Design and Optimization of Upright

Assemblies for Formula SAE

Racecar

Andrew Jen Wong

992200444

This thesis report is submitted in partial

fulfillment of the requirement for the degree

of

Bachelor of Applied Science

Thesis Supervisor: Prof. M. Bussmann

Department of Mechanical and Industrial

Engineering, University of Toronto

March 2007

I

Abstract:

Formula SAE is an annual international university-level design competition organized

by the Society of Automotive Engineers. The goal for the 140+ teams from around

the world is to design, manufacture, and compete with a small open-wheel, open-

cockpit type racecar. The purpose for this thesis project is to design and manufacture

the Formula SAE Vehicle Front and Rear Upright Assemblies.

The purpose of an upright assembly is to provide a physical mounting and links from

the suspension arms to the hub and wheel assembly, as well as carrying brake

components. It is a load-bearing member of the suspension system and is constantly

moving with the motion of the wheel. For the use on a high performance vehicle, the

design objective for the upright is to provide a stiff, compliance-free design and

installation, as well as achieving lower weight to maximize the performance to weight

ratio of the vehicle. This then is the goal for the optimization process.

The design of the 2007 upright assemblies achieved a total weight reduction of over

2.5 lb, which translates to a 22% reduction overall. This is achieved with no loss in

stiffness according to the Finite Element Analysis in the computer.

II

Acknowledgement:

The author would like to extend his gratitude to the following

individuals/organizations in helping the author to complete this complex project.

• Prof. Marcus Bussmann:

For agreeing to be the thesis supervisor of the author and provide his

assistance and guidance in general to the U of T Formula SAE team.

• Etobicoke Metal Company:

For graciously sponsoring the team with free laser cutting service, which

allows for the upright sheet metal parts to be easily manufactured.

• Vac Aero:

For graciously sponsoring the team with free heat treating service, which

allows welded suspension parts to be stress relieved post welding.

• Vince Libertucci:

For being suspension co-design leader for the FSAE racing team with the

author. Helping the author with other areas of suspension design when the

author was focused on this thesis.

• Stefen Kloppenborg:

FSAE drivetrain design leader. For providing assistance in using the CAD and

FEA software and being a general source for design and manufacturing

information, including providing his design calculations to aid the analysis in

this thesis. As well as helping to weld the upright assemblies

• Jason Kao:

FSAE braking system design leader. For doing most of the welding work on

the uprights as well as physical testing apparatus.

• Maggie Lafreniere:

FSAE Technical Director. For providing assistance in using CAD software, as

well as helping to check the packaging of the upright assemblies.

• For the U of T FSAE team:

For providing general support in the completion of this thesis.

