails.
3

Alternatively, a finite element analysis model can be constructed using the detailed mold geometry.
While such structural analysis techniques are very capable, modeling and computational burdens remain
significant barriers to routine implementation.

12.2 Analysis and Design of Plates

315

F/4
P
P
P
P
P
P
P
P
P

F/2
F/2
F/2
F/4

Figure 12.16: Compression and bending load cases

Once the load cases are developed for superposition, the previously presented compression
and bending analyses may be performed to estimate the stress in the support pillar, σ, the
deflection due to compression, δcompression, and the deflection due to bending, δbending. The
deflection across the surface of the mold cavity can be estimated as a function of the distance,
x, from the centerline of the support pillar as:
⎛ 3 L2 x − 4 x 3 ⎞
x⎞

δtotal (x) = δcompression ⎜1 − ⎟ + δbending ⎜


L⎠
L3



(12.12)

where L is the length of the span from the support pillar to the ejector rail and the range of
x is restricted to one-half the length of the span.
The maximum deflection of the mold will occur either at the center of the support pillar or
half-way between the support pillar and the ejector rail, depending on the relative magnitudes
of the deflections. This leads to the following formula for the maximum deflection under
superimposed compression and bending:
δcompression


δmax = max ⎜ δcompression ,
+ δbending ⎟
2



(12.13)

Example: Design a support pillar for the bezel mold so that the total deflection is less than
0.1 mm. Analyze the stress in the pillar and resulting deflections.
Since the support pillar will support the core insert and support plate underneath one side
of the bezel, only this local area of the mold cavity is analyzed as shown in Figure 12.17.
The top and bottom sides of the bezel are close to the ejector rails and thus will not cause
significant plate bending.

316

12 Structural System Design

Figure 12.17:

Area of mold cavity local to support pillar

Assuming a melt pressure of 150 MPa, the total force, F, exerted by the plastic on this
portion of the mold is:
F = P ⋅ A = 150 MPa ⋅ (168 mm ⋅ 13 mm) = 327,600 N = 33 tons
which is still a significant amount of force. A support pillar diameter of 37.5 mm is
initially analyzed. Given that the support pillar must convey one-half of the force, the
stress in the pillar is:
σ =

F /2
327,600 N
=
= 297 MPa
A
π (0.0375 m)2 /4

This stress is very close to the endurance stress for the support pillars if they are produced
from SAE1040 steel. The resulting strain is:
ε=

σ 297 MPa
=
= 0.014%
E
205 GPa

The length of the support pillar is 89 mm (3.5 in). The resulting deflection is:
δcompression = ε L = 0.014% ⋅ 88.9 mm = 0.13 mm
which is greater than the specified maximum deflection of 0.1 mm. To reduce the
deflection, the support pillar diameter is increased to 50 mm. The stress is thereby reduced
to 167 MPa while the deflection due to compression is reduced to 0.07 mm.
The analysis of bending is very similar to the previous example. However, the effective width
of the mold plate is conservatively estimated as the width of the mold cavity (13 mm).
The moment of inertia is then:
I =

1
0.013 m (0.120 m)3 = 1.9 ⋅ 10−6 m 4
12

With the use of the support pillar, the span has been reduced from 216 mm as shown in
Figure 12.11 to 108 mm as shown in Figure 12.17. Applying the bending equation for a
force of 33 tons in this area of the mold, the deflection due to bending is then estimated
as:

12.2 Analysis and Design of Plates

δbending =

317

33 tons ⋅ 9807 N/ton ⋅ (0.108 m)3
= 0.02 mm
48 ⋅ 205 GPa ⋅ 1.9 ⋅ 10−6 m 4

Since the deflection due to bending is quite small, the maximum deflection will occur
at the center of the mold due to compression of the support pillar. It should be noted
that the thickness of the B plate and/or support plate could be slightly reduced while still
meeting the deflection requirement. Furthermore, the deflection due to compression
could be greatly reduced by pre-loading the support pillars. Specifically, support pillars
of 88.97 mm (88.9 mm plus the 0.07 mm) can be used such that the pillars compress to
their nominal 88.9 mm (3.5 in) length so that cavity becomes flat during molding.

12.2.4 Shear Stress in Side Walls
The foregoing analysis focused on plate deflection across the parting plane. However, the
shear stresses in the side walls of the mold plates can also result in excess deflection and even
failure. This concern becomes especially significant for molds with deep cavities. The cup
mold represents a typical scenario with the load case shown in Figure 12.18. Specifically, the
deep cavity provides a tall side wall along which the melt pressure, P, is exerted. If the cavity
is very deep, then significant shear stresses and bending deflections can develop. The width of
the side wall, from the surface of the mold cavity to the side of the mold, is generally referred
to as the “cheek”.
A common guideline in the mold design is that the width of the cheek, Wcheek, should be
equal to the height of the mold cavity, Hcavity. The maximum shear stress in the side wall can
be estimated as a function of the height of the mold cavity, Hcavity, the width of the cheek,
Wcheek, and the molding pressure, P:
τ=

P ⋅ H cavity ⋅ Wcavity
σ
F
=
< limit
A
Wcheek ⋅ Wcavity
2

(12.14)



Bending

Figure 12.18: Shearing and bending of side walls

P
P
P
P
P
P

318

12 Structural System Design

To avoid failure, the shear stress should be less than one-half of the limit stress for the material.
Applying this constraint to Eq. (12.14) and solving for the width of the cheek provides:
Wcheek > 2 H cavity ⋅

P
σ limit

(12.15)

If the mold is made of SAE4140, then the endurance stress is 412 MPa. For a typical maximum
injection pressure of 150 MPa, the width of the cheek should be specified as:
Wcheek > 2 H cavity ⋅

150 MPa
= 0.73 ⋅ H cavity
412 MPa

(12.16)

Accordingly, the rule of thumb that the width of the cheek should equal the thickness of the
cavity provides a slight factor of safety under typical assumptions.
Even though the shear stress may not exceed the specified limit, the mold designer should
also verify the deflection of the side wall under load. Assuming that the side wall acts as a
simply supported beam with a uniform load, then the deflection due to bending of the side
wall can be estimated as:
δbending =

4
3 P H cavity
3
2 E Wcheek

(12.17)

Example: Estimate the shear stress and deflection of the side wall in the mold for the
cup.
Given the 3 mm wall thickness of the cup, a maximum melt pressure of 80 MPa is assumed.
The height of the cavity from the parting plane to the top of the cup is 50 mm, and the
width of the cheek is 45 mm. The shear stress in the side wall is approximately:
τ = 80 MPa ⋅

50 mm
= 89 MPa
45 mm

The maximum deflection of the side wall occurs at the parting plane, and will be
approximately:
δbending =

3 ⋅ 80 MPa ⋅ (0.05 m)4
= 4 ⋅ 10−5 m = 0.04 mm
2 ⋅ 205 GPa ⋅ (0.045 m)3

This stress and deflection should not be an issue so no changes are required to the mold
design.

12.2 Analysis and Design of Plates

319

12.2.5 Interlocks
In the previous example, the deflection of the side wall was not an issue. However, this issue
would likely be significant if the melt pressures were higher, the mold cavity was deeper, or
the molding tolerances were tighter. The mold designer could increase the width of the cheek
to reduce the side wall deflection. However, this approach adds significant size and expense
to the mold. Another alternative is to use interlocks on the parting plane near the edges of
the mold to transfer part of the bending load from the stationary half of the mold to the
moving half of the mold.
Round and rectangular mold interlocks are shown in Figure 12.19. Both types of interlocks
should be placed on the parting plane and as close to the mold cavities as possible. In general,
the rectangular interlock will provide greater resistance to deflection due to its larger size and
cross sectional area across the interlock. However, round interlocks are available in smaller
sizes and are easier to install in a mold.
A detail view of a mold design incorporating a round interlock is shown in Figure 12.20.
In this design, the male interlock is fit into a through hole in the B plate of the mold. The
female interlock is fit into a blind pocket in the deeper A plate of the mold. Both interlocks
tightly fit into the surrounding plates, and are retained in the height direction with socket
head cap screws. It is important that the mold designer does not jeopardize the structural
integrity of the side wall by removing excess mold material when incorporating the
interlocks. When the melt pressure is exerted on the side wall, the interlock will transfer part
of the load from the A half of the mold to the B half of the mold. The use of the interlock
effectively doubles the stiffness of the side wall, resulting in a halving of the amount of the
side wall deflection.

Figure 12.19: Round and rectangular interlocks

320

12 Structural System Design

Figure 12.20: Mold design with round interlock

Since larger interlocks can carry higher loads, the largest interlock should be used that can be
readily incorporated into the mold design. If the interlock is exposed to a lateral force, Flateral,
exerted by the side wall, then the shear stress in the interlock, τinterlock, can be estimated as:
τ interlock =

Flateral
Ainterlock

(12.18)

where Ainterlock is the cross-section area of the interlock at the parting plane. If the interlock
is made of S7 tool steel, then the design should provide a shear stress less than 300 MPa to
avoid failure.
Example: Estimate the shear stress in the 19 mm diameter interlock used to support the
side wall of the cup cavity.
The primary uncertainty in this analysis is the estimation of the lateral force applied to
the interlock. This estimation of the lateral force is complicated by the round shape of
the cup that provides a non-uniform cheek width between the guide pins. However, an
estimate can be provided by assuming that the interlock is exposed to the lateral force from
the nearby surface of the mold cavity. As shown by the hatched section of Figure 12.21
that represents the nearby plastic, the effective area can be estimated as the product of
the interlock width and the cavity height.

12.2 Analysis and Design of Plates

Figure 12.21:

321

Projected view of interlock and cavity

Of course, the interlock will not be exposed to all of the lateral force from the melt pressure
exerted on the side wall of the mold cavity. A conservative estimate is that half of the force
will be carried by the interlock, so:
1
Pmelt ⋅ φinterlock ⋅ H cavity
2
1
= 40 MPa ⋅ 19.05 mm ⋅ 50 mm = 19,050 N
2

Flateral =

The shear stress in the interlock can than be estimated as:
τ interlock =

Flateral
19,050 N
=
= 67 MPa
Ainterlock
π (0.019 m)2 /4

Since this shear stress is less than the 300 MPa limit stress, the interlock is structurally
sufficient to transfer half the loading from the side of the mold cavity to the moving half
of the mold.

12.2.6 Stress Concentrations
In mold plates, stress concentrations will occur wherever material has been removed between
the mold cavity and the supporting plates. Stress concentrations are especially common in
injection molds due to the installation of water lines and ejector holes. The resulting stress
distribution about the hole will be similar to that shown in Figure 12.22. In this example, a
hole has been provided in a mold plate at a distance of 1.5 times the hole’s diameter. A pressure
of 100 MPa has been applied to the top surface. The resulting maximum von Mises stress is
340 MPa, which corresponds to a stress concentration factor of 3.4.

322

12 Structural System Design

Figure 12.22: Stress concentration about hole

As the hole is moved further away from the mold cavity, the stress concentration is reduced.
To evaluate the stress concentration factor, a series of finite element analyses were performed
with varying mold geometries. Figure 12.23 plots the stress concentration as a function of
the number of hole diameters from the cavity surface to the centerline of the hole. A model
of the stress concentration factor, K, was fit to the data, providing:
⎛φ

K = 3.1 + 0.75 ⎜ hole ⎟
⎝ H hole ⎠

2.29

(12.19)

where φhole is the diameter of the hole and Hhole is the distance from the cavity surface to the
center of the hole. This model is plotted as the dashed line in Figure 12.23. Holes located close
to the cavity surface obviously cause significant stress concentrations. However, it is observed
that a stress concentration of 3 results even when a hole is located far from the cavity surface.

12.2 Analysis and Design of Plates

323

5

Finite Element Analysis
Model Fit

Stress Concentration Factor

4

3

2

1
0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Number of Diameters from Cavity to Hole Centerline

Figure 12.23: Stress concentration as a function of distance

This explains why many molds develop cracks emanating from the waterlines in molding
applications with high melt pressures, even when the cooling lines are located far from the
cavity surface. For this reason, molding applications with high melt pressures should be
constructed of materials with high endurance stresses such as A6, D2, or H13.
Example: A thin wall molding application will utilize a filling pressure of 200 MPa with
a core insert constructed of H13. Specify the closest allowable distance for a cooling line
with a diameter of 9.5 mm.
H13 has an endurance stress of 760 MPa. Since the melt pressure will provide a nominal
compressive stress of 200 MPa, the allowable stress concentration factor is:
K =

σ endurance 760 MPa
=
= 3.8
σ nominal
200 MPa

The distance may be evaluated using Figure 12.23 or calculated using Eq. (12.19). Solving
Eq. (12.19) for the distance, HHole, provides:
⎛ 0.75 ⎞
H hole = φhole ⎜
⎝ K − 3.1 ⎟⎠

2.29

⎛ 0.75 ⎞
= 9.5 mm ⋅ ⎜
⎝ 3.8 − 3.1 ⎟⎠

2.29

= 11.1 mm

324

12 Structural System Design

Cooling lines seem to cause more significant problems than ejector holes in practice. Cracks
emanating from cooling lines will eventually leak and cause quality issues with the moldings.
By comparison, cracks emanating from ejector holes may not ever cause a catastrophic failure.
The reason is that the deformation of the ejector hole under load can cause the plate around
hole to be supported by the ejector, thereby reducing the stress around the hole. As such,
cracks propagating from ejector holes will reach a critical length at which point the elastic
deformation of the core insert onto the ejector prevents further crack propagation.
Example: A prototype molding application will utilize a melt pressure of 100 MPa with
QC7. A mold designer is contemplating placing a 4 mm diameter ejector with 0.5 mm
of aluminum between the edge of the cavity side wall and the edge of the ejector pin.
Calculate the stress level and estimate the deflection of the ejector hole.
The distance from the cavity side wall to the center of the ejector, Hhole, is 2.5 mm. The
stress concentration factor, K, is:
⎛ 4 mm ⎞
K = 3.1 + 0.75 ⎜
⎝ 2.5 mm ⎟⎠

2.29

= 5.3

Given a melt pressure of 100 MPa, the von Mises stress level at the pin will be approximately
530 MPa. This stress level is just below the yield stress of 545 MPa provided in Appendix B
so the material should not immediately yield. However, the von Mises stress is far above
the endurance stress of 166 MPa required to prevent failure across one million molding
cycles. A review of the fatigue behavior of Figure 12.5 indicates that the design will likely
fail around 1,000 cycles.
To estimate the deflection of the ejector hole, the compressive stress in the mold plate
adjacent to the ejector hole must be estimated. One approach would be to assume that
the entire von Mises stress is compressive in nature. This approach will over estimate the
hole deformation since the von Mises stress also includes a component of the shear stress,
and is thus larger than the compressive stress. Continuing with this assumption, the strain
in the adjacent plate material is estimated as:
ε=

σ 530 MPa
=
= 0.73%
E 72.4 GPa

The material that is deforming about the ejector hole has a length equal to the hole
diameter. The deflection of the hole can then be estimated as:
δhole = ε φhole = 0.73% ⋅ 4 mm = 0.03 mm
This amount of deflection is on the order of the clearance provided around the ejector pin
for venting. Over many molding cycles, the hole will plastically deform and cause binding
of the ejector pin. For validation, a finite element analysis of this load case was conducted
and indicated that the deflection was actually 0.10 mm as shown in Figure 12.24.

12.3 Analysis and Design of Cores

Figure 12.24:

325

Deformation around ejector hole near the cavity

The reason for the large variance between the analysis and the simulation was that the close
proximity of hole to the cavity surface caused local bending at the top of the hole as shown
in Figure 12.24, which was not considered in the analysis. By counting the 0.01 mm displacement lines, the results do indicate that the vertical deflection of the mold plate to the
left and right of the holes is very close to the 0.03 mm predicted by the previous analysis.

12.3 Analysis and Design of Cores
For the purpose of structural design, a core can be considered shallow when the height of the
core is less than both the width and length of the core. Shallow cores, such as for the bezel
mold, will not be subjected to excessive stress or deflection caused by the application of the
melt pressure to the side walls of the core. As such, shallow cores can be designed according
to the previously described analysis for mold plates.

326

12 Structural System Design

12.3.1 Axial Compression
The vertical deflection of cores due to compression by the melt can be modeled as previously
discussed in Section 12.2.1, though with the compressive forces and cross-sectional areas
appropriate for the core.
Example: Estimate the vertical deflection of the core shown in Figure 12.25 assuming a
melt pressure of 80 MPa.
It may appear that the cooling insert in the design of Figure 12.25 will fully support the
core insert. While this may be fine in theory, a more robust design may be provided by
assuming that the cooling insert provides no support. There are two reasons for making
this assumption. First, the outer surfaces of the cooling insert may not tightly fit the inner
surfaces of the core insert. Any gap greater than the deflection of the core will completely
prevent the cooling insert from supporting the core. Second, the cooling insert may be
made from a different material than the core insert. As such, the cooling insert may not
be able to withstand the stresses imposed while supporting the core insert.
The total deflection of the top surface of the core can be estimated by superimposing the
compression of the side walls with the bending of the top surface. While the compressive
stress distribution in the side walls of the core is not entirely uniform, the average stress
is approximately:
σ side_wall =

Figure 12.25:

Fvertical
80 MPa ⋅ π (63 mm)2 /4
=
= 216 MPa
Aside_wall
π [(63 mm)2 − (50 mm)2 ]/4

Axial compression of hollow core

12.3 Analysis and Design of Cores

327

This is a fairly high stress level indicating that a mild steel or aluminum should not be used
in this application when considering the cyclic loading and possible fatigue. Assuming a
steel core insert, the vertical compressive strain in the side walls is:
εvertical =

σ side_wall
216 MPa
=
= 0.11%
E
205 GPa

The total height of the core insert is 58 mm. With a strain of 0.11%, the total vertical
deflection at the top of the side walls equal to:
δvertical = εvertical ⋅ H core = 0.11% ⋅ 58 mm = 0.06 mm
Bending from the edge of the top surface to the center of the core can be calculated using
beam or plate bending equations of Section 12.2.2 and added to the displacement due to
compression to estimate the total vertical deflection.
The structural design of deep cores is further complicated since deep cores can bend due to
the application of lateral forces from the melt pressure against their sides. Core bending may
be a significant problem when cores are slender and have a low stiffness associated with their
cross-section area, especially when the cores are hollowed out to provide for mold coolant.
Analysis and design of the core must ensure that the potential core deflection is not excessive
and that the compressive stresses around the perimeter of the core are acceptable. These two
concerns are next addressed.

12.3.2 Compressive Hoop Stresses
When a core insert includes a hollow section for a cooling line or other purpose, the side
walls must withstand the compressive forces imposed by the melt pressure. The load case is
shown in Figure 12.26.

Figure 12.26: Core insert loaded by melt pressure

328

12 Structural System Design

The compressive stress, σhoop, caused by the melt pressure is:
σ hoop =

P φcore
2 hcore

(12.20)

where P is the melt pressure, φcore is the outer diameter of the core insert, and hcore is the
thickness of the core’s side wall.
To avoid compressive failure in the side walls, the hoop stress must be less than the specified
limit stress for the material. This leads to the following constraint on the thickness of the
side wall:
hcore >

P φcore
2 σ limit

(12.21)

The constraint can also be used to find the maximum inner core diameter, φinner:

P ⎞
φinner < φcore ⎜1 −
σ limit ⎟⎠


(12.22)

A general guideline can be developed for inserts produced from P20 steel with an assumed
melt pressure of 150 MPa. Since P20 has an endurance stress around 450 MPa, the thickness
of the side wall should be greater than:
hcore >

φ ⋅ 150 MPa φ

2 ⋅ 456 MPa
6

(12.23)

and the maximum internal diameter of the core is:

150 MPa ⎞ 2
φinner < φcore ⎜1 −
≈ φcore
456 MPa ⎟⎠ 3


(12.24)

In practice, the mold designer should customize the above analysis by utilizing the maximum
melt pressure and endurance stress that are specific to the molding application.
Example: Compute the compressive hoop stress in the core insert for the cup mold
assuming that the outer diameter, φcore, is 60 mm, the wall thickness, hcore, is 10 mm, and
the melt pressure is 80 MPa. Also recommend a maximum inner diameter if the core
insert is made of aluminum QC7.
Given the above assumptions, the compressive hoop stress is:
σ hoop =

80 MPa ⋅ 60 mm
= 240 MPa
2 ⋅ 10 mm

This is a safe but significant amount of stress. If the core insert is to be made of aluminum
QC7, then two different loadings might determine the allowable inner diameter of the
core. First, the mold designer should consider the cyclic loading at the 80 MPa melt

12.3 Analysis and Design of Cores

329

pressure with an endurance stress of 166 MPa. This fatigue analysis indicates that the
inner diameter should be:

80 MPa ⎞
φinner < φcore ⎜1 −
= 0.51 φcore = 31 mm
166 MPa ⎟⎠


Second, the mold designer should consider an overpressure situation wherein the molder
accidentally injects the melt at the maximum pressure of the molding machine. A single
cycle at too high a pressure could cause the core insert to fail. To check this, a melt pressure
of 200 MPa can be used with QC7’s yield stress of 545 MPa. This yield stress analysis
indicates that the inner diameter should be:

200 MPa ⎞
φinner < φcore ⎜1 −
= 0.63 φcore = 38 mm
545 MPa ⎟⎠


Comparing the above two results indicates that cyclic fatigue is a more critical issue than
yield in an overpressure situation. The maximum inner diameter when using QC7 is
31 mm if a high number of molding cycles is desired.

