Design of a Formula SAE Racecar Chassis: Composite ... · PDF fileDesign of a Formula SAE...

Design of a Formula SAE Racecar Chassis: Composite Analysis Utilizing

Altair Engineering OptiStruct Software

Margaret Lafreniere

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

BACHELOR OF APPLIED SCIENCE

Supervisor: W. Cleghorn

Department of Mechanical and Industrial Engineering University of Toronto

March, 2007

ABSTRACT The overall scope of t his project can be broken down into two objectives. The first

objective of this thesis was to design, m anufacture, and test a Formula SAE racecar

chassis for use in th e 2007 Formula SAE desi gn series. This repo rt outlines the steps

taken to design this chassis, the fabrication process, and the subsequent integration of the

composite panels developed through the use of Altair Engineering OptiStruct software.

The second objective was to dev elop com posite pan els optim ized f or the

application in term s of t heir weight, core and laminate thicknesses, and also in term s of

the relative directions of each laminate ply. This was completed through the use of Altair

Engineering software, as well as another engineering software package to allow for a

comparison and provide a baseline for the evaluation of their software.

In conjunction with the Connections Program of the Ontario Centres of

Excellence, another parallel object ive of this the sis was to e valuate Alta ir Eng ineering

OptiStruct software in terms of its use f or the application of a rac ecar competing in th e

Formula SAE design series. The sp ecific application for the software was in the d esign

of composite sandwich panels for use in the 2007 Formula SAE racecar chassis.

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ACKNOWLEDGEMENTS I would like to acknowledge the following people for their help and support of this thesis. Professor Cleghorn – for accepting me as a thesis student in the Connections program, and for his support of my goals throughout university and beyond. Altair Engineering Canada Ltd – for providing software utilized in the design of the 2007 University of Toronto chassis, training opportunities, and in general, for their support of my thesis and my role in the Connections Program. Bob Little – for acting as my connection to Altair Engineering Canada Ltd., and providing me with information and software licenses needed to complete my report. Connections Program – for their support of the ties between academics and industry, giving us the experience we need to carry on into our future careers in engineering. The entire Formula SAE Team – for their dedication to the project, and for all of their help with the huge job of building a chassis, and an entire car each year. Astra Aero Ltd. – for providing composite manufacturing facilities and materials, without which it would not have been possible to complete the 2007 chassis, or this thesis. Andrew Wong – for providing many of the wonderful photographs shown throughout this report, and for his work with the Formula SAE team over the past 5 years.

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TABLE OF CONTENTS Acknowledgements……………………………………………………………………….. i Table of Contents…………………………………………………………………. ……... ii List of Figures……………………………………………………………………………... iv List of Tables……………………………………………………………………………… vi 1 Introduction and Background………………………………………………………. 1 1.1 Thesis Objectives…………………………………………………………... 1 1.2 Formula SAE Design Series……………………………………………….. 2 1.3 Altair Engineering OptiStruct Composite Analysis………………………... 3 1.4 Chassis Design……………………………………………………………... 4 1.4.1 Preliminary Design: Packaging……………………………………. 4 1.4.2 Chassis Design and Optimization………………………………….. 5 1.4.3 Chassis Fabrication………………………………………………… 6 1.5 Composites in Chassis Design……………………………………………... 6 1.5.1 Composite Sandwich Panel Design………………………………... 8 1.5.2 Composite Panel Fabrication and Integration ……………………... 8 2 Method and Approach………………………………………………………………. 12 2.1 Chassis Design Utilizing FEA Analysis…………………………….……... 12 2.1.1 Design of the Overall Structure……………………………………. 12 2.1.2 Design of the Composite Structure………………………… ……... 14 2.2 Chassis Design for Driver Safety…………………………………………... 16 2.2.1 Equivalence of Side Panel Structure……………………………….. 16 2.2.2 Equivalence of Forward Structure…………………………………. 18 2.2.3 Rollover Analysis…………………………………………………...20 3 Materials and Manufacturing………………………………………………………. 23 3.1 Material Selection………………………………………………………….. 23 3.2 Tubular Steel Chassis Manufacturing……………………………… ……... 25 3.3 Composite Panel Manufacturing…………………………………………... 26 3.3.1 Sandwich Panel Manufacturing……………………………………. 26 3.3.2 Panel Lay-up Process………………………………………………. 27 3.3.3 Composite Bonding Process……………………………………….. 29

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4 Validation and Testing………………………………………………………………. 32 4.1 Torsional Stiffness Testing………………………………………………… 32

4.2 Composites Testing………………………………………………… ……... 33 4.2.1 Test of Steel/Composite Attachment……………………………... 33 4.2.2 Bonding Epoxy Comparison Testing………………………………. 35 5 Results and Conclusions……………………………………………………………... 39 5.1 Evaluation of Altair Engineering Software………………………………… 39 5.2 Conclusions………………………………………………………… ……... 40 References…………………………………………………………………………………. 41 APPENDIX A: Additional Figures………………………………………………………..a1 APPENDIX B: Equivalency Calculations………………………………………………... b1 APPENDIX C: FEA Optimization Study of Chassis…………………………………….. c1 APPENDIX D: Torsion Test Procedure and Results…………………………………….. d1