III

Table of Contents: Abstract……………………………………………………………………………...……I

Acknowledgement……………………………………………………………………….II

Table of Contents………………………………………………………………………III

List of Figures……………………………………………………………………………V

Introduction………………………………………………………………………………1

Background………………………………………………………………………………3

Motivation………………………………………………………………………………..3

Section 1) Design……………………………………………………………………..…..5

Section 1.a) Design Objectives…………………………...……………………….5

Section 1.b) Design Considerations……………………………………………….5

Section 1.c) Design Constraints…………………..……………………………….7

Section 1.c.1) Physical Limits…………………………………………….7

Section 1.c.2) Material Choice…………………………………………….8

Section 1.c.3) Manufacturability…………………………………………..8

Section 1.d)Available Design Resources………………………………………….9

Section 1.d.1) Books and Publications……………………………………9

Section 1.d.2) Computer Software……………………………………….10

Section 1.e) Design Process and Methodology…………………………………..11

Section 1.e.1) Suspension Kinematics/Geometries……………………...11

Section 1.e.2) Mechanical Design……………………………………….13

Section 1.e.3) Manufacturing Process Design…………………………...15

Section 2) Finite Element Analysis…………………………………………………….16

Section 2.a) FEA Introduction…………………………………………………...16

Section 2.b) Model Simplification……………………………………………….16

Section 2.b.1) Wheel Bearing……..……………………………………..17

Section 2.b.2) Hub, Wheel, and Tire…………………………………….17

Section 2.b.3) Welded Joint……………………………………………...18

Section 3) Manufacturing………………………………………………………………22

Section 3.a) Upright Components………………………………………………..22

Section 3.a.1) Sheet Metal Face………………………………………….22

Section 3.a.2) Weld-In Clevice Inserts…………………………………..22

Section 3.a.3) Internal Tubular Gussets………………………………….23

Section 3.a.4) Wheel Bearing Housing…………………………………..23

Section 3.a.5) Lower Ball Joint Conical Insert…………………………..23

Section 3.a.6) Sheet Metal Brake Caliper Mount………………………..24

Section 3.a.7) Aluminum Bolt-On Upper Ball Joint Clevice……………24

Section 3.b) Welding Process……………………………………………………24

Section 3.c) Heat Treating Process……………………………………………...25

Section 3.d) Post-Machining……………………………………………………..26

Section 3.e) Installation………………………………………………………….26

IV

Section 4) Physical Testing and Validation…………………………………...………27

Section 4.a) Non-Destructive Testing………………………………………..…..27

Section 4.b) Physical Loading on Simplified Upright Assembly………..……....28

Section 4.b.1) Testing Upright Design…………………………….…….29

Section 4.b.2) Assumptions……………………………………………...29

Section 4.b.3) Physical Test Set Up……………………………………...30

Section 4.b.4) Results……………………………………………………31

Section 4.b.5) Analysis…………………………………………………..31

Section 4.b.6) Recommendation for Improvement………………………32

Section 5) 2007 Uprights………………………………………………………..………34

Section 5.a) Summary of 2007 Design ………………………………….………34

Section 5.b) Front Upright ………………………………………………..……..34

Section 5.c) Rear Upright …………………………………………………….…36

Section 6) Conclusion…………………………………………………………….……..39

References……………………………………………………………………………...VII

Appendix A: 2007 Upright Design…………………………………………….......…..A1

Appendix B: Upright FEA Graphs…………………………………..………….….....B1

Appendix C: Suspension Term Definitions…………………………………….…….C1

Appendix D: Upright Weight Comparison Matrix…………………………….…….D1

Appendix E: Calculations……………………………………………………….……..E1

Appendix F: FEA Setup………………………………………………………….….....F1

Appendix G: Manufacturing…………………………...……………………….…….G1

Appendix H: Physical testing and Validation………………………………….…….H1

Appendix I: Bearing Stiffness Calculations…...……………………………….….…..I1

V

List of Figures: Figure A1 2007 Front Upright Model……………………………...………………A1

Figure A2 2007 Rear Upright Model………………………………………………A1

Figure A3 Upright Welding Jig……………………………………………………A2

Figure A4 Upright on the Welding Jig………………………………….…………A2

Figure A5 Sheet Metal Box Section…………………………………………….…A3

Figure A6 Bolt-On Aluminum Clevice…………………………………….………A3

Figure A7 Welded Joint Design……………………………………………………A4

Figure A8 6813 and 6812 Wheel Bearings………………………………………...A4

Figure A9 Tripod Style CV Joint………………………………………………….A5

Figure A10 DOJ Style CV Joint…………………………………………………...A5

Figure A11 Assembled Front Upright……………………………………………..A6

Figure A12 Assembled Rear Upright………………………………………………A6

Figure B1 Front Cornering Displacement Graph………………………..………….B1

Figure B2 Front Braking Displacement Graph…………………………….……..…B1

Figure B3 Front Braking Stress Graph………………………………………………B2

Figure B4 Front Cornering Stress Graph……………………………………………B2

Figure B5 Rear Cornering Displacement Graph……………………………….……B3

Figure B6 Rear Braking Displacement Graph………………………………………B3

Figure B7 Rear Braking Stress Graph……………………………………………….B4

Figure B8 Rear Cornering Stress Graph…………………………………………….B4

Figure C1 Suspension Geometry……………………………………..……………...C1

Figure C2 Ackerman Steering Principle…..………………………………………...C2

Figure C3 Toe/Alignment…………………………………………………………...C2

Figure C4 Pushrod Suspension System……………………………………………...C3

Figure C5 Pullrod Suspension System……………………………….……………...C4

Figure F1 FEA Wheel Bearing………………………………………………………F1

Figure F2 FEA “Fake” Hub………………………………………………………….F2

Figure F3 FEA Setup and Constraints…………………………………………….…F3

Figure G1 Sheet Metal Face……………….………………………………………...G1

Figure G2 Weld-In Clevice Insert………………………………………………...…G1

Figure G3 Internal Tubular Gussets……….………………………………………...G2

Figure G4 Wheel Bearing Housing………..………………………………………...G2

Figure G5 Lower Ball Joint Conical Inserts………………………………………...G3

Figure G6 Sheet Metal Brake Caliper Mount………..……………………………...G3

Figure G7 Aluminum Bolt-On Upper Ball Joint Clevice…………………………...G4

Figure G8 Upright Being Welded on Jig………………….………………………...G4

Figure G9 In-Progress Front Upright………………………...……………………...G5

Figure G10 Bearing Bore Before and After………………….……………………...G5

Figure H1 Example of Suspected Welding Defect………………………………….H1

Figure H2 Example of Suspected Welding Defect……… …………………………H1

VI

Figure H3 Internal Structure of a Testing Upright………………………………….H2

Figure H4 Simplified Bearing Housing and Welded Joint……………………….…H2

Figure H5 Completed Testing Upright…………………………………………...…H3

Figure H6 Testing Upright and Actual Rear Upright……………………………….H3

Figure H7 Testing Upright and Actual Rear Upright…………………………..…...H4

Figure H8 Simplified Constraints and Loads……………………………………..…H5

Figure H9 Simplified Upright FEA Deflection Result……………………………...H6

Figure H10 Physical Testing Apparatus…………………………………………….H6

Figure H11 Physical Testing with Known Load…………………………………….H7

1

Introduction:

The purpose of the thesis is to design and manufacture the front and rear wheel

upright assemblies for the use of University of Toronto’s 2007 Formula SAE Race

Car. The goal is to produce a lighter design when compare with the highly successful

2006 car and not sacrifice performance in stiffness. Thereby contributing to making

the 2007 car better than its predecessor.

The function of a vehicle upright assembly is to provide a physical connection from

the wheels to the suspension links, and to provide mounting and installation for brake

caliper. In the case of the current design, it also provides a means of adjustment to

the suspension parameters such as camber (App. C2) and steering Ackerman (App.

C3) geometry. For the purpose of the application on a high performance, racing

vehicle, it has to meet the following criteria:

• Lightweight to maintain good performance to weight ratio of the race car

• Optimum stiffness to ensure low system compliance and maintaining

designed geometries.

• Ease of maintenance for enhancing serviceability and setup repeatability.

• And for the purpose of this team, ability to manufactured the components in

house to reduce turnaround time and outside dependability.

With the aid of the Pro/Engineer and Pro/Mechanica as the Computer Aided Design

(CAD) and Finite Element Analysis (FEA) program of choice in this project, the goal

2

is to design the 2007 FSAE Front and Rear Upright based on the similar layout in

2006 car to meet the aforementioned criteria. Quantitatively, the finalized 2007

upright should be lighter and maintain similar level of stiffness as the 2006 design. It

is also the aim of this project to attempt to correlate and validate the FEA results with

some form of physical testing.

3

Background:

The background for this thesis is based on design and manufacturing a high

performance racecar for the annual Formula SAE design competition. The

competition as organized by the Society of Automotive Engineers (SAE) is to allow

university and collegiate competitor to exercise their engineering skills to come up

with a functioning prototype for the hypothetical business proposal of a budget race

car that can be purchased for under $25,000 USD. The project consists of design,

manufacturing, business, and for the bulk of the score available, the dynamic on track

aspect of the vehicle. For the first 3 parts of the competition, the student will have to

justify their design decisions, manufacturability in a mass production environment,

and their project cost analysis to a panel of judges that were chosen from industry

professionals. And for the dynamic events the “prototypes” are put through their

paces on a closed course and their performance measured by a stopwatch. The winner

is determined by the cumulative scoring from all the events.

Motivation:

The motivation for the project comes as a culmination of my involvement with the

Formula SAE team. Being involved in the manufacturing of the 2004 upright

assemblies and observing the issues with 2005 upright design. The goals for 2006’s

upright then was to rectify the issues with the 2005 system in its stiffness,

manufacturing, and maintenance area, and to familiarize myself with the design

process utilizing the CAD/FEA program in Pro/Engineer and Pro/Mechanica. As such

a more conservative approach was taken in many features to increase its reliability

4

and robustness, with some sacrifice in weight. With a year of learning under my belt

it is then important to attempt to reduce some of the weight gained in the 2006 design

while not sacrificing the stiffness/reliability achieved in that design.

5

Section 1: Design

Section 1.a) Design Objectives:

The objectives for the design and optimization of the FSAE Vehicle Upright

Assemblies are listed as followed:

• Less Weight: Compare to 2006 design.

• Maintains Stiffness: Achieve the same level of stiffness when compared to the

2006 design.

• Maintain Serviceability/Reliability: Achieving the same serviceability and

reliability exhibited with the 2006 design.

These goals can be verified through FEA, physical testing, and actual on track

performance of the vehicle. Though for the purpose of the report and due to the

importance of the finished product, no actual destructive testing will be performed on

the finished assemblies.

Section 1.b) Design Consideration:

Being a racecar, the primary goal is to achieve the best performance to weight ratio.

The reduction of weight in any area will allow for better vehicle performance overall.

From basic Newtonian Physics, mass = force x acceleration, by reducing mass with a

given amount of force capable to be exerted from the vehicle, the acceleration can be

maximized. This is true not only for the obvious aspect such as straight-line

acceleration based on engine power, but also cornering grip available to a vehicle. As

there are a finite amount of cornering grip available from any given tire, it is just as

important to reduce the vehicle weight to better exploit the available grip from the tire

6

to achieve maximum amount of cornering acceleration possible. As such, weight is

inevitably a key constraint in designing any component in the racecar.

Weight is also an important consideration for any components in the wheel assembly

of the vehicle. As this part of the vehicle weight is defined as “unsprung weight”

(App C1). The importance of unsprung weight lies in the fact it dictates the response

of the suspension system to any given handling input. The higher the unsprung

weight, and more inertia there is in the given suspension system, and thereby

increasing its difficulty to change direction. In the case of the wheel assembly, the

spring/damper assembly of each corner is controlling the movement, with dynamic

inputs from road surface variation. The goal for the spring and damper is to keep the

tire firmly in contact with the road surface, in order to maximize the tire performance.

If the inertia of the wheel assembly is high, it will take more time for the system to

recover from a disturbance such as a bump on the track, and thereby not allowing

driver to exploit the performance from the vehicle. Therefore for any components in

the wheel assembly, weight carries extra significance.

Aside from unsprung weight and inertia, another important aspect in designing any

suspension components, and truly in any dynamic mechanical system, is its stiffness.

Through the vehicle design process, where a set of goals has been laid out for the

target vehicle to achieve, the only way for the vehicle to stay true to its design intent

is to ensure that all the key variables that the designer wants gets translated and

dynamically maintained in the final product. In the case of the suspension system that

7

means the geometries on paper has to be maintained by the components in the real

world when great loads are applied to them. If there are excessive amount of

deflection then all the key geometries will not be where the designer intended them to

be in a given situation. This is crucially important especially when dealing with

various adjustable parameters available on the racecar. As any adjustment an engineer

makes he expects to see certain effect on the vehicle. If the stiffness is not there then

the desired results cannot be obtained, as the system will not be in the state where the

engineer expects it to be.

With the above points in mind, the design goal for the vehicle suspension upright

assemblies then have to achieve an optimized stiffness to weight ratio. Such that the

unsprung weight in the assemblies will keep its effect to the wheel movement to a

minimum and that adequate stiffness is present in the system so that vehicle behavior

remains predictable and repeatable in the vehicle development process.