12.3.3 Core Deflection
Another common issue with deep cores is excessive deflection or “core bending” due to
variations in the melt pressure around the periphery of the core. The variation in melt pressure
is often due to the side gating as shown in Figure 12.27. However, slight variations in melt
flow can cause significant bending in center gated designs when the cores are very slender
(e.g., a core length on the order of ten times the core diameter). The problem is compounded
by the fact that the core bending effect is self-reinforcing, which means that a slight bending
of the core facilitates more melt flow and pressure to the thicker portion of the cavity and
further bending of the core.

Figure 12.27: Lateral loading of core insert

330

12 Structural System Design

Core bending can be analyzed through appropriate use of bending equations. Typically,
the core is held to the moving side of the mold, and the top of the core is free to bend. The
deflection due to the pressure difference, ΔP, across the core is:
δbending =

4
ΔP φcore H core
8EI

(12.25)

where I is the moment of inertia. For a hollow core with an outer diameter, φcore, and an inner
diameter, φinner, the moment of inertia is:
I =

π 4
4
(φcore − φinner
)
64

(12.26)

The magnitude of the pressure difference around the core will vary with the geometry of the
molding application. A shorter core, like that shown in Figure 12.27, will have a pressure difference that is a significant fraction of the pressure required to fill the mold (perhaps 50% of
the filling pressure). As the core becomes longer relative to its diameter, the pressure difference
around the core will become less compared to the pressure difference along its height (perhaps
10% of the filling pressure). However, the core deflection is proportional to the fourth power
of the core height, so a small asymmetry of the melt pressure can cause a large deflection.
Example: Estimate the magnitude of the deflection for the cup’s core assuming that the
outer diameter is 60 mm, the inner diameter is 40 mm, the height is 58 mm, and the
pressure difference around the core is 40 MPa.
The moment of inertia for the core is:
I =

π
[(0.060 m)4 − (0.040 m)4 ] = 5.1 ⋅ 10−7 m 4
64

Assuming a steel core with a modulus of 205 GPa, the deflection is:
δbending =

40 ⋅ 106 Pa ⋅ 0.06 m ⋅ (0.058 m)4
= 0.03 mm
8 ⋅ 205 ⋅ 109 Pa ⋅ 5.1 ⋅ 10−7 m 4

Since the deflection is small, core bending will likely not be an issue in this application
even if the pressure difference around the core was significantly greater.
Naturally, core bending becomes much more significant as the core becomes more slender. To
minimize core bending, the mold designer should utilize solid cores with a minimal length
to diameter ratio. When possible, slender core pins should be interlocked with the stationary
side of the mold as shown in Figure 12.28. Such interlocking of the core pin reduces the lateral
deflection of the pin to approximately 10% of the deflection for a pin that is supported on only
one end. When interlocking or increasing the size of the core is constrained by the geometry
requirements of the molding application, the mold designer should strongly recommend
using a center gate at the top of the corner or two opposing gates at the bottom of the core
to minimize the pressure gradient exerted on the core.

12.3 Analysis and Design of Cores

331

Figure 12.29 shows the use of flow leaders as another approach to reduce the core deflection.
In this design, the flow leaders will assist the melt to travel down the cavity with lower filling
pressures. At the same time, the melt will propagate into the thinner adjacent sections of the
cavity and partially freeze, thereby preventing the core from deflecting a significant amount
even if significant pressure differences arise later in the filling stage. The flow leaders shown on
the core in Figure 12.29 may be undesirable as protrusions on the inner surface of the molded
part if in contact with fluids. As such, the flow leaders may be integrated on the outside surface
of the molding according to a variety of design configurations set into the cavity insert.

Figure 12.28: Interlocking of slender core into cavity

Figure 12.29: Use of flow leaders to minimize core deflection

332

12 Structural System Design

12.4 Fasteners
The mold design must also include fasteners to rigidly fasten the multiple components of the
mold. There are three types of fasteners commonly used in molds. First, fits are used to tightly
locate one component within another, such as a cavity or core insert being located within
a retainer plate. Second, locating pins or dowels are used to locate one components above
another, such as the ejector housing to the support plate. These first two fastening methods
only provide fastening across the length and width directions of the mold. To fasten the mold
components together in the height direction, socket head cap screws are used wherein the
screw’s head is retained in a mold plate and the screw’s threads engage the component to be
fastened. Each of these fastening methods is next analyzed.

12.4.1 Fits
A “fit” refers to the mating of two components. A clearance fit refers to a mating in which a
nominal clearance between the surfaces of the two components. While a clearance fit provides
for easy assembly with no insertion forces, the clearance between the two components permits
the precise location of components to remain unknown. Since tight tolerances are required
in molds, interference fits are commonly used to locate the mold components.
Interference fits occur when the male component has a nominal dimension that is larger than
the nominal dimension of the female component, as shown in Figure 12.30 for a core insert
and a retainer plate. Since metals have a high elastic modulus, a rigid interference fit can result

Figure 12.30: Location-interference fit for inserts

333

12.4 Fasteners

when the difference between the nominal dimensions is very small, on the order of 0.01% of
the nominal dimension. The tightness and rigidity of the interference fit increases with the
amount of interference between the two components. Unfortunately, the implementation
of interference fits is impeded by the dimensional variations imposed in the components’
machining processes. For this reason, standard systems of fits have been developed to provide
limits on the dimensions of the components.
The fits analyzed here are based on a lateral hole basis and have been converted from U.S.
customary units to metric units.4 In this method, rectangular members with width, W, and
length, L, are modeled as a circular member with apparent diameter, D, computed as:
D=

W ⋅L

(12.27)

The tolerance limit, λ, on a given dimension is then calculated according to a formula:
λ = 0.001 ⋅ C ⋅ D

1
3

(12.28)

where C is a coefficient corresponding to the lower and upper limit for the male or female
component provided by international standards. Table 12.1 provides coefficients for locational-interference fits (LN1 to LN3) and drive-interference fits (FN1 to FN3). Locationalinterference fits are used when the accuracy of location is critical and the components require
lateral rigidity. However, locational-interference fits do not provide significant retention force
in the height direction, so the components must be secured in the height direction to another
component via screws or other means. FN1 to FN3 correspond to drive fits with increasing
interference and requiring increasing insertion forces. While drive fits provide semi-permanent
assemblies, mold designs usually provide screws or other means for positively retaining the
components in the height direction.
Table 12.1: Location tolerance interference coefficients [mm]

Fit

4

Cinterference

Female (hole in plate)

Male (insert)

Lower limit

Upper limit

Lower limit

Upper limit

5.67

9.05

LN1

4.89

0.00

4.93

LN2

7.14

0.00

7.84

8.59

13.52

LN3

12.22

0.00

7.84

13.67

18.60

FN1

13.57

0.00

4.93

14.34

17.73

FN2

22.02

0.00

7.84

23.47

28.41

FN3

30.85

0.00

7.84

32.30

37.24

Two of the most common standards for fitting include “Preferred Limits and Fits for Cylindrical Parts”,
ANSI B4.1-1967 (R1999), and “Preferred Metric Limits and Fits” ANSI B4.2-1978 (R1999). ANSI B4.1
is analyzed here due to its relative simplicity and broad applicability, though the mold designer may
conform to whatever standard is most appropriate.

334

12 Structural System Design

Example: The base of the core insert for the cup mold is 88.90 mm on each side. Specify
the tolerances for a light drive (FN1) fit.
The apparent diameter of the core insert is:
D=

88.90 mm ⋅ 88.90 mm = 88.90 mm

The lower tolerance limit for the insert dimension is computed with C equal to 14.34:
lower
λinsert

1
3

= 0.001 ⋅ 14.34 ⋅ 88.9 = 0.064 mm

The upper tolerance limit for the insert dimension is computed with C equal to 17.73:
1
3

upper
λinsert

= 0.001 ⋅ 17.73 ⋅ 88.9 = 0.079 mm

The lower tolerance limit on the mating hole in the retainer plate is 0:
λlower
plate

1
3

= 0.001 ⋅ 0.0 ⋅ 88.9 = 0.000 mm

The upper tolerance limit on the mating hole in the retainer plate is computed with C
equal to 4.93:
1
3

λupper
plate = 0.001 ⋅ 4.93 ⋅ 88.9 = 0.022 mm
The minimum and maximum dimensions on the insert are specified as 88.96 and
88.98 mm, respectively. The minimum and maximum dimensions on the hole in the
plate are specified as 88.90 and 88.92 mm. These dimensional limits are shown in
Figure 12.31.

Figure 12.31:

Insert and plate dimensions for an FN1 fit

12.4 Fasteners

335

It may be of interest to estimate the insertion force required to achieve various interference
fits, so that excessive insertion forces may be avoided. The insertion force may be estimated
by the compressive stress required to strain the components during assembly. The expected
amount of interference can be computed as the average male dimension minus the average
female dimensions. Alternatively, the expected amount of interference, λinterference, can be
computed using the formula:
λinterference = 0.001 ⋅ Cinterference ⋅ D

1
3

(12.29)

where Cinterference is a coefficient derived from the limit coefficients provided in Table 12.1.
Assuming that the plate is much larger than the insert, the compressive stress, σ, in the insert
is estimated as:
σ =

λinterference ⋅ E
2D

(12.30)

where E is the modulus of the material. The factor of 2 in the above equation stems from
the fact that the compressive stress in the insert will also drive a tensile stress in the plate.
Accordingly, the interference causes equal strain in both the insert and the plate.
The insertion force can then be estimated as the compressive stress multiplied by the contact
area and the friction coefficient:
Finsertion = f σ (π D H )

(12.31)

where f is the friction coefficient and H is the height of the contact zone between the two
components.
Example: Estimate the insertion force for the core insert for the cup mold. Assume an
FN1 fit with a contact height between the plate and the insert of 42 mm.
The expected dimension for the core insert is 88.97 mm while the expected dimension for
the hole in the retainer plate is 88.91 mm. The expected amount of interference, λinterference,
is 0.06 mm. The resulting stress in the steel components is:
σ =

0.06 mm ⋅ 205 ⋅ 109 Pa
= 69 MPa
2 ⋅ 88.9 mm

Assuming a coefficient of friction of 1.0, the resulting insertion force is:
Finsertion = 1.0 ⋅ 69 MPa (π ⋅ 88.9 mm ⋅ 42 mm) = 808 kN
An insertion force of approximately 808 kN or 180,000 lbs is required to drive the core
insert into the retainer plate. If a press is not available with this capacity, the mold designer
can utilize a location-interference fit. Also, it is desirable to provide a slight taper along
the leading edge of the core insert to assist in alignment during assembly.

336

12 Structural System Design

12.4.2 Socket Head Cap Screws
A ½″-13 socket head cap screw is shown in Figure 12.32. Socket head cap screws like this
screw are the most common fastener used in molds. The primary reason is that socket head
cap screws have been carefully designed such that the strength of the head, threads, and bolt
are matched. As a result, the socket head cap screw provides a standard and efficient method
for retaining multiple components along the screw’s axis.

Figure 12.32: Typical socket head cap screw

The sizes and load carrying capability of socket head cap screws are related to their size,
material, and treatments. Analysis of standard socket head screw designs indicates that the
head height is equal to the thread diameter, and that the head diameter is approximately
150% of the thread diameter. While the strength of the fastener varies somewhat with the
coarseness of the thread, the tensile strength of standard DIN/ISO screws can be fairly well
estimated by assuming an ultimate stress, σultimate, of 800 MPa multiplied by the cross-section
area of the outer thread diameter:
Ftensile = σ ultimate

2
π Dthread
4

(12.32)

Example: Specify the size of the socket head cap screws used to fasten the stationary and
moving halves of the laptop bezel mold shown in Figure 12.7.
Since this socket head cap screw is used in a critical application where failure may result
in loss of equipment or life, a worst case scenario is assumed. First, the maximum mass
of the mold is estimated assuming a solid block of steel according to the dimensions
provided in Figure 12.7. The maximum mass of the mold is:
M mold = ρmold H mold Lmold Wmold
= 7800

kg
⋅ 0.403 m ⋅ 0.381 m ⋅ 0.302 m = 362 kg
m3

12.4 Fasteners

337

Next, the worst case scenario is assumed. The worst case scenario occurs when the mold is
clamped to only one side of the molding machine without the support of the moving platen,
which may occur when the mold is being installed in the molding machine. Furthermore,
the worst case scenario will assume that the entire mass of the mold must be supported
by only one tightened screw, which may occur if the other cap screws are not tightened
or tightened to lesser amounts. The resulting load case is shown in Figure 12.33.
The exerted force on the screw by the mold can be estimated by summing the moments
about the locating ring to find:
Fscrew = M mold ⋅ ng ⋅ g ⋅

LCOG
Lscrew

where g is the acceleration due to gravity (9.8 m/s2), LCOG is the distance between the
platen and the mold’s center of gravity, and Lscrew is the distance from the locating ring to
the screw. The coefficient ng relates to the number of gravities that may be exerted on the
mold, and is usually set quite high for safety purposes. Due to the shock of a crane, ng is
set equal to 10. Substituting the approximate values from Figure 12.33 provides:
Fscrew = 362 kg ⋅ 10 ⋅ 9.8

Figure 12.33:

m 0.2 m

= 47,000 N
s2 0.15 m

Worst case analysis for screw loading

338

12 Structural System Design

Solving Eq. (12.32) for the diameter yields:
Dscrew =

4 Fscrew
=
π σ ultimate

4 ⋅ 47,000 N
3 ′′
= 8.65 mm → 10 mm or
6
8
π ⋅ 800 ⋅ 10 Pa

The analysis indicates that a 3/8″ or M10 socket head cap screw should be sufficient. For
reference, the mold base selected for this application was provided with ½” socket head
cap screws. Failure of cap screws in this mold base is not expected.

12.4.3 Dowels
Cap screws should not be relied upon to locate mold components given their relatively large
radial clearances. As previously discussed, an interference fit should be used to locate one
component within another. For parallel plates or components, however, dowels or other
locating pins should be used as shown in Figure 12.34. In this design, concentric holes are
provided into the coplanar surfaces of the two plates. A dowel then mates with the two holes
to locate the two components along the axis of the dowel.
Manufacturing variances in the holes’ location, diameter, and roundness limit the ability to
precisely locate the two components relative to each other. Equation (12.28) can be used for
various types of fits by varying the limit coefficients, C, for the dowel and holes according to
international standards. Table 12.2 provides coefficients for a locational-clearance fit (LC1),
locational-transitional fits (LT1 and LT3), as well as the loosest locational-interference fit
(LN1). Locational clearance fits are intended for parts that are typically stationary but can
be readily disassembled and reassembled. This fit provides the same order of tolerance as
threaded fasteners, so is not recommended for injection molds since the large clearance can
allow accelerated wear of sliding surfaces. Locational-transition fits provide for tighter control
of location, but with the possibility of interference between the dowel and the hole which
hinders the mold assembly.

Figure 12.34: Typical locating dowel design

12.4 Fasteners

339

Table 12.2: Location clearance and transitional coefficients [mm]

Fit

CInterference

Female (hole in plate)

Male (dowel)

Lower limit

Upper limit

Lower limit

Upper limit

LC1

–4.16

0.00

4.93

–3.39

0.00

LT1

–6.38

0.00

7.84

–2.43

–2.51

LT3

–0.73

0.00

7.84

0.72

5.65

LN1

4.89

0.00

4.93

5.67

9.05

Example: A 12 mm dowel is to be used to mate the ejector housing to the support plate.
Specify the dimensions for an LT3 fit. Estimate the expected clearance between the dowel
and the hole, as well as the insertion force in the event of the worst case interference.
The apparent diameter of the core insert is:
D=

88.90 mm ⋅ 88.90 mm = 88.90 mm

The lower tolerance limit for the dowel diameter is computed with C equal to 0.72:
1
3

lower
λdowel
= 0.001 ⋅ 0.72 ⋅ 12 = 0.002 mm

The upper tolerance limit for the dowel diameter is computed with C equal to 5.65:
1
3

upper
λdowel
= 0.001 ⋅ 5.65 ⋅ 12 = 0.013 mm

The lower tolerance limit on the mating hole in the retainer plate is 0. The upper tolerance
limit on the mating hole in the retainer plate is computed with C equal to 7.84:
1
3

λupper
plate = 0.001 ⋅ 7.84 ⋅ 12 = 0.018 mm

.

The minimum and maximum dimensions on the dowel are specified as 12.002 and
12.013 mm, respectively. The minimum and maximum dimensions on the hole in the plate
are specified as 12.000 and 12.018 mm. This design is shown above in Figure 12.34.
The average clearance between the two components is 0.0015 mm (or 1.5 μm, equal to the
hole’s average diameter of 12.009 mm minus the dowel’s average diameter of 12.075 mm).
Given that manufacturing variation exists, it is important to check on the magnitude of
the dowel’s insertion force when the hole and the dowel are at their specified limits. The
worst case interference will occur when the hole’s diameter is 12.000 mm and the dowel’s
diameter is 12.013 mm. The maximum amount of interference, λinterference, is 0.013 mm.
The resulting stress in the steel components is:

340

12 Structural System Design

σ =

0.013 mm ⋅ 205 ⋅ 109 Pa
= 111 MPa
2 ⋅ 12 mm

Assuming an insertion length of 12 mm and a coefficient of friction of 1.0, the application
of Eq. (12.31) results in an insertion force of:
Finsertion = 1.0 ⋅ 111 MPa (π ⋅ 12 mm ⋅ 12 mm) = 50 kN
This magnitude of insertion force for a dowel is clearly undesirable since separation of
the mold plates can not be accomplished manually. The mold assembler would require
grinding to reduce the pin diameter to avoid such excessive insertion forces.

12.5 Review
Molds are mechanical assemblies that must withstand high levels of stresses imposed by the
pressure of the polymer melt. Several constraints drive the structural design of the mold. First,
the mold must be designed to avoid yielding given a single over pressure situation. Second,
the mold must be designed to avoid failure due to fatigue associated with the cyclic loads
associated with molding thousands or millions of cycles. Third, the mold must be designed
to avoid excessive deflection while molding, which would lead to flashing of the molded parts
and accelerated wear on the mold’s parting line. Of these issues, fatigue and deflection tend
to dominate though the relative importance is a function of the number of mold cavities, the
molding pressures, the mold geometry, and the production quantity.
Analyses were provided to model the compression of mold plates, cores, and support pillars
as well as the bending of plates, side walls, and cores. Superposition of compression and
bending can be used to estimate the total deflection of the cavity surfaces. Analyses were
also developed for stress concentrations in mold plates. In general, all analyses indicate that
increasing the amount of steel between the load and support points provides for lower levels
of stress and deflection. As such, the mold designer must perform analysis to develop robust
designs that are not uneconomical. The uses of support pillars, interlocks, and other designs
were demonstrated to reduce deflection.
Common fastening means were also analyzed including interference fits, socket head cap
screws, and dowels with clearance and interference fits. The mold designer must remember to
provide means for fastening the cavity and core inserts to the rest of the mold while providing
tight control of location relative to other mold components. In practice, the provision of
fasteners may interfere with other subsystems of the mold including part ejection and mold
cooling. In such cases, iterative redesign of the mold may be required to efficiently locate all
the mold’s subsystems without increasing the size and cost of the mold.

12.5 Review

341

After reading this chapter, you should be able to:
• Describe the flow of forces from the mold cavity to the machine tie bars;
• State the relationship between modulus, stress, and strain;
• State the relationship between ultimate stress, yield stress, and endurance stress;
• Specify the limit stress and maximum deflection based an application’s requirements;
• Estimate the compressive, shear, and hoop stresses in various mold components;
• Estimate the deflection of a plate, core, or support pillar due to compression;
• Estimate the deflection of a plate, core, or side wall due to bending;
• Specify the plate thickness and use of support pillars to avoid excessive mold deflection;
• Specify the mold cheek and use of mold interlocks to avoid excessive stress or mold
deflection;
• Specify the design of mold cores to avoid excessive hoop stress and core bending;
• Specify the distance between the mold cavity and stress concentrations (such as ejector
holes and cooling lines) as a function of the material properties and application
requirements;
• Specify the dimensional limits on male and female components to achieve clearance,
transition, interference, and drive fits;
• Estimate the expected clearance or insertion force for a specified fit; and
• Specify the use of socket head cap screws to securely fasten mold components.
The analysis and design of each of the mold’s subsystems has been completed. The next chapter
is intended to increase the mold designer’s awareness by providing a critical examination of
available mold technologies.