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LIST OF FIGURES Figure 1.1: Side views of the standard Formula SAE mandated tubular steel structures for the front section of the vehicle (left), and the side impact structure (right) [1]…….. 2 Figure 1.2: A typical Formula SAE vehicle [6]…………………………………………… 3 Figure 1.3: Composite panel with carbon fibre laminate and Nomex core. [1]…………… 7 Figure 1.4: Polar plot of elastic modulus versus fibre orientation [2]……………………. 8 Figure 1.5: Composite panel fabrication setup, and vacuum-bag setup [2]………………. 9 Figure 2.1: Displacement plot of baseline chassis design………………………………… 13 Figure 2.2: Equivalent FSAE steel structure of 2007 UofT side panel [1]………………... 17 Figure 2.3: Rectangular approximation of UofT composite structure [1]………………… 18 Figure 2.4: FSAE equivalent steel structure and composite forward structure [1]………... 19 Figure 2.5: Simplified bulkhead support structure [1]…………………………………….. 20 Figure 3.1: Steel tube frame……………………………………………………………….. 23 Figure 3.2: Composite panels added………………………………………………………. 23 Figure 3.3: Balsa panel providing support of bellcrank mounts [6]………………………. 27 Figure 3.4: Example of a bend applied to a composite panel [1]…………………………. 28 Figure 4.1: Bond cross-section [1]………………………………………………………… 34 Figure 4.2: Diagram of the test panel geometry [1]……………………………………….. 34 Figure 4.3: Test fixture for side impact scenario [6]……………………………………… 34 Figure 4.4: Test sample with load attached [6]……………………………………………. 35 Figure 4.5: Sample after failure [6]………………………………………………………... 35 Figure 4.6: Magnification of steel to composite bond after failure [6]……………………. 35 Figure 4.7: Epoxy testing fixture………………………………………………………….. 36 Appendix A: Additional Figures Figure A1: FSAE standard tube structure…………………………………………………. a1 Figure A2: Deflection of FSAE tube structure……………………………………………. a1 Figure A3: UofT composite forward structure……………………………………………. a2 Figure A4: Deflection of UofT composite forward structure……………………………... a2 Figure A5: First layers being soaked with epoxy on the jig surface [6]…………………... a3 Figure A6: Uniaxial carbon cloth being placed on lay-up [6]…………………………….. a3 Figure A7: Nomex core being added to lay-up [6]………………………………………... a3 Figure A8: Beginning of symmetric layer on opposite side of panel [6]…………………. a4 Figure A9: Final panel lay-up enclosed in vacuum-bag [6]………………………………. a4 Figure A10: Final panel cut to shape, with material removed for bend lines [6]…………. a5 Figure A11: Bent panel being fit to steel tube frame [6]………………………………….. a5 Figure A12: All panels cut and fit into place on chassis [6]………………………………. a6 Figure A13: Steel chassis section…………………………………………………………. a6

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Figure A14: Panel bonded into chassis……………………………………………………. a6 Figure A15: Example of panels in chassis………………………………………………… a7 Figure A16: Carbon fiber wrapped around bond………………………………………….. a7 Figure A17: Torsion test setup for a Formula SAE vehicle [6]…………………………… a7 Figure A18: Close up of weight basket attached to front right suspension corner [6]……. a8 Figure A19: Measurement of deflection of bar attached to chassis [6]…………………… a8

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LIST OF TABLES Table 2.0: Final Composite Panel Lay-up………………………………………………… 16 Table 3.1: Panel Lay-up…………………………………………………………………… 26 Table 4.0: Epoxy Test: Number of Cycles to Failure…………………………………….. 36

CHAPTER 1:

INTRODUCTION AND BACKGROUND

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1 INTRODUCTION AND BACKGROUND

1.1 Thesis Objectives

The first objective of this thesis was to design, manufacture and test a Form ula SAE

racecar chassis, with particular focus on the integration of composite materials into the design.

The second objec tive o f this pro ject was to develop com posite sandwich panels optim ally

designed for use in this particular racecar ch assis, u tilizing Altair E ngineering OptiStruct

software. T his optimization process included consideration of com posite panel lam inate and

core materials, thicknesses, and the lay-up orientations of each ply.

The para llel goal of this thes is was to p erform an evaluation of Altair Engineering

software, with focus on the OptiStruct com posite analysis module. The software was applied

to the desig n of a For mula SAE racecar chas sis for use on the 2007 University of Toronto

Formula SAE Racing vehicle. Based on prel iminary resear ch of the sof tware, it was

established that the most appropriate area to benefit from the OptiStruct software applications

was through the development of composite sandwich panels for use in the chassis design.

Other sections of this report focus on key areas of chassis design including proof of a

safe structure in each of the impact or rollover situations that a racecar may undergo. As well,

in order to validate the computer analyses of structures, physical testing of various composite

components was completed, along with a full chassis torsion test to validate torsional stiffness

values from the finite element models.

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1.2 Formula SAE Design Series

Formula SAE is a collegiate design seri es in which team s design, build, and drive

open-wheel racecars in a field of international competitors. The se ries is dic tated by a se t of

rules set in place to ensure the vehicles and the competition is safe. In terms of the design of

the chas sis, the key ru les in clude m andated side and fronta l im pact structures, including

rollover protection, and certain specified m aterials. Below, in Figure 1.1, are representations

of the standard Formula SAE and frontal im pact and side impact structures. The rules dictate

that all chassis roll hoops m ust be made of 1” outer diam eter mild steel tubing, with a 0.095”

wall th ickness. All br acing must be constru cted of 1” outer diam eter mild s teel with eithe r

0.065” or 0.049” wall thickness, depending on the type of bracing. Though these materials are

stated in the rules, the competition does allow for these structures to be replaced by composite

materials as suming the chassis des igner is ab le to prov e that th e com posite structures are

equivalent in side impact, frontal impact, and in a rollover scenario.

Figure 1.1: Side views of the standard Formula SAE mandated tubular steel structures for the front

section of the vehicle (left), and the side impact structure (right). [1]

There are several benefits in using com posite structures as opposed to the S AE

standard steel structure. The predominant reason for replacing the steel is to reduce the m ass

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of the frame. The second advantage of composite sandwich panels is in the tors ional stiffness

the can be gained throu gh their use. In the field of motorsports, every bit of m ass removed

from the car increas es the power to weight ra tio of th e v ehicle. In term s of stif fness, if

implemented correc tly, com posite panels will im prove the overall tor sional s tiffness at a

fraction of the weight of a steel structure. Figure 1.2 shows a typical Formula SAE racecar.

Figure 1.2: A typical Formula SAE vehicle [6]

1.3 Altair Engineering OptiStruct Composite Analysis

The OptiStruct software package released by Altair Engineering has the ability to carry

out composite material analyses, allowing the designer to optim ize a panel geom etry for low

mass and hi gh stiffness, determ ining optim al lam inate and core thicknesses, as well as ply

orientations. OptiS truct is one of only a few software packages av ailable that can perform

fast, effective design studies of this particular type relating to optim ization of composite lay-

ups.

The software allows the engineer to choos e the lam inate and core m aterials, and

specify all initial displacem ent constraints and loading conditions. In a design study, the

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software applies a gene tic algorithm, avoiding the need to test all permutations of solutions.

