j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138

j our nal homepage: www. el sevi er . com/ l ocat e/ j mat pr ot ec

A study of computer-assisted analysis of effects

of drill geometry and surface coating on forces

and power in drilling

J. Audy

∗

School of Enterprise and Technology, Edith Cowan University, School of Enterprise and Technology, Bunbury, Western 6230, Australia

a r t i c l e i n f o

Article history:

Received 23 May 2007

Accepted 30 October 2007

Keywords:

Computer-assisted predictions

Drill point geometry

Rake angle distributions

Drill lips

Chisel edge

Surface coatings

Cutting performance

Predicted thrust

Torque

Power

a b s t r a c t

The success of continuous improved drill performance in cutting applications has to date

largely been based on signiﬁcant advances through tool surface coatings and modiﬁcations

of drill point geometry, i.e. optimisation of the rake angle distributions along the drill lips

and the chisel edge. It has been recognised that due to the complexity of equations for

the force and power predictions, computer assistance is needed. Consequently, this paper

presents the results of a systematic – computer-assisted – study focused on determining,

and describing, from a mathematical point of view, the relationship between the drill point

geometrical features and the performance measures as assessed by the cutting forces and

power in drilling. This is followed by a study of predicted inﬂuences of drilling variables

on the generated thrust, torque and power. The results are presented for different types

of modern commercial tool surface coatings and work-piece materials. It is suggested that

this sort of information may be used, by both tool manufacturers and users, to assist in the

optimisation, and selection, of the drill point geometrical features for ‘best’ performance.

Crown Copyright © 2007 Published by Elsevier B.V. All rights reserved.

1. Introduction to the effects of drill

geometry on forces and power in drilling

The models and/or software applications for prediction of

thrust, torque and power indrilling for commercially designed

drills are quite complex and include a set of equations which

relate the thrust, torque and power to the drill point features

(D, 2W, ı

0

, , 2P, and Cl

0

), cutting conditions (f, n), num-

ber of elements characterising the lip (M

L

) and chisel edge

(M

C

) regions and the basic cutting quantities (r

l

, ˇ, includ-

ing edge force coefﬁcients K

IP

, K

IQ

) as well as coefﬁcients C

IP

and C

IQ

for discontinuous chip formation obtained from the

∗

Tel.: +61 8 9780 7797; fax: +61 8 9780 7814.

E-mail address: [email protected]

orthogonal cutting data base for a particular tool/work-piece

material combination (Armarego, 1996). It has been stated in

the literature (Armarego, 1996; Zhao, 1994; Armarego et al.,

1997) that values of the geometrical drill point features such

as 2P, ı

0

and 2W vary from manufacturer to manufacturer

and more importantly from batch to batch. The geometry of

the chisel edge region also varies widely depending on the

point sharpening method used and the control of the sharp-

ener settings (Armarego, 1996; Zhao, 1994). Considering more

closely this information it seems to be crucial to obtain accu-

rate data about the actual speciﬁed drill point features, and, if

necessary, to use the ‘as measured’ data, rather than the nom-

inal values ‘provided’ by the tool manufacturer, in predictive

0924-0136/$ – see front matter. Crown Copyright © 2007 Published by Elsevier B.V. All rights reserved.

doi:10.1016/j.jmatprotec.2007.10.079

j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 131

Nomenclature

Symbols

D drill diameter

2W web thickness

f feed rate

r

l

chip length ratio

2P point angle

Cl

0

lip clearance angle

n drill revolutions

ˇ friction angle

chisel edge angle

ı

0

helix angle

ı

w

setting angle of the grinding wheel

shear stress in the shear zone (plane) (N/mm

2

)

drilling models for quantitatively reliable thrust, torque and

power predictions.

The drilling action itself is a complex cutting process con-

trolled principally by the geometry of a given drill dictated

mainly by the positions and lengths of the lips and chisel edge

regions. The cutting action on the drill lips has been reported

to be similar to that of the ‘classical’ oblique cutting process

but with variable cutting speeds, inclination angles and nor-

mal rake angles along the lip from the chisel edge corner to

the outer corner. By contrast, the cutting action at the chisel

edge has been found to be much closer to that of ‘orthogo-

nal’ cutting at relatively high negative rake angles and very

low cutting speeds resulting in discontinuous chip formation.

In the areas very close to the drill axis a type of ‘indentation’

process can be considered to occur where dynamic clearance

angle is zero or negative.

The work presented in the following Sections was under-

taken by the author of this paper and Dr. Armarego, from the

Melbourne University, was the supervisor until his death in

2003. Except where stated the work reported is the results of

the author’s own research work with reference to the source

(Audy, 2002).

