THE UNIVERSITY OF QUEENSLAND Bachelor of Engineering Thesis

NUMERICAL AND EXPERIMENTAL ANALYSIS OF

FORMULA SAE CHASSIS, WITH RECOMMENDATIONS FOR FUTURE DESIGN ITERATIONS

Student Name: JONATHAN PETER BLESSING

Course Code: MECH4501

Supervisor: Dr W. Daniel

Submission date: 11th June 2004

A thesis submitted in partial fulfillment of the requirements of the

Bachelor of Engineering degree program in the

Division of Mechanical Engineering

Jonathan Peter Blessing

27 Julia St

Highgate Hill 4101

11 June 2004

Prof. J. M. Simmons

Head of School

School of Engineering

University of Queensland

Brisbane

Queensland 4072

Dear Sir,

I hereby submit my Thesis titled Numerical and Experimental Analysis of Formula

SAE Chassis, with Recommendations for Future Design Iterations for

consideration as partial fulfillment of the Bachelor of Engineering degree.

All the work contained within this Thesis is my original work except where

otherwise acknowledged.

I understand that this thesis may be made publicly available and reproduced by

the University of Queensland unless a limited term embargo on publication has

been negotiated with a sponsor.

Yours sincerely

Jonathan Peter Blessing

Student Number 33627713

Executive Summary

The objective of this thesis is to analyze the design of the University of

Queensland Formula SAE chassis both experimentally and by numerical

methods. These experiments are based on the dynamic loads experienced by

the chassis under normal driving conditions, along with the torsional stiffness of

the chassis. The results from the testing of the 2003 chassis have been

implemented into the 2004 design, with a significant performance increase.

The mass moments of inertia in roll, pitch and yaw of the whole vehicle were

determined experimentally, and compared to the expected values from computer

modeling. There are strong correlations between the CAD calculations and the

experimental results, however, the testing equipment requires some modification

for future experiments about the pitch and roll axis. The experiments and

calculations in the yaw axis are sufficiently accurate at this stage.

The results from this experimentation will be used in future designs of Formula

SAE vehicles at the University of Queensland, with the recommendations made

that the 2005 design incorporate stressed aluminum and carbon-fibre skins on a

tubular spaceframe. This is in preparation for a future semi-monocoque design

from the University of Queensland. Improvements for the testing procedures

include a need for a lighter and more accurate car swing setup, along with a more

rigid torsional test rig.

Recommendations for the 2005 design include a stressed-skin of aluminum and

carbon-fibre on a tubular steel spaceframe, in preparation for a semi-monocoque

chassis design for the 2006 competition.

i

Table of Contents

Executive Summary ______________________________________________________ i

Table of Contents ________________________________________________________ii

Table of Figures_______________________________________________________ viii

List of Tables ___________________________________________________________x

Chapter 1 ______________________________________________________________1

1.1 Introduction___________________________________________________1

1.2 The University of Queensland FSAE team___________________________1

1.3 The Chassis ___________________________________________________1

1.4 Design Techniques _____________________________________________2

1.5 Design Validation ______________________________________________2

1.6 Design Options ________________________________________________3

1.6.1 Tubular Steel Space Frame ___________________________________3

1.6.2 Metal Monocoque __________________________________________4

1.6.3 Composite Semi-Monocoques ________________________________4

Chapter 2 ______________________________________________________________6

2.0 Test Equipment for Experiments __________________________________6

2.1 Torsional Test Rig______________________________________________6

2.1.1 Concept __________________________________________________6

2.1.2 Construction ______________________________________________7

2.1.3 Method __________________________________________________8

2.2 Car Swing ___________________________________________________10

2.2.1 Theory__________________________________________________10

2.2.2 Construction _____________________________________________12

2.2.3 Calibration of Swing System ________________________________13

2.2.3.1 Calculations____________________________________________14

2.2.4 Results of Calibration ______________________________________15

2.2.5 Inaccuracies______________________________________________15

Chapter 3 _____________________________________________________________16

ii

3.0 The 2003 Vehicle Design and Construction _________________________16

3.1 Design Objective of 2003 Chassis ________________________________16

3.2 Design Requirements __________________________________________16

3.3 Material Selection for 2003 _____________________________________17

3.4 Chassis Construction 2003 ______________________________________18

3.5 Rocker and Driveline Locations __________________________________19

3.6 Bodywork ___________________________________________________20

3.7 Post welding processes _________________________________________20

3.8 Non-Destructive Crack Testing of 2003 chassis______________________21

Chapter 4 _____________________________________________________________22

4.0 Numerical Analysis of 2003 Chassis _______________________________22

4.1 2003 FEA model______________________________________________22

4.1.1 Engine Model ____________________________________________22

4.1.2 Suspension model _________________________________________23

4.1.3 Weighted model __________________________________________23

4.2 2003 Load Cases for Modeling___________________________________24

4.2.1 Braking Case 2003 ________________________________________24

4.2.2 Lateral Load Case 2003 ____________________________________25

4.2.3 Acceleration case 2003 _____________________________________27

4.3 Finite Element Analysis of 2003 Chassis ___________________________29

4.3.1 Braking Case 2003 ________________________________________29

4.3.2 Lateral Loading Case 2003 __________________________________30

4.3.3 Acceleration Case 2003 ____________________________________31

4.3.4 Torsional Testing 2003 _____________________________________32

4.3.5 Rear Lower Engine Mounts _________________________________33

Chapter 5 _____________________________________________________________34

5.0 Experimental testing of 2003 chassis_______________________________34

5.1 Torsional Testing of 2003 vehicle ________________________________34

5.1.1 Method _________________________________________________34

5.1.2 Results__________________________________________________35

5.2 Measurement of Centre of Gravity ________________________________36

5.2.1 Method _________________________________________________36

iii

5.2.2 Procedure _______________________________________________37

5.2.3 Minimum Requirements for Competition_______________________38

5.2.4 Results__________________________________________________38

5.3 Calculation of Mass Moments of Inertia ___________________________39

5.3.1 Method _________________________________________________39

5.3.2 Results__________________________________________________40

5.3.3 Error and Inaccuracies in Experiments_________________________40

5.3.3.1 Location of Centre of Gravity______________________________40

5.3.3.2 Chain Friction __________________________________________41

5.3.3.3 Weight of Rig __________________________________________41

5.3.3.4 Recording of Period of Oscillations _________________________41

5.4 Nodal Deflections of 2003 Chassis________________________________42

5.4.1 Method _________________________________________________42

5.4.2 Locations measured _______________________________________43

5.4.3 Results__________________________________________________44

5.5 Strain Gauge Correlation of the 2003 Chassis Modeling _______________47

5.5.1 Gauge Selection __________________________________________47

5.5.2 Strain Gauge Setup ________________________________________48

5.5.3 Equipment_______________________________________________48

5.5.4 Strain Gauge Theory_______________________________________49

5.5.5 Calibration of Strain Gauge Amplifier _________________________50

5.5.6 Selection of Gauge locations ________________________________51

5.5.7 Expected stress in Gauge Locations ___________________________51

5.5.7.1 Strain Gauge Location 1 __________________________________51

5.5.7.2 Strain Gauge Location 2 __________________________________51

5.5.7.3 Strain Gauge Location 3 __________________________________51

5.5.8 Method _________________________________________________53

5.5.9 Results__________________________________________________53

5.6 2003 Wet Testing _____________________________________________55

5.7 2003 Competition _____________________________________________56

Chapter 6 _____________________________________________________________57

6.0 Design Objective of 2004 Chassis _________________________________57

6.1 Lessons learnt from 2003 Design _________________________________57

iv

6.1.1 Suspension mounting ______________________________________57

6.1.2 Driver compartment _______________________________________57

6.1.3 Packaging issues __________________________________________57

6.1.4 Location of Rear Sprocket and Disk___________________________58

6.1.5 Engine Mounts ___________________________________________58

6.2 Design improvements of 2004 chassis _____________________________59

6.2.1 Material Change for Minimum Requirements ___________________59

6.2.2 Cockpit Design ___________________________________________59

6.2.3 Engine Mounts ___________________________________________60

6.2.4 Diffbox design ___________________________________________60

6.2.5 General Chassis Improvements_______________________________61

6.2.6 Finalize Design before Construction __________________________61

6.2.7 Material Selection 2004 ____________________________________61

6.3 Construction Process 2004 ______________________________________62

6.3.1 Modular design ___________________________________________62

6.3.2 Bodywork 2004___________________________________________63

6.3.3 Non-Destructive Crack testing of 2004 chassis __________________63

Chapter 7 _____________________________________________________________64

7.0 Numerical Analysis of 2004 Chassis _______________________________64

7.1 2004 FEA Model______________________________________________64

7.2 2004 Load Cases______________________________________________64

7.2.1 Braking Case 2004 ________________________________________64

7.2.2 Lateral Load Case 2004 ____________________________________65

7.2.3 Accelerating Case 2004 ____________________________________65

7.3 Finite Element Analysis of 2004 Chassis ___________________________67

7.3.1 Braking Case 2004 ________________________________________67

7.3.2 Lateral Load Case 2004 ____________________________________69

7.3.3 Acceleration Case 2004 ____________________________________71

7.3.3.1 Change in Turnbuckle Location ____________________________72

7.3.4 Torsional Testing 2004 _____________________________________73

7.3.5 Suspension Pickup Forces 2004 ______________________________74

7.3.6 Rear Engine Mounts _______________________________________75

v

Chapter 8 _____________________________________________________________77

8.0 Experimental Testing of the 2004 chassis ___________________________77

8.1 Torsional Testing of 2004 vehicle ________________________________77

8.2 Strain Gauge Testing of 2004 Chassis _____________________________79

8.2.1 Strain Gauge Location 1 ____________________________________79

8.2.2 Strain Gauge Location 2 ____________________________________79

8.2.3 Strain Gauge Location 3 ____________________________________79

8.3 Dynamic Testing of 2004 Vehicle ________________________________82

8.4 Driveline Testing of 2004 Vehicle ________________________________83

8.4.1 Method _________________________________________________83

8.4.2 Results__________________________________________________83

Chapter 9 _____________________________________________________________84

9.0 Conclusions from Experimental Testing ___________________________84

Chapter 10 ____________________________________________________________87

10.0 Recommendations for 2005 Chassis Design and Construction _________87

Chapter 11 ____________________________________________________________88

11.0 Recommendations for Future Testing Procedures ___________________88

Bibliography___________________________________________________________89

Appendix A ____________________________________________________________91

Extract from 2004 Formula SAE Rules pertaining to Chassis Design and

Construction ________________________________________________________91

Appendix B ___________________________________________________________110

University of Queensland Safety Structure Equivalency ___________________110

Appendix C ___________________________________________________________113

Tube Selection for Minimum Requirements _____________________________113

Appendix D___________________________________________________________114

Calculations for Mass Moment of Inertia________________________________114

Appendix E ___________________________________________________________115

vi

Data plots for Dial Gauge Locations ____________________________________115

Appendix F ___________________________________________________________122

Strain Gauge Data Plots ______________________________________________122

Appendix G___________________________________________________________124

Calculations for 2003 Height of Centre of Gravity ________________________124

Appendix H___________________________________________________________125

2003 Chassis Layout _________________________________________________125

Appendix I ___________________________________________________________126

2004 Chassis Layout _________________________________________________126

vii

Table of Figures

Figure 1. The 2003 University of Queensland FSAE Chassis ____________________________________ 3 Figure 2. University of Wollongong with Stressed Carbon-Fibre Panels___________________________ 4 Figure 3. University of Western Washington's Composite Tub Chassis ____________________________ 5 Figure 4. Torsional Test Rig with 2003 FSAE Vehicle _________________________________________ 6 Figure 5. Front Left Stand of Torsional Test Rig _____________________________________________ 7 Figure 6. Front Right Stand of Torsional Test Rig ____________________________________________ 7 Figure 7. Swingarm on Central Bearing ____________________________________________________ 8 Figure 8. Schematic of Test Procedure _____________________________________________________ 8 Figure 9. Calibration of Torsional Test Rig _________________________________________________ 9 Figure 10. Plot of Calibration of Torsional Test Rig __________________________________________ 9 Figure 11. Huygens Theorem ___________________________________________________________ 10 Figure 12. Calculation of Mass Moment of Inertia of Platform_________________________________ 10 Figure 13. Mass Moment of Inertia of Vehicle______________________________________________ 11 Figure 14. Mass Moment of Inertia in Yaw with a Three-Point Swing ____________________________ 11 Figure 15. Trial 1 for Pitch Calibration ___________________________________________________ 13 Figure 16. Trial 3 for Yaw Calibration ____________________________________________________ 13 Figure 17. Mass moment of inertia of cylinder ______________________________________________ 14 Figure 18. Parallel Axis Theorem for Calibration___________________________________________ 14 Figure 19. Jig for 2003 Chassis Construction ______________________________________________ 18 Figure 20. Front Suspension Geometry 2003_______________________________________________ 19 Figure 21. Rear Suspension Geometry 2003________________________________________________ 19 Figure 22. Bodywork Construction 2003 __________________________________________________ 20 Figure 23. Non-Destructive Testing of 2003 Chassis _________________________________________ 21 Figure 24. Braking Load Case 2003 ______________________________________________________ 24 Figure 25. Lateral Load Case 2003 ______________________________________________________ 25 Figure 26. Acceleration Load Case 2003 __________________________________________________ 27 Figure 27. Schematic of Rear Sprocket ____________________________________________________ 28 Figure 28. Fibre Stress in Chassis under Braking ___________________________________________ 29 Figure 29. Fibre Stress in Chassis with Lateral Loads ________________________________________ 30 Figure 30. Fibre Stress in rear section of Chassis under Acceleration ___________________________ 31 Figure 31. FEA Torsional Test of 2003 Chassis _____________________________________________ 32 Figure 32. Schematic of Torsional Stiffness Calculation ______________________________________ 32 Figure 33. Torsional Test of 2003 Chassis with Modeled Lower Engine Mounts ___________________ 33 Figure 34. Torsional Testing of 2003 vehicle_______________________________________________ 34 Figure 35. Plot of Torsional Test of 2003 Chassis ___________________________________________ 35 Figure 36. Process for Finding Height of Centre of Gravity of Vehicle __________________________ 36

viii

Figure 37. Finding Centre of Gravity of 2003 Vehicle________________________________________ 37 Figure 38. Finding Mass Moment of Inertia in Yaw of 2003 vehicle _____________________________ 39 Figure 39. Locations for Nodal Displacements______________________________________________ 44 Figure 40. Comparison of Nodal Displacements to FEA______________________________________ 45 Figure 41. Wheatsone Bridge for Strain Gauge Wiring _______________________________________ 47 Figure 42. Strain Gauge Locations for 2003 Testing_________________________________________ 52 Figure 43. Axial Stresses In Torsional Testing ______________________________________________ 52 Figure 44. Bending Stresses in Torsional Testing ___________________________________________ 52 Figure 45. UQ FSAE at 2003 FSAE-A Competition _________________________________________ 56 Figure 46. 2001-2002 Georgia Institute of Technology _______________________________________ 60 Figure 47. Jigs for 2004 Construction ____________________________________________________ 62 Figure 48. Non-Destructive Testing of 2004 Chassis – Diffbox _________________________________ 63 Figure 49. Fibre Stress in 2004 Chassis Under Braking_______________________________________ 67 Figure 50. Axial Stress in 2004 Chassis under Braking _______________________________________ 68 Figure 51. Bending Stresses in 2004 Chassis under Braking ___________________________________ 68 Figure 52. Fibre Stress from Lateral Load Case 2004 ________________________________________ 69 Figure 53. Fibre Stresses in Rear Section Under Lateral Load _________________________________ 70 Figure 54. Fibre Stress in 2004 Rear Section Under Acceleration Load Case______________________ 71 Figure 55. Fibre Stresses in Rear Section with Alternate Driveline Support_______________________ 72 Figure 56. Torsional Testing of 2004 Model________________________________________________ 73 Figure 57. Von Mises Stress in Suspension Pickup Points _____________________________________ 74 Figure 58. Global Displacement of Rear Lower Engine Mounts ________________________________ 75 Figure 59. Global Displacement of Upper Engine Mounts_____________________________________ 75 Figure 60. Torsional Testing of 2004 Chassis ______________________________________________ 77 Figure 61. Plot of Torsional Testing of 2004 Chassis_________________________________________ 78 Figure 62. Strain Gauge Locations for 2004 Chassis ________________________________________ 80 Figure 63. Axial Stresses Under Braking__________________________________________________ 80 Figure 64. Axial Stresses in 2004 Chassis Under Lateral Forces _______________________________ 81 Figure 65. Bending Stresses under Acceleration ____________________________________________ 81 Figure 66. 2004 Vehicle under Initial Dynamic Testing ______________________________________ 82

ix

List of Tables

Table 1. 2003 Braking Load Case Parameters _____________________________________________ 24 Table 2. 2003 Lateral Load Case Parameters ______________________________________________ 25 Table 3. 2003 Acceleration Load Case Parameters__________________________________________ 27 Table 4. Torsional Stiffness Experiments __________________________________________________ 35 Table 5. Examples of Mass Moments of Inertia______________________________________________ 40 Table 6. Locations for Nodal Displacements _______________________________________________ 43 Table 7. Results for Nodal Displacements__________________________________________________ 44 Table 8. Calibration of Strain Gauge Amplifier _____________________________________________ 50 Table 9. Results of 2003 Strain Gauge Testing ______________________________________________ 53 Table 10. 2004 Braking Load Case Parameters_____________________________________________ 64 Table 11. 2004 Lateral Load Case Parameters______________________________________________ 65 Table 12. Analysis of 2003 Data, with Initial Rig Calibration __________________________________ 84 Table 13. Analysis of Testing Data, Including Dial Gauge Results ______________________________ 85 Table 14. Analysis of Testing Data for 2003, Applied Moment and Recorded Stress _________________ 85

x

Chapter 1

1.1 Introduction

Extract from the 2004 Formula SAE Rules:

“The Formula SAE® competition is for SAE student members to conceive,

design, fabricate, and compete with small formula-style racing cars. The

restrictions on the car frame and engine are limited so that the knowledge,

creativity, and imagination of the students are challenged. The cars are built with

a team effort over a period of about one year and are taken to the annual

competition for judging and comparison with approximately 120 other vehicles

from colleges and universities throughout the world. The end result is a great

experience for young engineers in a meaningful engineering project as well as

the opportunity of working in a dedicated team effort.”