In the initial design, the user is able to suggest a lay-up in terms of num ber of plies, ply

thickness, and ply direction, with each ply as a design variable. In the analysis, if any specific

ply thickness is directed to be come zero, that particular ply a nd its asso ciated ply orientation

can be removed from t he com posite panel design. [3] Analyses can also be perform ed to

determine the optimal thicknesses of the co re and laminate materials in various sections of a

structure.

1.4 Chassis Design

1.4.1 Preliminary Design: Packaging

Prior to the development of the composite pa nels to be utilized in the 2007 University

of Toronto chassis, it was necessa ry to develop an overall concep t for the vehicle, and ensure

that all p ackaging requ irements co uld be m et. A racecar chassis m ust be lightw eight, an d

torsionally stiff, but m ust also allow attach ment points and house all subsection components.

Before any optim ization could take place, a rou gh design of the fram e was created to ensu re

the weight distribution of th e vehicle was balanced, the de sired suspension geometry was

achieved, and in general, the overall placem ent of each vehicle com ponent was well thought-

out in terms of mounting and eventual m aintenance. The task of packaging an entire veh icle

is a crucial step in the chassis design process, particularly with the tight packaging constraints

of the relatively sm all Form ula SAE vehicles . Each co mponent and each section of th e

vehicle must be carefully considered in term s of its im pact in the general mounting area, as

well as the impact on the entire vehicle. Carefu l planning in this early stage of the design will

lead to a superior overall vehicle package further along in the design cycle of the racecar.

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1.4.2 Chassis Design and Optimization

Once all of the space co nstraints are decide d upon in the packaging phase, the actual

chassis design can be considered. The m ain goal of a racecar chassis designer is to produce a

lightweight structure with an optim al torsional stiffness as to allow suspension setup changes

to show their effects on the handling of the vehi cle, rather than sim ply being absourbed into

the frame. The key to this goal is in setting an “optimal” stiffness, as opposed to aim ing for

the “maximum” stiffness. When optimizing for low mass, and high torsional stiffness, there is

a tradeoff that m ust be m ade. For every b it of m ass added to the vehicle in the form of

additional tubes or structures, there will be a stiffness gai n, but the relationship is not

necessarily a linear one. The angular displacem ent of the chassis can be reduced by adding

mass to the chassis in the form of properly triangulated chassis tubes, or composite panels, but

as the theo retical “perfectly stiff” chassis is approached, the mass will becom e excessive f or

the given application. Essentially, there will be a point at which additional stiffness gains will

only come at the cost of extensive weight gain.

For the optim ization of the steel tubular frame of the chassis, Pro/Engineer and

Pro/Mechanica sof tware was utilize d. This is the standard software package used by th e

University of Toronto Formula SAE Racing Team in their designs. The main objective of this

optimization study was to focus on the steel portion of the chassis, using a simplified model of

the composite sandwich panels at first, and ev entually producing a more accurate model with

the final composite panel design fully incorporate d. The in-depth design and analysis of the

composite panels was developed using Altair Engineering com posite analys is cap abilities.

Both of these analyses are outlined in more detail later in this report.

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1.4.3 Chassis Fabrication

While the steel tube portion of the frame and the geometry of the composite panels

were being finalized, a steel chassis jig was concurrently designed to accurately locate the key

points of the frame; mainly being the suspension and engine mounting points.

With the foundation points of the chassis held in place, each steel chassis tube was

hand ground to fit and TIG welded into place. Mounting regions were left empty to later bond

in the designed and fabricated composite panels. While still on the jig, the chassis was stress

relieved to reduce twist of the frame upon removal from the jig structure. It is crucial that all

suspension points remain in their relative locations to ensure the proper handling of the

vehicle.

1.5 Composites in Chassis Design

A com posite sandwich panel refers to a laye red structural panel constructed of two

laminate layers separated by a core m aterial. Composite panels can be m ade from countless

types of m aterials, however, the panels that will be discussed in this report are carbon fibre

laminate co mposite pan els with a Nom ex honeycomb or balsa core m aterial. Figure 1.3

shows a sample of a carbon fibre laminate with Nomex core.

Figure 1.3: Composite panel with carbon fibre laminate and Nomex core. [1]

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A major goal of the 2007 University of Tor onto chassis design was to create custom

designed and fabricated carbon com posite panels for use in the 2007 fram e. Optimization of

these pane ls in te rms of lam inate thicknes s, core thickness, and pl y direction served to

increase the overall stiffness of the chassis, and reduce weight by replacing the equivalent

steel structure mandated in the Formula SAE rules.

Fibre orientation is a m ajor consideration in the design of com posite panels, and w as

one of the areas significantly im proved through the use of Altair Engineering softw are. Plain

weave carb on fibre clo th is fabricated with fi bres running in the directions of 0 and 90

degrees. As the cloth is loaded in differing dire ctions, the orientation of the f ibres will result

in different moduli. Figure 1.4 shows a polar plot of the re lative moduli of a plain weav e

cloth as a function of fibre orient ation. [2] In an isotrop ic material, this sam e plot would be

represented as a circle of the same modulus in any orientati on. Carbon lam inates, however,

are not homogeneous materials. By placing various layers of a similar laminate material in

differing ply orientations, a m ore circular plot can be developed. B y using optim ization

software to identify th ese key orientations, the plies can be placed in s tructure specific

directions, providing optimal stiffness gains.

Figure 1.4: Polar plot of

elastic modulus versus

fibre orientation [2]

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1.5.1 Composite Sandwich Panel Design

Upon completion of the overall geometry of the chassis, work progressed to the design

of the panels themselves. This design process formed the basis of the evaluation of Altair

Engineering OptiStruct software. The University of Toronto Formula SAE Racing team was

in a fortunate situation in 2007 to have the ability to fabricate panels to any specification.

Following the OptiStruct analysis of the composite panels, they were manufactured as per the

results of the design study.

As m entioned previously in this report, th e co mposite pan els utiliz ed in a Form ula

SAE chassis must also serve as side impact structures. The analysis of a side impact situation

presents a dyna mic loading co ndition, which differs greatly from general stiffness

optimization. The m ethod utilized to dem onstrate equivalency of the pa nels was to calculate

the energy absorbed, an d the maximum load accepted by the standard st eel structure required

in the Formula SAE rules, and to produce a com posite s tructure able to absorb at leas t the

same a mount of energy, and m aintain the sam e load. Generalized pane l calculations were

developed to estimate the minimum laminate and core thicknesses allowable to produce a safe

structure. T hese values were used as constraints in the OptiStruct an alysis. See Appendix B

for the calculations of the equivalence of the panels. A similar process was carried out for the

forward section of the composite chassis, and is also shown in Appendix B.