2. Analysis of cutting action at drill point

geometry

The investigations outlined in Sections 2.1 and 2.2 were set

up to analyse the lip design and chisel edge region of twist

drills prior examining the effects of drill point modiﬁcations

on predicted thrust, torque and power in drilling.

2.1. Lip design and its reported effects on the drilling

forces

Fig. 1 shows the geometry of, and the forces acting on an ele-

ment at, the lip region of a conventional general purpose twist

drill. From the mathematical point of view the drill lip region

can be considered as a sumof a number of different elemental

oblique cuts controlled principally by their own tool geometry

and cutting conditions (V

W

=V,

n

,

s

, t, ␦b

i

, r

i

, f, n). The ﬁrst

three values – namely V

W

,

n

,

s

– are found from the speci-

Fig. 1 – Geometry of, and the forces acted at, the lip regions

of a conventional drill. Refer Armarego (1996).

ﬁed drill point geometrical features (D, 2W, ı

0

, and 2P) at each

elemental radius r

j

; the oblique cutting forces are determined

from the ‘classical’ oblique cutting analysis for the element

radius of r

j

, areas of cut ␦A(=t␦b) found fromthe cutting condi-

tions, f and b; the fundamental oblique cutting tool geometry,

n

and

s

, and the basic cutting quantities, , ˇ and r

l

, and the

edge force coefﬁcients, K

IP

and K

IQ

, obtained from the orthog-

onal cutting data bank.

The thrust force (T

h

) and torque (T

q

) at the drill lip region

can be calculated via the sum of elemental values (␦T

h1j

) and

(␦T

qj

). The required values for both the elemental thrust force

(␦T

h1j

) and elemental torque (␦T

q1j

) can be calculated from

the ‘oblique’ cutting force components (␦F

P

, ␦F

Q

, and ␦F

R

) and

associated ‘edge’ force components (␦F

Pe

, ␦F

Qe

, and ␦F

Re

), the

meanradius (r

i

), the number of selectedelements (M) onthe lip

region, i.e. cutting edge length (

␦L), and the drill geometry

as documented by the same Fig. 1.

Mathematical expressions to calculate drilling forces from

a particular drill lip geometry and cutting conditions are

shown in Eqs. (1)–(18).

Thrust force (T

hl

) and elemental thrust force (␦T

hlj

) at the drill

lip region:

T

hl

=

M

j=1

ıT

hlj

(1)

where the elemental thrust force at the lip region

␦T

hlj

=(␦F

Q

+␦F

Qe

) cos ε sinp−(␦F

R

+␦F

Re

) (cos

s

cos p+sin

s

sinpsin), and the required angle (ε) canbe obtained by pro-

jecting the speed vector (V

w

) into the normal plane (P

n

), and

132 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138

calculated as

tanε =

V

W

sinωcos p

V

W

cos ω

= tanωcos p where ω = sin

−1

W

r

i

Torque (T

ql

) and elemental torque (␦T

lj

) at the lip region:

T

ql

= 2

M

j=1

ıT

qlj

where ıT

qlj

= r

i

(ıF

P

+ıF

Pe

) (2)

Cutting edge length (

L) and elemental cutting edge length

(␦L):

L = 2

M

j=1

ıL where ıL =

(D/2) cos ω

0

−Wcot (180

◦

−)

Msinp

(3)

(ω

0

) – given by Equation (1.36); and () is ‘as measured’ chisel

edge angle.

Mean radius (r

i

):

r

i

=

_

_

D

2

cos ω

0

−

_

i −

1

2

_

ıL sinp

_

2

+W

2

(4)

Cut thickness (t):

t =

f sinpcos ε

2

(5)

Elemental width of cut (␦b):

ıb = ıL cos

s

where

s

=

V

W

sinωsinp

V

W

= sinωsinp (6)

Elemental area of cut (␦A):

ıA = tıb (7)

Elemental oblique cutting force components (␦F

P

, ␦F

Q

and

␦F

R

):

ıF

P

=

ıA[cos (ˇ

n

−

n

)cos

s

+tanÁ

c

sin

s

sinˇ

n

]

_

cos

2

(

n

+ˇ

n

−

n

) +tan

2

Á

c

sin

2

ˇ

n

(sin

n

cos

s

)

(8)

ıF

Q

=

ıAsin(ˇ

n

−

n

)

_

cos

2

(

n

+ˇ

n

−

n

) +tan

2

Á

c

sin

2

ˇ

n

(sin

n

cos

s

)

(9)

ıF

R

=

ıA[cos (ˇ

n

−

n

) sin

s

−tanÁ

c

cos

s

cos ˇ

n

]

_

cos

2

(

n

+ˇ

n

−

n

) +tan

2

Á

c

sin

2

ˇ

n

(sin

n

cos

s

)

