Brake Toronto

Design of the 2007 University of Toronto Formula SAE Braking System Jason Kao 992448259

A thesis submitted in partial fulfillment of the requirements for the degree of

BACHELOR OF APPLIED SCIENCE

Supervisor: M. Bussmann

Department of Mechanical and Industrial Engineering University of Toronto

March 2007

ABSTRACT
This report describes the apt design process used to approach the manufacturing of the University of Toronto Formula SAE (FSAE) braking system. It is also the intent of this thesis is to develop a braking system that is specifically designed to meet the operating conditions of a 2007 University of Toronto FSAE racecar. This thesis has proposed caliper designs that are 22% stiffer than the 2006 calipers and 50% stiffer than the 2005 custom manufactured Aluminum calipers. These increased stiffness values are a result of extensive benchmarking from which well-placed stiffening ribs within the caliper models were exploited. Although this project has yielded front and rear brake discs that are 53% and 43% heavier, respectively, the new design incorporates a larger swept area that is anticipated to provide increased braking power as well as even pad wear. The design of the scalloping pattern is also expected to produce even brake pad wear, limiting the frequency of pad changes. The combination of stiff calipers and enhanced brake rotors should lead to a more reliable braking system, and thus lower lap times due to increased on track consistency.

ii

ACKNOWLEDGEMENTS
I would like to take this opportunity to thank the following people for their invaluable support and constructive counsel throughout the duration of this project:

Professor M. Bussmann, thesis supervisor and Formula SAE faculty advisor, for his patience and unconditional guidance during this undertaking. Futuretek-Bathurst Tool Inc, machining sponsor, for providing expertise CNC manufacturing hours towards the fabrication of the brake caliper and other related critical components. Etobicoke Metal Company (ETMECO), technology sponsor, for providing precise laser cutting services in the initial production of the brake rotors. Anchor Lamina, technology sponsor, for their unsurpassed and prompt blanchard grinding towards the complete manufacturing of the brake rotors. Jerry Zelinski, University of Toronto FSAE alumni, for his valuable input and direction during all stages of the design process. Stefan Kloppenborg, University of Toronto FSAE Drivetrain Leader, for his insight and input towards the manufacturing process of the calipers. University of Toronto Formula SAE, to every team member that has aided me in shaping my development in becoming a competent engineer over the past several years.

iii

TABLE OF CONTENTS
ABSTRACT ..............................................................................................................................ii ACKNOWLEDGEMENTS .....................................................................................................iii TABLE OF CONTENTS ......................................................................................................... iv LIST OF SYMBOLS ............................................................................................................... vi LIST OF FIGURES.................................................................................................................vii LIST OF TABLES .................................................................................................................viii CHAPTER 1: 1.1 1.2 1.3 INTRODUCTION......................................................................................... 1

Project Overview....................................................................................................... 1 Project Objectives ..................................................................................................... 2 Motivation ................................................................................................................. 2 PROJECT DESCRIPTION ........................................................................... 4

CHAPTER 2: 2.1 2.2 2.3

Context of Project...................................................................................................... 4 Scope ......................................................................................................................... 5 Schedule .................................................................................................................... 6

CHAPTER 3: 3.1 3.2

BRAKE SYSTEM DESIGN CRITERIA ..................................................... 7

Performance Specifications....................................................................................... 7 Design Life................................................................................................................ 7

CHAPTER 4: 4.1 4.2 4.3 4.4

CALCULATIONS ........................................................................................ 8

Assumptions .............................................................................................................. 8 Longitudinal Weight Transfer................................................................................... 8 Brake Torque........................................................................................................... 12 Brake System Temperature ..................................................................................... 14

iv

CHAPTER 5:

BRAKE SYSTEM DESIGN AND SELECTION ...................................... 15

5.1 Braking Forces ........................................................................................................ 15 5.1.1 System Compliance......................................................................................... 15 5.1.2 Brake Pedal Force ........................................................................................... 15 5.1.3 Pedal Ratio ...................................................................................................... 16 5.1.4 Hydraulic System Pressure ............................................................................. 18 5.2 Brake Rotor ............................................................................................................. 19 5.2.1 Brake Disc Material ........................................................................................ 19 5.2.2 Brake Disc Diameter ....................................................................................... 21 5.2.3 Brake Disc Modeling ...................................................................................... 22 5.2.3.1 Scalloping Pattern ........................................................................................... 22 5.2.3.2 Swept Area ...................................................................................................... 24 5.2.3.2 Stress and Deflection Analysis........................................................................ 26 5.3 Brake Caliper........................................................................................................... 27 5.3.1 Benchmarking ................................................................................................. 27 5.3.2 Caliper Placement ........................................................................................... 28 5.3.3 Design and Modeling ...................................................................................... 31 5.3.3.1 Fatigue Life and Allowable Stress .................................................................. 34 5.3.3.2 Stress and Deflection Analysis........................................................................ 35 5.3.3.3 Manufacturability ............................................................................................ 36

CHAPTER 6:

CONCLUSION AND RECOMMENDATIONS........................................ 37

LIST OF REFERENCES ........................................................................................................ 38 TABLES.................................................................................................................................. 39 APPENDIX A: APPENDIX B: APPENDIX C: MATERIAL GRAPHS AND CHARTS ................................................. 43 BRAKE ROTOR MODELS ................................................................... 47 BRAKE CALIPER MODELS ................................................................ 49

v

LIST OF SYMBOLS
AISI AMC AP Bf Br Dod Dash X cc CNC CG Dsf Dsr km ksi ma mm LWT lbs LP PR psi FEA FSAE FCF FCR Ft Fin Fout G in-lbs Reff RBr TFgen TRgen Treg UTXX Wc µ pad µt ” or in American Iron and Steel Institute area of master cylinder piston area of caliper piston brake bias setting to front circuit brake bias setting to rear circuit overall diameter of brake disc designation for diameter of pluming lines (in 1/16th of inch) cubic centimeters (derived unit of volume) computer numerically controlled center of gravity static weight distribution front of car static weight distribution rear of car kilometer kilo pounds per square inch mass x acceleration (from F=ma) millimeter longitudinal weight transfer pounds line pressure pedal ratio pounds per square inch Finite Element Analysis Formula Society of Automotive Engineers clamping force front calipers clamping force rear calipers tractive force or grip on tire driver input force at selected pedal ratio force applied to master cylinder Units of measuring deceleration / acceleration in gravity inch pounds effective radius of brake disc rolling radius generated braking torque front tires generated braking torque rear tires required brake torque University of Toronto FSAE vehicle year 20XX corner weight coefficient of friction of brake pad coefficient of friction of tires inches

vi

LIST OF FIGURES

Figure 1 Figure 2A Figure 2B Figure 2C Figure 3 Figure 4 Figure 5 Figure 6A Figure 6B Figure 7 Figure 8A Figure 8B Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure18 Figure 19A Figure 19B Figure 20