1.5.2 Composite Panel Fabrication

The composite panels were created by appl ying uniform pressure using a vacuum-bag

technique to ensure a uniform lay-up. The la yering consisted of th e carbon lam inate plies

determined in the OptiStruct optimization analysis, followed by a thin layer of fiberglass cloth

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to ensure an adequate bond to the core m aterial, and then the Nom ex core m aterial, with a

symmetric lam inate lay-up on the opposing face of the panel. The lam inate m aterial was

soaked in a two-part epoxy-resin to bond it to the core material. To ensure a firm bond of the

carbon laminate to the core, stiff plates were placed above and below the lay-up, and the entire

assembly was sealed an d pressed to gether through the application of vacuum pressure. The

process of “vacuum -bagging” a composite part is important in sealing th e layers together, as

well as in removing excess epoxy and air bubbles from the carbon cloth. In composite design,

the carbon cloth requires only sufficient epoxy to so ak into all of the fibres. All excess epoxy

will not add to the stif fness of the composite panel, but will only m ake the structu re heavier.

Figure 1.5 shows the fabrication assem bly, which will be com pleted under vacuum in a

similar manner to the vacuum-bag setup shown in the same figure, which shows the vacuum -

bag operation being carried out to create a curved panel rather than a flat one.

Figure 1.5: Composite panel fabrication setup, and vacuum-bag setup [2]

Once the composite panels were designed and fabricated, they were then bonded into

the chassis using a lightweight two-part epoxy. It was important ofr the epoxy used in this

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stage to have sufficient vibration damping properties to prevent the bonds from cracking under

the vibration loading of a racecar. Testing was completed on several epoxies to find one that

was optimal for the application. These results are shown later in this report.

CHAPTER 2:

METHOD AND APPROACH

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2 METHOD AND APPROACH 2.1 Chassis Design Utilizing Computer Analysis

2.1.1 Design of the Overall Structure

In the ove rview given in s ection 1.4.2 Chassis Design and Optimization, it was

explained that in chassis desi gn, it is im portant to determ ine the optim al torsional stiffness

range for the design of a racecar chassis. A good rule of thumb states that the chassis stiffness

should be around 6 to 8 tim es greater than th e difference between th e front and rear roll

stiffness values for the vehicle. [4] The intent of this is to ensure th at roll stiffness between

the sprung m ass (chassis) and unsprung m ass (out board suspension) is due m ainly to the

suspension. [5] The effects of a less than op timal chassis stiffness would be a vehicle for

which it is difficult to model and predict its behaviour and handling.

Based on front and rear roll stiffness values of 663 ft-lb/ deg and 343 ft-lb/deg,

respectively, for the 2007 Form ula SAE vehicle, this rang e was dete rmined to be between

1950 ft-lb/degree to 2800 ft-lb/degree. To desi gn beyond this range would create a fram e that

is heavier than is ne cessary, serving to only reduce the perform ance of the vehic le with little

gain to the predictabi lity of the handling. Appendix C shows one of m any iterative analyses

focusing on the steel p ortion of th e frame, in which a baseline design was analyzed, and a

series of small changes were made with a stiffness analysis performed for each iteration.

A baseline design of the f inite ele ment analysis m odel of the stee l tu be f rame was

created utilizing beam elem ents, and applying a linear analysis. In early m odels, th e

composite sandwich panels were modeled as simple shell elem ents with isotropic properties.

While in re ality, composite pane ls are not ac tually iso tropic, this assumption simplif ied the

model and allowed many iterations of the finite element analysis to be done consecutively for

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the steel portion of the frame. The goal of the early design studies was to develop the relative

stiffness values for various steel fram e geometries. Upon c ompletion of the com posite panel

design, it was integrated into the analysis model as an a dvanced shell w ith the exact

directional properties of the proposed lay-up. Figure 2.1 shows the deflecti on results of an

iteration of the chassis design.

Figure 2.1: Displacement plot of baseline chassis design

Constraints in the m odel includ ed lim iting the m ovement of the left, rear, low er

suspension point from translating in the x, y, and z directions. The right, rear, lower

suspension point was restricted in the x (longitudinal), z (vertical), but allowed to translate in

the y (lateral direction). Allowing this lateral movement serves to avoid over-constraining the

chassis, which would produce stiffness values much higher than is realistic. A torque of 2000

ft-lb was ap plied at a centrepo int o f the forwar d axle of th e chass is. Because all analyses

carried out in these s tudies were linear, the actua l va lue o f the torque applied is arbitra ry,

though the relative angular deflection values of each iteration of the chassis under this load are

of interest in optimizing the design.

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The final theoretical s tiffness value obtai ned for the 2007 University of Toronto

Formula SAE chassis design was approxim ately 2250 ft-lb/deg, which is within the desirable

range. This value was validated through a physical tors ion test upon comple tion of the entire

Formula SAE vehicle.

At the com pletion of this stage, th e act ual connections and m ounting points of the

frame were analyzed in more detail to ensure no local high stress ar eas existed, though this

process is outside the scope of this report.

2.1.2 Design of the Composite Structure

One of the objectives in the design of the 2007 Form ula SAE chassis was to produce

custom-designed and m anufactured com posite sa ndwich panels in an ef fort to increa se

stiffness of the chassis, while decreasing its weight. Com pletion of this objective included

choosing which composite materials were to be used in the design, as well as optim izing the

lay-up of these particular materials. Optimizing the lay-up included choosing the thickness of

the core material and of the lam inate skins, the number of layers m aking up these lam inate

skins, and the orientation of each respective layer.

In the optim ization of a com posite structur e, there are clearly m any variab les to be

considered, and with countless permutations of these variables, it can be a seem ingly endless

task attem pting to determ ine what the optim al layout for a giving structure and loading

situation is. Due to the complexity of this type of design study, it was determined that the use

of Altair En gineering OptiStruct sof tware w ould streamline this design process, and reduce

the tim e necessary to design com posite sandw ich panels for use in the 2007 University of

Toronto chassis.