13

Mold Technologies

13.1 Introduction
This book has sought to provide an engineering approach to mold design; the emphasis has
been on the examination and modeling of fundamental mechanisms that govern the use and
failure of injection molds. The examples have purposefully been made as simple and clear as
possible, so that the practitioner can apply the design and analysis methods to more specific
and advanced molding applications.
There are many advanced molding process technologies and corresponding mold designs. A
flow chart has been provided in Figure 13.1 to guide the selection of some of available mold
technologies. Such mold technologies can be used to compete effectively by providing molded
parts with higher quality in less time and at lower costs. Most of these technologies have been
developed for specific purposes, such as to produce a molded part with unique properties,
or to more economically produce large quantities of molded parts.
Many molding technologies are interwoven. For instance, multi-shot molding (in which a
molded part is made of two or more materials) has characteristics that are related to coinjection
molding, insert molding, stack molding, and even injection blow molding. Regardless of the
level of technology, the underlying physics and mold design fundamentals that have been
previously provided still apply. As such, this chapter provides an overview of some available
molding technologies, and discusses associated mold design issues. Examples of illustrative
mold designs have been sourced from the U.S. patent literature. The objective here is not to
provide an exhaustive survey of mold related technologies, or even to recommend specific
mold designs. Rather, the intent is to show some interesting examples that will imbue the
practitioner with specific insights into a range of mold technologies so that they may become
better mold designers.

13.2 Coinjection Molds
Coinjection molding is a process in which two materials are sequentially injected into a mold
cavity, typically through the same gate. Since the first material forms a skin and the second
material forms the core of the molded part, it is possible to use coinjection molding to produce
plastic parts with unique aesthetic or structural properties with potentially lower costs than
injection molding. Some typical coinjection molding applications include:


The use of a first virgin material having preferred cosmetic properties followed by a
second material having different structural properties and/or recycled content, as in the
fascia of a car bumper;

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13 Mold Technologies

Compete
effectively

Higher
quality

Multiple
materials

Hollow
parts

Aesthetic
surface

Complex
geometry

Lower
costs

Higher
yields

Plastic over
other

Insert
mold

Plastic over
plastic

Multi-shot
mold

Plastic within
plastic

Coinjection
mold

Fluid within
plastic

Gas/water
assist mold

Inflated
plastic

Injection
blow mold

Complex
interior

Lost core
mold

Decorated
surface

In mold
labeling

Glossy/clear
surface

Mold wall
temperature

No witness
marks

Reverse
ejection

Complex
exterior

Split cavity
mold

Interior
features

Rotating
core mold

Tight
tolerances

Injection
compression

Better flow
control

Dynamic
FeedTM
Melt
FlipperTM

Higher
productivity

Faster time
to market

Higher
cavitation

Hot runner
mold

Lower clamp
tonnage

Stack
mold

Less material
waste

Insulated
runner mold

Lower
tooling cost

Lower
cavitation

Two plate
mold

Faster mold
tooling

High speed
machining

Prototype
mold

Figure 13.1: Mold technology selection flow chart

13.2 Coinjection Molds




345

The use of a first material followed by a second foaming material to produce a cosmetic
part with lower density, as in structural foam applications;
The use of a first material followed by a second fluid, such as air or water, to produce a
hollow part like a door handle.

While this last example (commonly known as gas assist or water assist or fluid assist molding)
may not seem a coinjection process, the molding process and mold designs are sufficiently
similar to warrant a joint discussion.

13.2.1 Coinjection Process
In coinjection molding, two materials are sequentially injected, often similar to the sequence
provided in Figure 13.2 [42]. As shown, a first melt is partially injected into the mold through
a sprue 6 or some other feed system. After a desired volume of the first material 7 has been
injected, a second material 8 is injected at the same location. If the volume of the first material
is too small, then the second material may “blow through” the first material. Conversely, too
large an initial charge of the first material may leave too small a volume for the injection of the

Figure 13.2: Coinjection molding process

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second material. Since the first material is adjacent to the mold wall, and may have partially
solidified, the second material will tend to flow through the core of the first material. After
the second material has been injected, it is fairly common to then inject a small amount of
the first material 9. This latter injection of the first material serves to purge the feed system
of any undesired amount of the second material, which might otherwise contaminate the
subsequent molding cycle.
It is observed in Figure 13.2 that the mold core 2 is moving in and out of the mold cavity 1
during the injection of the materials into the mold to thereby adjust the wall thickness of
the cavity 3. This injection compression serves at least two purposes. First, in foam molding,
the compression and subsequent expansion of the mold cavity can be used to delay and
subsequently encourage the nucleation of gas cells, thereby controlling the distribution and
density of the injected foam. Second, in non-foam molding, the compression of the cavity can
be used to control the pack pressure throughout the mold and thereby control the shrinkage
characteristics of part features molded of the first material while injecting the second material.
The control of the cavity wall thickness can be accomplished by profiling the displacement
of the molding machine’s platen during the filling stage, or alternatively profiling the clamp
tonnage profile.
The mold uses a sliding fit (refer to Section 12.4.1) along the vertical sides where the mold
core mates with the mold cavity. While not discussed in this reference [42], the sliding fit
can be assisted through the use guide pins, interlocks, or keyways to mate the cavity and core
inserts to avoid accelerated wear on the sliding surfaces.

13.2.2 Coinjection Mold Design
A schematic for a coinjection mold and feed system is shown in Figure 13.3 [43]. As shown,
material is delivered to the mold from the barrels of two injection units 8 and 9 to the mold
10 via corresponding flow channels 15 and 16. These two channels converge at a control valve
17 prior to the sprue 11. The control valve uses a valve pin 18 with two skewed flow channels.
By rotating the pin, one of the two flow channels in the pin will register with the channels 15
or 16 to allow material to flow from the corresponding barrels 8 or 9 into the mold while also
preventing the materials from flowing between the barrels. A control system is required to
coordinate the actuation of the valve pin 18 with the injection of material from the barrels 8
and 9. Given this feed system design, a first and last injection of the first material is warranted
to avoid contamination of any material residing between the valve pin 18 and the sprue 11
as previously discussed with respect to Figure 13.2.
For the most part, design of coinjection molds is very similar to that of conventional
molds; many conventional molds can be successfully used in a coinjection process since the
mechanisms for coinjection are mostly integrated with the molding machine and not the mold
itself. However, the mold designer should modify the analyses for coinjection. With regard
to mold filling, the mold designer should ensure that the mold cavity is designed to achieve
the desired filling patterns at reasonable pressures. Analytical solutions and simulations have
been developed for the coinjection of two materials with dissimilar viscosities into a mold

13.2 Coinjection Molds

347

Figure 13.3: Coinjection mold and process

[44, 45]; however, in many coinjection applications, the mold will operate successfully if the
mold is designed to fill completely with only the more viscous material. Analysis of cooling,
shrinkage, and ejection should also be modified to consider the melt temperatures and
thermal properties of the two materials. Given the multi-layered structure of the coinjected
molding, a reasonable approach is to derive a “meta-material” that has material properties
in proportion to the layer thickness of the two constitutive materials.

13.2.3 Gas Assist/Water Assist Molding
Gas and water are both fluids, so both gas assist molding and water assist molding can
be considered as types of fluid assisted molding processes. Since these assisting fluids are
injected inside of a first material, all fluid assist molding processes can be considered a type
of coinjection molding process. Compared to traditional coinjection with polymer melts,
fluid assisted molding has two distinct differences. First, the second injected fluid (such as
nitrogen or water) has a very low viscosity compared to the previously injected polymer melt.
This low viscosity provides for a very low pressure drop along the flow path, and thus gives
excellent pressure transmission for packing out the previously injected polymer melt. Second,
the assisting fluid is later removed from the molded part so as to hollow out the inside of the
molded part. With careful mold design, fluid assisted moldings can have increased strength,
lighter weight, and reduced cycle times compared to conventional or coinjected molds.

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Fluid assisted molding is a fairly old process having served as an alternative to blow molding
[46]. Two variations of a more modern gas assist process with injection decompression are
shown in Figure 13.4 [47]. In the first method, two mold halves 10 and 11 form a mold cavity
12 into which the plastic melt will flow. The molding machine’s nozzle 13 has an internal core
16 with a sliding valve 19 that is actuated by compressed gas alternately introduced through
gas lines 20 and 21 through three-way valves 22 and 23. At the beginning of the process, the
plastic melt 24 is introduced into the mold cavity through the machine nozzle 13; at the same
time, the sliding valve 19 is in a position which blocks the gas inlet tube 18 compressing the
gas through line 21 decompressing the gas through line 20. After the mold cavity is partially
filled, gas line 20 is pressurized while gas line 21 is depressurized. This causes the sliding valve
to assume the position as shown so that gas inlet tube 18 is opens and delivers compressed
gas to the mold cavity. Once the gas has been injected, the sliding valve is then actuated to
prevent the undesired flow of the plastic melt. After the molded part cools, the opening of
the mold causes the sprue to break and the release of any compressed gas to the ambient
atmosphere.
A second method is also shown in Figure 13.4 in which the reverse of injection compression,
injection decompression, is used to form a hollow part with a very large cavity. In this design,
the plastic melt flows into a cavity formed between two mold halves 30 and 32. While not
shown, these mold halves can have fine details like bosses that are fully formed by the initial
filling of the cavity with the polymer melt. The compressed gas is then injected into a thicker
portion of the mold cavity. At the same time, the mold core 32 is retracted from its opposing
mold half 30 to enlarge the cavity. In this manner, moldings with very large internal gaps
(for example, 50 mm) can be formed while preserving fine features on the exterior surfaces
of the molded part.

Figure 13.4: Gas assist with injection decompression

13.2 Coinjection Molds

349

The mold design of fluid assisted molds needs to vary considerable from that of injection
and coinjection molds. In particular, the mold designer needs to consider the location for
the injection of the gas or water. As demonstrated in Figure 13.4, both the nozzle and cavity
are common locations. As importantly, the mold designer must carefully design the mold
to have appropriate flow channels to strategically direct the gas or water through the mold
cavity. In most mold designs, the cavity wall thickness is made as uniform as possible to avoid
non-uniform cooling and shrinkage. However, such a mold design will not lead to an effective
mold for fluid-assist. The reason is that the gas or water will permeate or “finger” in random
directions through a uniformly thick mold cavity, thereby weakening the molding without
significantly reducing the part weight. As such, thick flow channels as shown in Figure 13.5 are
commonly added to the mold cavity to direct the gas or water through the mold cavity [48]. All
the gas channels will exhibit some irregularity regardless of the magnitude of penetration. In
general, it is desirable to develop a gas channel to provide as uniform a molded wall as possible
while providing the necessary fluid flow and part stiffness. For this reason, the top right gas
channel in Figure 13.5 is least preferred. Since the other flow channels are cored out by the
fluid, the cooling and shrinkage is made relatively uniform without extended cycle times.
Water assist molding seems to have received renewed interest lately [49, 50]. Compared to gas
assist, water assist provides at least three key benefits. First, water has a very high specific heat
and so can be injected to reduce the cycle time compared with gas assist molding application.
In fact, in some water assist molding applications, the flow channels are designed with inlets
and outlets, such that the water can be circulated within the molded part and thereby greatly
reduce heat transfer via heat convection. Second, water is incompressible compared to gas, and
so can be used to provide higher melt pressures in the cavity with less energy and risk than
gas. Third, it has been shown that water assist provides more uniform and smooth surface in
the inside of the molded parts. With these advantages, however, water assist does bring two
significant disadvantages. First, the water must be removed from the interior of the molded
parts; various schemes have been developed to remove the water internal to the molding
prior to the mold opening [51]. Second, the use of water in the molding environment tends
to increase humidity and corrosion, so a corrosion resistant mold material such as SS420 is
recommended.

Figure 13.5: Flow channel sections for fluid assisted molding

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13.3 Insert Molds
Insert molding refers to a process in which a discreet component is placed within a mold, and
then at least partially encapsulated by the subsequently injected plastic melt. Some commonly
inserted components include electrical devices, nuts or other fasteners, stiffening members,
and other plastic components. After the insert molding process, the inserted component is
usually permanently joined with the molded plastic.

13.3.1 Low Pressure Compression Molding
One common method for encapsulation of delicate components is compression molding
as shown in Figure 13.6 for the production of a tantalum capacitor [52]. In this process, the
capacitor 19 is placed between two layers of plastic 17 and 18 prior to the mold closure. The
mold design provides matching cavities 16 and 22 to receive the plastic as well as grooves
21 to receive the lead wires 20. In any molding process, the mold designer should explicitly
consider the handling of the molded parts upon de-molding. In the design of Figure 13.6,
the lower cavity 22 is deeper than the upper cavity 16. In addition, the lower mold half 11
is provided with a flash well 23 for the collection of any plastic that flows out of the cavity
during the compression molding process. As a result of these design elements, the molded
part will remain on the lower mold half when the mold opens.
In this compression molding process, the plastic layers 17 and 18 were cut from sheet stock
in a form to fit into their corresponding cavities while also supporting the capacitor 19 and
lead wire, 20. It is desirable that the plastic fully contact the rear surface of the mold cavities
to facilitate heat transfer and plastic forming. Prior to mold closure, cartridge heaters in the
two mold halves 10 and 11 bring the temperature of the mold and plastic layers to above the
glass transition temperature of the plastic. Once the plastic is softened, the mold is slowly
closed with low force. As the mold slowly closes, the plastic slowly flows around the capacitor
until it is fully encapsulated – any excess plastic in the cavity will flow out the flash surface, 24,
and into the flash well, 23. Once the inserted component is fully encapsulated, full clamping
force may be applied to the two mold halves to compensate for shrinkage and achieve the
desired dimensions while the mold is cooled.
This mold design has some unique features. First, the grooves secure the insert component in
the mold to avoid undesired movement caused by the movement of the mold or the flow of the
plastic melt during the molding process. Second, this process was specifically designed to impart
low stress on the inserted component by the controlled heating of the mold and softening of
the plastic followed by the clamping and cooling of the mold. Given this heating and cooling
cycle, the mold should be carefully designed to minimize the size and thickness of the plates so
that energy consumption and cycle time are minimized. Third, this process used a flash surface
and reservoir to control flashing of excess plastic; it is clearly desirable to select an amount of
plastic stock that minimizes the amount of flashing while ensuring a fully filled cavity. In this
design, the mating flash surface, 24, on the lower mold requires a relatively large clearance
with mating surface on the upper mold half. If this clearance is too small, then the rate of the

13.3 Insert Molds

351

Figure 13.6: Compression molding with inserted component

compression molding process can be limited by the flow of the plastic melt out of the cavity.
The filling and cooling analyses of Chapters 5 and 9 can provide useful design support.

13.3.2 Insert Mold with Wall Temperature Control
Another example of insert molding is provided in Figure 13.7 [53], which is particularly
directed to the control and improvement of weld lines around an inserted component for
the production of a water faucet handle. The mold design consist of two separable mold
halves 30 and 31 having recesses 32 and 33 that together form a mold cavity. The inserted
component 35 is held in position by two opposing pins 36. After mold closure and prior to

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mold filling, a substantially uniform cavity thickness exists between the inserted component
35 and the mold halves 30 and 31. In this mold design, the mold wall temperature of the
mold is locally controlled by the flow of a controlled fluid through channels 40 and 42.
Different fluids such as water, oil, or steam can be provided to different portions of the mold
at different temperatures.

Figure 13.7: Insert molding with mold temperature control

13.3 Insert Molds

353

In the molding process, plastic melt is fed through the gate 38 and will follow the path of least
resistance through the mold cavity. Upon entering the cavity, the plastic melt will divide into
two streams 44 and 45 flowing around the insert. In Figure 13.7, the recess 33 in the lower mold
half is controlled at lower temperature compared to the recess 32 in the upper mold half. As
a result, the upper melt stream 44 will advance more rapidly than the lower melt stream 45.
Given the importance of aesthetics in this molding application, the melt front advancement
and knit-line location 50 can then be adjusted by specifying the difference between the mold
wall temperatures in each zone. Furthermore, a heating element 46 is used to locally heat the
mold wall to a temperature above the plastic’s glass transition temperature to melt and fuse
the area around the knit-line ensuring desirable aesthetic and structural properties.
The design of the multiple temperature control channels seems quite advanced, especially for
1937 when this patent application was filed. To facilitate the implementation of the cooling
channels, the recesses 32 and 33 are themselves provided as mold plates 48 and 49 that are
placed into the cavities in the two mold halves 30 and 31. This design is quite similar to the
bezel example of Figure 9.16 in which the cooling lines have been milled into the rear surface
of the core insert. The cooling and structural analysis of Chapters 9 and 12 should be applied
to determine the cooling channel’s hydraulic diameter and layout, as well as the required
amount of plate stock require to avoid excessive stresses. The local heating 46 by resistive
means will be discussed in more detail in Section 13.7.1.

13.3.3 Lost Core Molding
Lost core molding refers to a process in which a mold core is inserted into a mold cavity to
form the interior of a molded plastic part. After the molding with the core insert is ejected,
the core is melted out of the molded part to leave a complex interior cavity. One lost core
molding application is shown in Figure 13.8 [54]. This particular application molds a valve
housing with internal threads and an internal cavity containing a spring and ball check.
The lost core molding process requires two sets of molds. The first mold design consists of
two mold halves 4 and 6 which meet at a parting line 8. The mold cavity 10 includes threaded
ends 12, a central bore 14, and a valve seat 16. Prior to mold closure, a ball check 26 and a
compression spring 28 are inserted into the cavity 10 from the parting plane. After these
components are inserted into the cavity and the mold is closed, a pin 22, is lowered into the
mold cavity in opposition to the spring to lift the ball check from its seat. A low melting point
material 30 is then injected through an opening 20 to completely filly the mold cavity. Upon
solidification, the low melting point material has locked the ball check and spring in position.
The mold is then opened, and the molded part 32, is removed with the pin 22.
The molded part 32 is then inserted into the second mold’s cavity 46 formed by mold halves
40 and 42 for use as a core piece to form the inside surfaces of the valve housing. From the
previous molding process, the core includes externally threaded ends 34 and a central section
36 that encloses the ball check 26, spring 28, and a conical surface 38, which is used to form
the contour of the valve seat of the valve housing. The sliding fit of the pin 22 with the hole
52 serves to center the core 32 properly within the mold cavity 46. Plastic 56 is then injected

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13 Mold Technologies

Figure 13.8: Lost core molding with internal components

through the sprue 50 to fill the mold cavity and surround the core 32. Upon removal of the
solidified molding, the core 32 is melted away to leave the final structure 60. This housing
60 has internally threaded ends 62 and a central chamber 64, which contains the ball check
26 and the spring 28.
It may seem unlikely that such a lost core molding process is feasible. To melt the core from
the housing, after all, the first material 30 that makes up the core must have a lower melting
point than the second material 56, which makes up the housing. Then, why doesn’t the core
melt during the injection of the second material? The reason is that the first material 30 has
sufficient mass to act as a heat sink and absorb heat from the second material 56 without

13.4 Injection Blow Molds

355

melting. For example, the first material is suggested to be a metallic alloy of 58% bismuth
and 42% tin. Such an alloy melts at about 138 °C. For the second material, various plastics
with a wide range of melting points have been used, including acetal and polycarbonate. For
molding with higher temperature plastics, both the mold and the lost core can be cooled to
minimize melting of the core.

13.4 Injection Blow Molds
Injection blow molding is a process by which complex, thin-walled parts can be made including
large internal cavities. In this section, two different blow molding processes are presented. The
first design utilizes a conventional injection molding machine with a rotary mold while the
second design uses a four position indexing system with multiple molding stations.