Section 1.c) Design Constraints:

As with any design, there are a number of constraints that limits the physical layout,

material choice, and manufacturability of the upright. The constraints are highlighted

in the following sections:

Section 1.c.1) Physical Limits:

As the upright assembly exists entirely enveloped by the wheel, its size obviously

cannot be bigger than that of the space available in the wheel. Also, the primary

8

driving factors of the upright layout are the designed layout and geometries of the

suspension system. The upright has to incorporate all the pivots needed by the

suspension and allows the system to move within its designed range of travel without

obstructions and cause binding. Other physical limitation includes the choice of the

bearing sizes and the amount of suspension adjustments needed to be built-in to the

design. The finalized design needs to be within these limits while maintaining the

functional requirements of the upright.

Section 1.c.2) Material Choice:

In an open cheque book environment, the designer can have the free reign as to

choose whatever material that’s suitable and fits his/her needs. However with the

competition have a clear outline as to the cost of the vehicle, as well as FSAE team’s

budgetary constraint, material choice is not as free. For the purpose of this project and

for this team, the only materials that are realistically being considered are Aluminum

and Alloy Steel. This is due to their mechanical properties, availability and cost.

Section 1.c.3) Manufacturability:

With manufacturing resources being limited in terms of CNC capability outside of

using sponsorship resources, the use of billet aluminum as a material option is

difficult. While it is possible to use non-NC method to produce a billet aluminum

part, complicated geometry that’s often required in a optimized design is nearly

impossible to manufacture without the use of CNC. As such the geometries that can

be utilized is limited, thus reducing aluminum’s effectiveness as an ideal material for

9

the purpose. While utilizing sponsorship resources are not out of the question, the

turnaround time for this complicated part is bound to be excessive, and as such may

limit the overall vehicle progress. It is with these factors in mind that the design has

to be fully manufactured in-house, using methods available to the U of T FSAE team.

This also in terms limits certain material choices as well due to their potentially

difficult manufacturing process.

It is without question that the finalized design has to be within the constraints outlined

above in order to be feasible for the purpose of 2007 FSAE Race Car.

Section 1.d) Available Design Resources:

Since the design process is not done in a vacuum, the need exists to utilized

established information and aids. The following resources were used to aid the design

process and to provide guidance in making certain design decision.

Section 1.d.1) Books & Publications:

• Racecar Engineering and Vehicle Dynamic by Milliken & Milliken:

This is the established textbook in racing vehicle design. It provides the much-

needed science and engineering content into the racing vehicle design. This

book is used in the initial suspension system design stage to help analyze and

determine the overall design direction of the suspension system in terms of

kinematics and dynamic control of the system. The results will the drive the

design of the mechanical subsystem such as the upright assemblies.

10

• Tune to Win by Carroll Smith:

A more hands on, practical approach to the same subject as outlined by the

Milliken text, as well as other sub-systems of the vehicle. As the author is a

long time competitor in various form of racing, many of the points illustrated

are more experience based. Again this is more centered towards the initial

design of the suspension system.

• Engineer to Win by Carroll Smith:

Another book in the “To Win” series of books by the same author. This one

focuses more on the designing of mechanical sub-system of a racing vehicle.

This book also devotes a portion of it to material selection.

• Material Science and Engineering: An Introduction by William D. Callister

Jr.:

Standard in Material Engineering textbook, used here to reference material

properties.

• Machine Design: An Integrated Approach by Robert L. Norton:

Reference material for fatigue and various loading calculations.

Section 1.d.2) Computer Software:

• Susprog 3D:

A suspension kinematics design program used to design the overall vehicle

suspension geometry in terms of pivot location. The program also outputs the

parameter variation throughout the suspension travel in order to allow the

designer to understand the suspension geometry change under dynamic

11

conditions. The upright design parameters are established from the geometries

in this program.

• Pro/Engineer:

3D Solid CAD modeling program, used to model the actual upright

assemblies based on the Susprog 3D parameters. With accurately modeled

assemblies in the program important clearances can also be checked to ensure

the design meets the packaging requirement.

• Pro/Mechanica:

This is the FEA package for the Pro/Engineer. With properly defined loads

and constraints this can simulate the stresses and deformation experienced by

the assembly. Which provides objective basis to analyze the design.

Section 1.e) Design Process and Methodology:

Section 1.e.1) Suspension Kinematics/Geometries:

As the upright being the primary suspension component at the wheel side, its key

geometries are driven by the vehicle suspension parameters. As such, the geometric

layout of the suspension system is the first thing in the design process to be

completed for the design of the upright assembly.

In designing the suspension geometries of a high performance vehicle, the first thing

to be considered is the tire performance. The performance characteristics of the tire

are dictated by tire compound and carcass construction. As such there is a specific

way to utilize each type of tire. The goal for designing the suspension kinematics is to

12

maintain the tires in their preferred position as the vehicle experiences roll, pitch and

yaw movement as it is being driven around the track. Through iterative design

process with the help of Susprog3D, the kinematics of each iteration can be analyzed

in terms of their positioning of the tire throughout the ranges of travel of the wheel,

the amount of vehicle roll and the amount of steering input.

For the 2007 car, the geometries of the suspension system are evolution of the 2006

design. The system is designed with moderate amount of front camber compensation

(App C9) in roll to keep the tire perpendicular to the ground when the vehicle is

rolled and/or steered. Particular attentions have been paid to steering geometry to

reduce KPI (App C5) from the 2006 design as it induces unwanted camber change

when the front wheels are steered. By relocating the lower ball joint further towards

the inboard direction while doing the opposite to the upper ball joint, the KPI has

been reduced from 10 deg on the 2006 car to 6 deg in the 2007 car. Caster (App C6)

values of 6 deg have been retained from the 2006 design. The Ackermann adjustment

method of the 2006 car have also been retained with 3 different steering pickup point

representing 0-100% Ackermann steering, as opposed to –25% - 75% adjustment of

the 2006 car. This change has been driven by 2006 season’s on track testing results,

with observation made that the Hoosier tire performs better with more positive

Ackermann setup.

13

Section 1.e.2) Mechanical Designs:

With the suspension geometries fixed the focus shifts to the mechanical layout and

design of the upright assemblies. The goals are being able to package the necessary

components at their correct location and orientation within the confine of the wheel.

At the same time, the types of construction, material, sizing of bearing and pivots, as

well as adjustment method will have to be decided.

First of the details to be sorted out was the material and construction of the upright.

Taking into consideration with the aforementioned design constraints in terms of

manufacturability, CNC aluminum-based design is not feasible for the purpose or the

capability of the team. Therefore sheet metal welded box section design (Fig A5) of

the 2006 upright was retained. With the manufacturing process being further refined

to improve on manufacturing time. One major change from the 2006 design was the

wheel bearing size (Fig A8). This is driven by the drivetrain design of the new

vehicle. For 2007 season, the drivetrain design moves away from the traditional tri-

pod style CV joint (Fig A9) on the outboard side in favor of the DOJ-type CV (Fig

A10), advantage being the reduction in CV size. Therefore the wheel hub size was

reduced accordingly and thus facilitates the reduction in wheel bearing size. This

allows the 2007 upright to be smaller in width, and contributes to the goal of weight

reduction.

To allow for suspension adjustability, the use of detachable aluminum clevice was

retained from the 2006 design (Fig A6). This design offers several advantages over a

14

fixed pickup point design on the upright. First being decoupling the adjustment for

toe and camber. With the fixed pickup point, adjustment of one will have an effect on

the other. Thus increases setup time and introduce inconsistency in setup adjustment.

Secondly, the design allows for more design flexibility in suspension kinematics, as

throughout testing season the team may choose to adopt different tire construction

that requires different steering characteristic in terms of Ackermann response, and

this type of design can accommodate for on-demand design revision.

For the design of the different pivot joints, the use of spherical bearings is the

preferred option. The spherical bearing offers tolerance for angular misalignment,

which is required for the suspension system throughout the suspension travel range,

as well as allowing rotation in its axial direction. This is especially critical for the

front uprights as it will be steered and bumped at the same time. Sizing of the

bearings is primarily based on the manufacturer’s documentations against the known

loading condition. With 2006 and 2007’s suspension design, which moves from

2005’s pullrod actuated suspension system (App. C8) to pushrod-based design (App.