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The HyperLaminate module of the OptiStruct software package allows the engineer to

specify the number of initial layers, the material properties of each layer, its initial orientation,

and then the boundaries of how much each lay er can rotate. The software can run this design

study, testing com binations of lay-up orientat ions, and converging upon a specific lay-up

which results in the lowest overall deflection of the structure being analyzed.

In the early design stages, potential materials to be incorporated into the analyses were

selected based upon availability. Due to cost constraints, the design was lim ited to core

materials and carbon cloths that were availabl e in sm all volumes. In term s of carbon fibre

cloths, there are com panies that will design many different custom weaves, however these

customized fabrics must be purchased in large volumes. Upon determining the possible cloths

that could be used in the 2007 University of Toronto chassis design, the properties of these

materials were specified in the finite element analysis model.

The focus of the design studies carried out was to te st various combinations of cloth

types, and various lam inate and core m aterial com binations, allowing the design study to

optimize the orientation of each tested lay-up. Th e final composite panel design is outlined in

Table 2.0. Upon com pletion of the design of the co mposite lay-up, it was incorporated into

the full chassis model to determine the f inal theoretical stiffness value. This theoretical value

has been estim ated at around 2250 ft-lb/deg, whic h would represent an 8% stiffness increase

over the previous 2006 University of Toronto cha ssis. Application of the composite materials

in the design produced an overall w eight reduction of 7.5 lb over the Formula SAE m andated

steel structure.

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Table 2.0: Final Composite Panel Lay-up Layer Description

1 8.4 oz. plain weave carbon fibre cloth, fibres running 0º and 90º

2 6.0 oz. unidirectional carbon, fibres running at 45º

3 6.0 oz. unidirectional carbon, fibres running at -45º

4 3/4” Nomex honeycomb core, standard 1/8” cell




2.2 Chassis Design for Safety

While stiffness and weight are th e m ajor concerns in des igning a racecar chass is,

another im portant consideration is driver safety. Calculations and analysis carried out to

determine stiffness are very different from those com pleted to determine whether a vehicle is

safe in an impact or rollover situation. The Formula SAE series has developed a set of rules to

mandate what a minimum steel chassis must be comprised of. Chassis designers m ay diverge

from these rules, bu t o nly if equivalence of the designed chassis to the Formula SAE

mandated chassis can b e proven. The f ollowing sections outline the pr oof of equivalence o f

the side and forward structures of the vehicl e. These calc ulations determined the m inimum

core and la minate thicknesses, which were used as m inimum constraints in the design of the

composite sandwich panels.

2.2.1 Equivalence of Side Panel Structure

This section outlin es th e proof of equivalency of the 2007 University of Toronto

chassis side panel in the case of a side im pact. Equivalence was based upon a com parison of

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the energy absorption capabilities of the SA E m andated side structure versus the 2007

University of Toronto side com posite panel. See Appendix B: Side Impact Equivalency

Calculations.

Figure 2.2 represents the geometry of the For mula SAE equivalent steel structure that

2007 University of Toronto chassis would have run in the absence of a com posite sandwich

panel tub section. This structure m eets all sp ecifications def ined in the Form ula SAE rules

and was used in comparison to the 2007 University of Toronto composite structure.

Figure 2.2: Equivalent FSAE steel structure of 2007 UofT side panel [1]

Figure 2.3 represents an approxim ation of the co mposite sandwich panel side section

of the 2007 University of Toronto chassis. The side impact panels ca n be approxim ated as

rectangular in shape with averaged values of width and height. This geometry allows standard

equations and calculations to be used in determining the equivalency of the panels.

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Figure 2.3: Rectangular approximation of UofT composite structure [1]

2.2.2 Equivalence of Forward Structure

The process of proving the equivalence of the forward composite structure of the

chassis is slightly m ore complicated than the s ide panels due to the various im pact situations

that m ust be considered. The for ward structur e m ust be considered in the case of a side

impact, as well as a frontal im pact, in which the panels could potentially buckle under the

frontal load. The side impact case can be dealt with in a similar manner as for the side panels,

however the frontal im pact scenario m ust incl ude the possibility of panel buckling and the

associated com posite failure m odes. Calcul ations for these situations can be found in

Appendix B: Forward Structure Calculations: Side Impact Case, and Frontal Impact Case.

Diagrams from this section are referred to in the calculations.

Figure 2.4 (Left) represents the geom etry of the For mula SAE equivalent steel

structure that the 2007 Univers ity of Toronto chassis would ha ve run in the absence of a

composite sandwich panel forward chassis section. This structure m eets all specifications of

the Form ula SAE rules and was used in com parison to the 2007 University of Toronto

composite forward structure.

19

Figure 2.4 (Right) shows the forward structure of the 2007 University of Toronto

chassis, m ade up of c omposite sandwich pane ls. Bends in the composite panels are

represented as single solid lines in the figure below. The indicated panel which acts as the roll

hoop bracing were m ade with a ba lsa core material for added s upport. All other panels used

Nomex core.

Figure 2.4: FSAE equivalent steel structure and composite forward structure [1]

Figure 2.5 shows the simplif ied composite structure used in frontal an d side im pact

calculations ( Appendix B). The structure consists of a flat com posite sandwich panel of

representative size with an attached steel tube at the bottom, and free at the top. Calculations

were carried out considering only the two si de panels, disregarding the bends and upper

portion of the bulkhead support structure. This simplified model is actually more conservative

than the real-life situation, in which these panels are supported along the upper edge by the

closed-off top panel.

20

Figure 2.5: Simplified bulkhead support structure [1]

2.2.3 Rollover Analysis

To com pletely dem onstrate the equivale nce of the 2007 University of Toronto

composite forward structure to the F ormula SAE standard tube structur e, it was necessary to

look at the deflection of the enti re front section of the vehicle in a roll over situation. To

accomplish this, a comparative FEA study using Pro/Engineer and Pro/Mechanica was carried

out on the standard Form ula SAE structure as well as the 2007 University of Toronto

composite support structure. A lo ad approximately equal to the weight of the car and driver

was applied downward at the top of the front bu lkhead to sim ulate a rollover situation. The

frame assembly was c onstrained just behind th e forward structure to allow a comparison of

only the structure forward of the hoop. All figures referred to in this section can be found in

Appendix A: Additional Figures section of this report.