In addition to this, there are now competitions held in Australia, United Kingdom

and recently Japan that are available for all Formula SAE teams to compete.

1.2 The University of Queensland FSAE team

The University of Queensland started its first team in 2001, with an initial placing

in the Australian competition of 14th, followed by 10th in 2002. At the 2003

competition held at the Mitsubishi proving grounds in Talem Bend, the University

of Queensland placed 3rd overall, and 1st out of the Australian teams. At the time

of writing, the 2004 vehicle is under construction, with the intention of competing

in the 2004 Formula Student competition in the UK in July. The team has every

intention of another podium finish, and has its sights set on first place in both the

UK and Australian competitions in 2004.

1.3 The Chassis

One of the critical components in these vehicles is the chassis design and

construction. The initial chassis for the 2001 vehicle was the first time anyone at

the University had built this style of vehicle, and so was heavy, poorly designed

1

and suffered some initial failures. The design was modified for 2002, but the

chassis still suffered the same problems. The next iteration for 2003 was a

definite improvement on the 2002 design in terms of weight and component

packaging; however it was a very ‘floppy’ design, with a torsional stiffness that

affected the tuning of the suspension. The chassis design at the University of

Queensland has been improving with each year of the competition, with the 2004

design already proving itself as light, stiff and reasonably well packaged.

1.4 Design Techniques

The 2003 chassis design was made with the packaging of the other vehicle

components in mind, without significant finite element analysis used in the

design. FEA was used in the selection of wall thickness for the members in the

chassis to keep the predicted stresses in the chassis below 50% of the yield

strength of the material. The load cases used were calculated from the expected

dynamic forces that would be experienced by the vehicle in normal driving

conditions. The torsional stiffness of the chassis was only investigated once the

initial design had been finalized, which made options to stiffen the chassis fairly

constrictive. For the 2004 chassis, by designing for a target torsional stiffness of

3000Nm/deg, did not require significant modifications to handle the expected

dynamic loads. A minimum torsional stiffness of 2000Nm/deg was discussed as

a minimum requirement from discussions with the technical adviser for the

Australian competition, Pat Clarke. From computer modeling in Matlab treating

the chassis as a spring, a minimum torsional stiffness of 3000Nm/deg was

chosen.

1.5 Design Validation

The purpose of this thesis is to experimentally compare the design of the chassis

compared to the finite element model. The parameters of the entire vehicle,

centre of gravity and mass moments of inertia about the yaw, roll and pitch axis

will also be determined.

2

1.6 Design Options

During the years of competition of formula SAE, there have been 3 major styles

of chassis construction – tubular steel space frame, composite semi-monocoque

and stressed skin designs.

1.6.1 Tubular Steel Space Frame

Tubular steel space frames are possibly the most popular chassis design in

Formula SAE. Part of the competition process is the validation of your design to

the design judges; the tubular space frame is easiest. As the design judges have

only a limited amount of time to inspect the vehicles, they need to see that the

chassis performs as the team claims. As tubular steel structures are common in

motorsports, it is easy for judges (with or without motorsport backgrounds) to

visually access the design of a space frame. The University of Queensland has

only constructed tubular steel spaceframes for all of its vehicles to date.

Figure 1. The 2003 University of Queensland FSAE Chassis

3

1.6.2 Metal Monocoque

Metal Monocoque or stressed-skin designs can also be easily visually assessed

for load paths and expected forces, as they are usually a tubular space-frame

with bonded aluminum panels used to increase stiffness and to act as bodywork.

The aluminum sheeting is only ¼” to ½” thick, but the claimed stiffness increase

is significant. (Gadola 2003) Instead of aluminum, carbon-fibre panels can be

used to the same effect, which is more effective for complicated geometry and

sections that are out of plane.

Figure 2. University of Wollongong with Stressed Carbon-Fibre Panels

1.6.3 Composite Semi-Monocoques

Composite semi-monocoques are usually a tub design, with the material used a

carbon-fibre matrix with an epoxy resin. There are usually several materials

included in the lay-up process to modify the properties for strength, stiffness, and

weight. There is a wide scope in the properties of composite materials available

for chassis construction compared to the known and familiar properties of steel.

Because of this there are significant equivalency rules in place to ensure that the

minimum safety requirements for the chassis are met. (See Appendix A, section

3.3.3)

4

As the judges cannot easily assess the load lines and forces in the chassis when

looking at a composite construction, there is an inherent disadvantage from the

view of competition points. On the other hand, composite constructions have the

possibility of being lighter, stiffer, stronger and simpler to construct than any

tubular space frame.

Figure 3. University of Western Washington's Composite Tub Chassis

5

Chapter 2

2.0 Test Equipment for Experiments

2.1 Torsional Test Rig

2.1.1 Concept

The concept behind the torsional test rig is to apply a moment about the roll axis

of the vehicle, applied at the uprights. This is done with ‘dummy’ shocks

replacing the normal shock absorbers, and will measure the stiffness of the entire

vehicle.

The construction of this test rig was necessary for this research, as well as being

a useful tool for future years in the team. This is an excellent method for

comparing different chassis designs, even though the exact same loading is not

experience by the vehicle in normal use, it is more of a benchmark load case. As

the stiffness of the vehicle is dependent on the wishbone linkages, suspension

members, uprights and hubs, it’s a fair test of the stiffness of the whole vehicle.

Figure 4. Torsional Test Rig with 2003 FSAE Vehicle

2.1.2 Construction

The test rig was constructed out of 50mm SHS steel, with 3mm NWT and 40mm

SHS x 2mm NWT. The plate for the bolting of the hubs is 6mm mild steel, with

25.4mm SHS x 1.5mm NWT bracing. The rig was MIG welded in the Mechanical

Engineering Workshop at the University of Queensland.

There are 3 parts to the test rig, which are used to support the vehicle and apply

the moment. The rear uprights are bolted to the adjustable swingarm with the

front uprights bolted to the remaining two stands. The front left stand is bolted to

the ground. The mount for the swingarm and the front left mount are mounted on

castors, to allow movement in the horizontal direction(s) while resisting motion in

the vertical.

Figure 5. Front Left Stand of Torsional Test Rig

Figure 6. Front Right Stand of Torsional Test Rig

7

Figure 7. Swingarm on Central Bearing

2.1.3 Method

By applying weights to the cantilever on the end of the swingarm, a moment is

produced about the centreline of the vehicle, and the resulting deflection can be

measured. For this testing, a laser pointer was fixed to the swing arm and the

deflection measured on a vertical surface. This will give the rotation of the test

rig, which is proportional to the torsional stiffness of the chassis.

La

d

L

Rear of vehicle fixed to swingarm

F

θ

H

Figure 8. Schematic of Test Procedure

Moment about centreline

tan

Torsional stiffness

aM FLdLMK

θ

θ

= =

=

= =

8

The rig was first calibrated to find the effects of the stiffness of the rig itself,

this was done by rearranging the layout of the test rig to simulate a ‘dummy’

vehicle. As the rotation of the swingarm was measured the vertical

displacement of a laser pointer on a vertical board, the accuracy of the

measurement was difficult for small displacements. If the board were moved

further away to increase resolution, the laser point would spread, affecting the

accuracy of the readings.

Figure 9. Calibration of Torsional Test Rig

This gave an effective stiffness of the test rig as approximately 8509Nm/deg.

Torsional Test Rig Calibration

y = 8059.3x - 26.678R2 = 0.9704

0

500

1000

1500

2000

2500

0 0.05 0.1 0.15 0.2 0.25

LOADING

Linear (LOADING)

Figure 10. Plot of Calibration of Torsional Test Rig

9

2.2 Car Swing

2.2.1 Theory

The theory behind the car swing is that the mass moment of inertia of an object

can be determined by swinging the object like a pendulum and recording the

period of oscillations. The method used is from the OptimumG, Formula SAE

seminar presented by Claude Rouelle in 2003.

This is based on Huygens theorem, where

2

Inertia about axis AInertia about axis B

( )

A

B

A B AB

JJ

J J m dist

==

= + ×

Figure 11. Huygens Theorem

2

.(2 )

i ii

i

m g LJfπ

=

Figure 12. Calculation of Mass Moment of Inertia of Platform

10

( )( )

2

2

(2 )2

i car icar

m m gL J fJ

fπ

π+ −

=

Figure 13. Mass Moment of Inertia of Vehicle

iwhere m mass of stagef = frequency of ocillations

L = distance to pivot from centre of gravity of car

=

To find the mass moment of inertia in yaw, the swing is modified to be a three-

point swing, and the car is rotated about the centre of gravity of the vehicle and

the stage.

Figure 14. Mass Moment of Inertia in Yaw with a Three-Point Swing

11

For the calculations of mass moment of inertia in yaw using a three-point swing,

the formula used is

( )2 2 2

2 22 2

g4 4

Where T = Period of movementr = Distance from centre of gravity to platform supports

L = Vertical distance from pivot point to platform

car icar i

m r T m grI T TL Lπ π

= + −

2.2.2 Construction

The car swing platform was constructed out of 50mm SHS x 3mm NWT steel.

The platform was suspended from 10mm steel chain, fixed into eyebolts on the

platform. The chains were pinned to eye nuts that were bolted into the concrete

ceiling under the Mechanical Engineering building at the St Lucia Campus of the

University of Queensland.

The weight of the stage was 52kg, with 17.1kg of chain suspending the platform.

The horizontal centre of gravity of the platform was found by suspending the

platform from two corners, with a plumb line running vertical. Where the plumb

lines intersected was the centre of gravity of the platform. For the vertical

distance, a model of the platform and chain was made in Solid Edge, to confirm

the horizontal centre of gravity and to find the expected vertical centre of gravity.

The centre of gravity of the frame is in the centre of the three-point yaw setup and

for pitch and roll.

The swing can be pinned from either four or three points, allowing for testing in

the roll, pitch and yaw, however the swing must be dismantled between each set

of experiments, making it time and labour intensive. Each setup for the vehicle

required at least 3-4 people to shift the car into location.

12

2.2.3 Calibration of Swing System

To calibrate the swing system, experiments were done on weight stacks of known

weight and geometry. The mass moment of inertia of the stacks was calculated

by hand, and compared to a Solid Edge model. For the calibration, weight stacks

were used to represent the vehicle in the model of Section 2.2.1.

Trial 1 was a vertical stack of weights at the centre of gravity of the swing,

720mm tall and 180mm in diameter. The stack weighed 120kg, and was used for

the pitch calibration. Trials 2 and 3 were two weight stacks of equal dimensions,

spaced 1165mm apart across the axis of rotation. They were each 360mm tall,

180mm diameter and weighed 60kg. This was for the calibration in pitch and

yaw.

Figure 15. Trial 1 for Pitch Calibration

Figure 16. Trial 3 for Yaw Calibration

13

2.2.3.1 Calculations

The calculations for the mass moment of inertia for the stacks is

l

r

z’

x’

y’

2 2

2

' '12 4

'2

l rIx Iy m

mrIz

= = +

=

Figure 17. Mass Moments of Inertia of Cylinder

Where Ix’ is the mass moment of inertia about the horizontal axis of a cylinder

through the centre of gravity. For Trials 2 and 3 with two cylinders the mass

moment of inertia is calculated for each stack along an axis parallel to the centre

of the swing at distance x, using 2' ( )Ix Ix m dx= +

Where dx is the distance from the centre of mass of each individual stack to the

centre of mass of the load, and the axis of interest for finding the moment of

inertia.

dx

Pivot

Stage

Weights

Cog of weights

Figure 18. Parallel Axis Theorem for Calibration

This is also used for calculations about the y and z-axis. This will give the mass

moment of inertia about the centre of gravity of the weight stack(s).

14

2.2.4 Results of Calibration

Calculated MMOI in

Pitch (kgm2)

Experimental MMOI in

Pitch (kgm2)

% error

Calculated MMOI in

Yaw (kgm2)

Experimental MMOI in Yaw (kgm2)

% error

Trial 1 5.427 6.9 27% - - -

Trial 2 43.1 60.4 40% - - -

Trial 3 - - - 42.0 41.5 2%

From these results, it can be seen that there are significant inconsistencies in the

pitch and roll experiments, but that the yaw experiment is relatively accurate.

The pitch and yaw experiments give values that are consistently large (30-40%),

and will have to be taken only as a rough approximation.

2.2.5 Inaccuracies

There are some possible explanations for the errors in these measurements and

calculations, which are

• The stage and supporting chains are too heavy, which is reducing the

measurable effects of the load, affecting the calculated values

• There is excessive friction in the chain arrangement which is affecting the

results

• There were minor errors in the location of the load on the platform for the

tests

• Minor measurement errors in the dimensions of the platform and vehicle

may have affected this output.

• In the testing in pitch and roll there may have been development of

secondary oscillations in other axes.

• Errors in the recorded period of oscillation

These errors will be discussed in Section 5.3.3.

15

Chapter 3

3.0 The 2003 Vehicle Design and Construction

3.1 Design Objective of 2003 Chassis

The primary objective of the 2003 FSAE chassis was the reduction of weight from

the 2002 chassis design. The 2002 chassis was fabricated from mild steel and

weighed in at 55kg. The projected weight of the 2003 chassis was 30kg, which

would be a 25kg improvement. This would be obtained the use of thin-walled

High Tensile 4130 Alloy for the material selection. At final assembly, the 2003

chassis weighed in at 35kg.

3.2 Design Requirements

The primary requirements for the chassis as outlined by the rules of the

competition are to protect the driver of the vehicle from minor impacts and

rollover situations. (See Appendix A). The chassis has to allow for all of the

vehicle components to be appropriately contained on the vehicle. Packaging

issues should be kept to a minimum for the final assembly of the vehicle, and

access to components is critical during testing and on-track. In this competition,

the aesthetics of the vehicle plays a crucial role; with the winners of the

competition always producing very presentable vehicles. The layout of the

chassis is a major factor in the appearance of the vehicle, which is then

expanded upon by the bodywork.

From a structural perspective, the chassis is required to provide a stable base for

the mounting of the engine, driveline and suspension of the vehicle. Depending

on the suspension design, there should not be significant flex in the chassis.

Suspension design can be based on both stiff and flexible chassis designs; an

example of this is in go-kart design, where the frame of the go-kart acts as the

suspension. The design judges do not encourage flexible chassis design in this

competition. Another possible problem of a flexible chassis with a spool

differential is that there may be problems in tuning the vehicle for wet conditions,

again a go-karting comparison, which are notorious for understeer in wet

condition.

3.3 Material Selection for 2003

The 2001 and 2002 chassis were constructed out of 1” mild steel tubing, with a

minimum wall thickness of 1.6mm. This was a sturdy construction, and was fairly

tolerant of design flaws. However, it was heavy, at 55kg it was a significant

weight in the vehicle. For 2003 the team chose High Tensile 4130 Chrome-

Molybdenum steel for the frame construction. The primary advantage with this

steel is the high yield strength and its availability in thin-walled sections. This

was a new material for the team, and so some fairly conservative tube sizes were

used for the 2003 construction.

Including wishbones, the tubing used was (OD x NWT x total length used)

• 25.4 x 3.0mm x 3.63m

• 25.4 x 1.65mm x 10.6m

• 25.4 x 0.9mm x 9.6m

• 25.4 x 0.7mm x 6.2m

• 19.05 x 0.9mm x 6.3m

• 31.75 SHS x 1.65mm x 1.5m

• 25.4 x 44.45 RHS x 1.65mm x 0.34m

This steel is significantly more expensive than mild steel, with approximately

$AUD2000 spent for the material, with substantial excess. In the cost report

event in the competition, the costing for 4130 steel is rated at US$0.6/pound,

which makes the cost of the chassis material approximately US$35.