(10)

where tanˇ

n

=tan ˇ cos Á

c

and (

n

) can be calculated using

Eqs. (11)–(18).

tan

n

=

tanı[(cos ω +sinωtanωcos

2

p) −tanωcos p]

sinp

(11)

tan

n

=

sin ω

0

tanı

0

[(cot ω +tanωcos

2

p) −tanωcos p]

sinp

(12)

tan

n

=

tanı

0

(r

2

−W

2

sin

2

p) −(D/2)Wsinpcos p

(D/2) sin

_

r

2

−W

2

(13)

Shear angle ()

tan

n

=

r

l

(cos Á

c

/cos

s

) cos

n

1 −r

l

(cos Á

c

cos

s

) sin

n

(14)

tan(

n

+ˇ

n

) =

tan

s

cos

n

tanÁ

c

−sin

n

tan

s

(15)

Elemental ‘edge’ force components (␦F

Pe

, ␦F

Qe

and ␦F

Re

)

ıF

Pe

= K

IP

ıb (16)

ıF

Qe

= K

IQ

ıb (17)

ıF

Re

= K

IR

ıb = K

IP

sin

s

ıb or ıF

Re

∼

= 0 (18)

Other required variables (r

l

, ˇ, and ) and coefﬁcients (K

IP

,

K

IQ

and K

IR

) are taken from the actual database that needs

to be established for a particular tool–work-material–surface

coating combination at different cutting conditions.

2.2. Chisel edge region and its reported effects on the

drilling forces

Fig. 2 shows the geometry of, and the forces at, the chisel edge

region of a conventional drill. Armarego (1996) wrote that it is

possible to create force prediction model for any chisel edge

region if the speciﬁc drill point features 2P and 2W are known

or measured.

In such model the chisel edge region is represented by a

number of ‘classical’ orthogonal cutting elements each oper-

ating at its own tool geometry and cutting conditions (V

W

,

ne

,

˛

ne

, t, ␦b, r

k

, f, n, and M

C

) in a particular region (r

limit

<r <r

c

).

The values of the thrust force (T

hc

) and torque (T

qc

) can be cal-

culatedvia summing a number (M

C

) of elemental values (␦T

hck

)

and (␦T

ck

) using Eqs. (19) and (20); and the indentation thrust

force (T

hI

) can be calculated using Eq. (21).

Thrust force at the chisel edge region (T

hc

)

T

hc

=

M

k=1

ıT

hck

where ıT

hck

= ıF

Pc

sinÁ +ıF

Qc

cos Á (19)

Torque (T

qc

) at the chisel edge region and the elemental

torque (␦T

qc

)

T

qc

= 2

M

k=1

ıT

qck

(20)

where ıT

qck

= r

k

(ıF

Pc

cos Á −ıF

Qc

sinÁ) andr

k

= r

c

−

_

k −

1

2

_

ıb =

Lc

2

−

_

k −

1

2

_

ıb and

ıb = (r

c

−r

limit

)/M = (L

c

−2r

limit

)/2M

c

The r

limit

is the radius for ˛

ne

(=0), Á (=90

◦

−

2

), feed (f), and

wedge angle

W

=

1

+

2

.

j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 133

Fig. 2 – Geometry of, and the forces acted at, the chisel edge region of a conventional drill. After Armarego (1996).

Indentation thrust force (T

hI

)

T

hI

= ıT

hck

_

2r

limit

ıb

_

(21)

Cut thickness (t)

t =

f cos Á

2

(22)

The chisel edge length (L

c

) is equal to 2r

c

following a

data associated with the drill tool geometry, i.e. L

c

= 2W/sin

(180

◦

−)

The elemental forces (␦F

Pc

and ␦F

Qc

) can be determined

from Eqs. (23) and (24).

ıF

Pc

= C

IP

ıb (23)

ıF

Qc

= C

IQ

ıb (24)

where C

IP

and C

IQ

are the cutting coefﬁcients (forces per unit

width) for discontinuous chip formation taken from the data-

bank of a particular tool-work-material investigated.

Armarego (1996), for instance, reported that C

IP

and C

IQ

coefﬁcients for a HSS tool – 1020 – steel work-material combi-

nationhadthe mathematical expressions similar those shown

by Eqs. (25) and (26).

C

IP

(N/m) = 1.88.10

6

t

6.51

(90

◦

+

ne

) (25)

C

IQ

(N/m) = 19.14.10

6

t

6.35

(90

◦

+

ne

)

−0.62

(26)

Finally the thrust (T

Ht

) and torque (T

Qt

) for a drill can be

determined by summing all the corresponding values of both

the drill lip region and chisel edge region, as shown in a simple

form in Eqs. (27) and (28).