13.4.1 Injection Blow Molding
An injection blow mold design is shown in Figure 13.9 [55]. The design includes two injection
molds 48 and 50 which are positioned at equal radial distances from the axially located main
sprue. The injection molds each include gating 54 and 56, an injection molding cavity 58 and
60, and other common mold components. The design also includes two sets of split cavity
blow molds 140 a/b and 142 a/b so that undercut parts may be readily ejected after inflation.
The injection blow molds are located diametrically opposite each other on the same radius
as the injection molds 48 and 50. All four molds in this design spaced at 90 degree angles.
The mold cores are spaced on the same radius as the mold cavities so that the four cores can
engage the four mold cavities simultaneously upon mold closure.
A manifold delivers melt from the nozzle of the molding machine to the mold cavities.
The manifold rotator 18 is designed to oscillate between two orthogonal positions through
actuation of a hydraulic drive cylinder 124 pivoted at one end by a pin 126 to the bearing
block 78. A piston 128 having a clevis end 130 pivotally engages a crank arm 132 which is
secured by screws or other suitable means to the circumference of the manifold axle 15.
Stops 134 and 136 are fastened to the bearing block to limit the travel of bellcrank arm to a
90 degree sweep. This design ensures that the mold cores 114 and 116 engage the injection
mold cavities 58 and 60 at one position of the manifold unit, while the other two mold cores
engage the injection blow molding cavities 65 and 67.
During the molding process, the machine clamps the mold cores against the mold cavities.
The injection unit of the molding machine provides plastic through the main sprue 42 and
runners 44 and 46 of the manifold 14 to the injection mold cavities 58 and 60 where the blow
molding parisons or pre-forms are molded. Afterwards, the cores carrying the hot parisons,
are reciprocated out of the cavities by action of the clamp. The manifold assembly then
rotates 90 degrees to align the injection blow mold cavities with the molded parisons. The

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machine then clamps the mold and injects compressed air through the bores of the parisons
to inflate the parisons and form the blow molded products while the injection unit fills the
two injection mold cavities to form the next set of parisons. Upon mold opening, the split
blow molds open and the finished parts are ejected.
This design utilized a rotating set of mold cavities with a reciprocating set of mold cores. A clear
alternative would be to utilize a stationary set of cavities with a rotating and reciprocating
set of mold cores. Either design strategy provides a method for compactly and economically
performing injection-blow molding through the modification of a conventional molding
machine. The design may be guided by filling analysis to ensure appropriate runner system and
cavity design, cooling analysis to control the temperature of the hot parisons, and structural
analysis to minimize the size and stress of the injection and blow molds.

Figure 13.9: Injection blow mold with rotating cavities and reciprocating core

13.4 Injection Blow Molds

357

13.4.2 Multilayer Injection Blow Molding
A different machine configuration for injection blow molding is shown in Figure 13.10 for the
molding of a two layered product [56]. The inner and outer layers are chosen for particular
reasons related to the use of the product. For example, the inner layer 44 may be made of
material which resists reaction with the contents of the container while the outer layer 44′
may be made of a material of substantially greater strength than the inner layer. In this design,
the injection molding system includes a first injection station 10, a second injection station
12, a blowing station 14, and a stripper station 16. The system has an indexing head 18 with
four faces. A set of core rods 22 extends from each of the four faces. The indexing head rotates
intermittently about a center shaft 20 to sequentially index each set of cores with the different
stations. Due to its configuration, this design is known as a “four position machine”.
At the first injection station 10, the injection mold 26 is supplied with plastic melt from an
injection unit 28 via a runner system 30. The injection mold is a split cavity design with a
stationary lower section 32 and a movable upper section 34. When these mold sections are
closed together, each of the core rods 22 extends into a cavity. The neck portion 38 of each
core rod is firmly gripped by the wall of the opening 36. The plastic is injected into the cavity
at an opening opposite the top of the core rod, and flows around and down the length of the
core rod to form a parison 44. As the plastic flows down the length of the cavity, the melt
loses some of its heat to the mold 26 and the core rod 22. Because the core is slender and
has a large thermal resistance as analyzed in Section 9.3.5.5, the highest temperature of the
parison will occur at the end of the core rod 40 near the gate and runner 30.
After the molding of the parison in the first station 10, the mold 26 opens and the core rods 22
are lifted clear of the mold cavity in the lower section 32 by rising movement of the indexing

Figure 13.10: Two layer injection blow molding

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head. The indexing head turns 90 degrees in the counterclockwise direction and brings the
core rods with the parisons 44 on them over the lower section of a second injection mold 48
at the second injection station 12. The second injection mold closes on the neck portion 38
to form mold cavities 42a which are larger in cross-section than the corresponding cavity 42
if the first molding station.
As previously noted, the tip of the first parison 40 is at the highest temperature and so most
easily deformed. If the second layer of the parison were gated from the same location, then
the direct impingement and high flow rates of the second layer could wash some or all of the
first parison off the core rod and thereby lessen the value of the molded product. For this
reason, the plastic for the second layer 44′ is introduced into the cavity 42 from a manifold
50 and individual runners to the neck end of the cavity. The plastic flows around the first
layer to form a parison with two layers.
The second mold is then opened, and the indexing head moves the core rods to a blow
mold, 58, at the blowing station, 14. The blow mold holds the neck portion of the laminated
parison. The mold cavity, 42b, is in the form of the desired article which is to be blown from
the laminated parison. The blowing operation then fully inflates the two layer parison 60. The
blown products 60 next advance to the stripper station 16 where a stripper plate 64 pushes the
molded products 60 off the core rods, 22. With the next rotation of the indexing head, the bare
core rods are presented to the first forming station to begin the next round of moldings.
There are three suggested benefits of this mold design. First, the witness mark formed by the
gating at the tip of the core is wiped away by the flow of the second layer. Second, the design
reduces the cycle time associated with the molding of the first layer by gating the second
layer into a location away from the hottest portion of the first layer. Third, the improved
consistency of the first layer facilitates the molding of a thinner first layer and with it a lower
cost product.

13.5 Multi-Shot Molds
Multi-shot molding sequentially injects different types of plastic, to mold a part with distinct
regions. There are several potential advantages for the use of a multi-shot molding process.
These include the use of multiple shots with:





different shot capacities to sequentially mold very large parts;
different colors to mold multi-color parts, such as automotive taillights;
different structural properties to mold parts with improved living hinges, tactile feel,
etc.;
and others.

There are many different methods to accomplish multi-shot molding. Perhaps the oldest
and simplest is overmolding, which can be considered a variant of insert molding. Another

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approach is the core back method, which lends itself to a relatively simple mold design.
However, multi-station mold designs are the most common method in use today due to the
capability of this process to economically produce more complex part geometries. Each of
these mold design strategies will be discussed.
Regardless of the type of multi-shot mold design, the provided mold design and analysis
methods generally apply with a few special considerations. First, multi-shot molds may
require extended cooling times. The reason is that the first layer will not be at the mold coolant
temperature when the second layer is injected. Furthermore, the first layer will largely prohibit
the transfer of heat from the second layer to the mold. For these reasons, the mold designer
should consider multi-shot molding using the analysis for one-sided heat flow as discussed in
Section 9.3.5.6; the second layer should be 40% thinner than the first layer to avoid extending
the cycle time. Second, multi-shot molds provide the mold designer the opportunity to utilize
the second injection of plastic to melt and wipe out small imperfections or witness lines on
the first layer of plastic. Because of this effect, however, the mold designer should avoid the
placement of fine details on the some surfaces of the first molding that may be degraded by
the second injection of the plastic melt.

13.5.1 Overmolding
A multi-shot mold design using an overmolding approach is shown in Figure 13.11 [57]. In
this design, a separate mold has used a branching runner 4 to fill two lateral runners 2 and a
series of mold cavities for the production of key caps, B. Each key cap has a window 7 molded
into its top surface 6 in the form of that key’s desired character, such as the number “5”. This
particular design is directed to the bonding of incompatible plastic materials through the use
of a solvent such as acetone applied to the key caps’ rear faces 5. Accordingly, the branching
runner 4 is intended to be used as a handle by the operator during the application of the
solvent; more modern designs may use bosses or shoulders to assist automated part handling
systems.
Once the solvent has been applied to the key caps’ rear faces 5 the key caps are placed in the
cavities 1 of the lower half of a mold, A. The upper half of the mold, C, provides cores 12 that
mate with the cavities in the upper half of the mold for the molding of the keys. After the mold
is closed, the second plastic material is injected through the primary runner 13 and secondary
runner 14 into the mold cavities. A portion of the material will fill the back 9 and window 7
of the key cap as well as the key’s boss 17 for later assembly with other components.
This type of mold design is quite common for production of keys and signs to avoid noticeable
wear. Specifically, the number “5” is formed by two materials, each with the same thickness as
the window 7. The key cap’s entire top face 6 will have to be worn away before the character
disappears. On a side note, this mold design has two features that may be useful in other multishot molding applications. First, the projections 11 increase the surface area and therefore the
bond strength between the two materials; these same projections will also tend to increase the
lateral strength of the molded parts. Second, a rib 10 is placed below the window 7 to undercut
the second molded material and ensure that the two pieces are not separable.

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Figure 13.11: Two layer injection blow molding

13.5.2 Core-Back Molding
Core-back molding refers to a multi-shot molding process in which a portion of the mold,
typically a core, is moved to create or reveal a mold cavity into which a second plastic melt
can be injected adjacent to a previously molded first plastic melt. A design for a mold with
core-back capabilities used to make front or tail indicator lights for vehicles is shown in
Figure 13.12 and Figure 13.13 [58]; the molded piece in this application may consist of
three different colors such as red, clear, and amber. The mold consists of an upper mold half
4 and a lower mold half 5 that together form a cavity. The cavity is split into three different
portions 11, 12, and 13 through the use of four blades 14, 15, 16, and 17 that are independently
actuated by pistons 18, 19, 20, and 21 integral with cylinders 22, 23, 24, and 25. Each cavity
is fed polymer melt through runners 7, 8, and 9.

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Figure 13.12: Plane view of mold with core-back

b

Figure 13.13: Section view of mold with core-back

In the molding operation, the mold and the blades are closed to isolate the different portions
of the mold cavity so that the different plastic materials can be sequentially injected. To reduce
cycle time, it is preferable to concurrently inject polymer melts from nozzles 1 and 2 through
the runners 7 and 8 into the areas 11 and 12. Once these materials are sufficiently solidified,
the cylinders are actuated to retract the blades 14, 15, 16, and 17. The third plastic may then be
ejected through runner 9 into the third area 13 of the mold cavity. In this manner, a molded
part can be produced consisting of multiple materials without ever opening the mold.

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There are two items of note regarding this core-back design. First, it is possible to have
designed a mold utilizing a single set of blades 16 and 17 to reduce the size and complexity of
the mold. Indeed, for strength reasons a preferred design would use a single set of blades that
interlock with a slot on the opposing face of the mold cavity. However, one possible reason
for the design of Figure 13.12 and Figure 13.13 is that the retraction of the blades into both
sides of the mold provides a means for the molding of protruding ribs into the upper and
lower sides of the mold 4 and 5. In any case, structural analysis should be used to ensure that
the blades are of sufficient thickness to avoid excessive shear stress and bending in the blades
given the thickness of the cavity and the operating melt pressure.
The second item of note concerns the use of two sets of blades as opposed to a single central
core that could be withdrawn. An alternative mold design could avoid the use of blades
altogether by making the entire center section 13b of Figure 13.13 a single actuated member.
In this alternative design, the center section 13b would be in a forward position upon mold
closure, closing the cavity area 13 of Figure 13.12 from the melt and providing the same
cavity side walls effectively provided by the blades 14, 15, 16, and 17 in the previous design.
After the left and right areas 11 and 12 were filled with plastic, the center section 13n could
be retracted and the cavity area 13 filled with a third plastic via runner 9. It may seem that
this alternative design would require extremely high actuation forces for the center section
13b given its large projected area subjected to melt pressure. However, this is not the case
since the center section will not see significant pressure when molding areas 11 and 12, and
can be supported by a shoulder or other mold components when retracted and exposed to
high melt pressures.

13.5.3 Multi-Station Mold
Parts consisting of multiple materials are also often molded in multi-station molds. One
such design is shown in Figure 13.14 to produce a replica of the Canadian national flag [59].
In this design, a first mold is composed of a transfer plate 47, a cavity plate 48, and a runner
plate 49. The cavity plate 48 defines a cavity 51 including lateral panel segments 52, a central
maple leaf image segment 53, and bridges 54 that connects all of the segments together. In
operation, the first plastic melt is injected from a runner 58, into a sprue 56, through a gate
57, and into the cavity 51. Once this plastic solidifies, the mold is opened and the transfer
plate is removed from the first mold. Because of the mold design, the solidified runner 68
and molding 61 remain with the transfer plate.
The transfer plate 47 with the solidified runner 68 and molding 61 is then transferred to a
second mold. In this design, the transfer plate inserts the solidified molding 61 into another
cavity 70 in a second mold cavity plate 69. The transfer plate is then moved laterally to strip
the feed system from the molding 68. Additional plates 71 and 75 are then positioned with
the mold cavity plate 69 to completely form a second mold. The second material is then
injected adjacent and over the first material to form a single part integrating the two plastic
materials.

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Figure 13.14: Multi-station mold design

Compared to a core back mold design, the multi-station mold provides for greater flexibility
in the molded part design. Specifically, multi-station molds allow for complex parts to be
molded, and then inserted into other arbitrarily complex cavities for injection of additional
plastic materials adjacent to, above, and around the prior molding(s). Accordingly, several
different mold and machine designs have been developed to support multi-station molds.
These include the transfer of parts via rotating mold sections similar to the designs shown
in Figure 13.9 and Figure 13.10.
More recently, dedicated two-shot molding machines have been developed as shown in
Figure 13.15 [60]. In this type of design, the injection units provide material to two sets of
mold cavities mounted on two opposing platens. Because the platens oppose each other, a
single clamping mechanism can be used to provide the mold closure force for both sets of
cavities, very similar to stack molds as discussed in Section 13.6.2. Different drive mechanisms
have been developed to index the cores including turret drives as shown in Figure 13.15, rack
and pinion arrangements [61], and others.

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Figure 13.15: Turret style molding machine and mold design

13.6 Feed Systems
13.6.1 Insulated Runner
As presented in Chapter 6, the most common types of feed systems are cold runners and
hot runners. Both types of feed systems have disadvantages. With cold runners, there is
considerable material waste associated with the formation of the feed system as well as the
potential for extended cycle times.With hot runners, there is the additional cost and complexity
associated with the temperature control systems as well as the potential for temperature
variations and color change issues.
As an alternative to both cold runner and hot runner designs, the insulated runner was
designed in an attempt to eliminate these disadvantages. An insulated runner design is shown
in Figure 13.16 [62]. The design layout is very similar to a three plate mold with a runner
section 15, a cavity section 16, and core sections 17. The runner layout is also similar with a
sprue 19 conveying the melt through the plate thickness to primary and secondary runners
18 that convey the melt across the parting plane to a second set of sprues, 22 and 23, which
convey the melt down to the mold cavities. Compared to a traditional three plate mold,

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Figure 13.16: Insulated runner design

however, all segments of the feed system are purposefully designed to have large diameters.
In addition, the runner section 15 is secured to the cavity section 16, and does not open at
all during normal molding.
During the molding process, the melt is injected from the nozzle of the molding machine and
completely fills the feed system. A skin, 18a and 18b, immediately forms on the surface of the
runners. However, the solidified skin does not fully propagate throughout the runner since



the thermal conductivity of plastic is very low, and
each molding cycle conveys heated polymer melt from the molding machine throughout
the feed system.

As a result, the diameter of the molten core remains nearly consistent during the molding
cycle. In this manner, the insulated runner can be operated as a hot runner albeit without
any heaters, thermocouples, or temperature controllers. The color change issue is resolved
by removing the fully solidified feed system with the release of runner section 15 from the
cavity section 16.
The design of Figure 13.16 [62] was specifically intended for the molding of semi-crystalline
polymers such as polyethylene and polystyrene. Experiments were conducted with runner
diameters of approximately 25 mm and cycle times in the vicinity of 60 s; the thickness of
the skin was approximately 6 mm. Of course, the optimal specification of runner diameters
will depend on the material properties, the melt and mold temperatures, and the flow rates
and cycle times. The use of internal heaters and insulating layers (such as the airs gaps 40a
and 40b around the sprue inserts 39a and 39b as shown in Figure 13.16) can provide greater
process robustness albeit with increased design complexity. Perhaps because of these processing
uncertainties, the use of insulated runner systems has decreased with the commoditization
of hot runners. Even so, insulated runners can provide good performance at low cost.

13.6.2 Stack Molds
When the plastic melt is injected into the mold cavity at high pressure, significant clamp force
is required to keep the mold closed so that the melt does not escape the mold cavity. Because

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Figure 13.17: Early stack mold design

the clamp force is proportional to the projected area of the mold cavities, the clamp force
increases proportionally with the number of mold cavities across the parting plane. However,
if the cavities are “stacked” one on top of another, then the clamp force used to close one set
of cavities can also be used to close any sets of cavities that are in the stack.
One such stack mold design is shown in Figure 13.17, which was to designed to mold two
vinyl records with the clamp force and cycle time normally used to mold one vinyl record
[63]. In this design, two sets of stampers are mounted between an inner plate 12 and two
outer plates 14 and 16; the inner plate 12 is guided by bearings 20. The melt flow from the
nozzle 54 of the molding machine through extended sprue 40 to two sets of cavities where
the records are formed. After the plastic solidifies, the melt shut-off rod 65 is actuated to
seal the sprue inlet 51 with the shut-off 66. This action also connects the sprue 40 to the
chute 64, such that the sprue may be stripped from the moldings with actuation of the sprue
knock-out rod 75. The molded records are then ejected after retracting the sprue knock-out
rod and opening the mold.
There are two deficiencies in the mold design shown in Figure 13.17. First, the stack mold
requires the formation of a sprue, which is scrap. Second, the melt flow to the two cavities is
not balanced due to the additional length of the sprue to the left cavity. Both these deficiencies
are resolved in modern stack mold designs that utilize hot runner systems; one such stack
mold design is shown in Figure 13.18 [64]. In this design, a central moving plate 56 houses
two sets of cavities 60 on opposing parting planes 62 and 64. A hot manifold 65 delivers the
polymer melt to the cavities through the runner 70 and subsequent drops. The design uses
two single axis valve gates to deliver the melt from the molding machine nozzle 17, across the
parting plane 62, and to the manifold 65. During filling and packing stages of the molding
process, the actuators 50 and 54 retract the valve pins 24 to deliver the melt from the nozzle to
the manifold. Otherwise, the valve pins seal the feed system during the plastication, cooling,
and mold reset stages.

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Figure 13.18: Hot runner stack mold design

While the design increases the size and complexity of the mold, it enables the molding
of two sets of cavities with the same cycle time and clamp force as a single set of cavities.
Furthermore, the flow to both sets of cavities is completely balanced and there is no material
waste associated with the hot runner feed system. Given the significant part cost reductions
afforded by this type of stack mold design, stack molds are now quite common with two,
three, and four levels of cavities. Clearly, the stack mold design requires carefully balancing
of potential processing cost savings with issues related to investment, maintenance, color
change, stack height, and injection volume.

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13.6.3 Branched Runners
A potential issue in “naturally balanced” branched runners, such as shown in Figure 13.19
[65], is flow imbalances due to thermal variations caused by the flow and related shearing of
the melt [27]. Despite the geometrical balance of the feed system, it has been observed that
parts formed in cavities may be larger and heavier depending on their location in the branched
feed system. The flow imbalance is created by a non-symmetrical shear distribution within
the laminar plastic melt as it flows through the runner system. Specifically, in the feed system
there is a distribution of shear rates and temperatures across the radius of the runner: a hot
polymer melt at the center of the runner is surrounded by a layer of higher sheared, hotter,
and lower viscosity plastic melt. When the laminar melt flow reaches a branch in the runner
system, the lower viscosity melt remains in its outer position while the more viscous melt at the
core is split and flows to the opposite side of the branch 14. This lateral variation in viscosity
will cause a non-uniform flow distribution at the next downstream branch, 16 and 22.
To resolve the flow imbalance, it is necessary to eliminate the lateral viscosity variation in the
polymer melt. One approach shown in Figure 13.20 [65] imposes a level change just prior to
the branch. Specifically, the upstream section 100 of Figure 13.20 corresponds to the primary
runner 12 of Figure 13.19 while the downstream section 104 corresponds to the secondary
runner 14. Prior to the branch, a flow diverter 106 forces the melt upwards into the runner
extension 102. When the melt subsequently flows down into the runner 104, the more viscous
inner core is directed to the side of the runner that is opposite the level change. Since the
viscosity variation is now distributed vertically through the runner, the melt flow is balanced
when the downstream runners branch laterally.
Figure 13.20 provides a design for a set of inserts to accomplish the level change. The cavity
insert 150 and the core insert 156 are placed at any necessary junction between the upstream
and downstream runners. An indented cavity 164 and a protruding core 162 accomplish
the level change. Because the viscosity variation is only reoriented and not eliminated, the
use of multiple level changing inserts at consecutive runner branches will re-establish the

Figure 13.19: Branched runner system

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Figure 13.20: Level change mold inserts, also known as Melt Flipper

flow imbalances. More recently, research has shown that the flow imbalance and the ability
to control the melt flow is related to the melt rheology and the processing conditions [28].
For this reason, additional designs have been developed to adjust the viscosity distribution
in the feed system [66].