The chassis was TIG welded, using CroMo1 ER70S-6 filler rods. For some

sections of the framework, depending on the weld operator some stainless steel

filler was used. Various combinations of inert gas were used in the welding of the

chassis, with an argon mix the most common.

17

3.4 Chassis Construction 2003

The chassis construction in 2003 was intended to be as fast as possible. The

suspension points and roll hoops were fixed to a board on a seismic block, which

ensured that the suspension points were fixed relative to the ground. The rest of

the chassis was then built around these suspension points, ensuring that

everything was aligned and restrained. The welding was done in stages, as each

set of tubes was prepared by hand they would be welded on.

Figure 19. Jig for 2003 Chassis Construction

The major disadvantage of this method was that it created difficulties for access

to the weld area. The chassis would have to be taken off the jig and rotated to

allow for welding access, which resulted in some unrestrained warping of the

frame due to weld cooling.

18

3.5 Rocker and Driveline Locations

Due to the restrictions of the suspension design, the front and rear rockers and

shock mounts had to be orientated at difficult angles to the chassis. To ensure

that the suspension performance was not compromised, the rocker and shock

mounts were directly jigged to the board on the seismic block, ensuring the

relative location from the board and the suspension points were fixed

Figure 20. Front Suspension Geometry 2003

Figure 21. Rear Suspension Geometry 2003

19

3.6 Bodywork

Once the chassis was completed, the suspension pickup points were trimmed to

size, allowing the construction of the seat, nosecone and drivers cockpit. For the

bodywork and cockpit a ‘plug’ was built around the chassis from plaster and

foam. This was then filed and smoothed, with an overlay of fiberglass for a

female mould. This female mould was used for the final carbon-fibre lay-up.

This resulted in a perfectly fitting bodywork, however the chassis and rest of the

vehicle was unusable during the lengthy construction of the plaster and foam

mould.

Figure 22. Bodywork Construction 2003

3.7 Post welding processes

Minor heat-treating was done on the large section welds, using an oxy-acetylene

torch. The welds were brought up to a cherry red colour, and left to cool slowly,

minimizing any hardening effects. Ideally, the welds should be wrapped in an

insulated welding blanket, to slow the cooling of the welds as much as possible.

To manipulate and adjust brackets and tubes on the chassis after welding, the

20

oxy-acetylene torch was used to soften the area before bending into shape.

However, as the majority of welds on the frame are less than 0.120” thickness,

substantial stress relief and heat-treating was not necessary. (ref

http://www.lincolnelectric.com)

3.8 Non-Destructive Crack Testing of 2003 chassis

The team undertook a thorough NDT of the 2003 chassis before testing and final

assembly. All the welds were inspected and hand-filed to remove the stress

concentrations, with only 3 weld beads needing minor re-welding. The NDT

process was fairly laborious, mainly due to the number of joints and restrictive

geometry of the chassis.

The process used was a Magnetic-Particle inspection, a process suitable for

ferromagnetic materials such as steel. This is suitable for locating discontinuities

in the weld bead at the surface and within the weld.

Figure 23. Non-Destructive Testing of 2003 Chassis

21

Chapter 4

4.0 Numerical Analysis of 2003 Chassis

4.1 2003 FEA model

The FEA model of the 2003 chassis was constructed from beam members, with

cross sectional areas and material properties to correspond with the material of

the frame. After several design iterations of the suspension, the initial chassis

design was determined based on the suspension pickup points for the

wishbones. The model was then built around the expected location of the driver

and engine. The suspension geometry for the front and rear of the vehicle had

not been finalized, so an approximate orientation of the suspension hardware

was made.

After the construction of the chassis, and the orientation and location of the

suspension was finalized, a complete model of the chassis was generated in

Strand7, a finite element program. Strand7 was chosen as it is suitable program

for the analysis of beam structures such as in this style of chassis.

4.1.1 Engine Model

Discussions with the University of Swinbourne Formula SAE-A team suggest a

torsional stiffness of the engine at approximately 9000Nm/deg, when bolted at

the engine mounts. The actual experiments conducted and final results were not

available, and the University of Queensland team hasn’t yet repeated the

experiment. Because of this, the engine has been approximated as a rigid

member in all of the finite element analysis of the chassis. The engine mounts

for the 2003 vehicle have been included in the model; with the rear lower engine

mounts modeled as both rigid and as a meshed element.

4.1.2 Suspension model

The milled aluminum uprights and rockers will be approximated as rigid links, as

there should not be significant deflection in these components. The outboard

pushrod connection on the lower wishbone has been approximated to be at the

upright, which is a reasonable approximation, as the line of force of the pushrod

is close to the lower spherical housing on the wishbones.

The rocker location has been modeled as a mechanism, with the rocker restricted

to motion in the plane of the shock-rocker-pushrod system. All of the suspension

wishbones and push/pull rods were included in the model. (Not modeled as solid

links). The tyre stiffness was not included in the model, as the dynamics of the

vehicle were not specifically under investigation.

4.1.3 Weighted model

For the dynamic analysis of the 2003 vehicle, the model was fully weighted with

an engine mass, driver mass and peripheral masses to simulate the whole

vehicle. The location of these lumped masses was to correspond to the expected

centre of gravity of the actual vehicle. The model was then subjected to

appropriate global accelerations with reactive forces applied at the tyre patches.

This will give a good approximation of the forces experienced about the

suspension points of the vehicle. To prevent the whole model acting as a

mechanism the model is restrained at a non-critical member away from the area

of interest. The tyre patch forces and the global acceleration forces should

closely match, resulting in minimal reactive forces or moments at the restraint.

The reactive forces about the restraints were kept at a minimum by slight

modification of the applied forces in order to keep the models balanced.

23

4.2 2003 Load Cases for Modeling

4.2.1 Braking Case 2003

Assuming that the maximum braking acceleration of the vehicle is 1.1g, the

maximum forces in the vehicle will be found about the front uprights.

Lt Lf

Hc

ac

mc

Ha Hb

Va Vb

BA

Half car model – Side view

Figure 24. Braking Load Case 2003

Table 1. 2003 Braking Load Case Parameters

Height of centre of gravity, Hc = 0.293m

Weight distribution Front:Rear= 55:45

Distance from front axle to CoG Lf = 0.732m

Wheelbase Lt = 1.525

Max deceleration ac= 1.1g

Tyre Coefficient of friction u = 1.1

Mass of vehicle + driver, mc= 360kg

Gravity G = 9.81m/s2

Moments about A = 00

As the coefficent of friction between tyre and road limits the braking rate, the maximum horizontal force at the front is

a b c

a b c c

c c c c f b t

a a

V V m gH H m a

m a H m gL V L

H uV

+ =+ =

− + =

=

∑

24

Vrear = 949N

Vfront = 2583N

Hrear = 1044N

Hfront = 2841N

Moment about front uprights = 373Nm

4.2.2 Lateral Load Case 2003

The maximum cornering forces expected from the suspension part of the team is

a sustained 1.32g corner. This has also been verified through track testing of the

2003 vehicle, using a skid pad test track.

Assuming the car can be modeled as a half car from the rear, the lateral weight

transfer of the vehicle can be determined. As the track of these vehicles is

different front to rear, there will be different calculations for the front and the rear.

It is assumed that the centre of gravity of the vehicle is the same over the front

and rear wheels.

Vo Vi

Ho Hi

al

mc

Tc

Half Car Model – from rear

O I

Hc

Figure 25. Lateral Load Case 2003

Table 2. 2003 Lateral Load Case Parameters

Height of centre of gravity, Hc = 0.293m

Track front Tf = 1.2m

Track rear Tr= 1.15m

Max lateral cornering rate al = 1.32g

Weight Split Front:Rear 55:45

Mass of vehicle + driver mc= 360kg

25

Moment about I = 0

( ) 02

As the horizontal forces correspond to the vertical forces by the maximum cornering acceleration,

i o c

cc o c l c c

o l o

V V m g

Tm g V T a m H

H a V

+ =

− + =

=

∑

Vorear = 1420N

Virear = 277N

Horear = 1874N

Hirear = 366N

Vofront = 1596N

Vifront = 346N

Hofront = 2107N

Hifront = 457N

26

4.2.3 Acceleration case 2003

The maximum acceleration expected from the vehicle is 0.9g, which is what the

driveline section of the FSAE team is expecting to produce.

Lt Lf

Hc

aa

mc

Ha Hb

Va Vb

BA

Half car model – Side view

Figure 26. Acceleration Load Case 2003

Table 3. 2003 Acceleration Load Case Parameters

Height of centre of gravity, Hc = 0.293m

Track front Tf = 1.2m

Track rear Tr= 1.15m

Maximum acceleration al = 1.32g

Weight Split Front:Rear 55:45

Mass of 2003 vehicle + driver mc= 360kg

Gravity g = 9.81m/s2

The inline force Hb at the tyre patch will be restricted by the maximum

acceleration,

b

F maH m

== a

=

The vertical force Vb at the tyre patch is found by the rear weight transfer in

acceleration,

Moments about A = 00

1981c a c c f b t

b

m a H m gL V L

V N

+ −

=

∑

27

These forces are evenly split between the two rear wheels. This acceleration

corresponds to a torque transfer from the axle to the ground through a tyre of

radius 0.263mm, resulting in a moment about the rear axle of 857Nm. This

torque is reacted in the chain tension and the bearing hangers. The rear

sprocket has a 230mm diameter, which results in a chain tension of 7.5kN. The

chain angle from rear sprocket to the main gear is 37°. It is assumed that the

chain forces act directly through the bearing hangers, as the rear sprocket is

bolted directly to the bearing shaft.

θ

Va

HaTc

TH TV

Figure 27. Schematic of Rear Sprocket

Using statics,

00

sincos

a V

a H

V c

H c

V TH T

T TT T

θθ

+ =+ =

==

The chain force is then reacted at the main gear, with a diameter of 70mm,

resulting in a torque reduction of 3.2. The reaction forces in the horizontal and

vertical directions are the same at the main gear as at the sprocket, with a

moment of 261Nm about the engine output shaft. Reaction forces about the rear

axle, with chain angle = 37°

Vrear = 4374N

Hrear = 5805N

Moment about motor output shaft = 261Nm

28

4.3 Finite Element Analysis of 2003 Chassis

4.3.1 Braking Case 2003

As the maximum braking force in the vehicle is found about the front uprights, this

will be the section of the vehicle that is under investigation. The entire weighted

model is subjected to a global acceleration of 1.1g in the braking direction, along

with the vertical acceleration of gravity. The tyre patch loads from the load case

are then applied to the tyre patch in the model. The vehicle is then restrained

about the rear tyre patch to prevent the model acting as a mechanism. This

should balance the forces in the chassis, and result in only minimum reaction

forces about the restraints, minimizing artificial stiffness.

Figure 28. Fibre Stress in Chassis under Braking

There were peak stresses around the driver mounts; however the model was run

with rigid links as replacements without change affecting in the members around

the front suspension. From inspection of the members under interest, the

maximum fibre stress found was 293MPa, which was on the vertical member

between the top and bottom forward suspension pickups. This is a significant

stress in the vehicle, especially as it is a frequent force, as the vehicle tends to be

driven either hard on the throttle or hard on the brakes. However, in the short life

of the 2003 vehicle, there were no noticeable effects from this loading. If the

2003 chassis is stripped and crack tested again however, some serious fracture

developments may be found.

29

4.3.2 Lateral Loading Case 2003

The maximum forces experienced by the vehicle in a cornering situation are

found on the tyres on the outside of the corner. For this modeling, the vehicle is

subjected to a global acceleration of 1.32g across the vehicle along with a vertical

acceleration due the gravity. The tyre patch loads from the load case are applied

to the four uprights, and the model is restrained on the front bulkhead. As the

tyre patch forces will balance the forces from the global acceleration, there

should be minimal forces about the restraint.

Figure 29. Fibre Stress in Chassis with Lateral Loads

The forces due to the wishbone loads seem to be fairly well distributed in the

frame. The wishbone and pushrod forces correspond to the expected forces

from the suspension analysis. The stress about the front suspension points is

fairly evenly distributed, mainly within the range of 80-110MPa. The front engine

mounts experience some strong bending stresses up to 130MPa. This bending

force is mainly due to the angle that the supports make with the engine,

cantilevering the beams.

30

4.3.3 Acceleration Case 2003

The maximum acceleration loads of the vehicle are broken into tyre patch forces

(upright forces) at the rear wheels and reactions of the driveline. Again, the tube

across the main roll hoop was an anomaly with highly stressed seat restraint, so

the model was run both with a rigid link and the original member. The maximum

loads experienced in this model were in the forward lower front diffbox bulkhead,

and in the bracing around the driveline. The maximum stress experienced in the

lower diffbox bulkhead was close to 350MPa, with the maximum stresses in the

diffbox bracing of 300Mpa. These are extremely high numbers, and even though

the vehicle competed and survived testing without incident there was

redevelopment for the 2004 design to lower these stresses.

Figure 30. Fibre Stress in rear section of Chassis under Acceleration

31

4.3.4 Torsional Testing 2003

To determine the torsional stiffness of the 2004 chassis, the vehicle is restrained

at the rear tyre patches, one point fixed in three-directions and the other in one,

to allow for displacement across the centerline of the car and to have the same

restraints as the test equipment. The rear two uprights are displaced 9.59mm to

simulate a 1° twist of the chassis. This model is run without any gravitational

forces. The vertical reaction force at the front tyre patches will be used to

determine the moment applied about the centerline of the vehicle.

Figure 31. FEA Torsional Test of 2003 Chassis

θ

θ

Fr

Fr

d

Lt

Figure 32. Schematic of Torsional Stiffness Calculation

7631.29.591

Torque = K

916 / deg

r

t

r t

F NL md mm

F L KK Nm

θθ

θ

==== °

×=

=

32

4.3.5 Rear Lower Engine Mounts

One of the areas of interest in the model is the rear lower engine mount, as they

were initially modeled as rigid links. The torsional test model was remade with an

approximation of the lower engine mounts included. The two lower engine

mounts were each modeled as 2 sections of 30x3mm plate.

Figure 33. Torsional Test of 2003 Chassis with Modeled Lower Engine Mounts

(Global Beam Displacments Shown)

There was no significant difference in the overall torsional stiffness of the chassis,

only dropping to 915Nm/deg, suggesting that the lower engine mounts were

sufficient to not affect the stiffness of the vehicle. When the model is run with

without rear lower engine mounts, the torsional stiffness only drops to

889Nm/deg, suggesting that these are low stressed members. As these

members are heavy the lightening of these will be one of the changes for the

2004 design.

33

Chapter 5

5.0 Experimental testing of 2003 chassis

5.1 Torsional Testing of 2003 vehicle

Figure 34. Torsional Testing of 2003 vehicle

5.1.1 Method

The 2003 vehicle with engine was loaded on the test rig and a moment of up to

1275Nm was applied about the centreline of the vehicle. The torsional stiffness

of the chassis was found after taking into account the deflection of the test rig,

and taking a linear interpolation of the data points. The test was completed four

times, with the deflection recorded in loading and unloading, to check for

irregularities in the data recording. There were only minor deviations between

the loading and unloading data plots, suggesting the test was valid.

5.1.2 Results

This experiment was repeated for consistency and stiffness values for the

torsional stiffness of the chassis were determined from both the unloading and

loading cases. The stiffness of the chassis appeared to be linear. Over all of

these tests, an average of 746Nm/deg was found for the entire vehicle. This is

80% of the torsional stiffness of the finite element model in the same load case.

2003 FSAE Vehicle Torsional Testing

y = 614.03x - 33.248R2 = 0.9902

y = 621.41x + 1211.2R2 = 0.9888

-200

0

200

400

600

800

1000

1200

1400

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

Loading

Unloading

Linear (Loading)

Linear (Unloading)

Figure 35. Plot of Torsional Test of 2003 Chassis

Table 4. Torsional Stiffness Experiments

Loading Nm/deg Unloading Nm/deg

Average

Test 1 638.5 772.4 705.5

Test 2 670.4 661.8 666.1

Test 3 670.4 645.9 658.15

Test 4 755.6 779.4 767.5

Test 5 - 8 769 769 769

Average 746Nm/deg

35

5.2 Measurement of Centre of Gravity

The vertical height of the centre of gravity of a vehicle is required in the tuning of

the suspension of the vehicle, along with the calculations of the mass moments of

inertia. For the 2003 vehicle, the rollover angle of the vehicle dictates the height

of the centre of gravity.

Figure 36. Process for Finding Height of Centre of Gravity of Vehicle

5.2.1 Method

For the 2003 vehicle, the original plan for finding the height of the centre of

gravity was to utilize the swing platform constructed for the mass moment of

inertia testing. As there were some time constraints before the 2003 competition

in Adelaide, an effective temporary method of simulating a rollover situation was

devised. With the suspension members locked with dummy shocks, the car was

tilted until it reached the balance point. As there is a track difference from front to

rear, the rear tyre was spaced with a 50mm offset. The two tyres that the car

was balancing upon were sat in sections of angle to give a smaller balance point.