T

Ht

= T

hl

+T

hc

+T

hI

(27)

T

Qt

= T

ql

+T

qc

(28)

3. Computer-assisted software and

numerical simulation studies for prediction of

forces and power in drilling

Armarego (Armarego, 1996; Armarego and Zhao, 1996;

Armarego and Kang, 1997) and his research scholars (Zhao,

1994; Audy, 2002; Wright, 1981; Wu and Armarego, 1996)

developed the computer software and carried out extensive

numerical simulation studies over a large number of cutting

combinations and drill point geometrical features to study the

effects of these practical variables on the thrust, torque and

power in drilling. The predicted trends have been shown to be

reasonable suggesting that the models were plausible. It has

also been possible to use multivariable regression analysis to

curve-ﬁt the thrust and torque predictions and to establish

‘empirical-type’ equations, which include the cutting condi-

tions, as well as, the many individual drill point features.

Empirical-type equations similar to that given by Eqs. (29) and

(30) have been established for different drill designs modelled

for a given tool–work-piece–material combination.

thrust force (T

Ht

)

T

Ht

= C

1

f

a

1

D

b

1

_

2W

D

_

C

1

2p

d

1

ı

e

1

0

˛

b

1

0

or

m

1

W

n

1

(29)

torque (T

Qt

)

T

Qt

= C

2

f

a

2

D

b

2

_

2W

D

_

C

2

2p

d

2

ı

e

2

0

˛

b

2

0

or

m

2

W

n

2

(30)

The associated constants (regressioncoefﬁcients) are given

inTable 1 for both‘general’ and‘plane’ ﬂankmodels anda Type

1020 steel work-material (Armarego, 1996).

134 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138

Table 1 – Regression coefﬁcients for Eqs. (29) and (30) valid for ‘general’ (a), and ‘plane’ (b) ﬂank models and a Type 1020

steel work-material

(a) Drill: general ﬂank model Work-material: 1020 steel

C

(1, 2)

a

(1, 2)

b

(1, 2)

c

(1, 2)

d

(1, 2)

e

(1, 2)

h

(1, 2)

m

(1, 2)

n

(1, 2)

T

Ht

47.5 0.545 1.036 0.339 0.168 −0.206 – 0.311 0.266

T

Qt

4.56 0.660 2.004 0.149 −0.241 −0.263 – −0.008 −0.188

(b) Drill: plane ﬂank model Work-material: 1020 steel

C

(1, 2)

a

(1, 2)

b

(1, 2)

c

(1, 2)

d

(1, 2)

e

(1, 2)

h

(1, 2)

m

(1, 2)

n

(1, 2)

T

Ht

99.7 0.546 1.027 0.279 0.518 −0.210 – – 0.05

T

Qt

3.71 0.661 2.004 0.113 −0.226 −0.263 – – −0.177

After source Armarego (1996).

Armarego (1996) further mentioned that the thrust and

torque characteristics exhibited monotonic trend, and their

prediction has been possible for any particular drill/work-

material combination after determining the coefﬁcients

required for Eqs. (29) and (30). These equations were exper-

imentally veriﬁed (Verezub, 1996) and found to be reliable for

prediction purposes rather than running the more complex

analyses and computer software.

Audy (2002) established empirical force equations for the

general purpose twist (GPT) drill force model and web pro-

ﬁle ground (WPG) drill design model (see Fig. 3a and b)

when drilling a Type Bisalloy 360 steel work-piece mate-

rial.

In the study (Audy, 2002) the six drill point variables

(D, 2W/D, , 2P, ı

0

and f) were considered giving the total

3

6

or 729 combinations of thrust and torque values indi-

vidually for a particular database used, see the evaluated

Eqs. (31) and (32). For WPG drill force model the helix angle

was replaced with the two extra variables – the ˛

g

and the

ı

w

– giving such 3

7

or 2187 computed values of predicted

thrust and torque for each database chosen, see Eqs. (33) and

(34).

Uncoated general purpose twist drills (Audy, 2002, 2006a)

T

h

= 101.892f

0.67

D

0.967

_

2W

D

_

0.379

2P

0.397

0.265

ı

−0.233

0

(31)

T

q

= 28010.23f

0.732

D

2.004

_

2W

D

_

0.202

2P

−0..388

−0.282

ı

−0.427

0

(32)

Uncoated web proﬁle ground drills (Audy, 2002, 2006a)

T

h

= 354.5f

0.691

D

0.964

_

2W

D

_

0.577

2P

0.313

0.295

˛

−0.313

g

ı

−0.0779

w

(33)

T

q

= 20944.68f

0.718

D

2.001

×

_

2W

D

_

0.309

2P

−0.288

−0.128

˛

−0.469

g

ı

−0.119

w

(34)