C7), the bottom ball joint becomes the primary source of loading in the upright. This

allows for a reduction in spherical bearing size for the upper ball joint. The 2007

upright uses a ¼” ID upper ball joint and a 5/16” ID lower ball joint. The upper ball

joints are loaded in double shear to ensure the reliability of the aluminum clevice,

while the bottom ball joints are loaded in single shear to provide for extra clearance

for the steering requirement.

15

Section 1.e.3) Manufacturing Process Design:

For the manufacturing requirements of the upright, the primary consideration being

geometric accuracy of the manufacturing process. Being a fabricated design without

the use of CNC machinery, a reliable welding fixture needs to be made to ensure the

crucial geometric dimensions of the final product are maintained during the welding

process. The fixture itself also needs to be of substantial structural stiffness to ensure

zero distortion when the parts are bolt onto the fixture and undergoes post welding

stress relief heat treatment. For this reason all of the fixture parts are made with solid

steel components with dimension designed alongside the actual upright in the CAD

model. The fixture is manufactured using manual machining method on a 3-axis

milling machine to ensure geometric accuracy of the fixture components, and they are

assembled using dowel pins to facilitate accurate assembly of the fixture components

(Fig A3, A4).

The manufacturing process requirement of the upright also impacts the design of the

upright itself. Critical geometry such as the bore for the wheel bearings are post-

machined after the heat treatment process as to ensure the thermal distortion of the

heat-treating process will not effect such critical dimension(Fig G10).

16

Section 2: Finite Element Analysis:

Section 2.a) FEA Introduction:

Finite Element Analysis or FEA is the method used to optimize the design of the

2007 upright. The FEA package of choice for this project is Pro/Mechanica, the FEA

suite for the CAD software Pro/Engineer. This arrangement allows for easy

integration between the CAD model to the FEA software and quick changes and

analysis can be performed in the design process to optimize the design.

The accuracy of the FEA results is largely dependent on the constraints and setup for

the analysis. Since real world loading conditions and constraint can be incredibly

complex, simplified representative conditions are often used to model the real world

constrain. “Fake” parts are usually including in the FEA model to replace those parts

in which may exist on the real assembly but their performance are not important to

the model of interest. The results of the FEA then require the designer to interpret

with that knowledge in mind.

In Pro/Mechanica, the sheet metal faces on the upright are analyzed using “shell

element”, which is used specifically to model parts with thin cross sections. While

certain internal features and bearing bosses are modeled as solid elements.

Section 2.b) Model Simplifications:

Being the primary physical link between the tires and the suspension system, the real

world loading condition of an upright consists of the following: Forces are applied

17

from the tire and transmitted through the wheel to the hub and applied on the upright

through the wheel bearing mounts. While upright is being constrained at the upper

and lower ball joint by the suspension links that connects to it. With multitude of

connection joints and complex part geometry, it would not be feasible to analyze the

accurate reproduction of this setup. Thus a simplified model will have to be used

instead. The following simplifications are used to in the FEA model to represent this

type of loading condition.

Section 2.b.1) Wheel Bearings:

The actual upright uses deep groove ball bearing made by NTN bearing. The complex

interaction between the ball bearings and its multitude of contact region is not what

the focus of the upright design. Therefore a simplified “FEA Bearing” is used in the

model. The representative bearing is made of a solid part of the exact dimension of

the actual bearing. To compensate for the reduction of structural stiffness compared

to a solid part as seen in the real bearing, the FEA bearing is modeled with a reduced

Young’s Modulus as opposed to that of the solid steel components (App. I, Fig F1).

Section 2.b.2) Hub, Wheel, and Tire:

In the real world the cornering loads are transmitted by the combination of the 3 parts

to the upright assembly. What upright itself sees is a force and a moment load.

Therefore the complex relations between the 3 parts are not important for the result of

the thesis. To replicate the loading condition, a simplified FEA part is made to

represent the 3. The part consists of a fake hub portion that is connected to the upright

18

via the FEA bearings, and a long moment arm that extends to the tire contact patch

center location of the actual tire, at which point the loads are applied to the model

(Fig F2). This part is modeled as solid steel part to minimize its own deflections and

transmits all the loads to the upright assembly.

Section 2.b.3) Welded Joints:

Although the fabricated parts are consists of primarily welded joints, in the FEA the

relationship can be hard to replicate. The assumption made is that since the upright

will be stress relieved in post-welded state, the joint condition will be homogenous to

that of a regular material. Also, in using the Pro/Mechanica, the program has some

difficulty in dealing with joints that connects solid elements to shell elements, and

with most welded joints being welded along multiple seams such a connection will be

difficult to model. Therefore the joints in the model are kept as homogenous

connection, and the results in those areas are not used in the analysis.

Section 2.c) Model Loading and Constraints:

With the simplifications applied to the upright model, the loading and constraints can

be applied. The loading will be based on the loads experienced in the car during

cornering and hitting a bump on the track, while the constraints will be based on the

ball joint location and the links that connects to the joint.

Section 2.c.1) Model Loading:

19

The loads applied to model are based on the data collected in the previous years from

the vehicle data acquisition system. The system records the maximum cornering force

and this information is used in conjunction with the vehicle layout and weight

distribution to determine the forces on the front and rear tires. For the cornering

scenario, a lateral force (model y-axis) of 400lbf is applied to the front upright at the

contact patch center, along with a 800lbf of combined bump and lateral weight

transfer caused by the lateral acceleration of the vehicle, applied to the vertical

direction at the contact patch center (model z-axis). For the rear upright, the load is

scaled back to account for the smaller loads experienced by the rear tire.

Section 2.c.2) Model Constraints:

The upright model is constrained at the upper and lower ball joint plus the

steering/rear toe pickup points. Since all the joints are made with spherical bearing,

they do not offer any resistance to moment; their rotational constraints are all left to

be free. For the lower ball joint on the racecar, it is connected to the lower a-arm and

also the pushrod. Under load, the a-arm will resist the movement in lateral and

longitudinal direction, while the pushrod will resist the load in the vertical direction.

Therefore the lower ball joints are constrained in the model in the displacement in x ,

y, and z axis. For upper ball joint, since there are no pushrod connection, it resists

movement only in longitudinal and lateral direction, therefore it is assigned with

constraints in x and y axis. For the steering/toe-link pickup, the only link that

connects to this joint is either the steering link or toe-link. They only resist movement

in the lateral direction, so only y-axis is constrained in the model (Fig F3).

20

Section 2.d) Model Stresses:

The FEA package allows for the computation of stresses in different ways, the

stresses can be represented in principle stress, component stress, or Von Mises stress.

Since it is important to know the yield and material limit, as well as the computation

of safety factor, Von Mises stress is used in presenting the stress results. The FEA

results are compared against the fatigue strength of the material corrected for a known

service life. The correction factors followed that of a standard fatigue calculation and

takes into account of load factor, size factor, surface quality, operating temperature,

and reliability. For full calculations please refer to Appendix E.

Section 2.e) Optimization Parameters:

The deflection of the upright assembly will be the basis for the optimization process.

With stiffness being the performance standard and weight being the concern, the

design goals are defined to be reduction in weight over the 2006 design with

comparable stiffness. To optimize for weight, sheet metal thickness for different faces

of the upright are changed iteratively based on the previous run’s stress distribution

and deflection value, the material thickness were reduced in the areas where stresses

are low. The limiting factor being stresses cannot exceed the material limit. With

available thickness value based on available stock material, a number of combinations

were analyzed and the optimum front and rear upright designs were selected as the

final designs.

21

Section 2.f) Results:

The finalized designs and their associated FEA results can be seen in the Appendix A

and B. Knowing the aforementioned issue with FEA results interpretation in the

boundary region of the mating edges between solid and shell element, the focus then

is on the region that’s around the boundary. As such, the stresses in those region

combined with calculated endurance limit resulted in the fatigue safety factor of 1.07

for the front (Fig B4), and 1.28 for the rear (Fig B8). The value may sound to be too

risky, but knowing the conservative estimate for the fatigue cycle, as well as the

actual joint design being more robust with multiple weldments, these values should

be more than adequate.