This also helped to minimize the deflection of the tyre at the balance point.

36

5.2.2 Procedure

To find the angle that the car was balanced at, firstly a plumb was used to find

the horizontal distance from the outside edge of the raised tyre to the pivot point.

This was repeated front and rear of the vehicle, with the angle calculated using

trigonometry. This was repeated with a digital inclinometer on the main roll hoop.

Both methods gave an angle of 66° to the horizontal, which resulted in a height of

centre of gravity of 280mm with a 78kg driver. This value is low, as the expected

centre of gravity from the modeling process was 293mm. The data from this

experiment can be found in Appendix G.

Figure 37. Finding Centre of Gravity of 2003 Vehicle

37

5.2.3 Minimum Requirements for Competition

For the competition there is a similar event where the vehicle is tilted to 57° and

checked for leaks and the likelihood of rollover. This is to simulate the vehicle

taking a 1.5g corner. There has been a rule change for the 2004 competition that

will require a tilt test of 60° to be passed, however this will not affect the design of

future cars designed by this university, as the team aims to keep the centre of

gravity low.

5.2.4 Results

The measured centre of gravity of the vehicle with driver is 13mm lower than the

expected height of centre of gravity from the CAD drawing system. This is an

excellent result from the perspective of the performance of the vehicle; however

this is a significant difference to the expected value. This might be explained by

errors in the modeling and construction process, or possible deflections in the

suspension members may have skewed the measurements.

38

5.3 Calculation of Mass Moments of Inertia

5.3.1 Method

For the experiments in pitch, roll and yaw the 2003 vehicle was sat above the

centre of gravity of the platform, with dummy shocks installed. The centre of

gravity of the vehicle was found from the wheel weights of the vehicle using

scales with accuracy to 0.5kg. The vehicle was tested with both an 82kg driver

and without. For the experiments in yaw, the vehicle was again sat on the centre

of gravity of the platform.

The installation was given a small displacement, and the time taken to swing 30

oscillations was recorded with a stopwatch, with the frequency of the oscillations

calculated from that. This was repeated 4 times for each test, in order to check

for consistency.

Figure 38. Finding Mass Moment of Inertia in Yaw of 2003 vehicle

39

5.3.2 Results

From this it can be seen that the experimental values are all slightly different to

the expected values from Solid Edge, however the data is within the same order

of magnitude as the expected values. (Example data supplied in OptimumG

seminar notes) as can be seen below. If the variations from the calibration of the

test rig are taken into account, the value for the yaw moment of inertia should be

very accurate, with the pitch and roll calculations larger than expected.

Table 5. Examples of Mass Moments of Inertia

Prototype Car kgm2

CAD –empty

car kgm2

Test results – empty car

kgm2

CAD – with

driver kgm2

Test results – with driver

kgm2

Roll 70 31.5 46 36 49

Pitch 290 107 135 127 156

Yaw 450 121 125 144 151

5.3.3 Error and Inaccuracies in Experiments

The length of the chain was made as long as possible, with the intention to keep

the angle of oscillation as small as possible. This will help keep the

approximations made in the calculations close to the actual values.

5.3.3.1 Location of Centre of Gravity

The centre of gravity of the vehicle must be located above the centre of gravity of

the stage for this experiment to work. The centre of gravity of the vehicle was

found using wheel weights, using scales that an accuracy within 0.5kg. There

could be some error in the location of the centre of gravity of the vehicle in the

correct spot on the platform. Small differences in the height of the centre of

gravity of the vehicle had a significant effect on the pitch and roll experiments,

15mm difference in the vertical centre of gravity measurement would affect the

pitch and roll by 7kgm2. Any errors in the measurements of the stage and

equipment will have a significant effect on the final calculations

40

5.3.3.2 Chain Friction

There is excessive friction in the chains that the platform is swung from, which

should be accounted for in the calibration of the equipment. There is significant

decay in the amplitude of the oscillations of the experiment, which is directly

linked to friction at the pivot point. This is definitely a place for improvement for

the design of the test rig, most likely using light cable, preferably with roller

bearings at the pivots.

5.3.3.3 Weight of Rig

The weight of the test rig is definitely an issue in the experiment, and should be

kept as light as possible. A rig weight of 69kg when measuring a vehicle of only

240-360 kg could prove to be a problem. Again, this would be a factor in any

redesign of the equipment, with a lighter platform and cable system.

5.3.3.4 Recording of Period of Oscillations

For the calibration experiments, the time taken for 50 oscillations was recorded,

and this process was repeated four times. For the recordings of the period in

pitch and yaw, a difference of one second over the average recorded period of

160 seconds (0.64%) will cause a difference of approximately 10kgm2 over the

calibration of the test pieces.

The system in pitch and roll is very sensitive to errors in the recorded time; this

can only be improved by increasing the number of recorded oscillations and more

accurate recording methods. The same error in the calculation of yaw

experiments only affected the final value by 1.5kgm2. The strong decay in the

amplitude of the oscillations of the car swing restricted the number of oscillations

that could be confidently recorded.

The only way to verify this process is a repeat of the experiment with a lighter

platform and chain or cable system, with preferably a solid axle on bearings at

the pivot point of the swing. This will minimize the decay of the amplitude of the

swing, and allow the time for more oscillations to be recorded.

41

5.4 Nodal Deflections of 2003 Chassis

To compare the nodal deflections of the chassis in the FEA model to the actual

displacement of the nodes of the chassis. This will help determine which parts of

the vehicle deviate from the model of the chassis. The vehicle was loaded into

the torsional test rig, and the displacements of nodes measured for each of the

load cases.

5.4.1 Method

The chassis was loaded the same as for the torsional stiffness test on the test rig,

with the deflection of the chassis recorded in several locations by dial gauges. At

each of these locations a flat measuring surface perpendicular to the measured

direction was arranged. This was done with flat pieces of aluminum or steel

temporarily but rigidly fixed to the frame. This would minimize errors due to the

surfaces finish of the material, and account for the shape of the member being

measured.

Each measurement was repeated for the both loading and unloading cases,

again checking for validity of the measurement.

42

5.4.2 Locations measured

The locations to measure were chosen on a combination of ease of access to the

node and magnitude or expected displacement, with preference for locations of

large displacement.

Table 6. Locations for Nodal Displacements

Number Description

A1vert: Vertical displacement relative to ground of left fore lower front suspension

pickup

A2hoz Horizontal displacement of left fore upper front suspension pickup

B1vert: Vertical displacement relative to ground of left fore lower rear suspension

pickup

B3hoz: Horizontal Displacement of upper cockpit member and front roll hoop

C1vert: Vertical displacement relative to ground of left main roll hoop base

C1hoz: Horizontal displacement of left main hoop base

C2hoz: Horizontal displacement of left upper SIP and main hoop node

C3hoz: Horizontal displacement of left widest node on main roll hoop

D1vert: Vertical displacement relative to ground of rear left engine cage

E1vert: Vertical displacement of left rear aft engine mount/suspension pickup

E3hoz: Horizontal displacement of the rear rocker mount member

F1vert: Vertical Displacement of aft lower rear suspension pickup

G1vert: Vertical displacement of left front engine mount

G1hoz: Horizontal displacement of left front engine mount

H1vert: Vertical displacement of left rear upright

J1hoz: Horizontal displacement of right fore upper rear suspension pickup and

centre of fore lower rear pickup beam (SHS)

K1vert Vertical displacement of rear engine mount, (Engine end (front))

43

Figure 39. Locations for Nodal Displacements

5.4.3 Results

Table 7. Results for Nodal Displacements

Location

FEA displacement (mm/deg) - twist

of chassis Experimental Set 1

(mm/deg)

Experimental Set 2

(mm/deg)

Average Displacement

(mm/deg) %

of FEA

A1vert(mm) 0.25 0.14 0.156 0.148 59.20

A2Hoz(mm) 0.27 0.78 N/A 0.78 288.89

B1vert(mm) 0.5 0.31 0.33 0.32 64.00

B3Hoz(mm) 0.68 0.93 N/A 0.93 136.76

C1vert(mm) 4.12 1.89 2.09 1.99 48.30

C1Hoz(mm) 0.89 0.3 0.284 0.292 32.81

C2Hoz(mm) 4.41 1.7 1.9 1.8 40.82

C3Hoz(mm) 8.66 2.88 3.706 3.293 38.03

D1vert(mm) 4.38 2.57 3 2.785 63.58

E1vert(mm) 0.44 N/A 0.075 0.075 17.05

E3Hoz(mm) 2.01 0.67 0.9 0.785 39.05

F1vert(mm) 1.01 0.59 N/A 0.59 58.42

G1vert(mm) 3.3 1.45 1.47 1.46 44.24

G1Hoz(mm) 4.2 2.78 1.16 1.97 46.90

H1vert(mm) 9.59 5.5 6.04 5.77 60.17

K1vert(mm) 1.1 0.32 0.4 0.36 32.72

44

This data seems to be loosely equating to 35-60% of the expected displacement

in FEA. The closest correlations are in the vertical displacements on the bottom

members of the chassis along the length of the chassis.

There are several recordings that are significantly different from the expected

results in FEA, almost 300% difference in the experimental values. These

extreme measurements deviate significantly from the norm, and will be treated as

errors in measurement.

Figure 40. Comparison of Nodal Displacements to FEA

When the relative displacement compared to the FEA predictions are shown on a

diagram of the chassis, there is some consistency in the deflections. The

majority of the vertical displacements correspond to 60% of the expected FEA

per degree of test rig twist, with the horizontal displacements only deflecting 40%.

This either suggests that the chassis is nearly twice as stiff as the FEA suggests,

that there is excessive deflection in the test rig or the approximation of the

suspension, engine mounts and other peripheries is inaccurate. When the

displacement of the upright is used to determine the actual twist of the chassis

compared to the test rig, using trigonometry,

45

Vertical displacement of rear

hub per deg rig twist =

6mm

Rear track = 1150mm

Angle of rotation per deg twist = 0.6°

This suggests that the actual twist of the chassis at the rear uprights is 60% of

the rotation of the test rig. This doesn’t correspond to the initial calibration of the

test rig, but using this approximation the majority of the measured locations

match the expected displacements from FEA. To investigate this further, some

experiments with strain gauges were conducted to find the stresses in the

members under torsional loads.

46

5.5 Strain Gauge Correlation of the 2003 Chassis Modeling

As the 2003 vehicle had been disassembled and cannibalized for the 2004

vehicle since the competition in Adelaide, the only further feasible testing

available for the 2003 chassis is on the torsional test rig. To verify the FEA

process, the strain gauges will measure the strain of members of the chassis

compared to the expected strain in the model under similar conditions.

5.5.1 Gauge Selection

The strain gauges selected for this testing were CEA-06-250UT-350 gauges,

primarily chosen for their ease of use (they are a relatively large gauge). These

are dual gauges, with the second gauge aligned perpendicular to the first. The

University workshop is also familiar with these gauges, and was able to offer

support and instruction in the mounting and wiring of the gauges. The gauges

were wired in a Wheatstone bridge circuit, which allowed for temperature

compensation in the axial gauges and tensile force compensation in the bending

gauges. The two resistors used to complete the Wheatstone bridge were 390Ω,

matched within 1ppm temperature variance. This would minimize any errors

generated by the temperature variations between experiments.

Rg

Rg R1

R2

Vsource

Vm + -

+

-

Figure 41. Wheatsone Bridge for Strain Gauge Wiring

47

5.5.2 Strain Gauge Setup

The surface preparation for the strain gauges is a critical process in the

experiment. The surface must be cleaned of all paint, rust and any impurities,

and should ideally not be grit-blasted. The surface is then sanded with 320 to

400-grit paper, finishing with the sanding perpendicular to the intended

measurement of strain. The surface is then cleaned with a solution of phosphoric

acid, and then neutralized with a mild alkaline solution. The gauge is aligned

along the intended axis with tape, before being bonded with a fast curing glue.

The gauge is then soldered into the circuit shown above; with care taken to not

overheat the gauges. The maximum working temperature of these gauges is

275°C, however the glue used to attach to the chassis is only rated to 65°C. The

circuit is then coated in a resin to help protect the gauge and wiring from

mechanical and environmental damage.

5.5.3 Equipment

The voltage change measured at Vm is amplified through an analogue signal

processor with a variable gain. The output voltage can be adjusted with a rotary

potentiometer to be ‘zero’ at a set voltage before each experiment. The team has

built a custom data logger to record the data, however the data acquisition

program is still under development, requiring the data to be manually recorded.

The resistance of the lengths of the leads within the bridge itself was assumed to

have a negligible effect on the system, as they were kept short and with a high

quality, low resistance cable.

48

5.5.4 Strain Gauge Theory

The data collected from the strain gauges is a change in voltage; this is

converted to a strain of the gauge through

2 1 For Bending

-4= (1[(1 ) 2 ( 1)]

and

lr

g

lr

r

m mr

source sourcestrained unstrained

RVGF R

RVGF v V v Rg

V VVV V

ε

ε

−= +

++ − −

= −

) For Axial

m

source

g

l

With:Poisson's Ratio

GF = Gauge FactorV = Measured voltage

V = Applied VoltageR = Gauge resistance

R = Lead resistanceε = Strain

v =

0

0

axial

bending

This simplifies to 4 . .

with

With BF = Bending Factor,BF 1.3

BF 2.0

source

m strained

e GF BFV

V VeGain

ε =

−=

==

49

This strain can be related to an axial or bending stress, through Young’s

Modulus, where = stressE= Young's Modulus

Eσ εσ

=

5.5.5 Calibration of Strain Gauge Amplifier

To confirm the gain of the amplifier, a known dimensioned test piece with a pair

of transverse single gauges was loaded axially and the strain gauge data

collected. The test piece used was a wishbone from the 2002 vehicle; all the

forces experienced by this piece will be purely axial. The gain on the amplifier to

be verified was set at 1000.

Table 8. Calibration of Strain Gauge Amplifier

Weight (kg) 56

Force (N) 549.4

Area (mm2) 107.3

Stress (MPa) 5.1

GF 2.09

BF 1.3

Gain 1000

Vsource 10

Vm 2.66

V0 2.5

e0 -0.00016

Strain -2.5E-05

Stress (MPa) -4.98

50

5.5.6 Selection of Gauge locations

The strain gauges can be used to measure the tensional and bending forces in

the members of the chassis. The first choice of strain gauge location is in

members that are axially loaded, with minimal bending forces. There are not

many members in the 2003 chassis that experience pure axial loading, however

some of the frame members do experience single plane bending in a torsional

loading situation. The axial loaded strain gauges were located at the point of

minimum bending stress, on a single side of the tube. For the gauges in bending,

a gauge was placed on either side of the member under investigation

5.5.7 Expected stress in Gauge Locations

The expected stress at each of these points was found by inspection of the FEA

model.

5.5.7.1 Strain Gauge Location 1

In the centre of the member between the lower fore suspension pickup points at

45° to the vertical there is only axial stress. Expected axial stress per degree of

rotation of chassis = 58Mpa

5.5.7.2 Strain Gauge Location 2

At 445mm from the front roll hoop along the bracing member of the side impact

protection there is minimal bending stress compared to the axial stress.

Expected axial stress per degree of rotation of chassis = 36Mpa

5.5.7.3 Strain Gauge Location 3

One of the maximum bending forces observed in the FEA and initial testing was

in the members running alongside the driver and above the side impact

protection. There is negligible axial force in this location. This is Location 3, at

40mm from the end of the beam. Expected bending stress per degree of rotation

of chassis =145Mpa

51

Figure 42. Strain Gauge Locations for 2003 Testing

Figure 43. Axial Stresses In Torsional Testing

Figure 44. Bending Stresses in Torsional Testing

52

5.5.8 Method

The 2003 vehicle was loaded into the test rig as per the test for torsional

stiffness. The moment arm was loaded incrementally with the strain gauge

readings taken manually at each addition of weight to the moment arm. The

gauge readings were also recorded for the unloading cases to validate the

experiment. Each experiment was repeated to ensure consistency.

5.5.9 Results

A linear response was recorded from all of the strain gauges, with strong

consistency between the repeated experiments. The data plots for the strain

gauges can be found in Appendix E. (In the manipulations of this data, it is

assumed that for small angles of rotation sinθ =θ). Assuming the rig stiffness is

8509Nm/deg, for an applied moment of 746Nm, the rig will account for 9% of the

measured rotation. This is used to find the actual rotation of the chassis.