Point distribution of FSAE competitions Diagram of geometry and forces acting on car Longitudinal weight distribution static conditions on front and rear axle Longitudinal weight distribution under 1.6G of deceleration (LWT = 168 lbs) Linear relationship of traction and load on a FSAE tire Definition of pedal ratio (mechanical advantage) Diagram of bias bar and brake bias adjustment Brake pad coefficient of friction vs temperature for steel rotor material Brake pad coefficient of friction vs temperature for aluminum rotor material Effective radius of brake disc Uneven pad wear (top and bottom of pad exhibit less wear than middle of pad) Uncharacteristic brake disc attrition due to undersized swept area Wide scalloping pattern in UT06 rotor Narrow scalloping pattern UT07 rotor Swept Area of brake disc Swept area of manufactured front rotors for 2006 and 2007 Locations of critical stress on UT07 rotor design Pressure distribution on brake pad due to number of pistons View of inside front left wheel assembly Definition of inboard and outboard mounting styles Definition of axial and radial mounting Final UT07 caliper assembly Caliper mounting tab prior to adjustment Caliper mounting tab after 0.05” adjustment Illustration of external brake line on caliper

vii

LIST OF TABLES
Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Anticipated UT07 braking system timeline Comparison of 2006 and 2007 vehicle Parameters Life span of 2007 racecar Vehicle braking requirements for 2007 Comparative table listing rotor and caliper temperatures for 2006 and 2007 Mass comparison chart of 2006 and 2007 brake discs Caliper benchmarking data UT07 Brake caliper design criteria Tabulated fatigue strength comparison of aluminum alloys Spreadsheet of vehicle parameters and output values for braking system

viii

CHAPTER 1: INTRODUCTION
1.1 Project Overview

The following report details the design process and methodologies used for the 2007 University of Toronto Formula SAE (FSAE) braking system. A typical FSAE braking system is comprised of an assembly of components: brake calipers, brake discs (rotors), master cylinders, brake pads, brake line, etc. This report will primarily focus on the comprehensive design of a custom brake caliper and brake rotors for UT FSAE applications. The approach to the design for the UT07 Braking system is systematic and has been investigated in a structured manner. First, the complete tear down and analysis of previous designs and systems was scrutinized. The pros and cons of each braking system were investigated and compared to those of previous years. The design of certain components and selection of non in-house manufacturable components depends on the design criteria, which combines both vehicle parameters and braking requirements. Because many of the vehicle parameters such as top speed and mass were to remain fairly similar for UT07, a baseline for the braking system requirements was set. Next, all necessary theoretical calculations needed to stop UT07 where determined given specific input data. Lastly, once all the required information is gathered, the incorporation of vehicle parameters, operating conditions, and packaging restraints are combined into a proposed design.

1

1.2

Project Objectives

The intent of this thesis is to design a braking system that is balanced, reliable, cost effective, and specifically designed to meet the operating conditions of a 2007 University of Toronto FSAE racecar. The design of the custom components will be in response to the specific requirements to the 2007 University of Toronto FSAE racecar design goals while preserving the following characteristics: High stiffness to weight ratio Reliable Ease of manufacturability In addition, this project will serve as a reference for future FSAE teams to assist in designing (and selecting) brake components and how these relate to the overall braking performance.

1.3

Motivation

Brakes are an essential system to any racecar or vehicle. They are the most important component on any vehicle second to tires. Historically, the U of T racing team has not given high priority to the braking system, rather using inherited designs that were given insufficient consideration in terms of how the system would affect the performance of the overall vehicle. Although past systems accomplished the bare minimum goals of a braking system, they did not facilitate to promote on track performance gains. Contrast to road circuits FSAE tracks exhibit scores of corners and turns, which require extensive use of the brakes to decelerate from high rates of speed. Furthermore, a braking system that is powerful and consistent instills confidence in the driver (and race team) [1]. Respective racecar engineering experts [2] often suggest that improved braking performance can result in enhanced on track performance of racing vehicles. Furthermore, [4] asserts that the overall time spent on the

2

brakes is only 10% during a race, but this often equates to the difference between second place and a championship in racing. Major components including the brake calipers in previous years have been purchased and are often designed to exceed the performance needs of a FSAE vehicle. This leads to an overly robust, but more concerning an undesirable heavy component. While part of the design intent is to develop custom calipers for the 2007 racecar, the overall design hopes to allow for next generation teams to easily retrofit the design into future vehicles.

3

CHAPTER 2: PROJECT DESCRIPTION
2.1 Context of Project

The Formula SAE® (FSAE) competition is for students and aspiring engineers, to conceive, design, fabricate, and compete small formula-style racing vehicles. The FSAE series competitions challenge students and their respective teams in terms of their design choices and validation techniques, and on track performance in comparison to other universities around the world. Governed by a strict safety rules to protect participants from any foreseeable injury, the overall design on FSAE cars are only limited by the knowledge, creativity, and imagination of the students. The FSAE competitions enforce certain vehicle requirements and restrictions; the major design requirements being the following: Open wheeled and open cock-pit (formula style body) configuration Four wheel independent suspension Engine air intake restriction to 20mm in diameter Maximum four-stroke engine displacement of 610cc Braking system must act on all four wheels Each team will have the chance to demonstrate their hard work and prove their analysis and design through their engineering work, presentation, and driving skills. The SAE currently

sanctions a multitude of international competitions that continues to expand globally. As with previous years, the 2007 season’s “big three” main competitions of the series include (only that latter of the two are participated in due to scheduling logistics): Formula SAE Australia – Melbourne, Australia (Dec 14-18, 2006) Formula SAE – Detroit, Michigan, USA, Ford Proving Grounds (May 16-20, 2007) Formula Student – Northhamptonshire, UK, Silverstone Circuit (Jul 12-15,2007)

4

All the competitions in the FSAE series consist of a series of dynamic and static events in which points are distributed accordingly as illustrated in Figure 1. Of the allotted points, Autocross and Endurance are worth the most adding up to 50% of the competition’s points, both exploiting the vehicle to punishing on-track conditions. These and the other remaining dynamic events necessitate superior dynamic vehicle performance.

Figure 1 – Point distribution of FSAE competitions

With this notion in mind, it is the motivation for the UT FSAE team to develop each new vehicle with greater power, handling, and superior stopping power to improve on track performance and thus, maximize the points awarded in these events. As mentioned in Chapter 1, the consistency of the driver’s performance can be dramatically increased through well-designed brakes.

2.2

Scope

The scope of this thesis is intended to develop a design framework for the UT07 FSAE braking system including the potential manufacturing and implementation of the proposed design into the indicated vehicle. The design and selection of all braking subsections excluding pedal tray will be investigated. Techniques and methods of retrofitting custom components into future FSAE racecars and brake system tuning is beyond the scope of this project.

5

2.3

Schedule

This project intends to follow a timeline built around the technical schedule of the overall UT07 racecar. The project will adhere to a 12-month schedule, incorporating the following milestones as shown in Table 1. The manufacturing and implementation of the complete braking system lies outside the timeline of the thesis schedule due to turn around times of machining sponsors. Therefore, final on track verification of the proposed braking design will no be included in this report but will be diligently performed thereafter.