Based on the FEA model, maximum deflection of the upright assembly based on the

given loading condition for cornering and bump is 0.0021” (Fig B1), which is better

than 0.005” of 2006 design. The gain can be contributed to the closer proximity of the

bearing support housing to the outer perimeter of the upright body, since this where

the maximum deflection occurs (Fig B1).

The resulted design also weighs less in the model from than the 2006 design, due to

the material reduction in the less critical area along the upper ball joint. The front

upright is 2.03lb in the model compared to 2006 model’s 2.39lb. While the rear is

also 2.03 lb compare to 2006’s 2.67lb (App D).

22

Section 3: Manufacturing

The manufacturing of the 2007 upright design is done in several stages. It starts with

the manufacturing of different components that goes into the construction of each

upright. Then the components are placed on the welding fixture to be welded. The

finished uprights are then subjected to stress relieving process to alleviate induced

thermal stresses in the welding process. The post-treatment uprights are then post-

machined to achieve the required dimension for the wheel-bearing bore.

Section 3.a) Upright Components:

Section 3.a.1) Sheet Metal Face (Fig G1)s:

The sheet metal faces are the unique feature for a welded sheet metal upright. Cold

rolled, 4130 Chrome Moly alloy steel sheets are used in thickness ranging from

0.035”to 0.090”. Due to the availability of a laser-cutting sponsor in Etobicoke Metal

Company (EtMeco), the upright’s overall shape and geometry can be made more

complicated than if it were to be made entirely through conventional means. The laser

cut sheets are then bent on a manual break based on the designed specification

generated from the CAD model.

Section 3.a.2) Weld-in Clevice Inserts (Fig G2):

These inserts are the pickup points for the upper ball joint clevice. The inserts provide

the required bearing area for the fasteners used to bolt on to the aluminum clevice to

the steel upright body. The inserts are machined on a manual lathe. The flanges on the

23

inserts are to provide adequate welding joint for the weldment on to the sheet metal

faces as well as the internal gusseting tubes.

Section 3.a.3) Internal Tubular Gussets (Fig G3):

These gussets are welded between the back face of the upright and the weld-in clevice

inserts. Made with stock size, 4130 Chrome Moly alloy steel tube, 5/8”OD, 0.050”

wall tube are used for the front, and ¾”OD, 0.050” wall tube are used for the rear.

These tubes are simply cut to length then they are ready to be welded.

Section 3.a.4) Wheel Bearing Housing (Fig G4):

Along with the sheet metal faces, the wheel bearing housing forms the most

structurally critical portion of the upright assembly. Machined from a thick-wall,

4130 steel tube of 3.25” OD, the housing features weldment flanges near the faces of

the upright to facilitate welding joints (Fig A7). The housing is machined to

incomplete state in pre-welding stage, with the bearing groove not finished to the

final dimension. The reason being that this portion will be bored out after welding

and heat-treating process(Fig G10).

Section 3.a.5) Lower Ball Joint Conical Insert (Fig G5):

Machined from solid round ¾” stock of 4130 steel, the conical inserts are designed to

allow for full range of misalignment of the lower ball joint spherical bearing. The

bore on the insert are tapped half way and the rest are reamed to 5/16” to provide a

24

threaded joint and support for the 5/16” stud that’s used in the installation of the

spherical bearing.

Section 3.a.6) Sheet Metal Brake Caliper Mount (Fig G6)s:

Like the faces on the upright, the caliper mounts are also made from 4130 sheet

metal, laser cut to exacting specification. The caliper mount provides a double

sheared mounting for the custom brake caliper design of the 2007 FSAE car. The

mount is reinforced with additional sheet metal gusset to provide stiffness for

supporting the caliper under loads.

Section 3.a.7) Aluminum Bolt-On Upper Ball Joints Clevices (Fig G7):

The bolt-on clevices are made from 6061-T6 aluminum billet, machined on a manual

3-axis milling machine. The thickness of the sections are reduced from 2006’s design,

but a minimum thickness of 0.200” are specified to ensure manufacturability as to not

crush the part during setup on the mill. The holes on the clevices are upsized to allow

the use of steel bushings. The bushing maintains the bearing location as well as

increasing the bearing area to prevent ovalizing aluminum part.

Section 3.b) Welding Processes:

The welding process is the primary fabrication process of the sheet metal upright (Fig

G8) . The fixture are designed to locate the inserts and bearing housing of the upright

to maintain the fixed relation between the critical dimension, then the sheet metal

faces and gussets are welded on to their respective location (Fig A3, A4, G9). Most

25

critical welded joints are by designed to be welded on both side of the sheet metal

face (internal and external weld), these would require the semi-welded parts to be

taken off the fixture then reinstalled after adding on the necessary weld. This step also

adds on an additional check to ensure the part would still be within the geometric

tolerance of the design as it needs to be re-installed onto the fixture. The welding

process of choice is TIG welding with 4130 filler to ensure uniform material in the

upright assembly to allow for heat-treating of the welded joints. Each upright takes

about 5 hours to be welded fully. The welding process adds about 0.3lb of weld to the

each upright.

Section 3.c) Heat Treating Process:

The finished upright assemblies are heat-treated offsite at Vac Aero, a local heat-

treating service provider for many aircraft manufacturer. The heat treatment specified

for the parts are stress reliving. The process involves heating the entire assembly and

the fixture to below the steel austenizing temperature then slowly cooled in the oven

over a long period of time. This process removes majority of the residual stresses

induced by welding. This process also does not have the adverse effect of the higher

temperature heat-treating process that adds material hardness but at the same time

makes them more brittle. This is especially a concern with thin-walled material as

used here. Small holes are drilled in the non-critical area of upright to allow for

venting of heated gas in the otherwise enclosed upright cavity, this prevents distortion

caused by gas expansion.

26

Section 3.d)Post-Machining:

As previously mentioned, the upright requires being post-machined to obtain accurate

bearing bore to provide the correct transitional fit for the wheel bearings. The upright

assemblies are setup on a CNC milling machine and the center of the existing bore

are located, then the correct bearing bore at the right depth are machined onto the

upright (Fig G10).

Section 3.e) Installation:

Suspension links are connected to the upright via fastened joints. Each joint are

torqued to specified spec recommended by fastener manufacturer. Lower ball joint as

mentioned before uses a 5/16” stud. The stud is secured in the lower insert via the use

of thread locking compound coupled with positively securing lock wires to prevent

any possibility of backing off (Fig A11, A12).

27

Section 4: Physical Testing and Validation

With majority of the design work being done on computer, it is necessary to ensure

that the design method is representative of real world conditions, as well as ensuring

the completed part are to the designed standard. To this extend, two types of physical

testing methods are used to validate the design and manufacturing processes. First is

the non-destructive dye penetration testing for welding quality, and the second is a

simplified upright loading test to validate FEA results.

Section 4.a) Non-Destructive Testing:

Dye-penetration testing is a common non-destructive method to validate the quality

of weld. As welding quality is extremely important in structural application, it is

desirable and necessary to have welds with limited porosity and good continuity to

ensure the integrity of the welded joints. Dye-penetration test provides a simple visual

method to allow for quick post welding inspection for quality of weld. The following

are the steps taken in dye-penetration testing:

1. Spray on colored dye evenly around the welded parts; focus on welded seams

and joints. The dye will seep into any surface defects along the weld .

2. Clean the welded part completely; ensure that no more dye can be seen by

eye. This will ensure the only places that the dye will remain are around the

surface defects.

3. Spray on the dye indicator around the welded parts. This indicator will form a

powdery layer on the surface of the parts, and any dye still remained after the

28

cleaning operation will reveal itself as spots or lines around the defect (Fig

H1, H2).

4. Inspect and identify the problem region, with reference to the testing manual.

The manual will classify the type of defect, if indeed it is a defect, at the

indicated region

With the limited time allocated for the construction of the FSAE vehicle as well as

the limited resources available for manufacturing any component on the car, any

destructive testing for the fabricated components will not only be undesirable, but not

feasible as well. Dye-penetration testing provides a simple and effective method for

validating quality of the single most important manufacturing process for the upright

assembly.