13.6.4 Dynamic Melt Control
The goal of injection molding process control is to specify the pressure and temperature
distribution across the entire cavity. There are many possible concepts for adding the necessary
degrees of freedom but one generic approach is to provide a means for instantaneously
modifying the flow resistance in each branch of a runner system. As shown in Figure 13.21
[67], one design uses a set of strategically located, variable impedance melt valves each
individually controlled with a rapid-response hydraulic actuator. The valves are designed with
an adjustable annular clearance 81 between a tapered valve stem 45 and a tapered surface 47
of a bore 19. Since the resistance to flow is determined by the annular gap between the valve
stem and the mold wall, axial displacement of the valve stem can be used to selectively vary the
flow rate and pressure drop through each valve. When used in a closed loop control system,
this method can provide simultaneous control of multiple cavity pressures.
This system implementation introduces three new characteristics into the molding process
[68]. First, the independent control of each valve allows the pressure and flow in multiple
regions of the cavity to be decoupled. Previously, changes aimed at improving one area of
the part could result in detrimental effects elsewhere in the cavity since process changes
could not be controlled independently. With this process, the flow through each valve can be
controlled independently, bringing extra degrees of freedom to the molding process. Second,
the capabilities of this system can be leveraged by dynamic re-positioning of the valve within

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Figure 13.21: Dynamic feed control

the molding cycle. This strategy can be used, for instance, to specify one set of valve positions
to profile flow rates in the filling stage followed by a completely different set of valve positions
to profile pack pressures. Third, the dynamic capabilities of this process allow the valves
to be quickly controlled in response to feedback from process sensors in the mold cavity,
thus providing closed loop control of the cavity state variables which directly determine
the product quality. Variation in molding machine input parameters, machine behavior, or
material properties can be dynamically compensated to produce consistent parts. Moreover,
the control of cavity variables directly enables the use of pressure measurements as a process
control technique for automated detection of quality problems. This could eliminate the
need for manual inspection of part quality in many circumstances. Since the dynamics of the
molding machine are decoupled from the cavity, details of molding machine performance
are made less significant.
The size, complexity, and cost of a closed loop melt control system can raise significant barriers
to implementation in many molding applications. To reduce the cost and complexity of the
system, a self-regulating valve design was developed as shown in Figure 13.22 [69] to work with
an open loop control system design and not require any melt pressure transducers. The melt
entering the flow channel 14 will flow into the aperture 20b and around the head of the valve
pin to apply a dynamic force 24 against the projected area of the valve pin, which will tend to
shut-off the melt flow and reduce the melt pressure. At the same time, an opposing control

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26

24

14b
Figure 13.22: Self-regulating valve design

force 26 is applied to the stem 16 of the valve pin, which will tend to increase the melt flow and
the melt pressure. As a result, the pin will move until equilibrium is established between the
dynamic force 24 and the control force 26. In other words, any difference between the control
force 26 and the dynamic force 24 will cause movement of the control member 16 until the
control force and the dynamic force equilibrate, thereby regulating the melt pressure.
The outlet melt pressure will be approximately equal in magnitude to the control force divided
by the projected area of the valve. Previous research [70, 71] has shown that shear stresses and
pressure drops along the length of the valve pin 16 may contribute to errors in the output
melt pressure of a few percent. If the control force is provided via a hydraulic or pneumatic
cylinder, then the output melt pressure is equal to the pressure supplied to the actuator times
an intensification factor, typically on the order of 100 : 1 as determined by the ratio of the
push area of the actuator to the area of the head of the valve pin. By controlling the actuation
pressure to each valve cylinder during the molding process, the molding process can be made
more consistent and more flexible compared to conventional injection molding while not
requiring cavity pressure transducers or a closed loop control system.

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13.7 Mold Wall Temperature Control
The analyses and designs presented in Chapter 9 for cooling systems are adequate for most
injection molding applications. However, there are some applications in which the use of
conventional cooling designs is unacceptable. Normally, the development of a solidified skin
occurs when the hot polymer melt contacts the cold mold wall. In some molding applications,
the solidified skin may lead to premature freeze-off of the melt in the cavity, excessive
birefringence in the molded part, or inadequate levels of gloss or surface replication. In other
applications, mold wall temperature fluctuations across the surface of the mold cavity may
lead to a lack of dimensional control. As such, some molding applications involving lenses,
airplane cockpit canopies, optical storage media, and fiber reinforced materials may seek to
improve the quality of the moldings through dynamic control of the mold wall temperature.
Several different strategies are next discussed.

13.7.1 Pulsed Cooling
One approach to controlling the mold wall temperature is to use one or more sets of cooling
channels to actively heat and then actively cool the mold. One such mold design is shown in
Figure 13.23, which was developed to provide tight tolerances when molding highly sensitive
plastic materials or very thin walled moldings [72]. In this design, a mold cavity 7 is formed
by a cavity insert 10 and a core insert 9. The core insert is purposefully designed to be as thin
as possible, and surrounds an internal core 12 so as to provide a channel 14 for circulation
for temperature controlled fluids. The cavity insert 10 is similarly designed to mate with the
cavity plate 28 and the outer insert 29 to form channels 24 and 25.
In operation, two fluids are separately temperature-controlled with a heating device 35 and a
cooling device 34; two separate fluids are recommended to reduce the cost and time associated
with sequentially heating and cooling a single fluid. Prior to the injection of the polymer
melt, the control valves 36 and 37 will direct the heated fluid to the inlet 18 and through the
mold core via channels 14 and 15 before returning via the outlet 16; a similar heating circuit
is formed for the mold cavity via elements 26, 22, 25, and 27. Once the inserts 9 and 10 are at
a temperature above the freezing point of the plastic melt, the plastic melt is injected into the
cavity 7. The control valves can then be actuated to direct the cooling fluids from the cooling
device 34 through the same channels previously used for heating.
The success of this mold design is highly dependent on minimizing the mass of the mold steel
and coolant required to form and cool the walls of the mold cavity. It is clearly desirable to
minimize the thickness of the mold inserts, the length of the cooling channels and lines, and
the heat transfer to adjacent mold components. In this design, air gaps 20, 29, and 38 are used
to reduce the amount of heat transfer and so improve the thermal efficiency and dynamic
performance of the mold; insulating sheets (not numbered) are also provided adjacent the
top and rear clamp plate to minimize heat transfer to the platens. Unfortunately, the size of
the cavity and the structural requirements on the mold components necessitates the use of
fairly large mold components that need to be heated and subsequently cooled. The dynamic

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Figure 13.23: Mold design for pulsed cooling

thermal response is limited. For example, a 100 kg section of P20 that needs to be heated
100 °C and subsequently cooled will require a minimum of 10 MJ (2 times the specific heat
of 500 J/kg°C times the mass of 100 kg times the temperature change of 100 °C) or 3 kW h
of energy. At a cost of $0.10 per kW h, the energy cost for heating and cooling alone is on
the order of $0.30 per molding cycle. For this reason, pulsed cooling is not commonly used
except in very demanding applications.

13.7.2 Conduction Heating
Given the large thermal mass of the mold and the cooling system, another strategy to control
the mold wall is to use conduction heaters at or near the surface of the mold. One design is
shown in Figure 13.24 which was developed to provide a smooth surface finish to one side
of a foamed plastic product [73]. The mold consists of a cavity insert 12 and a core insert 10,
both including a network of cooling lines 34 and 36 as per conventional mold design. A thin
metallic sheet 38 conforms to the surface of the mold cavity 12, with a thin insulating layer of
oxide deposited between the sheet and the cavity insert. The thin metallic sheet 38 includes an

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Figure 13.24: Mold design with conduction heating

opening 40 to deliver the plastic melt from the sprue 32 to the mold cavity 14. Electrical cable
attachments 46 and 48 attach the sheet 38 to low voltage, high current electric cables 50 and
52. Because a very high current load is applied for a short period of time during each cycle
and then disconnected by switch 54, a bypass load in the form of heating pipe 62 is provided
to minimize arcing in the switch with current surges applied to the current source 56. The
electrical resistance of the pipe 62 is high relative to the resistance of the sheet 38 so closure
of the switch 54 effectively creates a short circuit path through the sheet 38. The bulk of the
current from source 56 passes through the sheet 38 when the switch 54 is closed.
Just prior to mold closure, the switch 54 is closed to pass a high current through the sheet. In
this design, a 0.2 cm thick steel plate was used with a length and width of 30 cm and 10 cm,
respectively. Given an electrical resistivity of 30 μΩ cm for the steel plate, the electrical resistance between the cables 50 and 52 would be 450 μΩ. The specification of the patent indicates
that experiments were conducted which yielded a temperature rise of 200 °C in 0.4 s with

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a current of 500 A. With this electrical current and resistance, the driving voltage would be
0.23 V leading to a power dissipation in the sheet of 113 W. Given the 0.4 s heating time, the
energy consumption per molding cycle would be 0.013 kW h. For comparison, the mass of the
steel sheet would be 4.68 kg and would require a minimum of 0.5 MJ or 0.13 kW h of energy
to heat. There is a large discrepancy between the supplied and the required heater power.
To further analyze the heating requirements, consider a typical molded part with a heat
capacity of 2000 J/kg °C, a 3 mm thickness, a melt temperature of 240 °C, an ejection
temperature of 100 °C, and a cycle time of 30 s. In this case, the heat load imposed on the
mold by the ABS melt is 28 kW/m2; given that the cooling lines are placed on two sides of
the mold, the cooling power is approximately 1.4 W/cm2. As such, a 30 cm by 10 cm heating
plate must deliver at least 420 W simply to overcome the heat transfer to the cooling lines
before the temperature of the heating plate begins to increase significantly.
It is noted that conduction heaters are widely available with power densities exceeding
250 W/cm2. Such a heater, if placed on the surface of a mold cavity, could increase a 0.2 cm
by 30 cm by 10 cm steel plate’s surface temperature by 200 °C in 6 s. Attempts have been made
to incorporate higher power, thin film heaters directly into the mold surface [74]. However,
such efforts to incorporate conduction heaters into molds have not been widely successful for
at least three reasons. First, the large, cyclic pressure imposed on the heater(s) by the polymer
melt tends to fatigue the heaters. Second, it is difficult to configure the heater(s), mold cavity,
and cooling channels to provide the uniform wall temperature required to deliver aesthetic
surfaces with tight dimensional controls. Third, the heaters are located between the mold
cavity and the cooling channels, tend to reduce the rate of heat transfer during cooling, and
so extend the cooling time.

13.7.3 Induction Heating
Induction heating is another approach to increasing the mold wall temperature prior to mold
filling. One design is shown in Figure 13.25 [75], which was developed to injection mold
reinforced thermoplastic composites with superior surface gloss and substantially no surface
defects. To reduce energy consumption and heating time, only a small portion of the mold’s
surface is selectively heated by high-frequency induction heating. As shown in Figure 13.25,
a conventional injection molding machine 3 delivers polymer melt to a mold consisting of a
stationary mold half 4 and a movable mold half 5.
Prior to mold closure and filling, a high-frequency oscillator 1 drives alternating current
through an inductance coil (inductor) 2 temporarily placed near the surface(s) of the mold.
When a high frequency alternating current is passed through the inductor 2, an electromagnetic field is developed around the inductor which subsequently generates eddy currents
within the metal. The resistance of the mold metal subsequently leads to Joule heating of
the mold surface. Traces A and B in Figure 13.25 demonstrate the increased mold surface
temperature at locations A and B caused by induction heating; traces C and D show no initial
effect at location C and D away from the induction heating but later increase with the heat
transfer from the injected polymer melt into the mold cavity.

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13 Mold Technologies

Figure 13.25: Mold design with induction heating

As with all the previously described schemes for mold wall temperature control, it is desirable
to elevate the surface temperature of the mold as quickly as possible. The heating power
through a high-frequency induction heating is proportional to the square of the alternating
frequency, the square of the current, and the square of the coil density, among other factors. As
such, the inductors must be carefully designed to locally heat the mold surface in a controlled
manner to avoid an undesirable temperature distribution. For example, an inductor was
made from copper tube of 5 mm diameter and wound as a spiral with a pitch of 5 mm. The
distance between the surface of the metal mold and the inductor was set to 1 cm. Experiments
indicated that a driving frequency of 400 kHz yielded a heating power at the mold surface
on the order of 1000 W/cm2, which required approximately 10 s to increase the surface of
the mold by 50 °C.
Compared to conduction heating, induction heating provides for increased heating rates and
the potential for very little additional mold complexity. The primary issue in implementation
is the design of the inductor, and in particular the spacing of its coil windings and their
relation to the mold surfaces. If the design is improper, then the heating may be limited to
low power levels. Experiments [75] indicated that a heating power less than 100 W/cm2 did
not significantly increase the mold surface temperature and eventually caused the overload
breaker to actuate. On the other hand, when the power output exceeded 10,000 W/cm2, the
rate of the surface temperature increase became too steep to control such that uniform heating
was no longer possible; defects such as gloss irregularities, sink marks, etc. were observed with
temperature differences of more than 50 °C across the surface of the mold.

13.7 Mold Wall Temperature Control

377

13.7.4 Managed Heat Transfer
Given the difficulties associated with active mold wall temperature control, a “passive” cooling
design has been developed; the term “passive” is used to imply that the mold does not utilize
any external power to control the mold wall temperature. The design shown in Figure 13.26
was specifically developed to control the mold wall temperature during the molding of optical
media [76]. The mold includes two halves 12 to form a mold cavity 14. Cooling lines 20 are
provided per conventional design to remove the heat from the polymer melt. However, a
thermal insulating member 22 is placed between the mold halves 12 and the stampers 31 and
33. The thermal insulating member 22 is made from a low thermally conductive material,
preferably a high temperature polymer, such as polyimides, polyamideimides, polyamides,
polysulfone, polyethersulfone, polytetrafluoroethylene, and polyetherketone. The insulating
polymer is typically spin coated in an uncured form to provide a layer with a thickness on the
order of 0.25 mm and subsequently heat cured. The stamper 33 is typically fabricated from
nickel, and provides the surface details for replication while also protecting and providing
the insulator with a uniform, highly polished surface during molding.
During molding, the insulating layer 22 behind the stamper 33 slows the initial cooling of
the resin during the molding operation. Because of this insulation, the stamper’s temperature
increases and so the skin layer retains heat longer during the mold filling stage, thereby

Figure 13.26: Mold design with managed heat transfer

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13 Mold Technologies

avoiding the surface irregularities created by rapid surface cooling. The temperature of the
stamper:melt interface can be controlled by specification of the process conditions as well
as the layers’ thicknesses and material properties; one-dimensional cooling analysis can be
used to understand the physics and assist in the design optimization. In this example, it was
found that the centerline temperature 51 of the disc dictates the minimum cooling time for
the part to cool below the glass transition temperature of the polymer melt. The temperature
52 at the stamper:melt interface impacts the thermal stress and pit replication on the disc’s
surface and is measured. The temperature 53 in the mold behind the insulator suggests that
the mold acts as a heat sink and is maintained at a substantially constant temperature.
The mold designer and process engineer should intuitively understand that the addition of
an insulating layer will tend to reduce the rate of heat transfer from the melt to the mold,
and therefore require extended cooling times. To alleviate this issue, the cooling lines can be
operated at a lower temperature to provide for higher rates of heat transfer after the initial
heating of the stamper. Accordingly, this design strategy provides a reasonable level of mold
wall temperature control without any additional energy consumption or control systems.
However, the level of temperature control is limited compared to the other active heating
designs. In addition, this approach may be difficult to apply to complex three dimensional
geometries.

13.8 In-Mold Labeling
Injection molding generally provides highly functional and economical parts. In many
applications, however, there is a requirement for decorating, detailing, or otherwise labeling
the molded parts according to the consumer’s needs. In some cases, the decorating may be
provided by post-molding processes such as hot stamping, pad printing, painting, screen
printing, and others. In other cases, these techniques are not feasible since some plastic resins
such as polypropylene, polystyrene, polyethylene, and others are inherently resistant to dies,
inks, and paints.
One approach might be to utilize two-shot molding with different types of plastics to achieve
the necessary detail. However, this approach is relatively expensive to implement. In addition,
two shot molding does not provide for the level of drawing detail or the number of colors that
may be desired. As such, molds can be designed to incorporate printed labels that are secured
to the molded part during the molding process. There are several advantages related to such
in-mold labeling. First, the labels themselves can have very fine graphic details with multiple
colors produced by screen printing or offset lithography. Second, the labels can provide for
wear resistance through the use of an acrylic or polycarbonate layer laminated over the printed
surface. Third, the cost of in-mold labeling is relatively small and little additional tooling cost,
only slight extensions of the molding process, and requires no post-molding processes.

13.8 In-Mold Labeling

379

13.8.1 Statically Charged Film
In this design, labels are typically printed on a film with a thickness on the order of 0.15 mm
(5 mils), and of a polymer (such as polypropylene or polystyrene) that is compatible with
the plastic being molded. Since a thin film is made of flexible plastic, the thin film can be
placed onto curved surfaces. Different approaches may be used to secure the film in place
during the molding process including adhesives, compressed air, vacuum, and static charge.
Figure 13.27 shows a method for in mold labeling using a film that is statically charged prior
to its placement in the mold [77]. In this design, two mold halves 17 and 19 form a cavity 23.
Prior to molding, a film 11 is placed in the mold cavity and secured by static charge applied
to either the film or the mold block; most often, the film is charged by ionizing the air around
the film with a high voltage from a nearby electrode. The film 11 is made of the same material
as the molded part 25, and has a printed design 13 facing the mold cavity.
Once the film is placed in the mold, the molding process continues as normal. The heat of
the polymer melt causes the film 11 to melt and fuse with the part 25, such that the printed
design 13 appears without any evidence of the film 11. Although the printed areas 13 may not
fuse into the plastic, these areas can be adequately bonded by the fusion of the surrounding
non-printed areas. If necessary, the printing may be imperceptibly dithered to facilitate fusion
between the molded part and the film.
A few comments are warranted about the film thickness and the processing conditions. The
mold designer should recognize that the film must withstand both thermal and structural
loadings. The structural loading is driven by the shear stress applied by rate of the polymer
melt flowing across the film and not the magnitude of the melt pressure; the analysis of
Section 5.3.1 can be used to estimate the shear stress as a function of the polymer properties,
part geometry, and processing conditions. The thermal loading is related to the heating and
melting of the film by the polymer melt. If the film is too thin, then the printed design may be
destroyed by the complete melting and flow of the film during the molding process. Analysis
and experimentation may be required to optimize the film and process.

Figure 13.27: In mold labeling with static charge

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13 Mold Technologies

13.8.2 Indexed Film
Statically charged films are quite common with in-mold labeling. One potential issue, however,
is the placement of the films into the mold by either human or robotic operation. If a human
operator is used, then issues may arise pertaining to processing delays, safety, or repeatability.
If a robot is used, then issues may arise related to processing delays and cost. For molding
applications with higher production volumes, it may be better to resolve these issues through
the use of a mold design that automatically indexes the printed film through the mold with
each molding cycle. One such design is shown in Figure 13.28 [78] for the production of
bottle cap with a retaining ring. In this design, the mold 25 includes a top clamp plate 26, a
movable cavity plate 28, and a conventional moving half of the mold, 30.
The cavity plate 28 is retained to the top clamp plate 16 via fasteners 37. However, a counterbore
is provided in the top clamp plate to allow the fasteners to slide such that the cavity plate
is moved away from the top clamp plate by compression springs 39 when the mold opens.
The resulting gap is approximately 0.5 mm in height, and provides clearance for the carrier
ribbon 55 or 90 to slide between the cavity plate and the top clamp plate. The carrier ribbon
is supplied from roll 58, around guide rolls 59, through the gap 41, to the mold cavities 50.

Figure 13.28: In mold labeling with indexed film

13.9 Ejection

381

When the printed film 60 is properly positioned, the mold closes and the film is secured by
the clamping of the carrier ribbon between the mold cavity plate and the top clamp plate.
With the mold filling, the printed design is transferred from the carrier ribbon to the molded
part 72 which subsequently solidifies. After the opening of the mold and the removal of the
molded part, the used carrier ribbon is indexed by the drive motor 64 and the feed rolls 62
and 66, then directed to a suction tube 68 where it is recycled or discarded. As such, this mold
is designed to operate very rapidly.
More recently, advanced mold and process designs have been developed to allow for very
complex in-mold labels that may be shaped and contain cut-outs. These designs may utilize
an indexing mechanism to consecutively handle thicker printed sheets. In such an operation,
each sheet is thermoformed to conform to the surface of a complex mold cavity. Then, one or
more punches may provide holes or otherwise size the formed and printed sheet to the shape
of the mold cavity. Finally, each completed label is placed into the mold where it is bonded
to the molded part. As such, in-mold labeling can be used to provide nearly any appearance
(such as marble, national flags, etc.) to nearly any part (such as cell phones, etc.)