2007 Braking System Design Timeline

Milestone/Activity On track preliminary data collection Preliminary tests started Braking system component design and selection started FEA analysis completed Brake caliper design/drawings complete Brake rotor designs/drawings complete Braking system sub components selection finalized Calipers and Rotors sent out to manufacturer Pedal Tray fabrication started Braking Lines installed Manufactured components completed* All components of braking system installed* Initial on track testing begins* Component and system verification* Competition Formula SAE East (Detroit) Competition Formula Student

Implementation Date 20-Jul-06 10-Aug-06 20-Aug-06 30-Sep-07 6-Oct-06 12-Oct-06 20-Oct-06 25-Oct-06 15-Nov-06 20-Dec-06 10-Feb-07 26-Feb-07 15-Mar-07 20-Mar-07 16-May-07 12-Jul-07

* subject to change pending sponsor machining time Table 1 – Anticipated UT07 braking system timeline

6

CHAPTER 3:
3.1

BRAKE SYSTEM DESIGN CRITERIA

Performance Specifications

The design of any braking system must begin with the collection of all relevant data regarding the vehicle’s specifications and performance requirements. A comparison between the 2006 and 2007 vehicle parameters show minor changes in the overall geometry, none of which should negatively influence the braking system design. The data shown in Table 2 indicates an estimated decrease in UT07’s weight by 75 lbs, which should allow for quicker deceleration. These values will be used in defining the brake torque, weight transfer, and brake disc and caliper temperature characteristics.

3.2

Design Life

As mentioned previously in Chapter 2.3, the design of the braking system must encompass multiple testing and competition dates. The braking system is to be used for a service life of 1200 km as indicated in Table 3. The system is to be designed for a minimum of one racing season (five months), after which servicing of major mechanical components such as the brake caliper piston seals should be carried out to ensure proper future operation.

7

CHAPTER 4:

CALCULATIONS

4.1 Assumptions
Deceleration is the measure of how rapidly a vehicle slows down. The maximum achievable velocity of the UT07 racecar is limited to 150 ft/s (~160 km/h). Although observed competition speeds are considerably lower, this value is taken as the worst possible condition during hard braking since energy dissipation is a function of velocity squared (E = ½mv2). Deceleration (and acceleration) is measured in units of gravity or “G’s”. To determine a baseline G value, the racecar should stop from 150 ft/s in approximately 2.5 seconds. Assuming constant deceleration, Equation 4-1 yields:
v f = vo + at

(4-1) a = -55.56 [ft/s2]

0 ft s = 150 ft s + a(2.7 s )

We can now establish the deceleration in terms of G’s through the use of Equation 4-2. G’s of deceleration = a/g = 55.56 ft/s2 / 32.2 ft/s2 = 1.72G (4-2)

Values from derived from data acquisition equipment on past FSAE vehicles show a sustained deceleration of 1.5G with short spikes of maximum 1.65G braking. Thus accounting for potential errors such as data acquisition irregularities of onboard computer systems and actual stopping time, a compensated value of 1.6G will apply for all other calculations within this report.

4.2 Longitudinal Weight Transfer
The center of gravity (CG) is a point on an object where all its mass is concentrated and it is completely balanced. The CG also serves as a location where the combination of all inertial forces summed into a focused single inertial force [1]. Since the CG of UT FSAE racecars

8

are located closer to the rear wheels for purposes of tractive acceleration as a result of engine packaging and driver placement, more weight of the car is distributed to the rear wheels while the car is static. Under deceleration forces due to rotational inertia tend to load the front tires and lift the rears (i.e. car rotates about the CG) as the CG is located above the ground (tire contact patch) [2]. The actual weight of the car does not change, rather the amount of load witness by the front and rear tires varies with dynamic conditions.

Ff = force on front tires B = Wheel base Bf = distance from CG to front tire Fr = force on rear tires CG = center of gravity Br = distance from CG to rear tire h = distance from CG to ground Wc = weight of car µ = coefficient of friction Figure 2A – Diagram of geometry and forces acting on car

Figure 2A illustrates how weight transfer occurs through the forces acting on the racecar while decelerating. Under static conditions, ma is nil and the weight distribution Dsf and Dsr is calculated by summing the moments about the front and rear tires at the contact patch with the road as described in [7].

9

Moment about front tires

Moment about rear tires

CW +

∑M

front

= − Fr B + Wc B f = 0

CW +

∑M

rear

= F f B − Wc Br = 0

Fr =

Wc B f B

(4-3a)

Ff =

Wc Br B

(4-3b)

Note that forces on the front and rear tires can be expressed in terms of W and G. F = ma = mg*a/g = W*G (4-4)

As a result, the static weight distributions of the front Dsf and rear Dsr, respectively, are:
Dsf = Bf Wr G= Wc B

(4-5a)

Dsr =

Wf Wc

G=

Br B

(4-5b)

Since G is a constant, it can be ignored in subsequent weight transfer equations.

To account for the weight transfer during deceleration, the same process is repeated but now
ma is taken into considering.

Moment about front tires

Moment about rear tires

CW +

∑M

front

= − Fr B + Wc B f − mah = 0

CW +

∑M

rear

= F f B − Wc Br − mah = 0

− Fr B + Wc B f − Wc Gh = 0 Fr = Wc B f B − Wc Gh B

F f B − Wc B f − Wc Gh = 0 Ff = Wf Wc Wc Br Wc Gh + B B Br Gh + B B

Wr B f Gh = − Wc B B Ddr = Dsf −

=

Gh B

(4-6a)

Ddf = Dsf +

Gh B

(4-6b)

10

The results illustrated in Equation 4-6 show an increase load transfer to the front wheels about the CG under deceleration. Consequently, the amount of braking force required at front and rear wheels will not be equal.

Figure 2B – Longitudinal weight distribution static conditions on front and rear axle

Figure 2B represents the longitudinal load distribution under static conditions. With data gathered from using weight scales to measure UT06’s weight distribution, the static weight distribution resulted in 45% and 55% to the front and rear, respectively, and is shown in Table 2. Modifications to the chassis and wheelbase indicate UT07 to have a static weight distribution of 56% to the rear, also shown in Table 2. The longitudinal weight transfer is proportional to rate of deceleration, weight of the vehicle, and CG height and is inversely proportional to the wheelbase. Thus, the governing equation for longitudinal weight transfer is given by:

LWT =

weight × CG wheelbase

[lbs ][inches ] [inches ] 11

(4-7)

From utilizing Equation 4-7, under a constant linear deceleration of 1.6G, Figure 2C illustrates an increase of 168lbs to both front wheels (each front wheel increases by 84lbs). Again, the amount of braking force must be designed accordingly to coincide with this difference in weight transfer.