Table 9. Results of 2003 Strain Gauge Testing

Experimental Stress

MPa/deg rig twist

Experimental Stress*

MPa/deg chassis twist

FEA Stress

MPa/degchassis

twist

% of expected

values from FEA

% of expected

MPa/deg**

Gauge 1, Axial

27.1 29.9 58 52% 78%

Gauge 2, Axial

15.3 16.9 36 47% 71%

Gauge 2, Bending

87.1 94.6 145 66% 100%

*assuming rig accounts for 9% deflection

**assuming 60% difference between rig and chassis rotation

53

These values are all approximately half of the expected values from FEA. There

is some correlation between the relative magnitudes of the three measured stress

values and the expected value. However, if the rotation of the rear uprights is

only 60% of the rotation of the test rig (from the dial gauge testing results), the

axial stress of location 1 and 2 are both 71-78% of the expected FEA result, with

the bending case at 100% of the expected stress. This seems to be a

reasonable value when compared to the nodal displacements.

The axially loaded members may be experiencing slightly different stresses than

the FEA suggests, as they are experiencing a combination of bending and axial

forces that could be affecting the gauge output. The strain gauge in bending

however is loaded in almost pure bending, which should result in fairly strong

correlation between the calculated and expected stresses.

54

5.6 2003 Wet Testing

The inherent problem of a spool differential driven vehicle such as the 2003

design is that the vehicle will understeer and ‘plow’ into a corner if there isn’t

sufficient weight transfer at the rear of the vehicle. The 2003 vehicle suspension

is designed to unload the inside rear wheel during a corner, giving the outside

wheel full contact. This will allow the outside wheel to maintain full traction and

torque transmission to the ground, with the inside wheel slipping to complete the

turn. This works very similarly to a go-kart suspension.

In normal conditions, the roll stiffness ratio from front to rear dictates this weight

transfer, and for this vehicle it was set at 55/45 front/rear, which worked well.

In wet conditions, for vehicles with a spool differential, the roll stiffness ratio

should be changed, with the rear roll stiffness increased in respect to the front, to

perhaps 53/47 or 52/48. This will tend to make the vehicle oversteer in corners,

which from a racing perspective is a preferable situation than understeer.

The 2003 vehicle was subjected to ‘wet testing’ at Willowbank raceway in March

2004, as an experiment for the suspension team. This was tested on wet

bitumen, on the same track that all the previous testing had been done. During

all this testing the vehicle would not oversteer until the roll stiffness ratio was set

to at least 46/54 f/r, which is a significant change from the original 55/45. The

theory put forward by the suspension team is that the chassis is acting as a

spring, and that the roll stiffness ratio is dictated by the weight distribution of the

car, which is 55/45. This was the first sign that the torsional compliance may be

affecting the handling of the vehicle. When the 2004 car is complete, the

suspension team will be able to determine if increased stiffness of the chassis

affects the tuning, as the suspension and layout of the 2 cars is very similar.

55

5.7 2003 Competition

Prior to the competition at Talem Bend in South Australia in 2003, the vehicle

was stripped and all the components cleaned, polished and painted, including the

chassis. After the re-assembly of the chassis, the engine did not sit in the same

location, whether this was due to the thickness of the paint, or the engine mounts

had been shifted or bent. This resulted in the gearshift selector clashing with the

chassis, restricting the gear changes. This problem went unnoticed during

testing until the first day of the competition, when the gearbox began ‘falling out’

of gear. This was strongly linked to the clash of the gear selector with the

chassis.

During the static events at the competition the judges were impressed with the

design of the diff-box section of the chassis; however there were comments

about the front suspension mount geometry, and the load lines through the

cockpit from the engine bay. Overall, there was no particular criticism from the

design judges, and the vehicle came 4th in design and third overall in the

competition.

Figure 45. UQ FSAE at 2003 FSAE-A Competition

56

Chapter 6

6.0 Design Objective of 2004 Chassis

6.1 Lessons learnt from 2003 Design

The 2003 chassis was a significant improvement over the 2002 chassis, with

some obvious design improvements, however there were some major design

flaws.

6.1.1 Suspension mounting

The orientation of the front suspension was not finalized before the chassis was

completed, which led to severe packaging issues. The need to construct rocker

mounts away from the main body of the chassis resulted in extra weight and

improperly loaded members, which possibly resulted in some yielding of the

chassis either in testing or at the competition. See Section 3.5 for front

suspension geometry.

6.1.2 Driver compartment

The most compliant section of the chassis in the 2003 vehicle was the driver

compartment. This part of the chassis is prone to flexing, as the requirement

that a driver can easily egress the vehicle requires a large open section of the

frame. The 2003 chassis did not adequately accommodate for this problem,

resulting in a very flexible centre of the vehicle. Lack of triangulation in three

dimensions was the major cause of compliancy.

6.1.3 Packaging issues

The position of the battery was not accounted for in the design of the vehicle,

resulting in the battery being placed on the top of the diffbox. However, this

turned into an advantage for the team, as the electrical section of the vehicle

required frequent access to the battery for modifications and testing.

The radiators were kept outboard of the major structure of the chassis, and were

integrated into the side pods. The design of the driver's cockpit made the

construction and location of side pods a simple process.

6.1.4 Location of Rear Sprocket and Disk

Running the main gear and rear disk outside the body of the chassis – very good

from the view of the driveline section of the team. This allowed for easy access

to the main bearings, axles, spool and CV joints, and allowed the chassis to save

weight by having a smaller profile in that section. However this generated some

issues in the location of the rear suspension. Again, this was caused by the

suspension not being finalized before the construction of the chassis, but the

solution taken to mount the shock absorbers off the upper engine mounts was

neat and efficient. A slightly modified suspension layout to this will be used in

the 2004 vehicle.

6.1.5 Engine Mounts

For the 2003 vehicle, the engine was a structural member of the chassis, with

the framework surrounding the engine mainly used to locate the rear diffbox. For

the 2004 chassis, the framework allows for easy access to the engine, with the

members there for torsional stiffness. The engine will account for approximately

half of the stiffness of the rear section. Due to the rear suspension location, a

custom rear engine bolt and shock absorber mount had to be manufactured.

This was a 10mm bolt to support the engine, turned down to a 6mm bolt to

mount the shock absorber. This meant that the torque applicable to an M6 fine

thread restricted the torque on the M10 course rear engine bolts. This restricted

the possible joint stiffness at this node.

58

6.2 Design improvements of 2004 chassis

There are some significant design improvements for the 2004 chassis over the

2003 design.

6.2.1 Material Change for Minimum Requirements

Increasing the outer diameter of the main roll hoop, front roll hoop and side

impact protection tubes to 11/8“. The wall thickness of the main hoops and SIP

can be reduced with this increased outer diameter, the equivalency submitted for

the 2004 formula student competition can be found in Appendix B. The other

advantage of this section tubing is that 300g is saved in weight as compared to

using the baseline steel section.

6.2.2 Cockpit Design

Significant changes had to be made to the cockpit design to increase the

torsional stiffness in driver compartment, this included the inclination of the front

roll hoop, widening of the base of the front and main hoops, and addition of a

cross member from the front to rear roll hoops. These changes had a huge

effect on the stiffness of the vehicle. For example, the cross-member from the

front to rear hoops adds 400Nm/deg of stiffness alone, based on FEA in

Strand7. The cockpit design also allows for more cockpit space and driver

comfort, helping in the drivability of the vehicle. One of the options considered

for the 2004 designs was bracing from near the top of main roll hoop to the front

roll hoop. This would increase the torsional stiffness of the chassis by

approximately 400-500Nm/deg, but there are some concerns about visibility and

driver egress. This geometry has been used in many of the successful Georgia

Institute of Technology chassis designs.

59

Figure 46. 2001-2002 Georgia Institute of Technology

6.2.3 Engine Mounts

As the engine is a significant structural member of the chassis, the need for joint

stiffness at the engine mounts is important. To overcome the suspension

mounting problems of 2003, heli-coil inserts were fitted to the rear upper engine

mounts, with the rear engine bolts threading directly into the engine. The shock

absorber location at the engine is then mounted in a supported cantilever

fashion, effectively in double shear. The use of 4mm steel plate as the engine

mount between the chassis and the frame, with inserts welded into the tube

sections of the diffbox allow for much simpler engine removal and replacement.

6.2.4 Diffbox design

Slightly modified diffbox design to allow for better battery positioning, with the

battery and overflow tanks kept within the diffbox itself. The battery has been

lowered, and is now suspended under the diffbox, helping to lower the centre of

gravity. The rear geometry and pickup points were slightly modified for the 2004

suspension, mainly affecting the roll centres of the vehicle.

60

6.2.5 General Chassis Improvements

There is a dramatic reduction in weight due to the use of ‘matchstick’ tubing (5/8”

OD, 0.9mm NWT) in all non-critical and bracing members. To keep the

construction as easy as possible, the majority of tubes had a minimum wall

thickness of 0.9mm, this was mainly for ease of welding. (Two members of

0.7mm wall tubing). There are fewer joints, with less welding and simpler

geometry. There is a significant reduction of number of frame members at each

joint.

6.2.6 Finalize Design before Construction

This is possibly one of the most important factors in the current success of the

construction of the 2004 vehicle. With the suspension design finalized before

the construction of chassis serious construction, packaging and logic issues

were avoided.

6.2.7 Material Selection 2004

The material used in 2004 is High Tensile 4130 Chrome-Molybdenum steel; with

both ER80S-2 and ER70S-6 weld filler rods. The tube sizes chosen for 2004 are

thinner wall sections than 2003, (including wishbones)

OD (mm) x NWT x total length used

• 28.6 x 2.11mm x 4m

• 28.6 x 1.25mm x 2.5m

• 25.4 x 0.9mm x 3.3m

• 25.4 x 0.7mm x 3.2m

• 19.05 x 0.9mm x 2.6m

• 15.9 x 0.9mm x 8.6m

• 19.05 SHS x 0.9mm x 1.1m

• 25.4 SHS x 1.25mm x 1.6m

• 25.4 SHS x 0.9mm x 3.3m

61

6.3 Construction Process 2004

As the UQ racing team is planning on competing in the 2004 Formula Student

competition in the UK in July, The new vehicle would have to be constructed in 3

months. The chassis needed to be built quickly and accurately, without the

issues faced in 2003.

6.3.1 Modular design

The chassis was built in separate sections, using an 8mm steel plate for a jig.

The plate was pre-drilled allowing for the jigging of bulkheads in plane, and for

the final assembly. As the chassis and suspension is designed with tolerances

in millimeters, it was critical that there was minimal weld distortion during

welding. Minor distortions of the welds can be rectified through ‘tube

manipulation’ with an oxy-acetylene torch; however the thin walled tubing used

does not handle this process as well as the thicker sections.

Figure 47. Jigs for 2004 Construction

62

Each section was then aligned and bolted to a seismic block, ready for welding.

The frame was welded around the engine, and the chassis was complete.

The increased use of SHS tubing for the chassis members is a definite bonus for

the manufacturing of the chassis. The SHS tubing allowed for much faster

construction of the chassis, with the attachment of peripheral components (pedal

box area, driveline, shock absorbers) a much simpler and accurate process.

6.3.2 Bodywork 2004

At the time of this writing the bodywork had not been completed, however due to

time and access to the chassis restraints, the bodywork would have to be made

without using the chassis as a mould. This is significant challenge for the

bodywork section of the team, however it is not in the scope of this study.

6.3.3 Non-Destructive Crack testing of 2004 chassis

The team again completed a full NDT of the 2004 chassis after completion of the

welding of sections and of the final chassis. There were very few welds that

needed serious attention, suggesting that the overall weld quality was high. The

crack testing of each of the sections was a much simpler process than the 2003

chassis, with the sections easier to test in pieces than all together.

Figure 48. Non-Destructive Testing of 2004 Chassis – Diffbox

63

Chapter 7

7.0 Numerical Analysis of 2004 Chassis

7.1 2004 FEA Model

The 2004 vehicle was modeled the same as the 2003 in Strand7, in order to

maintain consistency

7.2 2004 Load Cases

The method for finding the vehicle load cases for 2004 are identical to the

method for 2003, with the minor differences in the longer wheelbase, lighter

vehicle and smaller track.

7.2.1 Braking Case 2004

Assuming that the maximum braking force of the vehicle is 1.1g, the maximum

forces in the vehicle will be found about the front uprights. The assumptions used

by the suspension section of the team are

Table 10. 2004 Braking Load Case Parameters

Height of centre of gravity, Hc = 0.293m

Weight distribution Front:Rear= 52:48

Distance from front axle to CoG Lf = 0.756m

Wheelbase Lt = 1.575

Max deceleration ac= 1.1g

Tyre Coefficient of friction u = 1.1

Mass of vehicle + driver, mc= 312kg

Gravity g= 9.81m/s2

Vrear= 843N

Vfront = 2217N

Hfront = 2439N

These forces will be evenly split left and right for the front and rear wheels

7.2.2 Lateral Load Case 2004

Maximum sustained lateral acceleration expected from the 2004 vehicle is 1.32G

Table 11. 2004 Lateral Load Case Parameters

Height of centre of gravity, Hc = 0.293m

Track front Tf = 1.15m

Track rear Tr= 1.1m

Max lateral cornering rate al = 1.32g

Weight Split Front:Rear 52:48

Mass of 2004 vehicle + driver mc= 312kg

Gravity g = 9.81m/s2

For the front section of the vehicle,

1329

260

1754

ofront

front

ofront

V N

Vi N

H N

=

=

=

7.2.3 Accelerating Case 2004

The maximum acceleration expected from the vehicle is 0.9g, which is what the

driveline section of the FSAE team is expecting to produce. This is restricted by

the coefficient of friction between the tyre and the track. These calculations are

similar to the 2003 calculations.

27551981

r

r

H NV N

==

These forces are evenly split between the two rear wheels.

This acceleration corresponds to a torque transfer from the axle to the ground

through a tyre of radius 0.263mm, resulting in a moment about the rear axle of

725Nm. This torque is reacted in the chain tension and the bearing hangers.

The rear sprocket has a 230mm diameter, which results in a chain tension of

65

6.3kN. The chain angle from rear sprocket to the main gear is 35.5°. It is

assumed that the chain forces act directly through the bearing hangers, as the

rear sprocket is bolted directly to the bearing shaft.

Schematic of rear sprocket

θ

Va

HaTc

TH TV

Using statics,

00

sincos

36615132

a V

a H

V c

H c

a

a

V TH T

T TT TV NH N

θθ

+ =+ =

=== −=

The chain force is then reacted at the main gear, with a diameter of 70mm,

resulting in a torque reduction of 3.2. The reaction forces in the horizontal and

vertical directions are the same at the main gear as at the sprocket, with a

moment of 227Nm about the engine output shaft.

66

7.3 Finite Element Analysis of 2004 Chassis

7.3.1 Braking Case 2004

As the maximum braking force in the vehicle is found about the front uprights, this

will be the section of the vehicle that is under investigation. The entire weighted

model is subjected to a global acceleration of 1.1g in the braking direction, along

with the vertical acceleration of gravity. The tyre patch loads from the load case

are then applied to the tyre patch in the model. The vehicle is then restrained

about the rear tyre patch to prevent the model acting as a mechanism. This

should balance the forces in the chassis, and result in only minimum reaction

forces about the restraints, minimizing artificial stiffness.

Figure 49. Fibre Stress in 2004 Chassis Under Braking

There are some difficulties with the restraint of the driver mass, as the members

for the seatbelt mounts have not been finalized, however it will be fixed to a

structural part of the vehicle. There was a peak in stress at the driver mount on

the beam within the main roll hoop; however the model was run with a rigid link

as a replacement without change to the stresses in the members around the front

suspension. From inspection of the members about the front suspension, the

67

maximum fibre stress found was 152Mpa, which was found on the support for the

front rockers. This was a bending force, and found at the joint at the base of the

rocker mount. The majority of the loads found on the chassis were in bending,

with only small axial loads in most of the frame members.

Figure 50. Axial Stress in 2004 Chassis under Braking

Figure 51. Bending Stresses in 2004 Chassis under Braking

68

7.3.2 Lateral Load Case 2004

The maximum forces experienced by the vehicle in a cornering situation are

found on the tyres on the outside of the corner. For this modeling, the vehicle is

subjected to a global acceleration of 1.32g across the vehicle along with a vertical

acceleration due the gravity. The tyre patch loads from the load case are applied

to the 4 uprights, and the model is restrained on the front bulkhead. The reason

for the single restraint about the bulkhead is that as the tyre patch forces should

balance the forces from the global acceleration, there should be minimal loads

about the restraint.

Figure 52. Fibre Stress from Lateral Load Case 2004

The highest loads found in this load case are the restraints of the driver. These

are localized stresses, which reach a maximum fibre stress of 220Mpa. The

actual restraints for the driver have not been finalized, but the expected mounts

will be distributed along the side impact protection members. This will minimize

the localized stress, as these members have substantial wall thickness. The

forces due to the wishbone loads seem to be well distributed in the frame. The

wishbone and pushrod forces correspond to the expected forces from the

suspension analysis. The stress about the suspension points is in the range of

69

50-75Mpa, with the maximum stress found in the aft SHS member between the

upper and lower pickup points. The maximum peak stress is at the rear of the

vehicle at the tube supporting the lower engine mount and turnbuckle for the

driveline. This gives a maximum bending stress of 100Mpa.