13.9 Ejection
There are many types of ejection systems, and Chapter 11 provided guidelines for analysis
and design of the most common types. In addition to these previously discussed designs,
many specialized ejection system designs have been developed to provide molded parts with
very complex exterior details, very complex interior details, an aesthetic surface completely
free of defects, and other purposes. Some of the relatively common ejection systems are next
discussed.

13.9.1 Split Cavity Molds
As discussed in Sections 11.3.6 and 11.3.7, core pulls and sliding inserts are commonly used
when there is one or more external undercuts. If the section of the cavity with undercuts is
very large, or if the exterior of the molded part necessitates a parting plane that is transverse
to the mold opening direction, then a split cavity mold is often designed. As the term “split
cavity” implies, a split cavity mold is a mold design in which the cavity insert is split into two
or more pieces, such that the walls of the cavity can be moved away from the molded part
during the ejection stage of the molding cycle.
One split cavity mold design is shown in Figure 13.29 for the molding of bowling pins [79]. The
mold includes a top clamp plate 14, a cavity retainer plate 16, and a support plate 12, among
others. The split cavity is formed by two moving cavity inserts 23 and 24 that mate with the
conical bore 21 in the cavity retainer plate 16 when the mold is closed. Four elongated angle
pins 30 are fastened in the top clamp plate and extend through the cavity inserts 23 and 24.
Each cavity insert is fastened to two gibs 28 that can traverse in slideways 26.

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13 Mold Technologies

Figure 13.29: Split cavity mold design

When the mold opens, the support plate 12 is moved away from the cavity retainer plate 16.
Since the angle pins 30 are stationary and inclined relative to the mold opening direction,
the cavity inserts 23 and 24 are forced to move away from each other through a cam action.
Ultimately, a sufficient clearance is produced between the molded part 66 and the cavity side
walls 44 so that the molded product may be removed.
There are a few interesting items to note regarding this particular split cavity mold design.
First, there is a significant amount of mold cheek provided in the cavity retainer plate 16. The
thickness of the cheek is required to avoid excessive shear stress and deflection of the cavity
side walls 44. It is observed that the thickness of the cheek is approximately the same as the
depth of the mold cavity, as suggested by the analysis of Section 12.2.4. Second, wear can be an
issue in this mold design due to the large mass of the inserts, the length of travel, and the high
number of molding cycles. For this reason, the gibs should be specified to include lubricity and
be easily replaced when necessary. In addition, wear plates should be incorporated between
the support plate 12 and the cavity inserts 23 and 24. Third, internal cooling of the core is
provided through the use of a large bubbler 75 with coolant inlet 74 and outlet 76.

13.9 Ejection

383

Split cavity molds have been designed for quite some time, and this design was not selected
solely due to its incorporation of a split cavity design. Another interesting feature of the design
is the forward actuation of the core pin 50 during the filling and packing stages to provide
injection compression molding. This actuation is needed to compensate for the very high
volumetric shrinkage during the solidification of the thick side walls 54 of the molded part.
As such, the mold design includes a bearing 46 that supports the shoulder 65 of the core
pin. Since the molded part 66 will tend to shrink onto the core pin 50, the core pin must be
retracted after the mold is opened as shown in Figure 13.29 to release the molded part.

13.9.2 Collapsible Cores
Split cavity molds are often used when the part design includes complex and undercutting
external surfaces. Collapsible cores are often used when the part design includes complex
and undercutting surfaces on the interior of the part. The design of a mold which includes a
collapsible core is shown in Figure 13.30, which was developed to mold the head of a doll with
a nearly uniform wall thickness [80]. The mold cavity (14 and 15 together) is formed by two
cavity inserts 12 and 13, which are hollowed out by a collapsible core 17. In this design, the
collapsible core is comprised of eight segments 18, 19, 20, 21, 22, 23, 24, and 25. Four of the
segments, 18, 19, 20, and 21 are mostly triangular in section and fitted at the corners with a
contoured outer surface in the desired form of the core. The other four segments, 22, 23, 24,
and 25 are mostly planar in section and fitted between the corner segments with a contoured
outer surface to complete the desired form of the core. A core rod 37 is located at the center
of the core, and prevents the radial displacement of the eight segments when the collapsible
core is assembled. To prevent the axial displacement of the collapsible core, all eight segments
have a stem 35 with external threads 35a that engage the internal threads 39 in a sleeve 38.
The operation of the collapsible core relies upon the threads 37b of the core rod 37, and their
engagement with the threaded passageway 41 of the sleeve 38. Specifically, prior to molding
the core rod is rotated within the sleeve so that it fully extends until its distal (far) end is flush
with the ends of the eight segments to form a rigid core 17. The sleeve with the rigid core is
then placed in the mold cavity and the part is molded according to conventional practice.
Once the part is solidified, the mold is opened and the molded part is removed along with
the core and sleeve. The core rod 37 is then unscrewed from sleeve 38 and removed from the
inside of the core 17. Without any support, the eight segments can collapse and be removed
from the inside of the molded part. The segments, core rod, and sleeve are then reassembled
for the next molding cycle.
The collapsible core design of Figure 13.30 allows very complex and undercutting features to
be formed internal to the molded part. Because of its design, however, a significant amount
of time is required to assemble and disassemble the moving core. To facilitate the design and
manufacture of molds with collapsible cores, standard collapsible core designs have been
developed and are available from a number of mold base and component suppliers. In typical
designs, the actuation of the ejector plate slides the segments along a retaining sleeve, which
provides a cam action to collapse the core segments during the ejection of the molded part.

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13 Mold Technologies

Figure 13.30: Mold design with collapsible core

The diameter of commercially available collapsible cores ranges from 13 to 90 mm, with a
collapse of approximately 6% of the core diameter. While their collapse is not nearly as much
as the design of Figure 13.30, these standard components support fully automatic molding
of small features such as internal threads for molded closures.

13.9.3 Rotating Cores
Collapsible cores are relatively simple to incorporate into mold designs when using a purchased
assembly, and can be used for the forming of threads, dimples, windows, and other internal
features. However, one issue with collapsible cores is the formation of witness lines on the
interior of the molded part where the core segments interface. Depending on the application
requirements, these witness lines may prohibit the use of the collapsible cores. As such,

13.9 Ejection

385

Figure 13.31: Mold design with coarsely threaded rotating core

many different mold designs have been developed with rotating cores for the formation and
demolding of internal threads. One design is shown in Figure 13.31 for a 64 cavity mold for
the production of threaded caps [81]. The mold design includes cavities 16 that are formed
by matching sets of cavity inserts 10 and core inserts 15. The back of each core includes an
integral support 17, which is mounted upon a shaft 18 that extends from a coarsely threaded
helix 19. The helix is axially located between the rear clamp plate 21 and the support plate
23, and radially supported by bearings 20 and 26.
Follower pins 30 have been fitted to the actuated plate 29 that engage the threads of the helix
19. Since these pins can not rotate, the actuation of the plate 29 will cause the rotation of the
helix 19, and the subsequent rotation of the threaded cores 15. Regarding the design, a coarsely
threaded helix is necessary since the torque and wear will increase substantially as the pitch
decreases. As such, the required length of the helix is related to the friction between the helix
and the follower, as well as the number of rotations in the molding application.
Another mold design for rotating cores is shown in the plan view of Figure 13.32 [82]. In
this mold design, a central sun gear 84 simultaneously actuates multiple planetary gears 86,
which in turn drive shafts 88. The core inserts are not shown in Figure 13.32, but are keyed
to the drive shafts through slots 66. There are many possible designs to rotate the sub gear
84. In this design, a pinion 42 is attached to a shaft 74 which ends at a bevel gear 76. This
bevel gear 76 meshes with another bevel gear 78 that is locked to the central sun gear 84. In
operation, the mold opening stroke causes

386










13 Mold Technologies

the rack 44 to engage the pinion 42,
the pinion 42 to rotate the shaft 74,
the shaft 74 to rotate the bevel gear 76,
the bevel gear 76 to rotate the bevel gear 78,
the bevel gear 78 to rotate the sun gear 84,
the sun gear to rotate the planetary gears 86,
the planetary gears 86 to rotate the shaft 88, and
the shaft 88 to rotate the cores keyed to slot 66.

There are advantages and disadvantages of this mold design compared to the previous design
of Figure 13.31. The primary advantage is the use of multiple gearing stages to decouple the
actuation of the rack and pinion from the rotation of the cores. As such, it is possible to delay
and otherwise program the rotation of the cores during the mold opening while avoiding the
very large stack height associated with the coarse helix of the previous design. The primary
disadvantage is the large number, complex layout, and large volume of the gearing stages. In
addition, the planetary layout suggests a radial layout of cavities and so may require very large
molds for a high number of cavities. Accordingly, the planetary gear design may be preferable
in a mold with a relatively low number of cavities requiring high actuation torques.

Figure 13.32: Mold design with planetary gearing of rotating cores

13.9 Ejection

387

With either design strategy, the mold designer should ensure that the part geometry is designed
to prevent the rotation of the molded part with the rotating core. In some cases, the runner
and gate may provide sufficient strength to prevent the molded part’s rotation. In other
cases, however, this approach is inadequate since the ejection forces will tend to vary with
the material properties, processing conditions, and surface finish as analyzed in Chapter 11.
For this reason, the mold design may use some small undercuts or other non-asymmetric
features to prevent the part rotation.

13.9.4 Reverse Ejection
The cavity inserts in most molds are located within the stationary side of the mold and the
core inserts are located on the moving side of the mold. Since the molded part shrinks onto
the cores as the plastic cools, the molded parts will tend to remain with the cores on the
moving side of the mold when the mold is opened. Accordingly, molds are usually designed
with an ejector housing and ejector plate on the moving side of the mold such that ejector
pins can remove the part from the core. However, this conventional design is problematic in
that it does not provide for a purely aesthetic surface, completely free of defects, on either
side of the molded part. Witness marks will typically be left on the core side of the molded
part from the ejector pins while witness marks will typically be left on the cavity side of the
molded part from the feed system.

Figure 13.33: Mold design with reverse ejection

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13 Mold Technologies

To provide a completely aesthetic surface, molds can be designed with “reverse ejection”.
One such design is shown in Figure 13.33 [83], which includes a mold cavity plate 68 on the
moving side of the mold and a mold core plate 38 on the stationary side of the mold 36. The
sprue 76 conveys the plastic melt from the machine nozzle 14 through the mold core plate
38 to the mold cavity 40 and 74. Because the molded part will tend to remain on the mold
core, the stationary side of the mold 36 also includes ejector pins 48 and other components
that operate with an ejector plate 30 located between rails 18. Since the molding machine’s
ejector rod is located on the moving side of the molding machine and is useless with this
mold design, the mold design also includes hydraulic cylinders 32 for actuation of the ejector
plate. As a result of this mold design, the entire surface of the molded part opposite the core
is free of cosmetic defects.

13.10 Review
There are many technologies that can be incorporated into a mold’s design to:
• Enable extremely complex molded part geometries,
• Make molded parts containing multiple materials,
• Produce a hollow part with simple or complex internal features,
• Provide a molded part with aesthetic or decorative surfaces,







Control the flow of the melt in the molded part,
Increase the consistency of the molded parts,
Increase the molder’s productivity by increasing the number of cavities in a mold,
Increase the molder’s productivity by decreasing the required clamp tonnage,
Decrease the cost of the plastic consumed in molding the product,
And other objectives.

There seems to be almost no limit to what the injection molding process can accomplish with
advanced mold designs. For many molding applications, however, the issue to be deliberated
is not what can be done but rather what should be done for a specific application. The decision
as to how to develop a mold design is for the mold designer, who must strive to serve the
needs of the molder and end-user. For this reason, critical decisions about the mold design
and related technologies should be approved and documented between all the involved parties
with a common understanding of the costs, benefits, and risks.

Appendix

390

Appendix

Appendix A: Plastic Material Properties
Source: Moldflow (Walthan, MA). Used with permission.
Plastic material

ABS

Acetal

PA6

PA66

PA66-33%GF PC

Trade name

Cycolac

Delrin

Capron

Leona

Leona

Lexan

Grade

MG47

500

8202

1402

14G33

121

Supplier

GE Plastics

DuPont

BASF

Asahi

Asahi

GE Plastics

Description

Multipurpose,
injection
molding ABS
providing
a favorable
balance of
engineering
properties

Low friction,
wear resistant
grade with
high viscosity
for bushings
and engineering
applications

Non-impact
modified,
general
purpose
molding
grade of
Nylon 6

Unfilled
Nylon 6/6
with low
warpage,
aging resistance, and fast
cycle times

33% glass
fiber
reinforced
Nylon6/6 for
underhood
automotive
parts

Medium
viscosity
polycarbonate
with good
impact
properties

2.16

2.65

4.02

4.30

5.92

4.26

Approximate cost ($/m )

2011

3043

3900

4149

7160

4481

Modulus (MPa)

2280

2800

970

1200

4400

900

Yield strength (MPa)

44

50

36

67

132

62

Strain to yield (%)

2

12

16

35

3

7

DTUL (°C, 0.45 MPa, ASTM D648)

96.7

160

160

240

250

138

No flow melt temperature (°C)

132

175

216

263

254

143

Minimum melt temperature (°C)

218

180

230

260

275

280

Maximum melt temperature (°C)

260

230

300

300

300

305

Minimum coolant temperature (°C)

49

50

70

40

60

70

Maximum coolant temperature (°C)

71

105

110

80

120

95

1044

1435

1153

1151

1426

1192

Density at melt temp (kg/m )

930

1149

971

964

1210

1052

Specific heat (J/kg°C)

2340

2020

2630

1670

3100

1260

0.19

0.23

0.28

0.19

0.31

0.25

Thermal diffusivity (m /s)

8.73E–08

9.91E–08

1.10E–07

1.18E–07

8.26E–08

1.89E–07

Thermal expansion (m/m°C)

8.82E–05

1.00E–04

7.80E–05

8.00E–05

5.60E–05

6.80E–05

Minimum shrinkage (% m/m)

0.4%

1.4%

0.2%

0.8%

0.3%

0.4%

Maximum shrinkage (% m/m)

0.8%

2.6%

1.7%

1.6%

1.0%

0.8%

Approximate cost ($/kg)
3

3

Density at 20 °C (kg/m )
3

Thermal conductivity (W/m°C)
2

391

Appendix A: Plastic Material Properties

PE, LD

PE, HD

PET

PMMA

PP

PP-30%GF PS

PS-30%GF PVC, rigid PVC, soft

Lupolen

Alathon

Eastapak

Plexiglas

Inspire

Nepol

Styron

Questra

Geon

Geon

1800H

5370

9921

V052

702

GB303HP

478

WA212

M3000

C9000

Basell

Equistar

Eastman

Atohaas

Dow

Borealis

Dow

Dow

PolyOne

PolyOne

Low density polyethylene
with low
modulus
and high
elongation
for injection
molding

High density polyethylene
with good
impact
strength,
crack
resistance,
and color

Unfilled
polyester
for packaging applications

A general
purpose
acrylic with
good light
transmission and
high heat
stability

Unfilled,
high flow,
high
impact
grade for
consumer
products
and automotive applications

30% long
glass fiber
reinforced
polypropylene to provide high
strength
and impact
resistance

High
impact
polystyrene
resin typically used
in toys,
housewares, and
appliances

Syndiotactic polystyrene with
toughness
and heat,
moisture,
and
chemical
resistance

A medium
flow, rigid
PVC with
normal impact often
used with
potable
water
fittings

A general
purpose,
medium
gloss,
flexible
PVC

1.99

1.72

1.99

2.43

1.43

1.97

1.90

2.80

1.54

1.85

1490

1246

2304

2590

1120

1829

1818

3086

1900

1958

110

400

1400

2740

1740

7400

2110

7600

3200

570

9

28

55

70

21

150

23

92

51

9

15

7

4

2

6

2

1.4

1.2

1.6

350

41

72

68

98

80

160

87

240

73

55

106

142

74

215

176

170

121

248

77

130

205

230

270

220

200

220

180

290

190

170

245

260

300

260

240

280

220

330

220

210

20

18

16

50

20

20

40

50

20

40

60

30

40

90

50

60

60

80

40

60

894

952

1336

1186

929

1127

1036

1265

1350

1198

750

724

1160

1067

781

927

958

1101

1230

1056

3180

2890

1980

2093

2890

1969

1820

2400

1630

1580

0.23

0.33

0.23

0.157

0.184

0.13

0.133

0.25

0.185

0.22

9.64E–08

1.58E–07

1.00E–07

7.03E–08

8.15E–08

7.12E–08

7.63E–08

9.46E–08

9.23E–08

1.32E–07

2.30E–04

1.50E–04

7.50E–05

7.00E–05

9.50E–05

4.40E–05

9.00E–05

3.00E–05

7.50E–05

2.40E–04

1.4%

1.2%

0.5%

0.2%

1.2%

0.4%

0.3%

0.1%

0.2%

1.0%

3.0%

2.6%

1.0%

0.6%

2.2%

0.9%

0.7%

1.1%

0.6%

3.0%

392

Appendix

Plastic material

ABS

Acetal

PA6

PA66

PA66-33%GF PC

Parallel shrinkage (% m/m)

0.6%

2.1%

0.9%

0.9%

0.4%

0.6%

Perpendicular shrinkage (% m/m)

0.6%

1.5%

0.9%

0.9%

0.9%

0.6%

Maximum shear rate (1/s)

50000

40000

100000

60000

60000

40000

Mid-range melt temperature (°C)

239

205

265

280

288

293

Power law viscosity (Pa sn)

1.71E+04

6.24E+03

1.49E+04

1.51E+03

1.08E+04

4.47E+05

Power law index, n

0.348

0.538

0.314

0.680

0.434

0.213

WLF: n

0.247

0.122

0.191

0.679

0.400

0.211

WLF: τ* (Pa)

9.97E+04

4.43E+05

2.54E+05

3.81E+00

1.19E+05

6.97E+05

WLF: D1 (Pa s)

1.93E+13

1.20E+11

1.43E+08

7.16E+19

1.08E+18

5.06E+12

WLF: D2 (K)

373.15

263.15

323.15

323.15

323.15

417.15

WLF: D3 (K/Pa)

0

0

0

0

0

0

WLF: A1

31.4

24.1

18.025

44.24

43.215

31.41

WLF: A2 (K)

51.6

51.6

51.6

51.6

51.6

51.6

Zero shear rate viscosity, η0 (Pa s)

2210

745

134

25600

807

94400

b1m (m3/kg)

9.83E–04

8.49E–04

1.01E–03

1.03E–03

8.12E–04

8.66E–04

b2m (m3/kg K)

6.51E–07

4.21E–07

5.05E–07

6.94E–07

4.14E–07

5.67E–07

b3m (Pa)

1.35E+08

1.33E+08

1.78E+08

1.37E+08

1.65E+08

1.69E+08

b4m (1/K)

4.38E–03

3.37E–03

5.09E–03

3.51E–03

3.77E–03

4.23E–03

b1s (m3/kg)

9.83E–04

7.33E–04

9.41E–04

9.80E–04

7.58E–04

8.65E–04

b2s (m3/kg K)

3.47E–07

2.41E–07

3.83E–07

4.66E–07

2.49E–07

2.16E–07

b3s (Pa)

1.70E+08

3.59E+08

2.47E+08

1.68E+08

2.98E+08

2.58E+08

b4s (1/K)

4.21E–03

2.75E–03

3.67E–03

3.16E–03

2.57E–03

3.02E–03

b5 (K)

370.6

448.15

489.16

535.66

527.15

416.23

b6 (K/Pa)

2.30E–07

2.00E–08

6.05E–08

6.24E–08

6.40E–08

3.34E–07

b7 (m3/kg)

0

1.16E–04

6.50E–05

4.57E–05

5.41E–05

0

b8 (1/K)

0

1.24E–01

5.20E–02

1.13E–01

3.32E–02

0

b9 (1/Pa)