Figure 2C – Longitudinal weight distribution under 1.6G of deceleration (LWT = 168 lbs)

4.3 Brake Torque
Brake torque can be understood as the “braking power” of a vehicle. More specifically, it is the measure of friction force on a tire, multiplied by the rolling radius of that tire. Rolling radius is the distance from the center of the wheel to the pavement with the tire loaded [1]. The required brake torque for any wheel can be given by Treq = Ft × R Br (4-8)

where Ft is the maximum tractive force (i.e. grip) at any given tire. Tire testing data from 2005 revealed a linear relationship between tractive force with respect to vertical load (refer to Figure 3). Therefore, the threshold for traction can be considered at a maximum before

12

there is slippage between the tire and contact patch surface (i.e. skidding) and is shown by Equation 4-9. Ft = [(2.2338 × Wc ) + 32.64]µ t (4-9)

Max Tractive Force vs Vertical Load @ 1.5 deg Camber 3500

Max Tractive Force (N)

3000 2500 2000 1500 1000 500 0 0.00

y = 2.2338x + 145.2

200.00 400.00 600.00 800.00 1000.0 1200.0 1400.0 0 0 0

Vertical Load (N)
Figure 3 – Linear relationship of traction and load on a FSAE tire

Table 4 shows the minimum braking torques required for each wheel on the UT07 racecar to sustain a 1.6G deceleration. The actual generated brake torque by the braking system is directly proportional to the clamping force from the caliper, number of pistons in the caliper, effective radius, and brake pad coefficient of friction. TFgen = (FCF) x (number of pistons in caliper) x (Reff) x (µpad) TRgen = (FCR) x (number of pistons in caliper) x (Reff) x (µpad) Determining the clamping force FC is discussed in Chapter 5.2 (page 20). (4-10A) (4-10B)

13

4.4 Brake System Temperature
During braking applications, the vehicle’s kinetic energy is converted mainly into heat, but also noise and light. Heat generated from friction of the brake pads rubbing against the rotor is partially transferred to the caliper via the brake pads, pistons, and brake fluid. Accurate modeling of exact surface temperatures of the rotor is extremely complex, since heat is constantly being transferred from the rotor to the air/caliper through conduction, convention and forced convection. Temperatures from experimental data gathered during on-track simulations in Table 5 are averages of the rotor and caliper post endurance simulations. Caliper temperature data will be a useful determining factor for fatigue life of the material used in a custom caliper design. Determining the brake disc temperature experimentally will assist in the proper selection of brake pads, which their friction characteristics are dependant on specific temperature ranges.

14

CHAPTER 5:

BRAKE SYSTEM DESIGN AND SELECTION

5.1 Braking Forces
5.1.1 System Compliance
During braking applications, each component is linked together in some fashion of mechanical, hydraulic, or physical connection. Tremendous forces are exerted onto these components and thus each component must be as stiff as possible to limit the total physical compliance throughout the system. This allows each component to work to its full potential without having to compensate for system flimsiness. The brake pedal plays a crucial role in a robust braking system. As it is the only physical link connecting the driver to the braking system, a strong stiff brake pedal (and pedal tray) needs to be designed. In addition, the pedal needs to be large enough to accommodate the feet of every driver. As mentioned earlier, the actual design of the brake pedal and subsequent pedal tray will not be covered in this report, but rather only a discussion of the requirements related to determining braking force.

5.1.2 Brake Pedal Force
[1] states that the average person can stop a road car with 100 lbs of pedal effort. Since numerous drivers in competition pilot the FSAE vehicle, individual pedal efforts from current and potential drivers were collected by experimental trials. Participants were asked to produce medium to high braking inputs on previous cars simulating intermediate braking efforts to panic stops. Compiled data show all drivers can generate an average pedal effort of 110 lbs, more than enough to stop the racecar in any situation.

15

5.1.3 Pedal Ratio
Optimal braking torque requires careful manipulation of the brake bias, hydraulic force, and pedal ratios. The pedal ratio or mechanical advantage is the ratio of the distance from the brake pedal pivot point (commonly at the drivers heel) to the point of pedal input force application over the point of master cylinder attachment to the brake pedal to the pivot point. This is graphically explained with the aid of Figure 4. In essence, a greater amount of braking force can be generated by using minimal input force by adjusting the leverage of the pedal ratio.

Figure 4 – Pedal ratio (mechanical advantage)

Based on foot size of the largest and smallest drivers an average basis for “H” was determined for UT07. Bending load tests were conducted with varying dimensions of “h” to ascertain a maximum pedal ratio before the pedal would fail (yield). Average pedal dimensions consisting of an input height “H” of 7.5 inches and a distance “h” of 3 inches

16

give way to a pedal ratio of 2.5. This will allow for maximum force output without excessive driver input force, helping the endurance of the driver during numerous braking applications over a competition. Hydraulic ratio is the relative area of the master cylinder bore and the total piston area of the calipers [2]. Brake bias is the amount of brake line pressure distribution between the front and rear master cylinders. The brake bias fine tunes (changes) the brake force balance by moving the pivot point of the bias bar (refer to Figure 5) towards the master cylinder that requires more pressure.

Figure 5 – Diagram of bias bar and brake bias adjustment

Setting the bias bar ratio to 50% front and 50% rear is common practice in producing a balanced braking ratio between the front and rear wheels. A balanced bias setting will give a starting point for the design of the brake discs by assuming an equal amount of braking force will be distributed to each wheel.

17

5.1.4 Hydraulic System Pressure
Braking systems operate on the principles of hydraulics. The total hydraulic system pressure acting on a braking system at one time is dictated by the master cylinder bore size and pedal ratio. The master cylinder creates brake fluid movement and pressure through force manipulation and fluid displacement. It is connected to the brake pedal with a simple clevis linkage.

The maximum brake line pressure experienced can be found through calculations. Charting the maximum brake line pressure is essential in determining how much clamping force can be developed and will affect the extent of deflection in the caliper. The pressure developed within a braking system is found by:

Fout = Fin × PR FMC = Fout FMCF = FMC × B F FMCR = FMC × B R LPF = FMCF × AMCF LPR = FMCR × AMCR

(5-1) (5-2) (5-3A) (5-3B) (5-4A) (5-4B)

The maximum line pressure was found to be 540 psi. This information will be used for the caliper deflection analysis covered in Chapter 5.3 and in determining the optimal brake disc diameter. Furthermore, the maximum pressure will dictate the type and size of stainless steel braided brake lines to be used where solid brake lines are not suitable for installation. 18

In Chapter 4.3, the clamping force was needed to completely determine the generated braking torque in Equation 4-10. With the expressions developed in this chapter the preceding formulae can be calculated find the clamping force and thus generated braking torque:

FCF = LPF × APF FCR = LPR × APR

(5-5A) (5-5B)

Simultaneously solving these variables in a spreadsheet program (refer to Table 10) and returning to Equation 4-10 will result in arriving at an optimal solution that satisfies the braking torque requirements outlined in Table 4.