The first m odel consisted of a standard Formula SAE forward support structure as

defined in the rules; see Figure A1. The finite elem ent m odel was created using bea m

elements representing the 1” diam eter, .049” th ick steel tubing. The model was meshed and

21

analyzed resulting in a maximum deflection of .052”, measured at the bottom tube of the front

bulkhead; see Figure A2.

Figure A3 shows the geom etry of the 2007 Unve rsity of Toronto com posite forward

structure. T he composite panels of the 2007 University of Toronto chassis were m odeled as

advanced shell elements. For these shells, each layer (skins and core material) were defined in

terms of their directional proper ties. The same load was applied to the c omposite structure as

in the case of the Formula SAE tube structure. The model was meshed and analyzed showing

a deflection of .0051”, also measured at the lower front bulkhead tube; see Figure A4.

Each of the geometries was compared through linear analysis of the structures. Under

the given loading condition, stresses are far from the yield point of the materials, so this type

of analysis is accu rate for a com parison study. The results of the study demonstrate that th e

deflection is much smaller in the c ase of the composite pan el structure, concluding that it is

equivalent, and may safely replace the Formula SAE mandated structure.

CHAPTER 3:

MATERIALS AND MANUFACTURING

23

3 MATERIALS AND MANUFACTURING

3.1 Materials Selection

The base of the 2007 U niversity of Toronto chassis consists of a 4130 and m ild steel

tube frame chassis. The basic frame is shown in Figure 3.1. Added to this tub frame were the

custom-designed composite sandwich panels descri bed previously in this report, as shown in

Figure 3.2. Throughout this report, the benefits of utilizing composite materials in the design

of a chassis have been touched upon. These be nefits include increased stiffness, decreased

mass, and in general, com posites tend to produ ce a cleaner overall aes thetic for th e vehicle.

While these are all valid reasons to utilize composite materials, there are still many reasons to

retain the use of steel tubing in a chassis design.

Figure 3.1: Steel tube frame Figure 3.2: Composite panels added

In the early design s tages of the 2007 University of Toronto chassis, it was decided

that the rear structu re of the vehicle would be constructed of thin-walled steel tub ing, with a

simplified tube structure in the tub and forward section of the vehicle to which the com posite

panels would be bonded. The decision to retain the use of steel in these areas had several

justifications.

24

The first reason was to ensure the accurate placement of suspension po ints. A steel

chassis jig is a relativ ely easy fixtu re to des ign and build, whereas the jigging necessary to

accurately locate and bond in su spension po ints to a com posite chassis is much m ore

complicated, and very much depends on the skill level of the composite manufacturer.

The second reason deals with accessibility of vehicle components, and mounting. The

rear of the vehicle hou ses the engine and all of the m ajor powertrain subsystem s of the

vehicle. It is very im portant that these ar eas are fully ac cessible for easy m aintenance and

repair. A well-designed rear st eel tube s tructure can pro vide a stif f struc ture, while s till

allowing access to necessary co mponents. Steel m ounts and tabs can be easily welded in

place and can also allow a certain degree of fr eedom in packaging vehicle com ponents after

the chass is has been co mpleted. Com posite ma terials do not deal well with concentrated

loads, and must be precisely designed to do so. They do not allow leeway in term s of

changing the location of a component after the design stage has been completed.

The third reason has to do with the cost of composite materials and the accessibility to

the appropriate composite manufacturing facilities. The cost of a composite chassis versus the

cost of a Formula SAE steel chassis can easily reach ratios of 7 to 1, or even higher. Not only

are composites expensive, but they can be dangerous to use without the proper facilities.

Due to the above reasons, the comprom ise was made to c reate a chassis with a rear

steel sec tion, and a composite f orward se ction. It is f elt that th is co mbination d erived th e

benefits from both m aterials and produced and op timal chassis design in term s of stiffness,

weight, manufacturability, accessibility, and cost.

The decision to use specifically 4130 chrom ium-molybdenum steel was based upon

several justifications. 4130 is a low-carbon, high strength steel which is generally used in its

25

normalized state, and does not require heat treat ment. It is easily weld able, which is a key

factor in its use for this app lication. 4130 can be stress reliev ed after welding to reduce twist

in the chassis before removing it from the jig.

3.2 Tubular Steel Chassis Manufacturing

The steel portion of the frame was the first to be manufactured, and acted as a base to

which the composite sandwich panels would bond. The first step in creating the chassis was

the design and m anufacture of a jig. The purpose of this ch assis jig wa s to pick up the key

points of the car and ensure that throughout the manufacturing process, that they do not move.

These key points are the inboard suspension points, where the a-arm s of the vehicle attach to

the chass is. The design of the suspension geo metry of a r acecar is ve ry sensitive to sm all

changes. For example, if one of the inboard suspension points were to move by even 0.25”, it

could easily cause a change in the handling of th e vehicle. The clos er the car can be built to

the specifications of the suspension geom etry, the more closely the susp ension model will f it

the car, and the more predictable it will be.

Upon completion of the chassis jig, the very first steel chassis tubes were fastened in

place, and each addition al steel tube was hand ground and welded onto the fra me. Thin-

walled steel tubing was used for the chassis, with tube diameters ranging from 0.5” to 1.0” and

wall thicknesses ranging from 0.028” to 0.095” . These diam eters and thicknesses were

chosen based upon the FEA optimization of the steel portion of the frame.

Once all ch assis members were ground and welded into p lace, the k ey nodes of the

chassis were stress relieved. The steps of this process consist of heating up the node evenly

with an oxy-acetylene torch until it becom es a dark cherry red colour. This should m ean that

26

the steel is still below the annealing or normalizing temperatures. The goal of stress relieving

is not to ch ange the mechanic al pr operties of the stee l, b ut sim ply to rem ove the stres ses

induced by welding. Upon com pletion of stress relieving, the chassis was ready for rem oval

from the jig.

3.3 Composite Manufacturing

3.3.1 Sandwich Panel Construction

For the 2007 season, custom composite sandwich panels were manufactured for use in

the 2007 University of Toronto chassis. The la y-up orientation and thickness of these panels

was optimized through the use of finite elem ent analysis software. Th e final lay-up of the

panels is outlined in Table 3.0, Panel Lay-up.