It has been shown experimentally (Audy, 2002, 2006a) that

the web proﬁle ground drill design produced lower force levels

than the general purpose twist drill design. The quantita-

Fig. 3 – The GPT drill design (a) after Audy (2002), Audy et al. (2002a,b); and the CNC stub – web proﬁle ground (WPG) – drill

design (b) after Audy (2002), Audy et al. (2001, 2002b).

j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 135

tive comparison of such improvement has been determined

from the thrust and the torques values predicted using the

force models (Audy, 2002, 2006a; Audy et al., 2002b). When

comparing the thrust forces from the uncoated web pro-

ﬁle ground drill force model with those produced by the

uncoated general purpose twist drill force model the aver-

age percentage decrease (improvement) in the thrust values

was −13±4%. For the torque values the percentage difference

associated with decrease (improvement) in the torque values

was −15±2%.

In addition, Audy’s research (Audy, 2002, 2006a; Audy et al.,

2002b) has shown that the cutting action (drilling forces and

power) generated by the drill point geometry (D, 2W/D, , 2P,

and ı

0

) and feed rate is inﬂuenced by the elemental distribu-

tion of rake angles along the lip region and the chisel region.

This is outlined in Section 4.

4. Elemental rake angle distribution at the

lip and the chisel edge regions of GPT and WPG

drill designs

The elemental distribution of rake angles of each GPT and

WPG drill design has been studied separately for the lip region

and the chisel edge region by changing the values of the

drill point features, namely, the point angle 2P, the chisel

edge angle , the lip spacing to drill diameter ratio 2W/D,

the helix angle ı

0

, and the grinding wheel features, namely,

˛

g

and ı

w

. The drill speciﬁcations used were: D

(GPT)

=6.35mm;

D

(WPG)

=6mm; ı

0(GPT)

=25

◦

, 30

◦

, and 35

◦

; ˛

g(WPG)

=25

◦

, 30

◦

, and

35

◦

; ı

w(WPG)

=25

◦

, 30

◦

, and 35

◦

; Cl

0(GPT)

=14

◦

, Cl

0(WPG)

=12

◦

; then

for both drill designs: 2P=110

◦

, 120

◦

, and 145

◦

; =115

◦

, 125

◦

,

and 145

◦

; 2W/D=0.1, 0.18, and 0.3 were used. Furthermore, the

nominal cutting conditions were the speed of 4.33m/min, the

feedof 0.1mm/rev andthe work material was Bisalloy 360 high

abrasive and wear resistant steel.

The distribution of elemental rake angles at the drill lips

and the chisel edge region for GPT drill design and WPG drill

design has been studied for different values of 2P, ı

0(GPT)

,

˛

g(WPG)

, ı

w(WPG)

, , and 2W/D, and the patterns obtained were

similar to that shown in Fig. 4(a and b) for different 2P values.

From Fig. 4 it appears that for the GPT twist drill design the

normal rake angles,

n

, will vary from negative value(s) of

ni

at i =1 close to the outer chisel edge corner to highly positive

value(s) of

ni

at i =25 close to the lip outer corner radius. The

chisel edge represents series of negative rake angles that cut

from the smallest negative

ni

at i =1 close to the drill axis to

the highest negative

ni

at i =25 close to the outer chisel edge

corner. Comprehensive stresses created by the chisel edge will

contribute to the large percentage of the total thrust force in

drilling, while the drilling torque will, however, be not as great.

The lip region of WPG drills appears to be more favourable

for lower forces and power than that of GP-twist drills. This

is due to higher normal rake angles at radii along the drill

lip as seen in Fig. 4(a). The reduced chisel edge lengths of the

WPGdrills from1.24 to 0.75 contribute to the lower percentage

of the total thrust force and the torque values than expected

to be produced by the much longer chisel edges of the GP-

twist drills. Moreover, the normal rake angle distributionalong

the chisel edge region for the WPG drill design appears to be

qualitatively and quantitatively similar to that for the GPTdrill

design, as shown in Fig. 4(b).

The ‘as observed’ effects of different 2P, ı

0(GPT)

, ˛

g(WPG)

,

ı

w(WPG)

, , and 2W/D on the pattern of elemental rake angles

in the lip region and the chisel edge region can be described

as follows: (a) the larger values of 2P, for the whole drill, may

result in a small increase in the thrust and a little decrease

in the total torque; (b) the values increase the total thrusts

and the total torques are expected to decrease a little; (c) the

lower values of 2W/D reduce the drilling forces due to the pat-

tern of elemental rake angles on the lip and in the chisel edge

region which increases into less negative and more positive

values; (d) the increases in the ı

0

angle will result in lowering

the drilling forces along the whole lip region only because the

helix angle does not affect the geometry of the chisel edge; (e)

the feed is not expected to change the distribution of elemen-

tal rake face angles at the lip region, while the elemental rake

angles at the chisel edge may slightly decrease as the feed

values increase causing the thrust and the torque values to

increase approximately linearly with the feed due to the lin-

ear increases in the area of cut. The above rule was described

in more detail in sources (Audy, 2002, 2006b) and it has been

found, and reported, to be valid for the standard – GPT – drill

design (Armarego, 1996; Zhao, 1994; Audy, 2002, 2006b) and

point thinned drill design (Armarego, 1996; Zhao, 1994), and

also applied for the WPT drill design (Audy, 2002).