Section 4.b) Physical Loading Test on Simplified Upright Assembly:

As mentioned, with destructive testing being not feasible for the completed uprights,

another method for validating and testing the design method used in this project is

desired. With manufacturing a new, up to spec upright being time consuming and

difficult, the attention then turned to designing a simplified version of the upright

using the same design method, then replicate a simplified loading condition

performed in FEA and in real life to validate the FEA results. The testing upright will

be made from very similar overall construction (Fig G9, H3), but with vastly

simplified exterior geometry to compensate for the lack of laser cutting (Fig H5, H6).

While material choice will be limited to what is readily available to the existing

29

FSAE team stockpile. And with the time constraint in finishing the actual FSAE as

well as this thesis, the testing upright will not be go through the same heat treating

process as the actual part.

Section 4.b.1) Testing Upright Design:

The testing upright is constructed of similar design and layout of the actual upright.

The sheet metal welded box design is replicated in the design. The material used for

the sheet metal is the same as the actual uprights. 4130 steel sheets of varying

sectional thickness in the similar distribution as the actual upright (Fig G9, H3). The

machined wheel bearing housing with welding flanges are simplified and replaced

with a straight tube to facilitate quick fabrication (Fig H4).

Section 4.b.2) Assumptions:

• The lack of complex welded joint design will not affect the result between

FEA model and physical testing model (Fig A7, H4).

• The lack of heat-treating process will not introduce large discrepancies

between the FEA model and the physical testing model.

• The deflection of the testing upright will be linearly proportional to the load

applied.

30

Section 4.b.3) Physical Test Setup:

To validate the design method and processes, a simple test is performed under FEA

environment and then replicated in real world. The results are then compared to

validate the design.

• FEA Set Up:

The testing upright is constrained at the “bearing housing” for vertical and

longitudinal displacement, while the bolted joint on the upper part of the

testing upright is constrained in vertical, longitudinal, and lateral direction. A

simple force of 200 lbf is applied at the lower ball joint of the testing upright

in the longitudinal direction, with deflection measurement taken from at the

lower ball joint (Fig H8).

• Physical Testing Set Up:

A testing fixture is constructed in similar manner as the welding fixture for the

actual upright. The fixture provide a rigid bolted joint at the for the upper joint

of the testing upright, while the bearing housing is supported with a solid

round shaft with adequate fitting tolerance. A link is bolted to the lower ball

joint with a spherical bearing, and connected to a load arm. The load arm is

made have a built-in mechanical advantage such that a smaller load may be

scaled up to represent the required load for the testing. The load arm is

supported by ball bearing to minimize any mechanical friction that may

impede the load transferred to the test part. A dial indicator is set up at the

lower ball joint to measure deflection reading (Fig H10).

31

Section 4.b.4) Results:

• FEA:

The FEA testing yields a maximum deflection of 0.004” at 200lb of load (Fig

H9).

• Physical Testing:

The testing apparatus yields a deflection of 0.018” at 200lb of load (Fig H11).

Section 4.b.5) Analysis:

The tremendous discrepancy between the modeled result and physical testing is

somewhat unexpected, but perhaps not without basis. The following points outlines

the possible areas of contribution to this discrepancy:

• Welded joint design:

Knowing the difficulty for the FEA package for the analysis of joints, the

results around these areas are usually not analyzed too closely. While the

model usually represent a less robust joint design when compare to the actual

upright and how the joints are made, the simplified design maybe much

weaker than the modeled layout (Fig A7, H4).

• Heat Treating:

The lack of heat treatment, coupled with aforementioned simplified welded

joint, may further compromised the welded joint integrity and contributes to

the additional deflection of the physical testing upright.

• Ideal Installation Constrains vs. Real World Constrains:

32

In FEA model, constrains used in the model are idealized. Meaning they have

no deflection of their own and that all the deflection will be from the tested

part. On the real world apparatus though, each bolted joint will displace a

finite amount under load, and from the way the measurement is taken, all the

joint deflection could cumulatively affect the result.

Section 4.b.6) Recommendations for Improvement:

For future references, it is recommended that the following measures be taken to

possibly further validate this design processes:

• FEA modeling of the welded joint:

Due to the scope of this thesis, this particular area was largely assumed to be

adequate for the purpose of the analysis. But the complex relation of a welded

joint can obviously contribute greatly to the integrity of the parts that’s being

designed. Therefore it is desirable to establish a more accurate method to

validate the integrity and property of a welded joint. Possibly taking into

account of both heat-treated and non-heat treated joint.

• More robust testing fixture:

To minimize outside influence of the measurement, a more rigid and robust

fixture design is definitely recommended for further testing. This will bring

the test condition to be closer inline with the ideal setup under the FEA

environment.

• Investigate other FEA software package:

33

Due to Pro/Mechanica’s difficulty in modeling an accurate solid/shell element

joint, it maybe beneficial to investigate different FEA software to compare the

testing results.

34

Section 5: 2007 Uprights

Section 5.a) Summary of 2007 Designs:

The finalized designs for the 2007 FSAE uprights features evolutionary changes to

the successful 2006 design. Key features such as the sheet metal welded box structure

are retained, as well as the use of a removable aluminum upper ball joint clevice. The

goals set for the 2007 design was to reduce the weight of the 2006 design while

maintaining the stiffness achieved with that design. The following will break down

the changes between the 2006 and 2007 design and outline the gains made by the

2007 Uprights.

Section 5.b) Front Upright:

2007 front upright incorporates several key changes over the 2006 design due to the

necessity for the overall suspension system changes:

• Reduction in KPI through revised geometry:

KPI was changed from 10 degrees to 6 degrees by physically relocating the

lower ball joint further inboard of the vehicle on the upright by 1”, and

relocating the upper ball joint further outboard by 0.6”. This change was

driven by the need of suspension geometry to improve steering response (App

C3)

• Wheel bearing size change:

To allow for more efficient packaging of the 2007 hubs which features a

smaller DOJ-type CV design. The bearing was changed from NTN 6813 to

35

6812. This accounts for a reduction in size for wheel bearing housing and

affects the physical dimension of the upright (App A8).

• Aluminum upper clevice material reduction:

Due to the minimum amount of loading through the clevice based on the

pushrod suspension geometry, the flange thickness of the aluminum clevice

was reduced by 0.050” all around. As mentioned before, further reduction is

possible if it weren’t for manufacturing issue.

• Aluminum Clevice bolted-joint fastener size reduction:

The clevice bolts were changed from 5/16” size fasteners to ¼”. This is

possible due to the amount of camber we run on the front wheels. This puts

less bending load on the smaller fastener. This is not possible on the rear

upright due to the less amount of camber needed for the real wheels. This

change also affects the size of inserts as well as the size of the gusset tubes.

• Optimization of upright sheet metal thickness:

The sheet metal used around the upper clevice area has been reduced in

thickness, as the loads around this area are at a minimum according to the

FEA result. What used to be welded joint between 2 different thickness sheets

has been replaced with a single sheet. This also cuts down on the amount of

welds needed for the upright (Fig B4).

The final front upright weighs 2.873lb fully assembled. This value includes 2 wheel

bearings and the associated preload spacer, fasteners for the upper clevice, and the

36

lower ball joint stud. This compares favorably with the 2006 design, which at the

same level of assembly weighs 3.363lb.

Section 5.c) Rear Upright:

2007 rear upright features largely similar suspension geometry. As the 2006 layout

was satisfactory and most changes in suspension kinematics focuses on the front

suspension, and in particular steering. Therefore, most of the changes on the rear

upright are primarily driven by optimization of the structure and weight.

• Wheel bearing size change:

Like the front, the rear features the same type of hubs and therefore uses the

same wheel bearing.

• Symmetrical layout:

Aside from the brake caliper mount, the rear upright features symmetrical

layout between the left and right upright. The reason being to allow for the

efficient use of spare part.

• Aluminum upper clevice material reduction:

Similar to the front, the material thickness used on the aluminum clevice has

been reduced by 0.050”.

• Optimization of upright sheet metal thickness:

The sheet metal used around the upper clevice area has been reduced in

thickness, as the loads around this area are at a minimum according to the

FEA result. This is the same change done to the front upright. Also the face

for mounting the brake caliper mount has also been reduced in size in 2007, as

37

the loading from the caliper on the rear upright will not be as high as that of

the front (Fig B8).