5.2

Brake Rotor

5.2.1 Brake Disc Material
Various materials can be used for brake rotors, ranging from carbon steel, cast iron, aluminum, to even composite materials. For UT FSAE applications, low cost, strength, and manufacturability are commonly the compromising factors when selecting the appropriate materials. Mild (low carbon) steel contain up to 0.25% carbon content allowing for excellent wear resistance. They exhibit moderate strength to weight levels but also provide excellent “feel” during braking applications compared to other metals such as Aluminum. In addition to the improved modulation, mild steel (Figure 6A) offers greater coefficient of friction factors than aluminum (Figure 6B) when tested with various brake pad compounds. Aluminum is approximately only one third as rigid as steel, and becomes malleable at higher

19

temperatures making it a questionable rotor material choice. On top of this, an Aluminum rotor would need to be much thicker than a steel rotor due to its lower (42 ksi versus 68 ksi) compressive ultimate tensile strength than steel.

Figure 6A – Brake pad coefficient of friction versus temperature for steel rotor material

Figure 6B – Brake pad coefficient of friction versus temperature for aluminum rotor material

And because steel is inexpensive and is readily suitable for laser cutting, manufacturability of the rotors will only require a limited lead-time. These factors led to the material selection for the UT07 brake rotor to be of cold rolled SAE1025 – ¼” thick mild steel plate. The ¼” thick plate will be blanchard ground to a thickness of 0.120” to reduce its mass to an approximate final weight of 0.609 kg for a front rotor and 0.513 kg for one rear rotor.

20

5.2.2 Brake Disc Diameter
The brake disc diameter Dod is determined from the outside most edge to the center of the rotor, doubled. More importantly, the effective radius (Reff)) is the radial distance from the center of the rotor to the center of the brake pad contact patch as illustrated in Figure 7. This location is also the center of the caliper piston where the clamping force is applied by the caliper to the rotor.

Figure 7 – Effective radius of brake disc

To obtain the utmost possible braking torque, the brake disc diameter should be as large as possible, thus maximizing the effective radius. It should be noted that the maximum diameter of the brake disc is limited by the inner diameter of the wheel rim and caliper size. This will be kept in mind during the design of the caliper.

As discussed earlier in Chapter 4, the longitudinal weight transfer during deceleration influences the amount of braking torque required at the front and rear wheels. It was shown in Table 4 that the front wheels each required 3277 in-lbs of torque as compared to only 1442

21

in-lbs in the rear. Initially basing all torque requirements on the effective radius, one could deduce that the front rotor would be larger than the rear rotors. Due to the lower required torque values in the rear, the rear rotors should be made small as possible allowing adjustment of the appropriate master cylinder size to balance the rear braking torque with the front. With preliminary designs of the caliper having two pistons each and setting an equal brake bias ratio, the effective radius of the front and rear discs was set to the largest possible of 4.9 inches. Using data in Chapter 5 and Table 4, the optimal brake disc effective radii for the front and rear were calculated to be 4.3 inches and 3.8 inches, respectively. Incorporating the brake pad height, this gives a (resulting) maximum Dod of 10.38 inches in the front and 9.38 inches in the rear.

5.2.3 Brake Disc Modeling 5.2.3.1 Scalloping Pattern
The design inspiration of the UT FSAE braking rotor came from high speed racing motorcycles. Most automotive or motorbike racing brake discs contain a venting feature to help dissipate hot gases produced during braking applications and continuously sweep the pad clean of debris and brake dust build up. Conventional high performance rotor designs have either a slotted, cross drilled pattern, or both. As a result there is an increase in “bite” characteristics allowing for aggressive stopping. Drilling holes or machining slots require allocating many machining hours and can become expensive. On top of that, holes are a source for stress concentrators and induce crack propagation. The slotting patterns for the UT FSAE brake discs have been designed to provide a large reduction in rotating mass. However, there have been short comings to this approach. The amount of total actual swept

area is diminished by introducing too many sizable scalloping patterns that are ill placed. As
22

a result, unequal pad wear and tapering occurs as seen in Figure 8A and brake pads must be replaced more frequently.

Figure 8A – Uneven pad wear (top and bottom of pad exhibit less wear than middle of pad)

The UT07 rotor design investigates the optimal pattern that will limit accelerated irregular pad wear but maintain a low weight criteria. Figure 9 and 10 compare the 2006 rotor and the proposed design for 2007, respectively. The narrower and closely packed radial profiles of the scallops for the proposed 2007 rotor design is anticipated to promote even pad wear while providing extra “bite”.

Figure 9 – Wide scalloping pattern in UT06 rotor

Figure 10 – Narrow scalloping pattern UT07 rotor

23

5.2.3.2 Swept Area
The total area contacted by the brake pad on the rotor during one revolution is defined as swept area (refer to Figure 11), and is an important measure of the overall effectiveness of the brake disc. An increase in the potential stopping power can be harnessed through a larger swept area but at the cost of having a larger (and heavier) rotor.

Figure 11 – Swept Area of brake disc

Packaging becomes a concern since an increase of rotor diameter would have to be considered when packaging into a fixed wheel size. In addition, the overall pad size and thus caliper geometry would effectively change for a greater swept area.

Considerations into the swept area arose during testing of UT06 as closer observations revealed uneven pad wear and abnormal brake disc attrition (Figure 8B). The 2007 rotor design incorporates a larger swept area to provide increased braking power as well as even pad wear.

24

Figure 8B – Uncharacteristic brake disc attrition due to undersized swept area

As seen in the manufactured rotors from Figure 12, the overall swept area contacted by the brake pad has been enlarged by the redistribution of the scalloping patterns in hopes of promoting even pad wear. The larger swept area should also provide a bigger clamping area for the entire brake pad surface to adhere to. This will maximize the actual brake torque produced. Comparing the final mass values in Table 6, there has been an increase of approximately 53% in the front rotors and 43% in the rears from the new design to the 2006 rotor. This slight weight increase is a favorable tradeoff to improving pad wear and enhancing overall braking performance.

Figure 12 – Swept area of manufactured front rotors for 2006 and 2007

25

5.2.3.2 Stress and Deflection Analysis
Finite Element Analysis using Pro Engineer / Mechanica was the primary method used to analyze the stress distributions imparted on the brake rotors from applied brake forces. Frictional forces from the brake pads were modeled assuming all of the 804 lbs of generated clamping force was applied parallel to the swept surface of the rotor.

Figure 13 – Locations of critical stress on rotor design

The critical areas of stress seen in Figure 13 are located at the four mounting points to the hub and random small radial profiles within the scalloping pattern. This is due to the fact that the sharp corners or profiles with very small radius’ are regions of high stress concentration. Efforts to model corners and small profiles with larger radius’ were consciously made to reduce the amount and value of the resulting stresses. Although thermal properties play an important role in overall brake rotor and pad performance, the exact heat transfer coefficient due to (forced) convection while the rotor is rotating is extremely complex to determine and numerically model. It is therefore not included in the mechanical analysis of the brake disc and should not dramatically alter the results. The final version of 26

the proposed front rotor design yielded a Von Mises stress of 53 ksi and a maximum deflection along the rotor surface of 0.006 inches given a safety factor of 1.3. The FEA results of the brake disc iterations can be reviewed in Appendix B.

5.3 Brake Caliper
5.3.1 Benchmarking
The design of the caliper was initiated by a full inspection and break down of the 2005 physical caliper assembly and CAD model. Consultations with the designer yielded details behind the design that the CAD model did not intuitively reveal. Information gathered from initial benchmarking of braking systems from 2004, 2005, and 2006 was used to determine specific features and performance parameters required by the 2007 caliper design. Appendix C contains the benchmarked caliper models for UT04, UT05, and UT06.