From the above it is evident that the drill point geometry

and cutting conditions control the distributions of the rake

face angles and their mutual relationship can be studied by

varying the magnitudes of different inﬂuencing variables in

the input of the software. The value of corresponding angle

of WPG and/or GPT drills as well as other drill designs can

be determined for each particular element at the lip and

the chisel edge region so the illustrated trends may them-

Fig. 4 – Effect of the point angle 2P on the elemental normal rake angle distribution along the lip (a) and the chisel edge (b)

regions of GPT and WPG drill designs; after Audy (2002).

136 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138

selves indicate expected thrust and torque trends as described

earlier.

5. Studies of predicted inﬂuences of drilling

variables on the generated thrust and torque

Literature shows that the drilling action depends on the drill

point features, a large variety of tool–work-piece–material

combinations and the cutting conditions. It has also been

noticed that the experimental testing could not provide such

ﬂexibility as computer simulations using an appropriate pre-

dictive force and power model. The most complete research

concerning qualitative trends in the predicted thrust force

and torque for different drill geometry and uncoated drills

have been presented by various members of the research

group at the University of Melbourne supervised by Armarego

over 40 years. Whenever comparison of forces was possible,

considerable agreement between Melbourne’s research and

‘international’ research has been found.

Armarego (1982) and his research scholar Whitﬁeld

(Whitﬁeld, 1986) – studied a mechanics of cutting approach

for the prediction of forces and power in some commer-

cial machining operations. A part of his research work was

dedicated to study the general effects of drilling variables

on the thrust and torque. Noteworthy Fig. 5(a–h) has been

adopted from the study of these researchers (Armarego, 1982;

Whitﬁeld, 1986) because of illustrating the representative

thrust and torque predictions as inﬂuenced by drill geometry

(D, 2W, ı

0

, 2P, , and 2

W

) and drilling conditions (v, f) when

drilling a Type S1214 free machining steel work-material. Both

thrust andtorque increasedwiththe drill diameter, Fig. 5(a), as

a consequence of increases in the area of cut. Increases in the

web thickness 2W caused increases of both thrust and torque

values, as shown in Fig. 5(b), with the major increase occur-

ring on the thrust due to the wider and inefﬁcient chisel edge

region, whereas the torque is the largest at the lips where the

lever arm is largest. Whitﬁeld further reported that increases

in both the chisel edge angle and the chisel edge wedge

angle 2

W

increase the thrust but have only marginal effect

on the torque as illustrated in Fig. 5(c and d). Increases in

the point angle 2P had little inﬂuence on the predicted torque

but increased the predicted thrust as shown in Fig. 5(e). Both

the thrust and torque values were reduced with increases of

the helix angle ı

0

as shown in Fig. 5(f). Finally both thrust

and torque decreased little with increases in drilling speed,

Fig. 5(g). Increase in the feed, Fig. 5(h), resulted in increases

in both thrust and torque. Interestingly both the thrust force

and torque patterns similar to those shown in Fig. 5(a–h) were

achieved when the analysis was applied to the drilling of a

Type CS1040 steel work-material, and in this connection it has

been concluded that the pattern should remain qualitatively

the same for other common work-piece materials.

Armarego(1996) extendedthe researchinthis area. He used

a database for a Type 1020 steel work-material and predicted

thrust (T

Ht

) andtorque (T

Qt

) values as a functionof cutting con-

ditions (n, f) and drill point features (D, 2W/D, ı

0

, 2P, and ). A

set of typical graphs derived from the study of this researcher

were published in reference source (Audy, 2006b) and indi-

cated strong similarities to the qualitative trends pictured in

Fig. 5.

The knowledge and basis of the ‘Mechanics of Cutting

Approach’ primarily developed and examined by Armarego

(1996, 1982) has been extensively studied in recent years by

other scholars such as, for example, Audy (2002, 2006a), Audy

et al. (2002a, 2001, 2002b), Whitﬁeld (1986), Kata (1997), Gong

(1989) and Zhao (1994), Armarego and Zhao (1996). These

researchers conﬁrmed that this method can successfully be

applied for prediction of thrust force and torque in drilling

operations with general purpose, web-modiﬁed, four plane

facet point and circular centre edge drill point designs.