Final rear upright weighs 2.889 lb fully assembled. Like the front, this value includes

2 wheel bearings, preload spacer, associated fasteners for the clevice, and the lower

ball joint stud. The 2006 rear upright weighs 3.659lb at the same state of assembly.

Overall the uprights contribute to over 2.52lb of weight reduction on the 2007

vehicle. And as mentioned in the design consideration, this is all unsprung weight,

which is important for the response of the suspension system as a whole.

For stiffness, as the FEA results have shown (Fig B1, B5) , there is no loss of upright

stiffness between the 2006 and 2007 design, as the deflection values are comparable.

However as physical testing has shown, discrepancies do exist between the FEA

model and actual manufactured parts. Therefore this result is not certain. On the other

hand, based on the consistency between the 2006 and 2007 uprights in design and

manufacturing phase, although the ultimate values may not be what FEA results have

illustrated, the relative performance should be representative of the final parts. It is

my belief then that the 2007 design should be on par with the 2006 upright in

stiffness, and that the weight reduction contributes to the all-important performance to

weight ratio.

38

For 2007 season the team plans to conduct a full vehicle compliance test between the

2006 and 2007 vehicle, the result from this test should ultimately validate the design

gain of the 2007 design.

39

Section 6) Conclusion:

The purpose of this thesis project is not only to design and manufacture the upright

assemblies for the 2007 University of Toronto Formula SAE car, but also to provide a

in depth study in the process taken to arrive at the final design. While in FEA model

form the design seems to be a step forward from the highly successful, championship

winning design of 2006, the discrepancies in physical testing illustrate the limitations

of relying solely on a computer design tool. However, with the overall design being

carefully considered beforehand, the manufacturing process being controlled closely,

and that many design features have been proven effective by the 2006 design, the

2007 uprights should be well within the performance requirement of the vehicle. In

terms of quantifiable improvements, the 2007 design illustrates a significant weight

reduction over the 2006 design, with the 4 uprights contributes to over 2.5 lb of

weight loss on the 2007 vehicle, with the same level of deflection compare to the

2006 design in the FEA. Although actual gains cannot be seen until the vehicle hits

the track, I am confident that the design should prove to be superior to that of the

2006 design.

It is still recommended for future reference that the suggestions outlined in the

physical testing section of this report be implemented for future design. As the current

design relies heavily on welding, its integrity needs to be analyzed more closely to

increase the confidence level in the design of a welded component.

VII

References:

• Milliken, William F. & Doug L. 1995, Race Car Vehicle Dynamics.

Warrendale, PA: SAE International

• Smith, Carroll. 1978, Tune to Win, Fallbrook, CA: Aero Publishing Inc.

• Smith, Carroll. 1984, Engineer to Win, Fallbrook CA: Aero Publishing Inc.

• Callister, William D. Jr 2002, Material Science and Engineering: An

Introduction 6th Edition: Wiley.

• Norton, Robert L. 2006, Machine Design: An Integrated Approach 3rd

Edition, Upper Saddle River NJ: Prentice Hall.

• FSAE Rules Committee 2007, 2007 Formula SAE Rule Book, SAE

International.

• NTN Corporation 2002, Ball and Roller Bearing Catalogue, Japan: NTN

Corporation.

• Aurora Bearing Company 2000, Rod End and Bearing Catalogue, Aurora Il:

Aurora Bearing Company.

1

Appendix A: 2007 Upright Design

Figure A1: 2007 Front Upright Model

Figure A2: 2007 Rear Upright Model

2

Figure A3: Upright Weldment Jig

Figure A4: Upright on the Weldment Jig

3

Figure A5: Sheet Metal Box Section

Figure A6: Bolt-On Aluminum Clevice

4

Figure A7: Welded Joint Design

Figure A8: 6813 (Left) and 6812 (Right) Wheel Bearings

5

Figure A10: DOJ Style CV Joint

Figure A9: Tripod Style CV Joint.

6

Figure A11: Assembled Front Upright

Figure A12: Assembled Rear Upright

1

Appendix B: Upright FEA Graphs

Figure B1: Front Cornering Displacement Graph

Figure B2: Front Braking Displacement Graph

2

Figure B3: Front Braking Stress Graph

Figure B4: Front Cornering Stress Graph

3

Figure B5: Rear Cornering Displacement Graph

Figure B6: Rear Braking Displacement Graph

4

Figure B7: Rear Braking Stress Graph

Figure B8: Rear Cornering Stress Graph

1

Figure C1: Suspension Geometry

Appendix C: Suspension Term Definitions:

1. Unsprung Weight:

Unsprung weight is the weight of moving suspension components. The terms

comes from the fact that the weight on board the car are supported by the

spring of the vehicle, but any components that is part of the moving

suspension assemblies are not supported by the spring, hence the term

unsprung

.

2. Camber:

Camber (Fig C1) is the

measure of how much

the top of the wheel

tilts inward when

viewed from the front

of the vehicle. Most

tires generate more

cornering force when

the angle is

negative(the wheel tilts

inboard). This is caused

by the thrust force

generated by the

carcass deformation when tilted. On the upright this is adjusted by adding

shims between the bolt on clevice(Fig A6) and the body of the upright itself.

3. Ackerman Steering:

Ackerman Steering (Fig C2) is used when the steering linkage is setup in such

a way that it causes the wheel on the inside of the corner turns more than the

wheel on the outside of the corner. This is based on the fact that the inside and

outside wheel tracks curves of different radii. This is especially pronounced

2

Figure C3: Toe/Alignment

Figure C2: Ackerman Steering Principle

when the corner in question is tight, and that the distance between the inside

and outside tires(also known

as the Track) takes up a

significant percentage of the

radius of the curve. This is

adjusted on the upright by

different set of pickup point

available on the clevice(Fig

A1). The amount of

Ackermann steering

available is defined by the

imaginary line intersect

formed between the steering

pivot and steering axis of

both side of the car when viewed from the top. The distance of the intersect

when measured from the front axle and its percentage of the wheelbase of the

vehicle.

4. Toe/Alignment:

Toe (Fig C3) setting is the

alignment of wheels on the

vehicle. It is the measurement

where the wheel is pointing

relative to the straightaway

position when viewed from

above the vehicle. On the front

this is set by adjusting the

length of the steering linkage.

And on the rear this is set by adjusting the length of the toe link.

3

Figure C4: Pushrod Suspension System

5. Kingpin Inclination(KPI):

KPI (Fig C1) is the angle formed between line connecting upper and lower

suspension pivots, in other words, the steering axis of the wheel in relation to

the horizontal ground plane, when viewed from the front of the vehicle. KPI

adds positive camber to the outside wheel when the wheels are steered if the

angle is positive towards the inboard side of the vehicle.

6. Caster:

Caster (Fig C1) is the angle formed between line connecting upper and lower

suspension pivot, in other words, the steering axis of the wheel in relation to

the horizontal ground plane, when viewed from the side of the vehicle. Caster

adds negative camber to the outside wheel when the wheels are being steered

if the angle is positive in the clockwise direction.

7. Pushrod-Actuated

Suspension System:

Pushrod-actuated

suspension(Fig C4) is

defined as the suspension

system where the spring and

damper assembly is actuated

via a pushrod linkage from

the bottom ball joint. When

the wheel goes into bump,

the pushrod “pushes” the

bellcrank which in terms

compresses the spring/damper assembly.

4

Figure C5: Pullrod Suspension System

8. Pullrod-Actuated

Suspension System:

Pullrod actuated

suspension (Fig C5)

system is defined as

the suspension system

where the spring and

damper assembly is

actuated by a pullrod

linkage from the

upper ball joint.

When the wheel goes into bump, the pullrod “pulls” the bellcrank which in

terms compresses the spring/damper assembly.

9. Camber Compensation:

Camber compensation is defined as the change in camber value as the wheels

are either bumped or steered. The amount of camber compensation is based on

suspension kinematics and design. In bump this is governed by the relation

between the upper and lower control arm and their respective length. In

steering this will be governed by the caster and KPI. Caster adds more

negative camber to the outside tire when steered. While KPI adds more

negative camber to the inside tire when steered.