Caliper “flimsiness” occurs when the brakes are powerfully applied due to flexing in the

bridge of the caliper body. The bridge design determines the overall caliper stiffness, as it is
the major portion spanning the outside of the rotor. Aside from the UT04 design, prior brake calipers have been fixed calipers. Fixed calipers entail a rigid non-moving mount as opposed to a sliding caliper where the entire caliper assembly moves in the opposite direction of the applied clamping force (i.e. calipers similar to those on a production vehicle). It is difficult to manufacture a rigid upright brake mount that can facilitate the sliding motion (often referred to as floating calipers). Furthermore, floating calipers only have a single hydraulic piston and because of the motion this entails on the caliper, uneven pad wear may occur. Fixed caliper designs use one (dual piston design) or more pistons on each side of the caliper

27

body. Bigger caliper assemblies require more pistons to evenly spread the piston load against the brake pad and promote even pad to rotor pressure. Figure 14 exhibits the pressure distribution of the brake pad lining on the rotor in a single and dual piston caliper. Since the caliper must also package closely into a small FSAE wheel, conscious efforts were made to investigate brake pads with smaller dimensions that would make a compact dual piston design possible. Due to these reasons, a fixed dual piston caliper design was proposed and built off of.

Figure 14 – Pressure distribution on brake pad due to number of pistons

It is industry standard to use square piston seals within the cavity of the brake caliper bore instead of traditional (round) o-rings. A square “o-ring” seals the piston, prevents fluid to pass and forces it to push out the piston. Square seals control piston retraction and act as a return spring mechanism so that the brake pad does not drag against the rotor when the brakes are released. Thus, purchased high temperature square piston seals are preferred and will be used in the proposed design.

5.3.2 Caliper Placement
It is important to position the caliper in the most suitable arrangement around the rotor. Considerations should be made to allow for suspension and steering clearances and ease of

28

brake fluid bleeding. Examining Figure 15 as a clock, which shows a view of the inside front left wheel assembly, theoretically the caliper could be placed at any position. To completely remove all air within the braking system, calipers placed at 3 or 9 o’clock are ideal in typical racing caliper designs to facilitate bleeding. It should be noted that the brake bleeder location on the caliper should be the highest point relative to all braking system components to avoid creating air bubble traps since air rises.

Figure 15 – View of inside front left wheel assembly

Interference from the upright’s lower and upper components further dictates the caliper to be placed at 3 or 9 o’clock. In regards to bearing loads and weight transfer, front calipers are best placed behind the upright towards the rear of the car to offset the tremendous bearing loads encountered during deceleration. Rear calipers should be placed ahead of the upright

29

towards the front of the car to induce as much possible rear tire grip that is lost to weight transfer.

Figure 16 – Definition of inboard and outboard mounting styles

Proposals for inboard and outboard (refer to Figure 16) mounting schemes were analyzed using data presented in Table 2 and 4 and evaluating the impact on vehicle dynamics of both methods. The front wheels can only be of outboard mounting since there is no physical connection linking the two front wheels (i.e. drive shaft) in UT07. Mounting locations for the rear can be of either inboard or outboard styles. Important considerations towards a rear inboard mounting scheme must be acknowledged prior to implementation. [1] advises of several shortcomings leading to poor braking performance with a single rear inboard mounted caliper: It must provide enough braking torque to each wheel, and in addition overcome all rotating components of the power train (includes engine and differential). Inertial loads from components in the drive train add complexity to the accurate calculation of braking torque

30

Braking characteristics in the rear axle become a function of the differential torque bias ratio. Inboard rear mounting also places the caliper extremely close to the differential, exposing the brake disc to possible differential fluid and engine oils. Contaminants on the rotor surface such as lubricating oils are prone to dramatically reducing the braking effectiveness. Disadvantages to a rear outboard scheme would include the number of physical calipers to be manufactured or bought and the additional caliper mounts on the uprights would increase leading to possible prolonged turn around times. Additional brake pads, pistons, and brake line would also be required. Having analyzed the given circumstances, a compromise was made by selecting outboard mounting for superior and reliable braking performance over lead-time, which will be considered during physical modeling of the caliper.

5.3.3 Design and Modeling
The design and modeling of the caliper follow design requirements gathered in Table 4 and determined from the benchmarking stage. The caliper design and mechanical analysis were used simultaneously and iteratively to arrive at the desired parameters.

Preliminary calculations were performed to determine an initial suitable piston and master cylinder bore sizes. Various standard sizes of pistons come commercially available, but size constraints must be applied so that the caliper does not become bulky. Larger pistons provide a greater clamping force, and require lower line pressures to develop the same amount of brake force. This results in a firmer brake pedal feel from the reduction in radial brake line expansion. The larger pistons are comprised of Aluminum, instead of stainless steel to aid in mass reduction. But because Aluminum has a higher heat transfer coefficient

31

than steel, brake fluid boiling and piston seal crystallization becomes more likely. In effort to limit heat transfer, small (1.38” bore) short deep-cupped stainless steel pistons were chosen. Their small bore size of 1.38” produce a reduction in brake pedal travel resulting in quicker brake feel due to the increased pressure. To compensate for the increased line pressure as a result of using smaller pistons, stiffer Dash 2 (1/8” OD thick) the smallest possible stainless steel braided brake lines would be used.

Figure 17 – Definition of axial and radial mounting

The UT05 custom caliper was taken as an initial starting point for a rough model of the 2007 proposed design. The UT05 caliper utilizes radial mounting as opposed to axial mounts; both mounting schemes are described in Figure 17. Constraints developed from the upright design yielded axial mounting as the only suitable approach, even though radial mounting provides a more rigid caliper mount. The UT07 caliper axial mounting tab schemes were approached with the understanding that fasteners in double shear preserve a higher safety

32

factor (2.2) of those of single shear. Analysis from the 2006 axial mounting scheme showed that ¼” aircraft-grade steel bolts would suffice such shear stresses for the anticipated 2007 design. As previously mentioned, the maximum overall brake disc diameter of 10.38 inches for the front was used in modeling an optimal caliper bridge thickness that would not obstruct the wheel and also be mechanically stiff.

The detailed design process resulted in 10 distinct versions of the caliper, each an improvement of its predecessor. The greatest improvements are seen from iterations from 6, 7, 8, and the final 10th (Figure 18) iteration arriving at the optimal solution that will be used in for the 2007 design. Appendix C portrays caliper assembly versions 1, 6, 7, 8, and 10 respectively. The initial iterations will not be discussed in detail, as they did not satisfy the outlined criteria. Chapter 5.3.3.3 will reveal the approach detailing the improvements made towards ease of manufacturability.