Table 3.0: Panel Lay-up Layer Description

1 0.120 oz. fiberglass scrim cloth




5 0.120 oz. fiberglass scrim cloth

6 3/4” Nomex honeycomb core, standard 1/8” cell

7 Repeat of layers 5, 4, 3, 2, 1 on other side of core material

MGS L-135 epoxy with MGS 133 hardener was us ed to bond the skin layers to the

core material. Layers 1 and 5, the fiberglass scrim cloth, were added to ensure a secure bond

of the laminate layers to the core, and to provi de a smooth and damage resistant outer layer to

the panel.

27

The composite core consisted of 3/4" Nom ex honeycomb c ore material as listed for

layer 6 of the above table. This was the core m aterial used for all panels except the one

directly attached and forward of the front roll hoop. For this panel, 3/ 4" balsa core w as used

to increase stiffness in the roll hoop bracing region, which also serves as the bellcrank

mounting location. The increased density core pr events local failure of the skin and core

material beneath the singl e shear bellcrank m ount. Figure 3.3 shows the balsa core panel

being fit to the chassis.

Figure 3.3: Balsa panel providing support of bellcrank mounts [6]

3.3.2 Panel Lay-up Process

The following steps outline the general proce ss of laying up the co mposite panels that

were designed for the 2007 University of Toronto chassis. All figures referred to in this

section can be found in Appendix A: Additional Figures section of this report.

28

A) The panel manufacturing process begins with a clean alum inum jig plate to ensure the

final panel is flat and even. This surface is als o used for t he subsequent vacuum -

bagging of the panel. To ensure the pane l can be rem oved from the surface, it is

treated with a mould-release agent.

B) The primary layer of 0.120 oz. fiberglass sc rim cloth was laid down on the table and

soaked with epoxy. This will represent the outermost surface of the panel.

C) Starting with the plain weave carbon, the cloth was placed upon the lay-up surface and

soaked with epoxy and. The uni directional cloth was also ad ded to the lay-up in each

respective 45º, and -45º orientation, and soaked with epoxy. (See Figure A5, A6) The

final inner layer of scrim cloth was added to the lay-up, and soak ed with epoxy. At

this point, the entire laminate layer on one side of the panel has been completed.

D) The front and back surfaces of the Nom ex co re m aterial were ligh tly coated with

epoxy and added as the next layer. (See Figure A7)

E) Steps C and B were repeated, this tim e in reverse order to produce a symmetric lay-up

on the upper face of the panel. (See Figure A8)

F) At this po int, the pan el lay-up was com plete, and only the vacuum -bagging process

remained. For this, layers of peel ply and breather cloth were added. A final layer of

aluminum sheet was added to create a flat top surface, and to produce an even pressure

distribution over the surface of the panel.

29

G) The entire assembly was covered in vacuum-bagging plastic and sealed. The air was

then evacuated from the bag, pullin g the exces s epoxy thro ugh the peel ply and into

the breather cloth to be discarded after curing. (See Figure A9)

H) The assembly was allowed to cure for 24 hours, and then removed from the jig plate.

3.3.3 Composite Bonding Process

Upon com pletion of the com posite sandwich panels, templates were m ade of each

composite section to be bonded into the chassi s. Bends were crea ted in the panels by

removing the carbon lam inate layer on the inner side of the bend. Some of the Nom ex core

was also removed to allow the panel freedom to bend. The open cut was then filled with a

lightweight epoxy, bent to the appropriate geometry and held to cu re. Several layers of plain-

weave carbon fiber clo th were add ed to i nner side of the bend to add strength. Figure 3.4

shows an exam ple of this proces s. As well, see Additional Figures, Figures A11, A12 for

pictures of the actual panels used on the 2007 University of Toronto chassis.

Figure 3.4: Example of a bend applied to a composite panel [1]

Once all section panels were m ade for the frame, they were bonded into the chassis

using a two-part epoxy. This particular epoxy was chosen through cyclic load testing of

30

several different epoxy options (see section 4.3.2: Bonding Epoxy Comparison Test). This

section outlines the process of bonding the pre-fabr icated composite sandwich panels into the

chassis:

A) The bonding surfaces of the steel p ortion of the fra me were prepared b y abrading the

surface, and cleaning th oroughly. Figure A13 shows a typical welded tube section.

This view also shows a seat belt mount that has been welded together prior to bonding

the panels in.

B) Panels were cut and the edges were shap ed to f it the profile of the tubes. Figure A14

shows the panel bonded into place u sing the Hexion Paste epoxy, denoted as the blue

areas in the diagram.

C) Two layers of plain-weave carbon cloth were soaked in epoxy and applied around all

bonding areas. A vacu um-bag was placed around all edges to ensu re a secure bon d

between the panel and tube. Figure A15 shows the application of the additional

carbon, with Figure A16 representing an example of the final product.

CHAPTER 4:

VALIDATION AND PHYSICAL TESTING

32

4 VALIDATION AND PHYSICAL TESTING

4.1 Torsional Stiffness Testing

There are many reasons why theoretical stiffness values determined through the use of

FEA can be inconsisten t with rea l-world resu lts. Manufacturing qual ity, and in particula r

weld quality and steel/com posite bond quality , can accou nt for the g reatest difference in

theoretical and actual values. To validate the torsional stiffness determ ined through finite

element analysis, a physical torsion test can be carried out on the chassis.

In general, this test consis ts of locking the rear portion of the actual chassis at the rear

of the fra me, and applying a torque at the front. To avoid the need to fabricate a fixture for

this test, it can be carried out with the susp ension and wheels a ttached to the veh icle. Rear

wheels can be rested on the ground as a means of “locking down” the rear axle, while the front

can be rested on a pivot point. The torque is a pplied by resting the forwar d axle on a single

pivot at the centre, and hanging weights off the front right wheel attachment point (in a basket

hanging from the wheel studs). A bar is also att ached to the chassis itself and extended off to

the side of the frame for deflection measurement purposes. As varying weights are applied at

the front right corner, the vertical deflection of a bar attached to the chassis can be m easured.

Recording the dis tance from the pivot to the p oint of m easurement, as well as th e dis tance

from the pivot to the applied loa d, the ac tual to rsional stiffness o f the fram e can be

determined. Appendix D outlines the procedu re in m ore detail, as well as th e res ults of a

typical Formula SAE torsion test . Photographs of a Formula SA E torsion test are shown in

Appendix A: Additional Figures, Figures A17 to A19.