Appendix D: Upright Weight Comparison Matrix2006

Front Rear

Part Vol Density Mass Part Vol Density Mass

Forward Face 8.22E-01 0.28277100 2.32E-01 Forward_Face 9.64E-01 0.28277100 2.73E-01

Rear_Face 9.89E-01 0.28277100 2.80E-01 Rear_Face 9.60E-01 0.28277100 2.71E-01

Inboard Face 6.09E-01 0.28277100 1.72E-01 Inboard Face 6.90E-01 0.28277100 1.95E-01

Outboard Face 7.43E-01 0.28277100 2.10E-01 Outboard Face 8.42E-01 0.28277100 2.38E-01

Interface 2.20E-01 0.28277100 6.23E-02 Interface 2.49E-01 0.28277100 7.04E-02

Top Face 0.3190096 0.28277100 9.02E-02 Top Face 0.350104 0.28277100 9.90E-02

LBJ Plate 0.0763468 0.28277100 2.16E-02 LBJ Plate 0.0763468 0.28277100 2.16E-02

Brake 080 0.4091776 0.28277100 1.16E-01 Brake 065 0.4290943 0.28277100 1.21E-01

Brake 065 0.3324568 0.28277100 9.40E-02 Brake 065 0.4290943 0.28277100 1.21E-01

Brake Gusset 0.2129459 0.28277100 6.02E-02 Brake Gusset 0.2302115 0.28277100 6.51E-02

Gusset Tube 1.09E-01 0.28277100 3.09E-02 Gusset Tube 1.09E-01 0.28277100 3.09E-02

Gusset Tube 1.09E-01 0.28277100 3.09E-02 Gusset Tube 1.09E-01 0.28277100 3.09E-02

Insert 1.29E-01 0.28277100 3.64E-02 Insert 1.29E-01 0.28277100 3.64E-02

Insert 1.29E-01 0.28277100 3.64E-02 Insert 1.29E-01 0.28277100 3.64E-02

Bearing Housing 1.95E+00 0.28277100 5.53E-01 Bearing Housing 1.95E+00 0.28277100 5.53E-01

Clevice 3.37E+00 0.09791210 3.30E-01 Clevice 4.76E+00 0.09791210 4.66E-01

LBJ Spacer 1.30E-01 0.28277100 3.67E-02 LBJ Spacer 1.30E-01 0.28277100 3.67E-02

Total 2.39E+00 Total 2.67E+00

2007

Front Rear

Part Vol Density Mass Part Vol Density Mass

Forward_face 7.75E-01 0.28277100 2.19E-01 Side Face 7.55E-01 0.28277100 2.14E-01

Inboard_face 6.28E-01 0.28277100 1.77E-01 Side Face 7.55E-01 0.28277100 2.14E-01

Outboard_face 7.59E-01 0.28277100 2.15E-01 Inboard_face 6.24E-01 0.28277100 1.76E-01

Back_face 9.48E-01 0.28277100 2.68E-01 Outboard_face 7.62E-01 0.28277100 2.15E-01

Top Interface 3.48E-01 0.28277100 9.84E-02 Top Interface 3.76E-01 0.28277100 1.06E-01

Brake 065 2.56E-01 0.28277100 7.23E-02 Brake 050 0.1771565 0.28277100 5.01E-02

Brake 050 0.1967015 0.28277100 5.56E-02 Brake 050 0.1771565 0.28277100 5.01E-02

LBJ_plate 0.0763468 0.28277100 2.16E-02 LBJ_plate 0.0763468 0.28277100 2.16E-02

Brake Gusset 1.45E-01 0.28277100 4.10E-02 Brake Gusset 1.20E-01 0.28277100 3.39E-02

Bearing_housing 1.78E+00 0.28277100 5.04E-01 Bearing_housing 1.78E+00 0.28277100 5.04E-01

Gusset Tube 6.32E-02 0.28277100 1.79E-02 Gusset Tube 8.11E-02 0.28277100 2.29E-02

Gusset Tube 6.32E-02 0.28277100 1.79E-02 Gusset Tube 8.11E-02 0.28277100 2.29E-02

Insert 8.28E-02 0.28277100 2.34E-02 Insert 1.29E-01 0.28277100 3.64E-02

Insert 8.28E-02 0.28277100 2.34E-02 Insert 1.29E-01 0.28277100 3.64E-02

LBJ Spacer 1.22E-01 0.28277100 3.46E-02 LBJ Spacer 1.22E-01 0.28277100 3.46E-02

Clevice 2.42E+00 0.09791210 2.37E-01 Clevice 3.00E+00 0.09791210 2.93E-01

Total 2.03E+00 Total 2.03E+00

Unit: LB

1

Appendix E: Calculations:

Fatigue Cycle Calculations:

The following are the figures estimated for performing the fatigue cycle calculations.

The figures are conservative estimate in assuming all cornering force taken by the car

is at maximum value and that it is all experienced by only outside front tire. This is

ignoring the fact that the track has turns in different direction.

Variable Description Value

T # on turns per lap 20

L # of laps per race 22

R # of race per day 3

N # of days driving 80

Total Cycle = T x L x R x N

Total Cycle = 20 x 22 x 3 x 80

Total Cycle = 105600

This is a conservative figure, as this is assuming 80 full days of testing with 3 full

race distances completed, with each corner at maximum cornering load. Any rain

days, or other types of testing will drastically reduce this number. For full fatigue life,

this figure is multiplied by 3 to assume for a 3 year service life. Therefore a full cycle

of 3 x 105 will be adopted for fatigue calculation.

Endurance Limit:

Based on the above figure along with the known material properties for 4130 CrMo

Steel, the safety factor against fatigue can be calculated:

Sut = 81.2 ksi

Sy = 52 ksi

Sm = 0.9 Sut = 0.9 (81.2) = 73.1 ksi

2

Se’ = 0.5 Sut = 0.5 x 81.2 = 40.6 ksi

Cload = 1

Csize = 0.7

Csurf:

Assuming a cold drawn and machined surface => A = 2.7, b = -0.265

Csurf = 2.7(Sut)-0.265

= 27(81.2)-0.265

= 0.842

Ctemp = 1

Creliability:

Assume 99.9% Reliability => Creliability = 0.753

Se = Cload x Csize x Csurf x Ctemp x Creliability x Se’ = 18.01ksi

This is the endurance limit beyond 1000000 cycle. However with the interest being at

300000 cycle, the fatigue limit can be found for the material using S-N graph. And in

this case it is found on the graph to be 55ksi, and applying the correction factors it

becomes 24.4ksi.

1

Appendix F: FEA Setup

Figure F1: FEA Wheel Bearing

Figure F2: FEA "Fake" Hub

2

Figure F3: FEA Setup and Constraints

1

Figure G2: Weld-in Clevice Insert

Appendix G: Manufacturing

FigureG1: Sheet Metal Face

2

Figure G3: Internal Tubular Gusset

FigureG4: Wheel Bearing Housing

3

FigureG5: Lower Ball Joint Conical Insert

Figure G6: Sheet Metal Brake Caliper Mount

4

Figure G8: Upright Being Welded on Jig

Figure G7: Aluminum Bolt-On Upper Ball Joint Clevice (front)

5

Figure G9: In Progress Front Upright

Figure G10: Bearing Bore Before and After

1

Figure H2: Example of a suspected welding defect

Appendix H: Physical Testing and Validation

Figure H1: Example of a suspected welding defect

2

Figure H3: Internal Structure of the testing upright

Figure H4: Simplified Bearing Housing and Welded Joint

3

Figure H5: Completed Testing Upright

Figure H6: Testing Upright and Actual Rear Upright

4

Figure H7: Testing Upright and Actual Rear Upright

5

Figure H8: Simplified Constrains and Load

6

Figure H9: Simplified Upright FEA Deflection Result

Figure H10: Physical Testing Apparatus

7

Figure H11: Physical Test with known load @ 56lb with 3.6x mechanical advantage, which

equates to 201.6lb at the ball joint.

1

Appendix I: Bearing Stiffness Calculation

2

3