Figure 53. Fibre Stresses in Rear Section Under Lateral Load

70

7.3.3 Acceleration Case 2004

The maximum acceleration loads of the vehicle are broken into tyre patch forces

(upright forces) at the rear wheels and reactions of the driveline. Again, the tube

across the main roll hoop was an anomaly with highly stressed seat restraint, so

the model was run both with a rigid link and the original member. The maximum

loads experienced in this model were in the forward upper engine mount brace,

and in the bracing around the driveline. The maximum stress experienced in the

upper engine mount brace was 100Mpa, with the maximum stresses in the

diffbox bracing of 160Mpa.

Figure 54. Fibre Stress in 2004 Rear Section Under Acceleration Load Case

71

7.3.3.1 Change in Turnbuckle Location

There was a recent change to the geometry of the rear axle, with the mounting

for the bearing hanger turnbuckle being shifted to the lower part of the diffbox

bracing. This was due to loading concerns from the driveline section of the team.

This change has highly stressed the diffbox section, with a maximum stress of

233Mpa near the rear upper engine mount, with 265Mpa at the turnbuckle mount.

This is not a favorable situation, but over the short life of these vehicles there

should not be too many complications.

Figure 55. Fibre Stresses in Rear Section with Alternate Driveline Support

72

7.3.4 Torsional Testing 2004

To determine the torsional stiffness of the 2004 chassis, the vehicle is restrained

at the rear tyre patches, one point fixed in 3-directions and the other in 2, to allow

for displacement across the centerline of the car. The front two uprights are

displaced 10.04mm to simulate a 1° twist of the chassis. This model is run

without any gravitational forces. The reaction force at the front tyre patches will

be used to determine the moment applied about the centerline of the vehicle.

This is the same technique as for the 2003 model.

Figure 56. Torsional Testing of 2004 Model

The vertical reaction force at the front uprights was 2727N,

27271.1510.41

Torque = K

3136 / deg

r

t

r t

F NL md mm

F L KK Nm

θθ

θ

==== °

×=

=

73

7.3.5 Suspension Pickup Forces 2004

The suspension pickup points of the 2004 chassis are constructed out of 25.4mm

SHS x 0.9mm NWT. This is a reduction of 0.85mm in wall thickness since 2003.

The verification that these mounts will withstand the wishbone forces, FEA of a

model of the pickup point was done in Cosmos, an FEA program that integrates

well with Solid Edge. The maximum wishbone force found in Strand7 was

4200N, on a suspension pickup point that extended 30mm from the structure of

the chassis. The wishbone ends are rod ends fixed to 6.35mm bolts through the

tube. There are steel locators/spacers either side of the rod ends that will resist

deflection of the tube inwards, along with the compression of the nut and bolt.

Figure 57. Von Mises Stress in Suspension Pickup Points

This model restrained one end of the tube to simulate a rigid chassis mount, and

applied a 4200N pullout force in the direction of the wishbone evenly divided

between the boltholes. The maximum Von Mises stress expected is 294Mpa,

which is 45% of the nominal yield strength of the material. This is a large stress

at a worse case scenario, but for the short working life of these vehicles this

loading should not be an issue.

74

7.3.6 Rear Engine Mounts

The design of the rear engine mounts for 2004 are slightly different than the 2003

design, using 4mm plates to support the engine. To investigate the forces in

these mounts, the forces at the lower engine mounts in the torsional test of the

FEA model of the 2004 chassis were used in a Cosmos model of the mount. The

rear boltholes were restrained in the model as on the chassis.

Figure 58. Global Displacement of Rear Lower Engine Mounts

Figure 59. Global Displacement of Upper Engine Mounts

75

These appear to be large deflections for these components, suggesting that there

are significant forces in the lower engine mounts, with up to 5mm deflection of the

lower mounts, and 2mm in the upper. The model is not quite accurate, as the

face of the bolthole to the engine is flush against the engine block, adding to the

joint stiffness.

However, when the vehicle was loaded in the torsion test rig, there was no visible

deflection of that magnitude seen at the engine mounts, suggesting that perhaps

there are more factors involved. The stresses and deflections of the mounts do

correspond to the forces that are applied, with the forces taken from the end

forces of the engine mounts in the FEA model.

The model was run without the lower engine mounts, to investigate what effect

they had on the torsional stiffness. Without the rear lower engine mounts, the

torsional stiffness of the chassis is reduced by 300Nm/deg, down to

2803Nm/deg. This suggests that the maximum loss of torsional stiffness due the

engine mounts could possibly be is 10%.

76

Chapter 8

8.0 Experimental Testing of the 2004 chassis

8.1 Torsional Testing of 2004 vehicle

The torsional testing of the 2004 vehicle was conducted in the same manner as

the testing of the 2003 vehicle, with the vehicle restrained at the uprights and a

moment applied about the centerline of the vehicle.

Figure 60. Torsional Testing of 2004 Chassis

2004 Vehicle Torsional Testing

y = 1554.2x + 23.678R2 = 0.9981

y = 1596.1x + 889.55R2 = 0.9972

-200

0

200

400

600

800

1000

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

Loading

Unloading

Linear (Loading)

Linear (Unloading)

Figure 61. Plot of Torsional Testing of 2004 Chassis

Again, the data was recorded and repeated in unloading and loading, with a

value for the torsional stiffness found to be 2000Nm/deg, accounting for the

deflection of the test rig. This is 64% of the expected torsional stiffness from the

computer modeling of the chassis at 3130 Nm/deg. This is a significant

difference to the 2003 chassis testing, which was 80% of the expected stiffness.

78

As the 2004 vehicle was under construction for the UK competition, there were

some difficulties in the access to the vehicle for further testing before the

submission of this thesis. Ideally these experiments should be completed upon

the team’s triumphant return from the Formula Student competition in July 2004.

8.2 Strain Gauge Testing of 2004 Chassis

The intended strain gauge testing of the 2004 chassis was to find a correlation

between the dynamic forces approximated in the modeling and the actual forces

experienced in the chassis.

8.2.1 Strain Gauge Location 1

The SHS member between the front lower suspension pickup points. This will

measure the axial strain, which should correspond to a maximum stress of

30Mpa under 1.1G braking.

8.2.2 Strain Gauge Location 2

The member running from the base of the main roll hoop to the lower rear

suspension pickup at the rear of the vehicle. This should experience up to

33MPa of axial stress in a steady state corner.

8.2.3 Strain Gauge Location 3

The SHS member forming the top of the diffbox supporting the rear sprocket.

This will be to measure the bending forces in the member under full acceleration.

Depending on the accessibility to the location for fixing the gauges, the expected

stress should be around 100MPa in bending.

Figure 62. Strain Gauge Locations for 2004 Chassis

Figure 63. Axial Stresses Under Braking

80

Figure 64. Axial Stresses in 2004 Chassis Under Lateral Forces

Figure 65. Bending Stresses under Acceleration

81

8.3 Dynamic Testing of 2004 Vehicle

The feedback from the test drivers of the 2004 vehicle after the initial dynamic

testing suggests that the vehicle is more responsive, with more feel from what the

car is doing. The drivers feel that they have more feel of what the suspension is

doing. Whether this will make the tuning of the vehicle easier is yet to be seen,

as the initial driving suggests that the spring rates are too high, causing

excessive oversteer and unpredictable front weight transfer. In dynamic testing,

the vehicle is responding more to suspension tuning than the 2003 design, which

suggests that the chassis is stable and sufficiently rigid.

Figure 66. 2004 Vehicle under Initial Dynamic Testing

82

8.4 Driveline Testing of 2004 Vehicle

A concurrent project running at the same time as this thesis was an analysis of

the 2003 and 2004 driveline. Part of the testing of this project was strain gauge

testing of the 2004 driveline under dynamic conditions.

8.4.1 Method

Strain gauges to measure the torque in the 2004 driveline were attached to the

spool differential and the half-shafts. The voltage change measured by the strain

gauges was transmitted via a radio transmitter fixed to the driveline. This data

was then amplified through signal amplifier, and collected in the University of

Queensland’s custom data acquisition hardware. (ref. Myers, 2004)

8.4.2 Results

The primary load case for analysis was the stress under acceleration, with the

maximum driveline torque found to be 450Nm at the spool differential. This is

significantly less than the expected driveline torque calculated in the FEA load

cases of 835Nm. The experiments were completed without traction control, and

with worn drive tyres that would have affected the maximum acceleration

possible. From this initial result it appears that the assumptions made in the load

cases on the chassis under acceleration are conservative, but this can only be

confirmed by further testing.

83

Chapter 9

9.0 Conclusions from Experimental Testing

From the torsional testing of the chassis, without taking into considerations the

nodal deflections of the chassis, the actual torsional stiffness of the chassis was

80% of the FEA for the 2003 design, and 63% of the FEA of the 2004 design.

This difference between the two designs could be due to differences in the

suspension systems, uprights, wheel hubs, and the rockers of the two vehicles.

The vehicles were modeled the same way in the finite element program, so there

shouldn’t be too many differences from the FEA techniques.

Assuming that the torsional test rig has an effective torsional stiffness of

8510Nm/deg, this will correspond to 9% of a 1 deg twist of the rig with the 2003

chassis. This is not taking the dial gauge results into account. This gives stress

from the gauges that correspond to approximately half of the expected stress

from the FEA results.

Table 12. Analysis of 2003 Data, with Initial Rig Calibration

Experimental Stress

(MPa/deg rig twist))

Experimental Stress*

(MPa/deg chassis twist)

FEA Stress (MPa/deg chassis twist)

% difference from FEA Stress*

Gauge 1, Axial 27.1 29.9 58 52%

Gauge 2, Axial 15.3 16.9 36 47%

Gauge 2 Bending 87.1 94.6 145 66%

*Assuming rig accounts for 9% deflection

If the dial gauge experiments suggesting that the torsional test rig accounts for

40% of the deflection for 1°rotation of the test rig, the stresses in the chassis

correspond fairly well with the stresses expected in the FEA.

Table 13. Analysis of Testing Data, Including Dial Gauge Results

Experimental Stress

(MPa/deg rig twist))

Experimental Stress**

(MPa/deg chassis twist)

FEA Stress(MPa/deg chassis twist)

% of expected stress**

MPa/deg values from FEA

Gauge 1, Axial

27.1 49.8 58 78%

Gauge 2, Axial

15.3 25.5 36 71%

Gauge 2, Bending

87.1 145.1 145 100%

**Assuming 60% difference between rig and chassis rotation

However, comparing the recorded strain gauge data to the expected stresses

associated with the applied moment finds substantially less stress in the chassis

than expected.

Table 14. Analysis of Testing Data for 2003, Applied Moment and Recorded Stress

FEA Stress/applied

moment MPa/Nm

Experimental stress/applied

moment MPa/Nm

% of expected MPa/Nm values

from FEA

Gauge Location 1

0.0634 0.0408 64%

Gauge Location 2

0.0393 0.024 61%

Gauge Location 3

0.1583 0.129 81%

85

This data suggests that the stiffness of the chassis is greater than the FEA

model. This is not an unusual situation, as in a welded structure such as this; the

effective lengths of all of the beam members are shorter than in the FEA model.

In the FEA model, the beam member runs to the node, whereas in the actual

chassis the beam doesn’t reach the node, and welded joint is effectively stiffer in

reality. The FEA model can be modified to represent this, using rigid links at the

nodes, the lengths of which are dictated by the joint geometry. This shortening of

the members will account for some increase in chassis stiffness.

The stresses in the chassis correspond to the actual rotation of the chassis, along

with the nodal displacements; however the stresses in the chassis are less than

expected for the loads applied.

When using this information for future designs, the stresses calculated in FEA

should be assumed to be the actual stresses in the members. For the calculation

of torsional stiffness, the actual stiffness should be assumed to be 60-70% of the

FEA stiffness, to allow for flex in the suspension components, rod ends, engine

mounts, hubs and uprights. Until further testing using a modified torsional test

rig, this is the best method of approximating the actual torsional stiffness of the

chassis.

From the testing of the mass moments of inertia, the modeled value in yaw can

be confirmed by the swing test along with the approximate magnitude of the

values in roll and pitch. However, the swing setup needs to be improved for

experiments in pitch and roll, as the experimental values found were very

sensitive to small changes in measurement.

86

Chapter 10

10.0 Recommendations for 2005 Chassis Design and Construction

Provided that UQ racing continues to use a Honda CBR600 motor and is content

with the style and performance of the 2004 design, the 2005 chassis design

should be based on the current vehicle. Aesthetics should be included early in

the design process, along with accommodations for radiators, oil and fuel tanks.

The current cockpit layout is suitable for driver comfort; however the egress of the

vehicle is difficult with the low sides and non-structural floor under the driver’s

thighs. The construction process should be a similar to the 2004 process, with

each section of the chassis constructed separately on rigid rigs before final

assembly. Accuracy in the chassis construction is paramount, and the

construction should match the CAD design within 1mm for square sections, and

within 1-2mm for round sections.

From a structural viewpoint, a similar design to the 2004 should be used, with

accommodation for carbon-fibre ‘skin’ between the driver section and front

suspension section. All of the floor panels should be rigidly bonded to the

chassis where applicable, especially in the section under the front wishbone

pickups and the front bulkhead. By comparing the weight loss between

iterations of the spaceframe at the University of Queensland, it is feasible to

remove at least 2kg in chassis weight for the 2005 competition. After the

Formula Student competition in July 2004, it is recommended that the 2004

vehicle have some preliminary skin construction. This will allow for a comparison

in torsional stiffness between the stressed skin and straight spaceframe design.

This experiment into stressed skins will develop the team for a future semi-

monocoque composite chassis in preparation for the 2006 Australian competition.

Chapter 11

11.0 Recommendations for Future Testing Procedures

For future testing of the chassis design at the University of Queensland, an

improved car swing for pitch and roll is required. A lighter rig with roller bearing

supports at the pivots, or at least low friction pivot points is required. This will be

able to accurately determine the mass moment of inertia of the University of

Queensland FSAE vehicles.

For the torsional test equipment, it is recommended that a new swingarm

arrangement be constructed. As there appears to be inconsistencies in the

torsional testing using the current equipment, there are some inaccuracies in the

calculations of the torsional stiffness of the chassis. The current equipment is

useful for finding comparisons between different chassis designs that have been

tested on the same equipment. The other use of the current test rig is that flexible

areas of the chassis can be seen to flex, which can be used for finding areas

requiring addition bracing. A ‘dummy’ chassis of known stiffness should also be

constructed to further calibrate the test rig.

For calculations of the centre of gravity of the vehicle, the current test method is

satisfactory. However, a less laborious method should be devised to allow the

centre of gravity of the vehicle to be found by one operator. A similar rig to the tilt

test rig used at the FSAE-A competition could be constructed, utilizing a portable

rigid A-frame truss with a tilting table operated by a block and tackle

arrangement.

Strain gauge testing of the chassis under dynamic conditions is required for

further comparisons between the computer models and the actual stresses in the

chassis under driving conditions.

Bibliography

Campbell, J 2001, Chassis design and manufacture for the formula SAE

competition, Undergraduate thesis, Bachelor of Engineering, University of

Queensland, St Lucia, Australia.

Chang, E, Dover W.D 1999, ‘Prediction of stress distributions along the

intersection of tubular X and DT joints’ International Journal of Fatigue pp. 619-

635

Davisson, G 1995, Welding, Its not Black Magic, Sport Aviation, EAA Aviation

Centre,

http://www.eaa.org

Gadola, M, Granzotto, S, Structural analysis of a lightweight aluminum-

cladded(sic) racing car frame: Experimental and numerical results, viewed

August 2003,

<http://bsing.ing.unibs.it/%7Egadola/papers/romania95/romania.htm>

Kellar, M 2003, Mass Reduction of Space Frame, Semester Project Thesis,

University of Queensland, St Lucia, with Swiss Federal Institute of Technology,

Zurich

The Lincoln Electric Company, Welding Services, Weld 4130!

http://www.lincolnelectric.com/knowledge/articles/content/chrome-moly.asp

Milliken, F, Milliken, L 2002, Chassis design principles and analysis, based on

previously unpublished technical notes by Maurice Olley, Professional

Engineering Publishing Limited, Northgate Avenue, Suffolk UK

Myers, N 2004, Drivetrain design, Testing and Development for the 2003/2004

Formula SAE Vehicle, Undergraduate thesis, Bachelor of Engineering, University

of Queensland, St Lucia, Australia.

Patman, N 2002, Design System for the University of Queensland’s 2003

Formula SAE Chassis, Undergraduate thesis, Bachelor of Engineering, University

of Queensland, St Lucia, Australia.

Prater, Jr, Shahhosseini, A. M, State M. B, Furman, V.T, Azzouz, M 2002, ‘Use of

FEA concept models to develop light truck cab architectures and reduced weight

and enhanced NVH characteristics’, Presented to the 2002 SAE World Congress,

from the compilation Designing and achieving lightweight vehicles, SAE – 1684.