In addition, Audy (2002) has shown that the above method

for force and power predictions in drilling with uncoated

drills outlined in sources (Armarego, 1996, 1982; Zhao, 1994;

Whitﬁeld, 1986; Kata, 1997) will produce similar qualitative

trends for the effects of the individual, and common drill

point features, the tool substrate and more importantly tool

surface coatings (Audy, 2006b) on the thrust and torque val-

ues. These trends are reproduced in Fig. 6. The experiments

were conducted with TiN, Ti(C,N) and Ti(Al,N) coated drills.

Fig. 5 – Some reported predicted effects of the drilling thrust (T

Ht

) and torque (T

Qt

) on the drill geometrical features, D, 2W,

2P, ı

0

, , 2

w

, (a–f); drilling speed, v, (g); and drilling feed, f, (h). Unless indicated otherwise D=10mm, 2W=1.5mm,

=135

◦

, 2

w

, =110

◦

, 2P=118

◦

, ı

0

=35

◦

, v=20m/min, f =0.2mm/rev; after source Whitﬁeld (1986).

j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138 137

Fig. 6 – Effects of speciﬁed drill point features and feed on predicted thrust, T

h

, and torque, T

q

, values when drilling Bisalloy

360 steel with the uncoated and the coated GP twist drill(s): D=12.7mm, 2P=118

◦

, 2W/D=0.12, =125

◦

and ı

0

=30

◦

, at a

speed of 12.5m/min and a feed of 0.1mm/rev (Audy, 2002, 2006b).

For the prediction purposes the coated tools were treated as

one group (Audy, 2002). It was because when comparing the

effect of different coatings, one with another, in orthogonal

cutting tests (Audy, 2002) the quantitative differences in var-

ious performance measures namely, forces, power, friction

angle, shear angle, shear stress and chip length ratio values

were statistically equal at 95%and higher conﬁdence level, i.e.

there were no qualitative or quantitative differences between

the three coatings (Audy, 2002). Moreover, the group of coated

tools reduced, on average the torque by 24.9% and the thrust

by 14.5% indicating that the highest reductions were in the

thrust force not in the power force (Audy, 2002). This allowed

establishment of one combined database for coated tools and

use it for prediction of drilling forces and power.

Comparison of the predicted total thrusts and the total

torques for the relevant drill point geometry of the WPT-jobber

and the GP-twist drills has shown that the WPT drills reduced

the total thrust by ∼13% for the uncoated drills and by ∼20%

for the coated drills. The total torque reductions due to more

suitable WPT drill design were ∼15% for the uncoated drills

and ∼13%for the coated drills. Comparison of the total thrusts

and the total torques produced by a standard point geome-

try of the GP-twist drills and the WPT drills examined over a

wide range of the feed rates conﬁrmed again that the WPT

drill produced lower forces (and power) than the GP drills.

Moreover, in the same groups the coatings lowered the total

thrust by ∼20% and the total torques by ∼13% for both drill

designs.

The drilling force experiments were also carried out to con-

ﬁrm the validity of predictions. The results generated in this

way showed that all the three different coatings produced sta-

tistically equal variances and mean of the lip thrusts and the

lip torques at the 95% and higher conﬁdence levels, indicating

that the effects of each coatings have the same importance

in drilling Bisalloy 360 steel. This pattern has been proved

for the two different speeds one of 5.33m/min and another

of 12.5m/min supporting such knowledge that the speed has

no signiﬁcant effect on the drilling forces and power. Finally

it has been experimentally proved that the group of differ-

ently coated – TiN, Ti(Al, N) and Ti(C, N) – GP-twist drills of a

nominal diameter of 10mm was able to reduce the lip thrust

and the lip torque by a factor of ∼1.7 and ∼1.3, respectively

comparing to the uncoated drills when drilling Bisalloy 360

steel at a feed of 0.15mm/rev employing speeds of 5.33 and

12.5m/min. The predicted values and trends matched reason-

ably well with the experimental data, and the force tests have

conﬁrmed the advantage of various – single layer – coatings

over unprotected/uncoated tool substrate material.

6. Conclusions

This study has brieﬂy reviewed the concept and modelling

approach of the ‘Uniﬁed’ approach with particular reference

to drilling operations which have commonly been set to study

the effects of drill point geometry and tool surface coating

on cutting performance. Results showed that the computer-

assisted modelling allowed studying the changes in the drill

point geometry, namely, the rake angle distributions along the

drill lips and the chisel edge. In addition, this approach has

been shown to provide reliable means of quantitatively pre-

dicting all the force components, thrust, torque and power

for different drill design with particular reference to differ-

ent GPT and WPG drill geometries, and tool surface coatings.