Upon the final iterations of the brake caliper, it was discovered that a packaging issue would incur due to the brake mount location on the suspension upright. The physical mount on the caliper required an offset of 0.050 inches to obtain the correct mounting configuration for the brake assembly as illustrated in Figure 19. Although the change was not overly crucial to the structural integrity of the caliper, it demonstrates the importance of how systems on the car can affect one another and the need to allow for unexpected compromises throughout the design process.

33

Figure18 – Final UT07 caliper assembly

Figure 19A – mounting tab prior to adjustment

Figure 19B – mounting tab after 0.05” adjustment

5.3.3.1 Fatigue Life and Allowable Stress
Following the procedure outlined in [1] for establishing and determining the predominant failure mode (i.e. fatigue) and the maximum allowable stresses for aluminum under worse case FSAE scenarios, justification for opting 7075-T6 Aluminum as the material choice was clear-cut. By comparatively examining the Strength-Fatigue (SN) curves for both 6061-T6

34

and 7075-T6 aluminum in Appendix A, the maximum allowable stresses corresponding to the predetermined allowable caliper cycles is shown in Table 8 as 102,000 cycles. Important elements dictating accurate fatigue life including temperature, surface finish, and reliability were taken into account to correctly adjust for fatigue life of 7075-T6. Knowing the caliper would be machined finished (0.85), the operating temperature to be 90 Celsius (0.95), and a reliability factor of 90% (0.89), using formulae developed from [6], a calculated maximum allowable stress of 56 ksi will be used as a design constraint in the stress and deflection analysis.

5.3.3.2 Stress and Deflection Analysis
Similar to the brake rotor analysis, FEA was the main method employed to analyze the mechanical properties of the modeled caliper designs. The optimization of stress and deflection values is a result of implementing stiffening features in successive iterations. The FEA plots and detailed mechanical analyses of both deflection and Von-Mises stress for the caliper assemblies are tabulated in Appendix C. It is from version 6 to 7 where a significant increase in stiffness to weight ratio is observed through removal of excessive bridge material and remodeling of a stiffening rib. This stiffening rib is also a prominent feature on the 2006 Brembo motorcycle calipers allowing the caliper to maintain high stiffness, while reducing the overall bulkiness of the caliper. UT07 bare caliper assembly weighs 0.397 kg, a slight increase from UT05. From Table 7, the final version (10) caliper is expected to be 22% stiffer than UT06’s purchased calipers and 50% stiffer than the custom calipers of UT05. The FEA plots show a maximum Von Mises stress value of 42 ksi and an average value of 25 ksi at a sustained brake line pressure of 600psi, rendering it able to survive the prescribed cycles.

35

5.3.3.3 Manufacturability
As mentioned previously, pursuing outboard mounting locations necessitates possible longer lead times for CNC manufacturing. Minimizing the complexity of the caliper will limit the amount of tool/fixture set-ups needed and will greatly reduce manufacturing times and cost. The modeled calipers contain features that can be easily machined by a 3-axis CNC mill as opposed to a 5-axis mill that would require increased set ups. Modeling adequate internal brake line passages within the caliper would result in the need for a 5-axis mill. External fluid passages offer no performance gain nor do they negatively affect the braking performance of a caliper. The external lines are small diameter round aluminum or stainless steel hard line packaged around the outside of the caliper and can be made inhouse similar to the ones in Figure 20. For simplicity reasons, external fluid passages were chosen as part of the final caliper design. If needed, the caliper halves can be interchanged since they are identical with only minor post machining required to remove the mounting tabs. Each half can act as a spare to a complete assembly if one half should require replacing.

Figure 20 – Illustration of external brake line on caliper

36

CHAPTER 6:

CONCLUSION AND RECOMMENDATIONS

The stress and deflection values from the FEA plots of the 2007 caliper design show an improvement in stiffness to weight ratio over the 2005 design by 43% and a 51% to that of UT06. The increased swept area and narrower scalloping patterns on the brake disc are predicted to provide balanced braking with decreased pad wear. To further facilitate in a balanced braking set up, the diameter of the front and rear brake discs have been sized accordingly to the 2007 dynamic vehicle characteristics. Although there is a 53 % and 43% increase in front and rear rotor weight, respectively, increasing the swept area is estimated to result in consistent bite characteristics that will provide the driver with confidence during the most demanding braking scenarios. The methods used to approach the braking system design in this report have demonstrated a vital connection between the braking system and how each component influences the performance of a FSAE vehicle. Ample design time and unexpected modifications throughout the engineering design phases should be prepared for in advance. Investigation into the possible design and implementation of custom multi-sized piston calipers is encouraged to further enhance the braking performance of the UT FSAE racecars. Carbon composite and ceramic brake discs are also the norm for high end racing rotors offering superior stopping power and weight savings when compared to conventional metallic materials and is encouraged for future UT FSAE designs. Furthermore, custom manufacturing of current heavy outsourced components such as the master cylinders can be an excellent way to further reduce weight and have a component that is fitted accordingly to the vehicles specific requirements.

37

LIST OF REFERENCES
[1] [2] Fred Puhn, Brake Handbook, HPBooks, Los Angeles, CA, USA, 1985. Carrol Smith, Tune to Win: The art and science of racecar development and tuning, Aero Publishers, Inc., Fallbrook, CA, USA, 1978. Carrol Smith, Engineer to Win: Racing Car Materials Technology, MBI Publishing Co, Osceola, WI, USA, 1984. Carrol Smith, Drive to Win: The Essential Guide to Race Driving, Carrol Smith Consulting, Inc., Palos Verdes Estates, CA, USA, 1996. Jerry Zielinski, Design of the 2005 University of Toronto Formula SAE Brake Caliper, Undergraduate Thesis, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada, 2005. Robert L. Norton, Machine Design: An Integrated Approach, Third Edition, Prentice Hall, New Jersey, USA, 2006. Hoi Sum Iu, Design for the Brake System of the Formula SAE Vehicle 2001, Undergraduate Thesis, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada, 2001.

[3]

[4]

[5]

[6]

[7]

LIST OF SUPPLEMENTARY SOURCES

US Department of Defense, Military Handbook: Metallic Materials and Elements for Aerospace Vehicle Structures, Knovel Interactive Edition, 2003, available at HTTP: http://www.knovel.com.myaccess.library.utoronto.ca/knovel2/Toc.jsp?BookID=754 Wilwood Engineering, High Performance Braking Products, online catalog, Wilwood Engineering, Inc., Camarillo, CA, USA, available at HTTP: http://www.wilwood.com/Products/index.asp BrakeTech USA, Advanced Braking Systems, FAQ, BrakeTech USA. Inc, Lake Elsinore, CA, USA, available at HTTP: http://www.braketech.com/faq.html E. Oberg, F. Jones, et all., Machinery's Handbook: 27th Edition, Industrial Press, 2004. Society of Automotive Engineers, 2007 Formula SAE Rules, 2006, [online document], available at HTTP: http://students.sae.org/competitions/formulaseries/rules/rules.pdf