Rouelle, C 2003, OptimumG – Race Car Engineering with Motec Data

Acquisition, Proceedings from 2003 Formula SAE OptimumG seminar.

Smedley, P, Fisher, P, ‘Stress Concentration Factors for Simple Tubular Joints’,

Loyds Register of Shipping, Proceedings of the first (1991) International Offshore

and Polar Engineering Conference, pp. 619-635

Suh, M.-W., Lee, J.-H., Cho, K.-Y. and Kim S.-I. 2002, Section property method

and section shape method for the optimum design of vehicle body structures,

International Journal of Vehicle Design, Vol. 30, Nos 1/2 pp. 115-134.

90

Appendix A

Extract from 2004 Formula SAE Rules pertaining to Chassis Design and Construction

(Numbering system is not continuous with previous sections)

3.2 CHASSIS RULES

3.2.1 Ground Clearance

Ground Clearance must be sufficient to prevent any portion of the

car (other than tires) from touching the ground during track events.

3.2.6 Jacking Points

A jacking point, which is capable of supporting the car’s weight and

of engaging the organizers’ “quick jacks”, must be provided at the

rear of the car. The jacking point is required to be:

(A) Oriented horizontally and perpendicular to the centerline of the

car

(B) Made from round, 25.4 mm (1.0 inch) O.D. aluminum or steel

tube

(C) A minimum of 300 mm (11.8 inches) long

(D) Exposed around the lower 180 degrees of its circumference

over a

Minimum length of 280 mm (11 in)

The height of the tube is required to be such that:

(A) There is a minimum of 75 mm (3 in) clearance from the bottom

of the tube to the ground measured at tech inspection,

(B) With the bottom of the tube 200 mm (7.9 in) above ground, the

wheels do not touch the ground when they are in full rebound.

3.3 CRASH PROTECTION

The driver must be protected from car rollover and collisions. This requires

two roll hoops that are braced, a front bulkhead with crush zone, and side

protection.

3.3.1 Definitions

These definitions apply throughout Section 3.3.

A. Main Hoop--The main rollover protection (roll bar) alongside or

just behind the driver.

B. Front Hoop--Rollover protection (roll bar) in front of the driver

above his/her legs near the steering wheel.

C. Frame Member--A minimum representative piece of tubing as

defined by Section 3.3.3, Minimum Material Requirements.

D. Major Structure of Chassis--That portion of the chassis that is

within the envelope of frame members or structure that meet the

requirements of 3.3.3. The upper portion of the main hoop and its

bracing are not included in defining this envelope.

E. Crush Zone--A deformable area forward of the major structure/

Bulkhead of the chassis designed to absorb energy.

3.3.2 Safety Structure Equivalency

92

Designs that use alternative materials or tubing sizes to those

specified in Section 3.3.3.1 - Baseline Steel Material, and which

protect the driver to an equal or greater extent than required by

Section 3.3.3.1, will be allowed, provided they have been judged as

such by a technical review. Approval will be based upon the

engineering judgment and experience of the technical judge.

The technical review is initiated by completing the Safety Structure

Equivalency Form using the format given in Appendix A-1. The form

must be submitted no later than the date given in the “Action

Deadlines” located in the Appendix.

3.3.3 Minimum Material Requirements

3.3.3.1 Baseline Steel Material

The safety structure of the car, which comprises of the main

roll hoop, the front roll hoop, the side impact structure, the

roll hoop bracing and the front bulkhead, shall be constructed

of:

Either:

Round, mild or alloy, steel tubing (minimum 0.1% carbon) of

the minimum dimensions specified in the following table,

Or:

Approved alternatives per Section 3.3.3.2

93

Note: The use of alloy steel does not allow the wall thickness

to be thinner than that used for mild steel.

3.3.3.2 Alternative Tubing and Material

3.3.3.2.1 General

Alternative tubing geometry and/or materials may be

used. However, if a team chooses to use alternative

tubing and/or materials:

(A) The material must have equivalent (or greater)

Buckling Modulus EI (where, E = modulus of

Elasticity,

and I = area moment of inertia about the weakest

axis)

(B) Tubing cannot be of thinner wall thickness than

listed in 3.3.3.2.2 or 3.3.3.2.3.

Note: To maintain EI with a thinner wall thickness

than

specified in 3.3.3.1, the outside diameter MUST be

increased.

(C) A Safety Structure Equivalency Form must be

submitted per Section 3.3.2. The teams must submit

calculations for the material they have chosen,

demonstrating equivalence to the minimum

requirements found in Section 3.3.3.1 for yield and

ultimate strengths in bending, buckling and tension,

94

for buckling modulus and for energy dissipation. The

main roll hoop and main roll hoop bracing must be

made from steel, i.e. the use of aluminum or titanium

tubing or composites are prohibited for these

components.

3.3.3.2.2 Steel Tubing Requirements

Minimum Wall Thickness Allowed:

Note: All steel is treated equally - there is no

allowance

for alloy steel tubing, e.g. SAE 4130, to have a thinner

wall thickness than that used with mild steel.

3.3.3.2.3 Aluminum Tubing Requirements

Minimum Wall Thickness:

The equivalent yield strength shall be considered in

the

“as-welded” condition, (Reference: WELDING

ALUMINUM (latest Edition) by the Aluminum

Association, or THE WELDING HANDBOOK, Vol . 4,

7th Ed., by The American Welding Society), unless

the team demonstrates and shows proof that the

95

frame has been properly solution heat treated and

artificially aged.

Should aluminum tubing be solution heat-treated and

age hardened to increase its strength after welding,

the team must supply sufficient documentation as to

how the process was performed. This includes, but is

not limited to, the heat-treating facility used, the

process applied, and the fixturing used.

3.3.3.2.4 Composite Materials

If any composite or other material is used, the team

must present documentation of material type, e.g.

purchase receipt, shipping document or letter of

donation, and of the material properties. Details of the

composite lay-up technique as well as the structural

material used (cloth type, weight, resin type, number

of layers, core material, and skin material if metal)

shall also be submitted. The team must submit

calculations demonstrating equivalence of their

composite structure to one of similar geometry made

to the minimum requirements found in Section 3.3.3.1.

Equivalency calculations shall be submitted for energy

dissipation, yield and ultimate strengths in bending,

buckling, and tension. Submit the completed Safety

Structure Equivalency Form per Section 3.3.2. No

composite materials are allowed for the main hoop or

the front hoop.

3.3.4 Roll Hoops

The driver’s head and hands must be protected from contact with

the ground in any rollover attitude. This requires a main hoop (roll

bar) near the driver and a front hoop. Refer

96

to Figure 1 on the next page.

3.3.4.1 Main and Front Hoops – General Requirements

(A) When seated normally and restrained by the seat

belt/shoulder harness, a straight line drawn from the top of

the main hoop to the top of the front hoop must clear by 50.8

mm (2 inches) both the tallest driver’s helmet and the helmet

of a 95th percentile male (anthropometrical data). A two

dimensional template will be used to represent the 95th

percentile male and ensure compliance.

-A circle of diameter 200 mm (7.87 inch) shall represent the

hips and buttocks.

-A circle of diameter 200 mm (7.87 inch) shall represent the

shoulder/cervical region.

-A circle of diameter 300 mm (11.81 inch) shall represent the

head (with helmet).

-A straight line measuring 600 mm (23.62 inch) shall connect

the centers of the two 200 mm circles.

-A straight line measuring 150 mm (5.9 inch) shall connect

centers of the upper 200 mm circle and the 300 mm head

circle. With the seat adjusted to the rearmost position, the

bottom 200mm circle will be placed in the seat, and the

middle 200mm circle, representing the shoulders, will be

positioned on the seat back. The upper 300 mm circle will be

positioned up to 25.4 mm (1 inch) away from the head

restraint (i.e. where the driver’s helmet would normally be

located while driving).

97

(B) Both the main hoop and front hoop must each be formed

from closed section metal tubing. No composite materials are

allowed for the main hoop or the front hoop.

(C) Both the main hoop and front hoop must extend to the

bottom of the chassis. Each hoop shall extend from the

lowest frame member on one side of the car, up and over

and down to the lowest frame member on the other side.

(D) The minimum radius of any bend, measured at the tube

centerline, must not be less than three times the tube

diameter. The bends shall be smooth and continuous with no

evidence of crimping or wall failure.

(E) Proper gussets and tube triangulation must be used to

ensure that the main and front hoops are securely attached

to the primary structure.

(F) A 4.5 mm (0.18 inch) inspection hole must be drilled in a

non-critical location of both the main hoop and the front hoop

to allow verification of wall thickness.

3.3.4.2 Main Hoop

(A) The main hoop must be constructed of steel per Section

3.3.3.1 or 3.3.3.2.

(B) The use of aluminum alloys, titanium alloys or composite

materials is prohibited for the main hoop.

(C) The main hoop must be formed from a single piece of

uncut, continuous, closed section metal tubing that extends

98

from the lowest frame member on one side of the car, up and

over and down to the lowest frame member on the other

side.

(D) In the side view of the vehicle, the portion of the Main

Roll Hoop that lies above its attachment point to the Major

Structure of the Chassis shall be within 10 degrees of the

vertical.

(E) In the front view, the vertical members of the main hoop

must not be less than 380 mm (15 inches) apart (inside

dimension) at their attachment to the chassis.

(F) On all monocoque chassis, the main hoop must be

continuous and extend down to the bottom of the chassis.

Mechanical fasteners must be used to ensure positive

attachment of the Roll Hoop to the monocoque. All bolts (or

solid rivets) used must be 8mm (5/16 inch) minimum

diameter. The number of bolts used and their placement is

for the team to determine, but proof must be submitted to

show equivalency to a welded tubular chassis that meets

Section 3.3.3. Mounting plates welded to the roll hoop shall

not be less than 2.0 mm (0.080 inch) thick steel (or the

equivalent in aluminum). Backup plates of equal thickness

must be used on the opposing side of the composite

structure to prevent crushing the core. All teams are required

to submit a Safety Structure Equivalency report per Section

3.3.2, showing the integrity of their proposed design.

3.3.4.3 Front Hoop

-The front hoop must be constructed of material per Section

3.3.3.1 or 3.3.3.2.

99

-The front hoop must be formed from closed section metal

tubing. No composite materials are allowed for the front

hoop.

-The front hoop must be no lower than the top of the steering

wheel in any angular position.

-The front hoop must extend to the bottom of the chassis. It

must extend from the lowest frame member on one side of

the car, up and over and down to the lowest frame member

on the other side. With proper gusseting, it is permissible to

make it from more than one piece of tubing.

3.3.5 Roll Hoop Bracing

3.3.5.1 Main Hoop Bracing

-The main hoop bracing must be constructed of steel, with

dimensions per Section 3.3.3.1 or 3.3.3.2.

-The main hoop must be braced in the fore or aft direction on

the left and right sides.

-In side view, the main hoop and the main hoop bracing

cannot be on the same side of the vertical line through the

top of the hoop, i.e. if the main hoop leans forward, the

bracing must be forward of the main hoop, and if the main

hoop leans rearward, the bracing must be rearward of the

main hoop.

-Braces must be attached as near as possible to the top of

the hoop but must not be more than 160 mm (6.3 inches)

100

below the top and at an included angle of at least 30

degrees.

-The braces must be straight, i.e. without any bends.

3.3.5.2 Front Hoop Bracing

-The front hoop bracing must be constructed of material per

Section 3.3.3.1 or 3.3.3.2.

-The front hoop must have two braces extending forward to

protect the driver’s legs.

-These braces shall be attached as near as possible to the

top of the hoop, but must not be more than 50.8 mm (2 in.)

below the top of the hoop.

-The front hoop bracing should extend to the structure in

front of the driver’s feet; but in any case it must be integrated

into the chassis to provide substantial support for the front

hoop. When monocoque construction is used as bracing for

the front hoop, it must be approved on an individual basis.

Submit the “Safety Structure Equivalency Form”.

3.3.5.3 Other Bracing Requirements

-Braces attached to monocoque chassis must be welded to

plates not less than 2.0 mm (0.080 inch) thick and backed up

on the inner side by plates of equal thickness using solid

rivets or bolts 8mm (5/16 inch) minimum bolt diameter

through the nonferrous material.

101

-Roll hoop bracing may be removable. Any non-permanent

joint shall be of the double-lug design as shown in figures 2

and 3. Each lug shall be at least 4.5 mm (0.177 in) thick

steel, measure25 mm (1.0 in) minimum perpendicular to the

axis of the bracing, and be as short as practical along the

axis of the bracing. All joints must include a capping

arrangement (figure 2) and/or a doubler (figure 3), fabricated

of at least 1.65 mm (.065 inch) steel. If a doubler is used, it

must extend at least 120 degrees around the frame member.

The pin or bolt shall be 10 mm Grade 9.8 or 3/8in Grade 8

minimum. The attachment holes in the lugs and in the

attached bracing shall be a close fit with the pin or bolt. NO

SPHERICAL ROD ENDS are allowed.

REMOVABLE ROLL BAR BRACES ATTACHMENT DETAILS (FIGURES 2 & 3)

3.3.6 Frontal Impact Protection – Drivers

In order to provide protection from a frontal impact, the driver’s feet

shall be contained within the major structure of the chassis. While

they are touching the pedals no part of the driver's feet shall extend

outside of the major structure of the chassis as defined in 3.3.1.d.

102

The major structure of the chassis shall extend forward to a

bulkhead. Forward of this bulkhead shall be a crush zone.

3.3.6.1 Bulkhead

The bulkhead is required to:

(A) Be constructed of material per Section 3.3.3.1 or 3.3.3.2.

(B) Be formed of closed section tubing attached securely to

the major structure of the chassis.

(C) Be in front of all non-crushable objects (e.g. batteries,

master cylinders)

(D) Be located such that the soles of the drivers feet, when

touching but not applying the pedals, shall not be forward of

the bulkhead plane. (This plane is defined as the forward

most surface of the tubing.) Adjustable pedals must be in the

forward most position.

(E) Be supported by the major structure of the chassis within

50.8 mm (2 ins.) of the top.

(F) All monocoque chassis (composite monocoque or metal

monocoque) must provide the same protection as tube

frames built per Section 3.3.3. The team must submit

calculations demonstrating equivalence for energy

dissipation, yield and ultimate strengths in bending, buckling,

and tension. Submit the completed Safety Structure

Equivalency Form per Section 3.3.2.

3.3.6.2 Crush Zone

103

The crush zone is defined by two separated planes forward

of the main chassis structure. The planes defined are normal

to the fore/aft axis of the car.

Front Plane--The forward vertical plane of the crush zone

shall, as a minimum, be able to contain a rectangle of 100

mm (3.9inch) height and 200 mm (7.8 inch) width.

Rear Plane--The rearward vertical plane of the crush zone

shall be the front plane of the Bulkhead.

Distance Between Planes--There shall be a minimum

distance of 150 mm (5.9 inch) between the front and rear

planes of the crush zone.

3.3.6.3 Crush Zone Construction

The material providing the crush zone:

(A) Must be capable of decelerating the car within an

acceptable limit.

(B) Shall be attached securely and directly to the bulkhead

(no adhesive tape or Dzus type fasteners are allowed). It

shall not be attached to the vehicle by being part of non-

structural bodywork.

3.3.6.4 Non-Crushable Objects

All non-crushable objects (e.g. batteries, master cylinders)

must be rearward of the bulkhead. No non-crushable objects

are allowed in the crush zone.

104

3.3.7 Frontal Impact Protection – Others

People shall not be endangered by contact with sharp edges

on the forward facing bodywork or other protruding

components. All forward facing edges on the bodywork that

could impact people, e.g. the nose shall have forward facing

radii of at least 38 mm (1.5 inches). This minimum radius

shall extend to at least 45 degrees relative to the forward

direction, along the top, sides and bottom of all affected

edges.

3.3.8 Side Impact Protection

The driver must be protected from a side collision while

seated in the normal driving position. Side impact must meet

the requirements listed below. The material requirements are

given in 3.3.3.

3.3.8.1 Tube Frames

A minimum of three (3) tubular members must be

used for Side Impact Protection. These side impact

members must be located on each side of the driver

while seated in the normal driving position. See Figure

4. The three (3) frame members defined below must

meet the requirements given in 3.3.3.

Upper Member

A member must connect the main roll hoop and the

front roll hoop at a height between 200 and 350 mm

(7.87 and 13.78 inches) above the ground with a 77kg

(170 pound) driver seated in the normal driving

105

position. The upper frame rail can be used as the

upper side impact member if it meets the height,

diameter and thickness requirements of the latter.

Diagonal Member

At least one (1) diagonal member per side must

connect the upper and lower side impact members

forward of the main roll hoop and rearward of the front

roll hoop.