Finally it has been shown that computer-assisted modelling

allowed to establish simpler predictive equations for forces

and power in drilling with different drill designs which oth-

erwise would needed to be estimated by direct experimental

138 j ournal of materi als processi ng technology 2 0 4 ( 2 0 0 8 ) 130–138

or ‘empirical’ approaches, reported for being time consuming

and expensive.

Acknowledgements

The author would like to thank the Edith Cowan University

(ECU) and Professor Bill Louden and Dr. Elaine Chapman from

the University of Western Australia (UWA) for supporting his

research work on ‘Designing Technology Enriched Pedagogy in

Higher Education’.

r e f e r e nce s

Armarego, E.J.A., 1982. Economics of machining criteria,

constraints and selection of optimum cutting conditions. In:

Proceedings of the UNESCO-CIRP, Seminar on Manufacturing

Technology, Singapore, pp. 86–100.

Armarego, E.J.A., 1996. Material Removal Processes—Twist Drills

and Drilling Operations, Manufacturing Science Group,

Department of Mechanical and Manufacturing Engineering,

The University of Melbourne.

Armarego, E.J.A., Kang, D.C., 1997. Geometric Modelling of Twist

Drills for Modern Computer Based Design and Manufacture.

In: Proceedings of the CAD/CAM’97 Seminar, B8.1, July 24–25.

Bandung Institute of Technology, Bandung, Indonesia.

Armarego, E.J.A., Zhao, H., 1996. Predictive Force Models for

Point-Thinned and Circular Centre Edge Twist Drill Designs,

Manufacturing Technology, vol. 45, CIRP Annals 1/1996, pp.

6570.

Armarego, E.J.A., Verezub, S., Smith, A.J.R., 1997. Effect of TiN

Coating and Substrate on the Forces, Power, Friction and

Cutting Process in Classical Orthogonal Cutting.

Australasia-Pacifc Forum on Intelligent Processing and

Manufacturing of Materials, Gold Coast, Australia, pp.

1334–1341.

Audy, J., 2002. The inﬂuence of hard coatings on the performance

of twist drills. Thesis for Master of Engineering Science in

Research. The University of Melbourne,

Australia.

Audy, J., 2006a. Exploring the role of computer modelling and

image analysis in assessing drill design features and

performance. J. Manuf. Eng., 57 6, 1–17 (Strojnicky

Casopis).

Audy, J., 2006b. A study of the effect of variations in drill point

geometry on the experimental and predicted cutting forces

generated by uncoated and coated twist drills. Mater. Eng. 13

(4).

Audy, J., Doyle, E.D., Audy, K., 2001. A study of effects of geometry

and surface coatings on the experimental thrust and torque

of general purpose twist drills and deep hole jobber drills. In:

Proceedings of Asia-Paciﬁc Forum on Precision Surface

Finishing Technology, Singapore.

Audy, J., Audy, K., Doyle, E.D., 2002a. Estimation of sources of

variations and the toleration ranges in the manufactured

point geometry of general purpose twist drills. In: Proceedings

of the 2nd Asia-Paciﬁc Forum on Precision Surface Finishing

and Deburring Technology, PSFDT, Seoul, Korea, July 2002, pp.

194–202.

Audy, J., Doyle, E.D., Audy, K., Harris, S.G., 2002b. A study of the

effect of drill point geometry and physical vapour deposited

coatings on the cutting forces generated by twist drills. In:

Proceedings of the 5th Conference on “Behaviour of Materials

in Machining”, Chester, UK, November 11–14.

Gong, Z.J., 1989. A Study on Drilling and Four Plane Facet Point

Drills. MEngSC Thesis. The University of Melbourne.

Kata, R.K., 1997. Computer aided predictive performance models

for self-propelled rotary tool and circular stationary tool

turning. PhD Thesis. The University of Melbourne.

Verezub, S., 1996. A Study of the Effect of TiN Coating and

Substrate on the Orthogonal Cutting Process. MEngSc Thesis.

The University of Melbourne, pp. 57–86.

Whitﬁeld, R.Ch., 1986. A mechanics of cutting approach for the

prediction of forces and power in some commercial

machining operations. PhD Thesis. The University of

Melbourne.

Wright, J.D., 1981. A study of the conventional drill point

geometry its generation, variability and effect on forces. PhD

Thesis. University of Melbourne.

Wu, N.Z., Armarego, E.J.A., 1996. An investigation into

dimensional accuracy of holes drilled by asymmetric general

purpose twist drills. In: Proceedings of the ICPE ‘96’ at the 6th

Sino-Japan Joint Seminar on Ultraprecisin Technology, China,

September 23–25, pp. 281–284.

Zhao, H., 1994. Predictive models for forces, power and hole

oversize in drilling operations. PhD Thesis. The University of

Melbourne.