38

TABLES

2006 Vehicle Parameters

value

units 2007 Vehicle Parameters

value 80 11.5 47 46 65 595 56 1.6

units km/h in in in in lbs % g

Initial Vehicle Speed 60 km/h Initial Vehicle Speed C of G Height 12 in C of G Height Track Front 47 in Track Front Track Rear 46 in Track Rear Wheelbase 69.5 in Wheelbase Vehicle Weight (+ 200lb driver) 660 lbs Vehicle Weight (+ 180lb driver) Rear Weight % 55 % Rear Weight % Braking Deceleration 1.6 g Braking Deceleration Table 2 – Comparison of 2006 and 2007 vehicle Parameters

2007 Vehicle Lifespan Requirements
Service Life 5 months 17 test days / month 2 Endurance simulations / test day 40 laps / endurance simulation 15 braking zones / lap TOTAL MILES DRIVEN TOTAL BRAKING CYCLES Table 3 – Life span of 2007 racecar

1200 km 102,000

39

UT07 Braking Requirements
LF: LR: Longitudinal Weight Transfer (lbs) 84.22 RF: -84.22 RR: Corner Weights Under Braking (lbs) 215.12 RF: 82.38 RR: Max Possible Tractive Force (lbs) 335.1 RF: 143.32 RR: Tire Radius While Braking (in) 9.78 RF: 10.07 RR: Required braking Torque (in-lbs) 3277.71 RF: 1442.86 RR: 84.22 -84.22

LF: LR:

215.12 82.38

LF: LR:

335.1 143.32

LF: LR:

9.78 10.07

LF: LR:

3277.71 1442.86

Assumed Tire Coefficient of Friction LF: 1.56 RF: 1.56 LR: 1.74 RR: 1.74 Table 4 – Vehicle braking requirements for 2007

UT FSAE Temperature Data
Year Component 2004 Brake Caliper Brake Disc 2005 Brake Caliper Brake Disc Front Rear Event 66 Cels 58 Cels Endurance Simulation 110 Cels 100 Cels Endurance Simulation 90 Cels 86 Cels Endurance Simulation 135 Cels 115 Cels Endurance Simulation

2006 Brake Caliper 84 Cels 80 Cels Endurance Simulation Brake Disc 151 Cels 126 Cels Endurance Simulation Table 5 – Comparative table listing rotor and caliper temperatures for 2006 and 2007

40

Final Mass Comparisons for 2006 and 2007 rotors
Rotor Front Rear Year 2006 2006 Mass [kg] 0.398 0.357

Front 2007 0.609 Rear 2007 0.513 Table 6 – Mass comparison chart of 2006 and 2007 brake discs

Mass Benchmarking of Previous Calipers
Year 2003 2004 2005 2006 2007 Caliper Type Dual Opposing Piston Single Piston Floating Dual Opposing Piston Dual Opposing Piston Dual Opposing Piston Piston Size Manufacturer 1.5" 1.75" 1.75" 1.25" 1.38" CNC Wilwood FSAE UT05 Brembo FSAE UT07 Bare Assembly Stiffness Stiffness to weight ratio [psi / in] Mass [kg] 0.638 0.553 0.380 0.490 0.397 4.75E4 2.8E4 3.57E4 4.39E4 5.37E4 74451 50633 93947 89592 135264

Table 7 – Caliper benchmarking data

Caliper Design Criteria Design Parameter Value Max Caliper weight 400 g Material 6061-T6 Al or 7075-T6 Al Max Brake line Pressure 600 psi Min Life Span 102,000 cycles Max Deflection 0.012 in Min Stiffness 50,000 psi / in Max Operating Temp 150 Celsius Brake Fluid Passage Type External Table 8 – UT07 Brake caliper design criteria

41

Fatigue Strength of Aluminums (stress ratio = 0) Aluminum Alloy Fatigue life (N cycles) Maximum Stress 6061-T6 50,000 42 ksi 100,000 40 ksi 200,000 38 ksi 7075-T6 50,000 85 ksi 100,000 79 ksi 200,000 73 ksi Table 9 – Tabulated fatigue strength comparison of aluminum alloys

UT07 Vehicle Parameters and Calculated Outputs
Pedal Force From Driver (Fin) Height of (H) height of (h) Force Applied to MC's (Fout) Pedal Ratio % of Braking to Front Circuit Front MC Bore Rear MC Bore Front Caliper Piston Bore Rear Caliper Piston Bore Number of Pistons in Front Caliper Number of Pistons in Rear Caliper Coefficient of Pad Friction 110 lbs 7.5 in 3 in 275.00 lbs 2.5 60 % 0.625 in 0.750 in 1.38 in 1.38 in 2 2 Required braking Torque (in-lbs) 0.55 LF: 3277.71 RF: RR: 3277.71 1442.86 LR: 1442.86 LF: 3804.90 LR: 1556.70 Generated Braking Torque (in-lbs) RF: RR: 3804.90 1556.70 LF: LR: 4.30 3.80 Brake Disc Mean Radius (in) RF: RR: 4.30 3.80 LF: LR: 804.42 372.42 LF: LR: 537.82 248.99 Pressure in Brake Lines (psi) RF: RR: Clamping Force at Caliper (lbs) RF: RR: 804.42 372.42 537.82 248.99

Table 10 – Tabulated spreadsheet of vehicle parameters and output values for braking system

42

APPENDIX A:

MATERIAL GRAPHS AND CHARTS

Material properties of low carbon steel (AISI 1025)

43

Mechanical Properties of 6061 Aluminum

44

Mechanical Properties of 7075 Aluminum

45

Fatigue life of 7075 Aluminum

46

APPENDIX B:

BRAKE ROTOR MODELS

UT07 Front Brake Disc Version 1 - FEA Plot

UT07 front brake disc version 1 Von Mises Stress Distribution

UT07 front brake disc version 1 displacement

47

UT07 Front Brake Disc Version 3 - FEA Plot

UT07 front brake disc version 3 Von Mises Stress Distribution

UT07 front brake disc version 3 displacement

48

APPENDIX C:

BRAKE CALIPER MODELS

UT07 Caliper assembly version 1

UT07 Caliper assembly version 5

49

UT07 Caliper assembly version 6

UT07 Caliper assembly version 7

50

UT07 Caliper assembly version 8

UT07 Caliper assembly version 10 (final)

51

UTO7 Caliper Version 1 - FEA Plot

UT07 caliper version 1 Von Mises Stress Distribution

UT07 caliper version 6 Displacement

52

UTO7 Caliper version 6 FEA Plot

UT07 caliper version 6 Von Mises Stress Distribution

UT07 caliper version 6 displacement

53

UTO7 Caliper version 7 FEA Plot

UT07 caliper version 7 Von Mises Stress Distribution

UT07 caliper version 7 displacement

54

UTO7 Caliper version 8 FEA Plot

UT07 caliper version 8 Von Mises Stress Distribution

UT07 caliper version 8 displacement

55

UTO7 Caliper version 10 FEA Plot

UT07 caliper version 10 Von Mises Stress Distribution

UT07 caliper version 10 displacement

56

APPENDIX D:

BENCHMARKED CALIPERS

UT 2004 Floating caliper assembly

UT05 Fixed Caliper assembly

UT06 Fixed caliper assembly

57