0

4.65E–09

4.73E–09

7.96E–09

4.71E–09

0

393

Appendix A: Plastic Material Properties

PE, LD

PE, HD

PET

PMMA

PP

PP-30%GF PS

PS-30%GF PVC, rigid PVC, soft

1.6%

1.6%

0.6%

0.4%

1.5%

0.5%

0.5%

0.2%

0.4%

1.7%

1.6%

1.6%

0.6%

0.4%

1.5%

0.8%

0.5%

0.7%

0.4%

1.7%

40000

40000

50000

40000

100000

80000

40000

80000

32000

32000

225

245

285

240

220

250

200

310

205

190

2.06E+04

1.65E+04

6.989E+05 7.05E+04

5.30E+03

9.52E+03

7.87E+04

1.13E+04

8.32E+05

4.41E+04

0.292

0.378

0.101

0.237

0.378

0.332

0.346

0.360

0.306

0.291

0.291

0.360

0.100

0.237

0.377

0.329

0.346

0.358

0.306

0.291

2.35E+04

8.85E+04

8.46E+05

5.81E+04

3.90E+03

1.69E+04

1.03E+04

1.30E+04

9.20E+04

2.33E+04

2.64E+19

3.75E+17

1.26E+16

3.99E+20

1.99E+14

1.19E+15

1.00E+12

2.20E+15

1.02E+19

2.42E+13

233.15

153.15

351

377.15

263.15

263.15

373.15

373.15

353.15

360.15

0

0

0

0

0

0

0

0

0

0

44.335

38.78

39.12

51.858

30.02

33.317

25.29

34.19

49.42

33.79

51.6

51.6

51.6

51.6

51.6

51.6

51.6

51.6

51.6

51.6

15500

1460

136000

133000

9070

3300

3710000

9320

123000000 209000

1.23E–03

1.27E–03

7.54E–04

8.61E–04

1.24E–03

1.02E–03

9.97E–04

8.78E–04

7.51E–04

9.02E–04

8.78E–07

1.03E–06

5.104E–07

6.00E–07

8.72E–07

7.209E–07

5.98E–07

4.98E–07

4.95E–07

7.72E–07

1.05E+08

9.26E+07

2.46E+08

2.07E+08

8.05E+07

8.69E+07

1.56E+08

7.29E+07

2.19E+08

1.15E+08

4.12E–03

4.94E–03

3.80E–03

5.45E–03

4.93E–03

5.45E–03

4.58E–03

1.94E–03

5.05E–03

5.36E–03

1.17E–03

1.08E–03

7.53E–04

8.62E–04

1.17E–03

9.33E–04

9.94E–04

8.17E–04

7.51E–04

9.01E–04

6.60E–07

2.08E–07

1.00E–07

1.00E–07

6.14E–07

3.10E–07

2.96E–07

1.18E–07

2.32E–07

6.28E–07

1.71E+08

3.32E+08

3.77E+08

2.77E+08

1.10E+08

1.50E+08

1.92E+08

2.09E+08

2.67E+08

1.15E+08

2.42E–03

2.46E–06

5.87E–04

4.23E–03

5.12E–03

5.93E–03

4.96E–03

1.00E–04

4.96E–03

5.03E–03

379

414.5

346.88

386.15

449.15

443.15

394.25

521

350.15

403.15

2.39E–07

2.39E–07

1.75E–07

2.00E–07

6.25E–08

6.90E–08

8.10E–08

2.90E–07

1.33E–07

6.56E–08

5.44E–05

1.87E–04

0

0

7.44E–05

8.15E–05

0

6.14E–05

0

0

7.37E–02

5.16E–02

0

0

1.02E–01

1.42E–01

0

1.90E–02

0

0

2.28E–08

1.02E–08

0

0

8.67E–09

1.18E–08

0

1.22E–08

0

0

394

Appendix

Appendix B: Mold Material Properties
B.1

Non-Ferrous Metals

Mold material

Al 7075-T6

Al QC-7 Alloy

Cu 940

Description

Aircraft grade
aluminum alloy
with high strength
and corrosion
resistance

Aluminum alloy
developed for
molds with higher
strength, hardness,
and conductivity

Beryllium-free
copper alloy
with high strength
and thermal
conductivity

Cost ($/kg)

34.9

29.8

43.2

Cost ($/m3)

98,000

83,400

375,400

Ultimate strength (MPa)

565

579

689

Modulus (MPa)

71,000

72,400

120,000

Yield stress (MPa)

421

545

517

Fatigue limit stress (MPa)

149

166

290

Hardness, Brinell

150

167

210

Feed per tooth (mm)

0.0762

0.0762

0.0762

23,600

23,600

3,600

0.0091

0.0091

0.0014

Cutting speed (m/h)
3

Volume machine rate (m /h)
2

Area machine rate (m /h)

0.225

0.225

0.034

Thermal expansion (°m/m°C)

24

24

18

Thermal conductivity (W/m°C)

130

142

259

Specific heat (J/kg°C)

960

864

506

2,810

2,800

8,690

4.82E–05

5.87E–05

5.89E–05

3

Density (kg/m )
2

Thermal diffusivity (m /s)

Appendix B: Mold Material Properties

B.2

395

Common Mold Steels

Mold material

1045

4140

P20

Description

High strength
carbon steel,
low cost but poor
corrosion and
wear resistance

Chrome alloyed
steel with good
fatigue, abrasion,
and impact
resistance

Common mold
steel with good
fatigue, abrasion,
and impact
resistance

Cost ($/kg)

7.9

24.0

15.1

Cost ($/m3)

62,300

188,400

118,200

Ultimate strength (MPa)

752

778

965

Modulus (MPa)

207,000

200,000

205,000

Yield stress (MPa)

647

669

830

Fatigue limit stress (MPa)

291

412

456

Hardness, Brinell

225

259

300

Feed per tooth (mm)

0.0762

0.0508

0.0508

5,600

4,700

3,800

0.0021

0.0012

0.001

0.053

0.03

0.024

Thermal expansion (°m/m°C)

12.2

12.2

12.8

Thermal conductivity (W/m°C)

49.8

42.7

32

Specific heat (J/kg°C)

515

523

500

7,850

7,850

7,820

1.23E–05

1.04E–05

8.18E–06

Cutting speed (m/h)
3

Volume machine rate (m /h)
2

Area machine rate (m /h)

3

Density (kg/m )
2

Thermal diffusivity (m /s)

396

Appendix

B.3

Other Mold Steels

Mold material

A6

D2

H13

S7

SS420

Description

Heat treatable to be
very hard
with good
wear resistance and
fatigue life

High
carbon/
chrome
steel for
wear and
abrasion
resistance

Heavily
alloyed,
hard steel
with excellent temperature
and wear
resistance

Excellent
toughness
and high
strength
but lower
wear
resistance

Excellent
polishability and
corrosion
resistance
with good
hardness

Cost ($/kg)

40.2

21.4

32.2

19.0

29.7

Cost ($/m )

322,600

164,000

251,000

148,400

231,400

Ultimate strength (MPa)

2,380

2,200

1,990

1,620

655

Modulus (MPa)

203,000

210,000

210,000

207,000

207,000

Yield stress (MPa)

2,100

1,929

1,650

1,380

345

Fatigue limit stress (MPa)

834

755

760

528

190

Hardness, Brinell

650

685

528

369

195

Feed per tooth (mm)

0.0508

0.0508

0.0508

0.0508

0.0508

2,900

2,700

700

3,900

5,000

0.0007

0.0007

0.0002

0.001

0.0013

3

Cutting speed (m/h)
3

Volume machine rate (m /h)
2

Area machine rate (m /h)

0.018

0.017

0.004

0.025

0.032

Thermal expansion (°m/m°C)

11.8

11.8

11.5

12.1

10.8

Thermal conductivity (W/m°C)

27

21

24.3

29

24.9

Specific heat (J/kg°C)

460

460

460

460

460

8,030

7,670

7,800

7,810

7,800

7.31E–06

5.95E–06

6.77E–06

8.07E–06

6.94E–06

3

Density (kg/m )
2

Thermal diffusivity (m /s)

Appendix B: Mold Material Properties

B.4

397

Notes

The following methods and assumptions were used in providing these data regarding mold
metals:






Cost data was produced from commodity pricing for rectangular volumes on the order
of 100 cubic inches.
The fatigue endurance stress was analyzed using empirically fit S-N coefficients at 1,000,000
cycles with a safety factor of 1.0.
The volumetric removal rate assumes a carbide, two fluted, ¾ inch diameter end mill
with a depth of cut of 0.125 inches. The surface area removal rate assumes a carbide, four
fluted, ¼ inch diameter end mill operating at half the nominal feed rate.
Thermal properties were evaluated as the average of room temperature and 200 °C if data
was available, and at room temperature otherwise.

398

Appendix

Appendix C: Properties of Coolants
Coolant material

Water

Ethylene glycol

Oil

Formulation

100% H2O

100% C2H6O2

(CH4)n

Description

Typical plant
water, possibly
contaminated with
corroded metals

Undiluted ethylene
glycol with corrosion inhibitors

ISO grade 32 oil,
a lower viscosity
oil appropriate for
circulating systems

Cost ($/L)

0.0

3.2

1.9

Lower use temperature (°C)

1

–56

32

Upper use temperature (°C)

100

134

288

3

Density (kg/m )

1,000

800

900

Specific heat (J/kg°C)

4,187

2,261

1,842

0.6

0.18

0.16

Thermal diffusivity (m /s)

1.43E–07

9.95E–08

9.65E–08

Viscosity (Pa s, at 50 °C)

0.0010

4.8

23.5

Viscosity (Pa s, at 100 °C)

0.0002

3.4

4.6

Thermal conductivity (W/m°C)
2

Appendix D: Statistical Labor Data

399

Appendix D: Statistical Labor Data
D.1

United States Labor Rates

The average wages for various occupations related to mold design, mold making, and molding
are listed in Table D-1. These data are from the United States Department of Labor’s, Bureau
of Labor Statistics from national data as of November, 2005. These data do not include the
cost of benefits, indirect costs, or profit. To provide a realistic estimate of charged hourly
rates, multiple the wages below by a factor of three.
Table D-1: United States wage data

Position

Average wage (US$)

Mechanical engineer

31.88

Tool and die maker

23.94

Precision machine assemblers

20.65

Machinist

19.93

Tool and die maker apprentice

17.92

Lathe setup operator

17.41

CNC Milling operator

16.82

Milling machine operator

16.14

Lathe operator

15.88

Drilling operator

14.21

Machinist apprentice

13.96

Buffing and polishing operator

13.52

Molding machine operator

13.41

D.2

International Labor Rates

The average manufacturing costs rates for different countries are listed in Table D-2. Average
compensation is listed in U.S. dollars and local currency according to prevailing currency
exchange rates. Source: U.S. Department of Labor Statistics database as of November, 2005.
The above occupational labor rates of Table D-1 can be proportioned by the international
average manufacturing rates to estimate occupational labor rates internationally.

400

Appendix

Table D-2: International manufacturing cost data

Compensation
(U.S. Dollars)

Exchange rates

Compensation
(local currency)

Americas
United States
Brazil
Canada
Mexico

23.17
3.03
21.42
2.50

1
2.926
1.302
11.29

23.17
8.87
27.89
28.22

Asia and Oceania
Australia
Hong Kong
Israel
Japan
Korea
New Zealand
Singapore
Taiwan

23.09
5.51
12.18
21.90
11.52
12.89
7.45
5.97

1.358
7.789
4.482
108.2
1145
1.505
1.69
33.37

31.35
42.9
54.6
2370
13190
19.4
12.59
199.1

Europe
Austria
Belgium
Czech Republic
Denmark
Finland
France
Germany
Hungary
Ireland
Italy
Luxembourg
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom

28.30
29.99
5.43
33.75
30.67
23.89
32.52
5.72
21.94
20.47
26.57
30.76
34.64
7.03
17.10
28.42
30.26
24.71

0.804
0.804
25.7
5.989
0.804
0.804
0.804
202.7
0.804
0.804
0.804
0.804
6.74
0.804
0.804
7.348
1.243
0.546

22.75
24.11
139.5
202.1
24.66
19.21
26.15
1160
17.64
16.46
21.36
24.73
233.5
5.65
13.75
208.8
37.61
13.49

National currency units are:
United States, dollar; Brazil, real; Canada, dollar; Mexico, peso; Australia, dollar; Hong Kong, dollar;
Israel, new shekel; Japan, yen; Korea, won; New Zealand, dollar; Singapore, dollar; Sri Lanka, rupee;
Taiwan, collar; Austria, euro; Belgium, euro; Czech Republic, koruna; Denmark, krone;
Finland, euro; France, euro; Germany, euro; Greece, euro; Hungary, forint; Ireland, euro; Italy, euro;
Luxembourg, euro; Netherlands, euro; Norway, krone; Portugal, euro; Spain, euro; Sweden, krona;
Switzerland, franc; United Kingdom, pound.

Appendix D: Statistical Labor Data

D.3

401

Trends in International Manufacturing Costs

The historical trends of average manufacturing costs compared to manufacturing in the
United States is listed in Table D-3. Source: U.S. Department of Labor Statistics database as
of November, 2005.
Table D-3: Historical trends in manufacturing costs

Country
Americas
United States
Brazil
Canada
Mexico
Asia and Oceania
Australia
Hong Kong (1)
Israel
Japan
Korea
New Zealand
Singapore
Sri Lanka
Taiwan
Europe
Austria
Belgium
Czech Republic
Denmark
Finland
France
Germany, Former West
Germany
Greece
Hungary
Ireland
Italy
Luxembourg
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom

Year
1975

1980

1985

1990

1995

2000

2001

2002

2003

2004

100

99
24

100

92
23

100

88
12

100

110
11

100

96
9

100
18
84
11

100
14
79
12

100
12
78
12

100
12
87
11

100
13
92
11

91
12
33
48
5
50
14
5
6

88
16
35
57
10
53
16
2
10

64
14
29
49
10
34
20
2
12

88
22
52
84
25
54
25
2
26

89
28
55
137
42
57
44
3
34

73
28
58
112
42
40
37
2
131

65
28
60
94
37
37
34
2
29

72
26
52
87
41
40
31
2
26

89
25
52
91
45
50
32
2
26

100
24
53
95
50
56
32

26

73
94

101
75
73
102

27

50
75
101
107
112
25
41
116
98
54

92
122

112
86
92
126

39

63
84
120
125
123
21
61
129
114
78

60
65

64
65
59
74

29

47
60
59
69
82
12
36
76
75
49

121
120

124
143
104
146

46

79
116
108
121
147
24
76
140
139
85

147
149
15
147
141
112
182
175
53
16
80
91
136
140
144
30
74
126
168
80

97
102
14
111
99
78
120
115

14
65
70
89
98
115
23
54
102
107
85

93
96
15
107
96
76
114
109

15
66
66
84
96
113
22
52
89
105
81

97
102
18
113
102
80
118
113

18
71
69
87
103
128
24
56
95
111
85

114
119
21
135
122
95
139
133

22
86
81
104
123
142
28
67
113
125
95

122
129
23
146
132
103
147
140

25
95
88
115
133
150
30
74
123
131
107

402

Appendix

Appendix E: Unit Conversions
This book used the following system of units:
• Temperature: degrees, Celsius, °C
• Length: meter, m
• Mass: kilogram, kg
• Force: Newton, N
• Pressure: Pascal, Pa
• Flow Rate: cubic meters per second, m3/s
• Viscosity: Pascal seconds, Pa s
• Energy: Joules, J
Conversions from each of these units to other common systems are next provided to four
significant digits. To convert from degrees Celsius to degrees Fahrenheit, multiply the
temperature by 1.8 and add 32:
T (°F) = 1.8 ⋅ T (°C) + 32
T (°K) = T (°C) + 273.1

(E-1)

Appendix E: Unit Conversions

E.1

Length Conversions

Table E-1: Length conversion factors

To convert from

to

Multiply by

Meters, m

Millimeters, mm

1,000

Meters, m

Centimeters, cm

100

Meters, m

Micrometers, μm

1,000,000

Meters, m

Inches, in

39.37

Meters, m

Feet, ft

3.281

E.2

Mass/Force Conversions

Table E-2: Mass/force conversion factors

To convert from

to

Multiply by

Kilograms, kg

Newtons weight, N

9.807

Kilograms, kg

Grams, m

1,000

Kilograms, kg

Pounds force, lbf

2.205

Kilograms, kg

Ounce, oz

35.27

Kilograms, kg

Metric ton, t

0.001

Kilograms, kg

U.S. Short Ton, t (short)

0.0011023

Kilograms, kg

U.K. Long Ton, t (long)

0.0009842

E.3

Pressure Conversions

Table E-3: Pressure conversion factors

To convert from

to

Multiply by
2

Megapascals, MPa

Dynes per sq. centimeter, dyn/cm

Megapascals, MPa

Pascals, Pa

Megapascals, MPa

Kilopascals, kPa

1,000

Megapascals, MPa

Pounds per sq. inch, lb/in2

145.04

Megapascals, MPa

Bars, bar

10

Megapascals, MPa

Standard atmospheres, atm

9.86

10,000,000
1,000,000

403

404

Appendix

E.4

Flow Rate Conversions

Table E-4: Flow rate conversion factors

To convert from

to

Multiply by

Cubic meters per second, m3/s

Cubic centimeters per second, cc/s

1,000,000

Cubic meters per second, m3/s

Liters per minute, L/min

60,000

Cubic meters per second, m3/s

Gallons per minute, gal/min

15,840

Cubic meters per second, m3/s

Gallons per hour, gal/h

950,400

E.5

Viscosity Conversions

Table E-5: Viscosity conversion factors

To convert from

to

Multiply by

Pascal seconds, Pa s

Poise, P

10

Pascal seconds, Pa s

Centipoise, cP

1000

Pascal seconds, Pa s

Gram per centimeter second, g/(cm s)

10

E.6

Energy Conversions

Table E-6: Energy conversion factors

To convert from

to

Multiply by

Joules, J

Watt seconds, W s

1

Joules, J

Newton meters, N m

1

Joules, J

Foot pounds, ft lbf

0.7376

Joules, J

British thermal unit, Btu

0.000948452

Joules, J

Kilowatt hours, kW h

0.000000278

Joules, J

Ton hours of refrigeration, ton h

0.000000079

Appendix F: Advanced Derivations

405

Appendix F: Advanced Derivations
Derivation of Melt Velocity
The following analysis derives the melt velocity required to balance the heat lost from the
melt to the mold with the heat internally generated due to shear heating. As such, the plastic
melt should maintain a uniform melt temperature throughout filling if the suggested velocity
is maintained.
Power law flow is assumed. The one dimensional, steady, heat equation with internal shear
heating is:
d 2T q(z )
+
=0
κ
dz 2
where κ is the thermal conductivity. The internal shear heating, q(z), is:
q(z ) = η [ γ (z )] γ (z )2
For a power law fluid in a channel of thickness H, the shear rate as a function of the thickness
is:
1⎞

4 ⎜1 + ⎟ v z

n⎠
γ (z ) =
H2
Substituting the above terms for the viscosity and the shear rate, the shear heating as a function
of the thickness is:
1⎞
⎡ ⎛
⎢ 4 ⎜⎝1 + n ⎟⎠ v
q(z ) = k ⎢
H2

⎢⎣


z⎥


⎥⎦

3−n

1⎞ ⎤
⎡ ⎛
⎢ 4 ⎜⎝1 + n ⎟⎠ v ⎥

=⎢
H2


⎢⎣
⎥⎦

3−n

z 3−n

where k, n are the power law model coefficients. Substituting the shear heating term into the
energy equation and integrating once provides:
1⎞ ⎤
⎡ ⎛
4 1+ ⎟v⎥
k ⎢ ⎜⎝
dT ( z )
n⎠

=− ⎢
dz
κ⎢
H2

⎢⎣
⎥⎦

3−n

z 4−n
+ C1
(4 − n)

where C1 is a constant of integration. To find this constant, the temperature profile through
the thickness is assumed to be symmetric with respect to the centerline. Accordingly, C1 is:

406

Appendix

1⎞ ⎤
⎡ ⎛
4 1+ ⎟v⎥
k ⎢ ⎜⎝
dT (z = 0)
n⎠

=0=− ⎢
2
dz
κ⎢
H

⎢⎣
⎥⎦

3−n

04 − n
+ C1 ⇒ C1 = 0
(4 − n)

Integrating again,
1⎞ ⎤
⎡ ⎛
4 ⎜1 + ⎟ v ⎥


k
n⎠

T (z ) = − ⎢
κ⎢
H2

⎢⎣
⎥⎦

3−n

z 5−n
+ C2
(4 − n) (5 − n)

To find C2, the temperature at the mold wall is assumed constant. Then, C2 is:

C2 = Twall

1⎞ ⎤
⎡ ⎛
4 1+ ⎟v⎥
k ⎢ ⎜⎝
n⎠

+ ⎢
κ⎢
H2

⎢⎣
⎥⎦

3−n

(0.5 H )5 − n
(4 − n) (5 − n)