Lower Member

A member must connect the bottom of the main roll

hoop and the bottom of the front roll hoop. This lower

side impact member is normally the lower frame

rail/frame member. Alternative geometry to the

minimum requirements given above must be

approved prior to competition. Teams must submit a

Safety Structure Equivalency Form per Section 3.3.2.

3.3.8.2 Composite Monocoque

The section properties of the sides of the vehicle must

reflect impact considerations. Non-structural bodies or

skins alone are not adequate to meet the side impact

rule. Teams building composite monocoque bodies

must submit the Safety Structure Equivalency Form

per Section 3.3.2. Submitted information should

include: material type(s), cloth weights, resin type,

fiber orientation, number or layers, core material, and

lay-up technique.

3.3.8.3 Metal Monocoque

These structures must meet the same requirements

as tube frames and composite monocoque. Teams

106

building metal monocoque bodies must submit the

Safety Structure Equivalency Form per Section 3.3.2

Figure 4

3.4 SAFETY - DRIVER RULES

3.4.1 Driver’s Restraint System

All drivers must use either a five or six-point restraint harness

meeting the following specifications. Arm restraints are also

required. The restraint system installation is subject to approval of

the SCCA Chief Technical and Safety Inspector. The restraint

system must be worn as tightly as possible at all times.

(A) 5 Point System A five-point system consists of a 76 mm (3 inch) wide lap belt,

approximately 76 mm (3 inch) wide shoulder harness straps and a

single, approximately 51 mm (2 inch) wide anti-submarine strap.

The single anti-submarine strap of the five-point system must be

attached to the primary structure and have a metal-to-metal

connection with the single release common to the lap belt and

shoulder harness.

(B) 6 Point System

107

A six point system consists of a 76 mm (3 inch) wide lap belt,

approximately 76 mm (3 inch) wide shoulder harness straps and

two, approximately 51 mm (2 inch) wide leg or anti-submarine strap.

The double leg straps of the six-point system may be attached to

the primary structure or be attached to the lap belt so that the driver

sits on them, passing them up between his or her legs and

attaching to the single release common to the lap belt and shoulder

harness. The leg straps may also be secured at a point common

with the lap belt attachment to the structure, passing them under

the driver and up between his or her legs to the harness release.

(C) Material Requirements The material of all straps must be Nylon or Dacron polyester and in

new or perfect condition. There must be a single release common

to the lap belt and shoulder harness using a metal-to-metal quick-

release type latch. All driver restraint systems must meet either SFI

Specification 16.1, or FIA specification 8853/98. The belts must

bear the appropriate dated labels, and be no more than five years

old. It is recommended that driver restraint systems be replaced

every three years.

(D) Belt and Strap Mounting The lap belt, shoulder harness and anti-submarine strap(s) must be

securely mounted to the primary structure of the car (i.e. frame

tubes, roll structure). Such structure and any guide or support for

the belts shall meet the minimum requirements of 3.3.3. Bolting

through aluminum floor closeout panels, etc. is not acceptable. An

SSE form must be completed for all monocoque structures (see

3.3.2).

(E) Belt Position Requirements The lap belt must pass around the pelvic area below the Anterior

Superior Iliac Spines (the hip bones) (Figure 5a). Under no

108

condition may the lap belt be worn over the area of the intestines or

abdomen. The lap belts should come through the seat at the bottom

of the sides of the seat to maximize the wrap of the pelvic surface

and continue in a straight line to the anchorage point. The

centerline of the lap belt at the seat bottom should be approximately

76 mm (3 inch) forward of the seat back to seat bottom junction

(see Recommended Location in Figure 5). The lap belts should not

be routed over the sides of the seat. The seat must be rolled or

grommeted to prevent chafing of the belts.

(F) Shoulder Harness The shoulder harness must be the over-the shoulder type. The

shoulder harness must be mounted behind the driver and above a

line drawn downward from the shoulder point at an angle of 40

degrees with the horizontal to minimize spine compression injuries

under high “g” deceleration. Only separate shoulder straps are

permitted (i.e. “Y”-type shoulder straps are not allowed). “H”-type

configuration is allowed. It is mandatory that the shoulder harness,

where it passes over the shoulders, be 76 mm (3 inch) wide. The

shoulder harness straps must be threaded through the three bar

adjusters in accordance with manufacturers instructions.

Figure 5

109

Appendix B

University of Queensland Safety Structure Equivalency

110

111

112

Appendix C

Tube Selection for Minimum Requirements

Non-Dim In Bending

Suit Roll Hoops

Suit Side Impact

Protection

Suit Hoop

BracingOD

(mm) NWT (mm) kg/m Ixx stress/kg stiff/kg

= = 25.40 1.65 0.966 8.72 3.55 9.03

= = 25.40 2.11 1.212 10.55 3.43 8.71

= = = 25.40 2.41 1.366 11.63 3.35 8.51

= 28.58 1.25 0.842 10.04 4.17 11.92

= 28.58 1.47 0.983 11.54 4.11 11.74

= = 28.58 1.65 1.096 12.70 4.06 11.59

= = = 28.58 2.11 1.377 15.47 3.93 11.23

= = = 28.58 2.41 1.555 17.11 3.85 11.00

= = 30.16 2.11 1.460 18.39 4.18 12.60

= = 30.16 2.41 1.649 20.38 4.10 12.35

= 31.75 1.25 0.940 13.95 4.67 14.84

= 31.75 1.47 1.098 16.06 4.61 14.63

= 31.75 1.65 1.225 17.72 4.56 14.47

= = 31.75 2.11 1.542 21.69 4.43 14.06

= = 31.75 2.41 1.744 24.06 4.35 13.80

= 34.93 1.25 1.038 18.78 5.18 18.09

= 34.93 1.47 1.213 21.67 5.11 17.86

Baseline Material

2004 Material Selection

113

Appendix D

Calculations for Mass Moment of Inertia

Car Alone With 82kg Driver Gravity (m/s^2) 9.81 Gravity (m/s^2) 9.81Length from Pivot to CG of Stage (m) 2.175

Length from Pivot to CG of Stage (m) 2.175

Height from platform to Cog of platform 0.3

Height from platform to Cog of platform 0.3

Vertical height from stage to pivot(m) 2.475

Vertical height from stage to pivot(m) 2.475

Height of center of gravity of car (m) 0.243

Height of center of gravity of car (m) 0.28

Distance from pivot to CoG of car (m) 2.232 Distance from pivot to CoG of car 2.195Horizontal Distance from CG to pivots - Yaw (m) 1.34

Horizontal Distance from CG to pivots - Yaw (m) 1.34

Mass of Car (kg) 240 Mass of Car (kg) 322Mass of Stage (kg) 69 Mass of Stage (kg) 69Measuring Moments of Inertia Measuring Moments of Inertia Roll Roll Frequency of Oscillations - Empty (Hz) 0.3194

Frequency of Oscillations - Empty (Hz) 0.3194

Frequency of Oscillations - Loaded (Hz) 0.3266

Frequency of Oscillations - Loaded (Hz) 0.3294

Roll Moment of Inertia of stage about pivot kgm2 365.6

Roll Moment of Inertia of stage about pivot 365.6

Roll Moment of Inertia of stage 39.1 Roll Moment of Inertia of stage 39.1Roll Moment of Inertia of Car about pivot kgm2 1241.1

Roll Moment of Inertia of Car about pivot 1600.0

Roll Moment of Inertia of Car kgm2 45.5 Roll Moment of Inertia of Car 48.5Pitch Pitch Frequency of Oscillations - Empty (Hz) 0.3129

Frequency of Oscillations - Empty (Hz) 0.3129

Frequency of Oscillations - Loaded (Hz) 0.3164

Frequency of Oscillations - Loaded (Hz) 0.3196

Pitch Moment of Inertia of stage about pivot kgm2 380.9

Pitch Moment of Inertia of stage about pivot kgm2 380.9

Pitch Moment of Inertia of stage 54.5 Pitch Moment of Inertia of stage 54.5Pitch Moment of Inertia of Car about pivot kgm2 1331.0

Pitch Moment of Inertia of Car about pivot kgm2 1707.0

Pitch Moment of Inertia of Car kgm2 135.4

Pitch Moment of Inertia of Car kgm2 155.6

Yaw Yaw Frequency of Oscillations - Empty (Hz) 0.4296

Frequency of Oscillations - Empty (Hz) 0.4296

Frequency of Oscillations - Loaded (Hz) 0.5263

Frequency of Oscillations - Loaded (Hz) 0.5563

Yaw Moment of Inertia of Car kgm2 125.42

Yaw Moment of Inertia of Car kgm2 150.45

114

Appendix E

Data plots for Dial Gauge Locations

Displacement of A1vert vs Test Rig Twist

y = 0.1561x - 0.0492R2 = 0.968

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5

deg twist

mm

A1vert(mm)Series2Linear (Series2)

Vertical Displacement at Location A1vert per degree twist of chassis

y = 0.1434x + 0.0018

0.0000.0500.1000.1500.2000.2500.3000.350

0.000 0.500 1.000 1.500 2.000 2.500

(deg)

(mm

) LoadingUnloadingLinear (Loading)

Displacement of A2Hoz vs Test Rig Twist

y = 0.7874x - 0.4193R2 = 0.9869

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3

deg tw ist

mm

A2H(mm)

Series2

Linear (Series2)

115

Displacement of A3Hoz vs Test Rig Twist

y = 0.9306x - 0.0944R2 = 0.9829

-0.5

0

0.5

1

1.5

2

2.5

0 0.5 1 1.5 2 2.5

deg tw ist

mm B3H(mm)

Linear (B3H(mm))

Displacement of B1vert vs Test Rig Twist

y = 0.3319x - 0.0898R2 = 0.9675

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.5 1 1.5 2 2.5

deg tw ist

mm

B1vert(mm)

Series2

Linear (Series2)

Displacement of C1vert vs Test Rig Twist

y = 1.4166x - 0.065

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3

deg tw ist

mm C1vert(mm)

Linear (C1vert(mm))

116

Vertical Displacement at Location C1vert per degree twist of chassis

y = 2.9096x - 2.2968

0.0000.5001.0001.5002.0002.5003.0003.5004.000

0.000 0.500 1.000 1.500 2.000 2.500

(deg)

(mm

) Loading

Unloading

Linear (Loading)

Horizontal Displacement at Location C1Hoz per degree twist of chassis

y = 0.2843x - 0.0097

-0.1000.0000.1000.2000.3000.4000.5000.600

0.000 0.500 1.000 1.500 2.000

(deg)

(mm

)

LoadingUnloadingLinear (Loading)

Horizontal Displacement at Location C2Hoz per degree twist of chassis

y = 1.7965x - 0.0317

-0.5000.0000.5001.0001.5002.0002.5003.0003.500

0.000 0.500 1.000 1.500 2.000

(deg)

(mm

) LoadingUnloadingLinear (Loading)

117

Displacement of C3Hoz vs Test Rig Twist

y = 2.8834x - 0.1729R2 = 0.9971

-1

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5

deg tw ist

mm C3H(mm)

Linear (C3H(mm))

Displacement of D1vert vs Test Rig Twist

y = 2.5684x - 0.133R2 = 0.9959

-1

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5

deg twist

mm D1vert(mm)

Linear (D1vert(mm))

Vertical Displacement at Location E1vert per degree twist of chassis

y = 0.0746x + 0.0061

0.000

0.050

0.100

0.150

0.000 0.500 1.000 1.500 2.000

(deg)

(mm

) Loading

Unloading

Linear (Loading)

118

Vertical Displacement at Location D1v ert per degree tw ist of chassis

y = 2.9997x - 1.4129

0.0001.0002.0003.0004.0005.0006.000

0.000 0.500 1.000 1.500 2.000 2.500

(deg)

(mm

)

Loading

Unloading

Unloading

Linear (Loading)

Displacement of F1vert vs Test Rig Twist

y = 0.5919x + 0.0949R2 = 0.939

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.5 1 1.5 2 2.5

deg twist

mm F1vert(mm)

Linear (F1vert(mm))

Vertical Displacement at Location G1vert per degree twist of chassis

y = 1.4668x - 0.0417

-0.500

0.000

0.500

1.000

1.500

2.000

2.500

3.000

0.000 0.500 1.000 1.500 2.000

(deg)

(mm

) LoadingUnloadingLinear (Loading)

119

Displacement of G1vert vs Test Rig Twist

y = 1.0642x - 0.1237R2 = 0.9866

-0.5

0

0.5

1

1.5

2

2.5

0 1 2 3

deg tw ist

mm

G1vert(mm)

Linear(G1vert(mm))

Displacement of G1Hoz vs Test Rig Twist

y = 0.8912x - 0.0749R2 = 0.985

-0.5

0

0.5

1

1.5

2

0 1 2 3

deg twist

mm G1H(mm)

Linear (G1H(mm))

Horizontal Displacement at Location G1Hoz per degree twist of chassis

y = 1.157x - 0.0167

-0.5000.0000.5001.0001.5002.0002.500

0.000 0.500 1.000 1.500 2.000

(deg)

(mm

)

LoadingUnloadingLinear (Loading)

Vertical Displacement at Location H1v ert per degree tw ist of chassis

y = 6.0375x - 0.1512

-5.000

0.000

5.000

10.000

15.000

0.000 0.500 1.000 1.500 2.000

(deg)

(mm

) Loading

Unloading

Linear (Loading)

120

Displacement of H1vert vs Test Rig Twist

y = 5.324x - 0.5979R2 = 0.9704

-2

0

2

4

6

8

10

12

0 1 2 3

deg tw ist

mm H1vert(mm)

Linear (H1vert(mm))

Horizontal Displacement at Location Jhoz per degree twist of chassis

y = 0.0349x - 0.0015

-0.0100.0000.0100.0200.0300.0400.0500.0600.0700.080

0.000 0.500 1.000 1.500 2.000 2.500

(deg)

(mm

)

Loading

Unloading

Linear (Loading)

Vertical Displacement at Location K1vert per degree twist of chassis

y = 0.3117x - 0.0246

-0.1000.0000.1000.2000.3000.4000.5000.6000.700

0.000 0.500 1.000 1.500 2.000

(deg)

(mm

) LoadingUnloadingLinear (Loading)

121

Appendix F

Strain Gauge Data Plots

Axial Stress in Gauge Location 1 vs Applied Moment

y = 0.0408x - 0.8891

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 500 1000 1500 2000

Nm

MPa

test4test 3test 2test 5Linear (test 2)

Axial Stress In Gauge Location 2 vs applied Moment

y = 0.024x + 0.0912

0.005.00

10.0015.0020.0025.0030.0035.0040.00

0 500 1000 1500 2000

Nm

MPa

test4

test 3

test 2

test 5

Linear (test 2)

Bending Stress in Gauge Location 3 vs Applied Moment

y = -0.1219x - 37.442-250.00

-200.00

-150.00

-100.00

-50.00

0.000 500 1000 1500 2000

Nm

MPa

test 2test 5Linear (test 5)

122

Axial Stress in Gauge location 1 vs rig twist

y = 27.136x - 1.3824

-10.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

0 0.5 1 1.5 2 2.5

Deg twist

MPa

test4test 3test 2test 5Linear (test 3)

Axial Stress in Gauge Location 2 vs rig Twist

y = 15.368x - 0.3103

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

0 0.5 1 1.5 2 2.5

deg twist

MPa

test4

test 3

test 2

test 5

Linear (test 3)

Bending Stress in Gauge Location 3 vs rig Twist

y = -87.226x - 35.493-250.00

-200.00

-150.00

-100.00

-50.00

0.000 0.5 1 1.5 2 2.5

deg twist

MPa

test4test 5Linear (test 5)

123

Appendix G

Calculations for 2003 Height of Centre of Gravity

Empty car Front Rear

Horizontal length from pivot to outside of tyre (mm) 500.000 520

Vertical length from ground to outside of tyre (mm) 1270.000 1230

Width of pivot (mm) 8.000 8

Track (mm) 1200.000 1100

Tyre width (mm) 152.000 152

Effective track (mm) 1360.000 1310.000

Angle of tilt (tan) 68.510 67.083

Angle of tilt (sin) 69.039 69.873

Angle of tilt (cos) 68.429 66.613

Average 68.660 67.856

1.198 1.184 Average

Centre of Gravity 237.544 247.425 242.484

With 78kg Driver Front Rear

Horizontal length from pivot to outside of tyre (mm) 570.000 570

Vertical length from ground to outside of tyre (mm) 1240.000 1200

Width of pivot (mm) 8.000 8

Track (mm) 1200.000 1100

Tyre width (mm) 152.000 152

Effective track (mm) 1360.000 1310.000

Angle of tilt (tan) 65.313 64.592

Angle of tilt (sin) 65.750 66.353

Angle of tilt (cos) 65.221 64.207

Average 65.428 65.051

1.142 1.135 Average

Height of Centre of Gravity 278.004 282.860 280.432

124

Appendix H

2003 Chassis Layout

2003 Isometric view

2003 Top View

2003 Side View

125

Appendix I

2004 Chassis Layout

2004 Isometric

2004 Top View

2004 Side View

126