Accordingly, the temperature profile through the thickness is

T (z ) = Twall

1⎞ ⎤
⎡ ⎛
4 1+ ⎟v⎥
k ⎢ ⎜⎝
n⎠

+ ⎢
2
κ⎢
H

⎢⎣
⎥⎦

3−n

(0.5 H )5 − n − z 5 − n
(4 − n) (5 − n)

The goal in the selection of the linear melt velocity is to force the bulk melt temperature
during filling to equal the initial melt temperature. The average temperature can be evaluated
by integrating the melt temperature profile from the centerline to the mold hall and dividing
by the half thickness:
1⎞ ⎤
⎡ ⎛
4 ⎜1 + ⎟ v ⎥


2 Twall z
2k
n⎠


T =
+
2
H
κH ⎢
H

⎢⎣
⎥⎦

H /2

3−n

⎡ (0.5 H )5 − n z

z 6−n
⋅⎢


⎣ (4 − n) (5 − n) (4 − n) (5 − n) (6 − n) ⎦
0

which when evaluated at the integrands is:

T = Twall

1⎞ ⎤
⎡ ⎛
4 1+ ⎟v⎥
k ⎢ ⎜⎝
n⎠


+
2
κH ⎢
H

⎢⎣
⎥⎦

3−n



H 6−n
⋅ ⎢ 5−n

(4 − n) (6 − n) ⎦
⎣2

Appendix F: Advanced Derivations

407

Setting the average temperature equal to the melt temperature and solving for the linear melt
velocity provides:
1

⎡ (T
− Twall ) κ 25 − n (4 − n) (6 − n) ⎤ 3 − n
H2

v = ⎢ melt

1⎞

k H 5−n


4 ⎜1 + ⎟

n⎠
For a Newtonian material, n = 1, the linear melt velocity simplifies to:
v =

5 (Tmelt − Twall ) κ


It is a good idea to verify the solution by checking the units. For the Newtonian material:
1

1

1


1
⎡ W ⎤ ⎞ 2 ⎛ ⎡W⎤ ⎞ 2 ⎛ ⎡N ⋅ m⎤ ⎞ 2
⎛ ⎡ m2 ⎤ ⎞ 2 ⎡ m ⎤
⎜ ([°C]) ⎣⎢ m°C ⎦⎥ ⎟
⎜ ⎣⎢ m ⎦⎥ ⎟
⎜ ⎣⎢ s ⋅ m ⎦⎥ ⎟
v =⎜
⎟ =⎜
⎟ =⎜
⎟ = ⎜⎢ 2 ⎥⎟ = ⎢ ⎥
⎣s⎦
⎝⎣ s ⎦⎠
⎜ [Pa ⋅ s] ⎟
⎜ [Pa ⋅ s] ⎟
⎜ ⎡ N s⎤ ⎟




⎝ ⎢⎣ m 2 ⎥⎦ ⎠

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Subject Index
A
aesthetics 24, 353
– defect 93
– surface 24, 387
allowance, see layout design
aluminum, see materials selection
amorphous thermoplastic 251
angle pins 291, 381
anisotropic shrinkage 242, 252
annulus, see flow channel
ANSI 23
A plate 5, 80, 126
apparent diameter 333
apparent shear rate, see shear rate
artificially balancing, see feed system
automatic de-gating, see gate types
automatic molding, see injection molding
process
auxiliaries 11, 64
avoid uneven filling 92
axial compression, see structural design
axial mold opening direction 69

B
baffles, see cooling
banana gate, see gate types
barrel temperature, see melt temperature
beam bending, see also structural analysis
310
bending, see structural design
blush 65
boss design 25, 29, 282
B plate 5, 80
branched runners, see feed system
break-even analysis, see cost estimation
Brinell Hardness 85
bronze gib, see slide 291
bubbler 227, 382
buckling 255, 257, 278, 281

buckling constraint, see structural design
burn marks 65, 104, 114, 185
business development 19

C
cam 382, 383
carbon black 252
cashew gate, see gate types
cavity complexity 48
cavity filling analysis 91
cavity insert 67, 69, 74
cavity insert retainer plate 5, 382
cavity layout 77
chamfers 31, 276
cheek 75, 317, 382
circular layout 78, 79
clamp force 365
clamp tonnage 63, 64, 82, 92, 109
clearance 276, 283
clearance fit, see fits
closed loop control 369
coefficient of thermal expansion 234, 237
coefficient of volumetric thermal expansion
236
coinjection 343, 345
coinjection mold design 346
cold runner 41, 61, 121, 154, 364
collapsible cores, see cores
color change 42, 122, 149, 173
color matching 24
color streaks 173
common defects 65
complete filling 92
complexity factor, see cost estimation
compressed air 185
compressibility 233, 235
compression 313
compression molding 350
compression spring 293

414

Subject Index

compressive stress 269, 306, 326, 335
computer simulation 102, 104, 246, 256
concurrent engineering 14
conduction heating 373
conductive pin, see cooling
conformal cooling, see cooling
constraints, see structural design
contamination 65
contoured ejector pins 275
contracts 246
convective boundary 205
coolant 9, 398
– ethylene glycol 211, 398
– flow rate 208
– oil 211, 398
– temperature 250
– water 398
cooling 199, 238
– air channel 229
– baffles, 226
– circuit 219
– conductive pin 229
– conformal 222
– insert 222, 225
– line 9, 74
– line depth 211
– networks 219
– line pitch 213
– line routing 216
– manifolds 219
– plugs 211
– power 206
– stage 1, 2
– system 56, 199
cooling system design 201, 219
cooling time 3, 9, 148, 199, 206, 250, 359,
375
– required 201
copper, see also materials section 215
core 325
– collapsible cores 383
– deflection 329
– insert 67, 69, 74
– insert height 330

– insert retainer plate 5
core back molding 359, 360
core pull 262, 287
– bore diameter 290
corner design 30
cost estimation 34, 43
– amortized 60, 61
– break-even analysis 40, 41
– cavity insert costs 44
– cavity discount factor 51
– cavity machining cost 46
– cavity materials cost 45
– cooling system cost 57
– complexity factor 48, 49
– cost drivers 39
– cost plus quoting 37
– customization cost 57, 58
– cycle efficiency factor 62, 63
– defect cost per part 65
– discount factor 44
– ejector system cost 57
– feed system cost 56
– finishing cost 51
– finishing rates 52
– geometric complexity 47
– machine capability factor 64
– machining efficiency factor 50
– machining factor 49
– machining labor rate 46, 399
– machining rate 86
– machining time 47
– marginal cost 41
– material cost 21
– material cost per part 60, 61
– mold maintenance cost 13, 38, 43
– mold operating cost factor 87
– mold cost 21, 200
– processing cost per part 60, 62
– structural system cost 58
– total part cost 21, 41, 60
cracks 302, 324
critical buckling stress, see also structural
design 279
critical milestones 20

Subject Index

critical stress, see materials selection
critical tolerance 24
Cross-WLF model 96
CTE 252
Cu 940, see also materials selection 85
custom layout, see layout design
customization costs, see cost estimation
cycle efficiency, see cost estimation
cycle time 2, 13, 21, 22, 62, 199, 206, 358,
361, 375
cyclic stresses, see structural design

D
D2, see materials selection
daylight 11, 82, 129
dead pockets 188, 196
deep cores 225
deflection, see structural design
deflection temperature under load 203
degradation 82
delivery terms 37
density 202, 252
design changes 256
design details 195
design for assembly 18, 25
design for injection molding 25, 28
design for manufacturing 18
design requirements 20
detailed design 18, 282
detailing 276
diaphragm 136, 169
diaphragm gate, see gate types
dieseling 185
differential shrinkage 28, 199, 219, 252
dimensional adjustments 76
dimensions, see layout design
discount factor, see cost estimation
distortion 262
double domain Tait equation, see shrinkage
dowel pins 332, 338
draft angles 25, 33
– textured surfaces 34
drive-interference, see fits

415

drops, see hot runner
DTUL, see deflection temperature under
load
Dynamic Feed 122, 369, 370

E
early ejector return 294
edge gate, see gate types 165
effective area, see ejection
efficiency 47, 151
ejection 33, 234
– actuation force 289
– effective area 266, 268
– ejection force 262, 265, 267, 273, 285
– ejection stage 261
– ejection system 259, 381
– ejection system design 259
– push area 269, 270
– push pin 271
– temperature 203, 266
ejector
– assembly 259
– blades 280
– holes 321
– ejector housing 5, 81, 387
– knock-out rod 259, 294, 312
– locations 91
– pad 273
– pins 154, 188, 194, 259, 278, 312
– plate 9, 123, 259, 294, 387
– retainer plate 259
– sleeve 275, 282
ejector system design 265
– layout 273
– number 271
– size 271
– travel 80, 81
elastic deformation 285
elastic limit 285
elastic modulus 300
encapsulated 350
endurance limit, see materials selection
endurance stress 302, 397

416

Subject Index

ethylene glycol, see coolant
Euler theory 279
excessive deflection 340
external undercuts 381

F
factor of safety, see structural design
family mold 6, 22, 204
fan gate, see gate types
fasteners 332
fatal flaws 14
fatigue 84, 302, 329, 340
FDA 23
feed system 56, 119, 364
– artificial balancing 122, 135, 145
– branched runners 135, 368
– orifice diameter 81
– selection 12
– volume 121
– waste or scrap 62
filler 251, 252
fillet 30
filling pressure 238
filling patterns 112
filling stage 1, 7
filling time 2
fingering, see gas assist molding
finishing, see cost estimation
fits 332
– clearance fit 332
– drive-interference 333
– insertion force 332, 335
– interference 332
– lateral hole basis 333
– locational-interference 333, 338
– locational-transitional 338
– sliding fit 289, 346
fit for purpose 1
fixed core pin 282
flash 65, 70, 104, 185
flash gate, see gate types
flashing 304
flow channel 107, 349

annular 153
flow leaders 114, 116, 331
flow length 25
fluid assisted molding 347
foam molding 346
freeze-off 7
full round runners 150
fully automatic molding, see injection
molding

G
gantry robots 263
gas assist molding 347
– fingering 349
gas trap 113, 122
gate 7, 123, 161
gate freeze time 179, 181
gate types 176
– automatic degating 10, 161, 171
– banana gate 172
– cashew gate 172
– diaphragm gate 169
– edge gate 165
– fan gate 167
– flash gate 169
– pin-point gate 164
– sprue gate 163
– submarine gate 172
– thermal gate 11, 172
– thermal sprue gate 173
– tunnel gate 169
– valve gate 174, 366
– valve pin 153, 174
gate well 164
gating design 161, 175
gating flexibility 10, 11, 13
gating location 25, 91, 107
general relative tolerance 23
general tolerance 24
geometric complexity, see cost estimation
geometric distortion 28
gibs 381
glass bead 252

Subject Index

glass fiber 252
glass filled 242
gloss 24, 65, 372, 375, 376
grid layout, see layout design
gusset 29

H
H13, see materials selection 84, 88
Hagen-Poiseuille 138, 211
half-round runners 151
hardness, see materials selection
HDT, see heat distortion temperature
heat distortion temperature 203
heating element 353
heat load 375
heat pipes 227
heat transfer 9, 84, 199
– required rate 206
heel block 293
height allowance, see layout design
height dimension, see layout design
helix 385
hesitation 93
highly conductive inserts 223
hoop stresses, see structural design
hot runner 41, 61, 119, 121, 130, 172, 364
– drops 130
– manifold 130, 355, 366
– molds 11
– nozzles 130
– number of turns 149
– sprue bushing 11, 130
– thermal gate 11, 172
– thermal sprue gate 173
– thrust pads 131
– torpedo 172
– valve gate 174, 366
– valve pin 153, 174
hourly rate 63, 399
hourly labor wage 50, 399
hybrid layout, see layout design
hydraulic actuators 289
hydraulic diameter 151

417

I
IEC 23
improper color match 65
in-mold labeling 378
increased molding productivity 11
indexed film 380
indexing head 357
induction heating 375
initial investment 13
injection blow molds 355
injection compression mold 346, 348, 383
injection decompression 348
injection mold 3, 4
injection molding 1, 2, 13
– change-over times 12
– filling stage 1, 7
– filling time 2, 405
– fully automatic molding 10, 62, 155, 384
– mold opening time 129
– packing stage 1
– plastication stage 1
– plastication time 3
– process timings 2
injection pressure 82
inner core diameter 328
insert creation 74
insertion force, see fits
insert molding 350, 351
inspections 60
insulated runner mold 364
insulating layer 377
interference 263
interference fits, see fits
interlock 289, 319, 330
interlocking features 72
internal corners 224
internal manifold 220
internal tensile stresses 265
internal threads 384
internal voids 29
ISO 23
isothermal boundary 204
isotropic 241
iterative mold development 13

418

Subject Index

J
jetting 104, 162

K
keyway 289
knit-line 122, 353

L
laminar flow 138
lateral hole basis, see fits
lay flat 91, 107, 112
layout design, 67
– allowance 75
– custom layout 137
– conflict 79
– grid layout 78
– height allowance 74, 75
– height dimension 74
– hybrid layout 78, 79, 136
– length dimension 75
– line layout 78
– mold dimensions 23
– radial layout 78, 136
– series layout 78, 135
– width dimension 75
lean manufacturing 43, 220
length dimension, see layout design
limit stress, see materials selection
limit switches 291
linear flow velocity, see velocity
linear melt flow 168
linear melt velocity, see velocity
linear shrinkage, see linear
line layout, see layout design
locating dowel 283
locating pins 332
locating ring 6
location 273
locational-interference, see fits
locational-transitional, see fits
lofted surfaces 72
lost core molding 353

M
machine capability factor,
see cost estimation
machining efficiency factor,
see cost estimation
machining factor, see cost estimation
machining labor rate, see cost estimation
machining rate, see cost estimation
machining time, see cost estimation
maintenance, see mold maintenance
managed heat transfer 377
manifold, see hot runner
marginal cost, see cost estimation
material consumption 13
material removal rate 47, 48, 397
materials selection
– mold-maker’s cost 86
– molder’s cost 86
– aluminum, 215
– aluminum 7075-T6 85, 394
– aluminum QC7 85, 300, 394
– copper 215, 394
– Cu 940 85, 394
– critical stress 96
– endurance limit 84
– hardness 85
– limit stress 84, 302, 303
– modulus 266
– steel, 1045 88, 395
– steel, 4140 88, 395
– steel, A6 84, 396
– steel, D2 84, 396
– steel, H13 84, 88, 396
– steel, P20 84, 85, 88, 300, 395
– steel, SS420 88, 396
– steel, S7 396
material supplier 245
material waste 62
maximum cavity pressure 92
maximum deflection 315
maximum diameter 209
maximum shear stress 317
maximum stroke 281
Melt Flipper 136, 369

Subject Index

melt flow index 96
melt front advancement 91
melt pressure 91
melt temperature 235
– barrel temperature 250
MFI, see melt flow index
mica 252
microfinish 32
MIL-SPEC 23
minimum cooling line diameter 210
minimum cooling time 203
minimum draft angle 34
minimum wall thickness 108
mirror finish 32
modulus, see materials seclection
mold amortization schedule 43
mold base 14, 53, 67, 79, 83
– cost estimation 53
– selection 77
– sizing 79
– suppliers 83
mold cavity 68
mold commissioning 24
mold customer 37
mold customization 55
mold deflection 304
mold design 13, 17, 19
mold development process 14, 20
mold dimensions 54
Moldflow, see computer simulation
mold functions 3
molding cycle 238
molding machine
– capability 64
– mold compatibility 81
– platens 299
molding productivity 12
molding trials 14, 38
mold insert 287
mold interlocks 319
mold layout design, see layout design
mold maintenance 32, 83, 186
mold material properties 27

419

mold material selection, see materials
selection
mold opening
– direction 67
– stroke 11
mold operating cost factor, see cost
estimation
mold purchase agreement 37
mold rebuilding 60
mold reset time 3
mold resetting stage 1
mold setup time 220
mold size 305
mold structures 4
mold supplier 37
mold technology 343
– selection 344
mold temperature controllers 208
mold texturing 32
mold wall temperature control 351
– active 372
– passive 377
moment of inertia 279, 281, 311, 330
moving core 261, 288, 381
moving half 9, 319
moving side 264
multi-cavity molds 6, 77
multi-gated 11
multi-shot molds 358
multi-station mold 359, 362
multilayer injection blow molding 357

N
naturally balanced 131, 135, 138, 145, 368
naturally balanced feed system 78
net shape manufacturing 1
Newtonian limit 96
Newtonian model 98, 102, 139
nominal dimensions 249
nominal shrinkage rate 250
non-uniform shrinkage 248
normal force 265
nozzles, see hot runner

420

Subject Index

number of turns, see hot runner
numerical simulation, see computer
simulation

O
Oil, see coolant
one-sided heat flow 230, 359
opening time, see injection molding
open loop control 370
operating cost 12
optimal mold design 40
optimization 141
orientation 93
orifice diameter, see feed system
over-filling 122
over-packing 92, 244
overmolding 358, 359
overpressure 329, 340

P
PvT 235
P20, see materials selection
packing 238
packing pressure 235
packing stage, see injection molding
packing time 2, 163, 250
parison 356, 357
part cost estimation, see cost estimation
parting line 70, 71, 73
parting plane 6, 67, 69, 71, 79, 123, 185,
192, 319
part interior 188
part removal system 263
payment terms, see quoting
peak clamp tonnage 110
perimeter 271
pilot production 19
pin-point gate, see gate types
pin length 279
planetary gears 385
plastication 238
plastication stage, see injection molding

plastication time, see injection molding
plastic material properties 26
plastic part design 17
plate 306
– bending 309
– compression 306
Platens, see molding machine
positive return 294
power law index 96, 99, 101
power law model 96, 99, 102, 139, 142, 178
pre-loading, see support pillars
preliminary quote, see quoting
pressure drop 92, 95, 120, 138, 162, 178,
210
pressure gradient 254, 330
pressure transmission 11
preventive maintenance 60
primary runners 123
processing conditions 104
processing cost per part, see cost estimation
product definition 18
product design 13, 18
product development process 17, 19
production data 21
production flexibility 43
production planning 19
production quantity 22, 40
production rate 22
profile the packing pressure 250
projected area 64
projections 359
prototype mold 103, 246
prototype molding 24
pulsed cooling 372
purchase cost 12
purge 149
purging 12
push area, see ejection
push pin, see ejection

Q
QC7, see material selection
quick ship 83

Subject Index

quoting 19, 37, 133
– payment terms 20, 37
– preliminary quote 13
– requests for quotes 37

R
race-tracking 113
radial flow 168
radial layouts, see layout design
radial mold opening direction 69
radius of curvature 253
rails 259
rear clamp plate 5, 259
recommended melt velocity, see velocity
recommended vent thickness, see vent
dimensions
reduced material consumption 11
reduced setup times 43
regulatory agencies 20
regulatory compliance 23
requests for quotes, see quoting
residence time 121, 149, 150
residual stress 93
retainer plate 75, 291
retention force 333
return pins 259
reverse ejection 264, 387
Reynolds number 138, 209
RFQs, see request for quotes
rheology 96
rib design 25, 29
rotating cores 384, 385
round-bottom 151
rubber 252
runner 7, 119, 123, 126
– see also cold runner, hot runner, and
insulated runner
– shut-offs 155
– volume 140

S
S7, see materials selection

421

s-n curves 302, 397
safety margin 91
secondary runners 123
selective laser sintering 222
self-regulating valve 370
self-threading screws 29
semi-automatic 62
semi-crystalline 251
series layout, see layout design
sharp corners 25, 30
shear rate 94, 96, 162, 176
– apparent 99
shear stress 94, 269, 309, 317, 320, 379, 382
shear thinning 101
short shot 65, 104, 120, 162
shot volume 82
shot weight stability studies 2
shrinkage 93, 233, 234, 346
– analysis 235
– anisotropic 242, 252
– behavior 24
– data 245
– differential shrinkage 28, 199, 219, 252
– double domain Tait equation 235
– linear 241
– nominal rate 250
– range 244
– recommendations 245
– uniformity 256
shut-offs 73
shut-off surface 187
side action 287
side walls 317, 382
single cavity 11
single cavity mold 77
sink 29
sink marks 376
sintered vent 196
slender core 224, 230, 330
slides 291, 381
– bronze gib 291
– cores 291
sliding fit, see fits
snap fits 25

422

Subject Index

Society of the Plastics Industry 32
socket head cap screws 332, 336
solidification temperature 266
solidified plug 172
solidified skin 372
solvent 359
specific heat 202
specific volume 251
– change in 239
SPI 32
– surface finishes 32
splay 65, 162
split cavity 355, 357
sprue 81, 119
– break 125
– bushing 7, 123, 126
– knock-out pin 123
– pickers 263
– pullers 10, 126, 154
sprue gate, see gate types
SS420, see m