Due to m anufacturing delays for the 2007 hubs, actual stiffness values for the 2007

University of Toronto chassis could not be included in this report. Results shown in Appendix

33

D are from the torsion test of the 2006 University of Toronto chassis. T he results of this test

were within 7% of the theoretical stif fness values determined through finite element analysis.

Due to the similarities in the analysis proces s of 2006 and 2007, it is expected that the results

of the 2007 torsion testing will be within a similar range.

4.2 Composite Testing

The 2007 com posite sandwich panels were bo nded into a steel tube frame making up

both the side impact panels as well as the fo rward support structure. The FEA studies shown

in this report do not account for local effects of the att achment between the steel and

composite structures. This means that validation of the models through physical testing of the

materials and structures is a crucial step in the design process of a Formula SAE chassis, or in

any composite application. The following section outlines seve ral tests completed throughout

the design process of the 2007 University of Toronto chassis.

4.2.1 Test of Steel/Composite Attachment

Finite element analysis models of the chassi s do not take into ac count the attachment

strength of the composite panels to the steel chassis members. In an impact situation, a typical

failure mode could be delamination of the composite panels from the chassis tubes, so further

investigation into this a rea was nec essary. The following test serv ed to dem onstrate that the

attachment strength of the com posite panels to the steel fram e is greater than th e crush

strength of the com posite material itself. A physical test was perform ed on a representative

sample of the com posite panel. Figure 4.2 and 4.3 show the test sam ple geometry, which is

equivalent to the length of the side panel on the 2007 University of Toronto chassis. The

34

panel sam ple was bonded to steel tubing at each side in the exact m anner that the panels

would be bonded into the frame. A cross-section of this attachment is shown in Figure 4.1.

Figure 4.1: Bond cross-section [1] Figure 4.2: Diagram of the test panel geometry [1]

Mounting points were added to the tube s and they were secured to a m ounting

structure. A weight was applie d a t the cen tre of the panel to sim ulate the ef fects of a side

impact scenario. Figure 4.3 shows the actual test fixture from the top and side view.

Figure 4.3: Test fixture for side impact scenario [6]

Upon application of a 471 lb m ass, the panel failed at the load ap plication point, a s

shown in Figure 4.4. Figure 4.5 and 4.6 show the failed sample as well as a magnified view

of the attachm ent point of the steel tubing to the composite panel. The core m aterial shows

delamination from the carbon skins, however, the epoxy bond did not becom e detached from

35

the steel su rface, and the additional carbon bo nded aroun d the steel/com posite connectio n

remained intact.

Figure 4.4: Test sample with load attached [6] Figure 4.5: Sample after failure [6]

Figure 4.6: Magnification of steel to composite bond after failure [6]

Results from these physical tests demonstrate that the panel to steel attachment will not

fail before the com posite panel itself under the a pplicable loading cond itions. This is a key

point in the validation of the overall chassis as a safe structure.

4.2.2 Bonding Epoxy Comparison Test

To find the most suitable t ype of epoxy for use in bonding the composite panels into

the chassis, a com parison test was perform ed on four different potential bonding compounds.

36

The test se tup is s hown in Figure 4.7, consisting of a cyclic alternating tensile and

compressive load of 170 lb. The connecti on is the sam e as would be found on the 2007

University of Toronto chassis, without the ad dition of a carbon wrap layer. The test was

meant as a com parison of four epoxy types, so the additional carbon wrap is no t necessary.

The fixture was set up in the exact sam e manner for each epoxy tested. The epoxies tested

and their relative performances are listed in Table 4.0.

Figure 4.7: Epoxy testing fixture

Table 4.0: Epoxy Test: Number of Cycles to Failure Epoxy Type Cycles

to Fail. Notes

A Hexion Paste MGS 235/K 29830 Very easy to work with

B 3M 3524 Filling Compound 9213 Cracks formed within first 300 cycles

C MGS L-135 Adhesive, w/ filler 17982

D BetaMate 31288 Difficult to work with – runs off of part

Manufacturing quality is anothe r factor th at has a significan t effect on the strength of

the final bond using a particular epoxy. Higher viscosity epoxies can be very difficult to use

because they will flow away from the bonding surface. For this reason, epoxies A and B were

preferable due to their paste-like consistency.

37

Epoxy A, the Hexion P aste MGS 235/K was chosen for use on the 2007 com posite

panel bonding for several reasons. The Hexion Paste and the BetaMate epoxy cam e very

close in the cyclic lo ad test, however the th ick consistency of the Hexi on Paste allowed it to

remain in place during panel-bond ing, resulting in a higher quality bon d, free of gaps. The

Hexion Paste epoxy is produced specifically fo r com posite structures under high fatigue

loading conditions, having a high tear strength and high resist ance to crack propagation under

these conditions. It is also specifically m ade to be used in situations where som e bonding

surfaces will be v ertically oriented, and epoxy v iscosity is an i ssue. Regular conditions of a

racecar include heavy vibration from the e ngine and other moving components, m aking the

Hexion Paste specifically useful for this application.

CHAPTER 5:

RESULTS AND CONCLUSIONS

39

5.0 RESULTS AND CONCLUSIONS

5.1 Evaluation of Altair Engineering OptiStruct Software

After working with th eir sof tware, it is eas y to see th at the goal of OptiStru ct is to

streamline the design process by providing softwa re in which the engineer can input m any

design constraints, and run com plicated design studies which can quickly converge upon an

optimal result. The com posite m aterial anal ysis, HyperLam inate module of the software

allows inpu ts in cluding m aterial, weight restricti ons, ply thickness ra tios, etc. and run

multivariable design studies that would normally take weeks, and at great expense. Most FEA

software packages have the cap abilities of doi ng design studies, but with com posite lay-up

design, so m any variables need to be changed, that there are very few powerful com posite

analysis packages that can quickly carry out this type of analysis.

Most FEA software packages run design stud ies by setting a variab le that will change

and iterating this variab le through a series of pre-defined values. This m ethod can provide

very accurate results, but can be very tim e consuming and memory intensive. The benefit of

the OptiStruct software is that it applies a ge netic algorithm to the design study, m eaning that

not every single perm utation of the variables n eeds to be tested to con verge on an optimal

result. This makes OptiStruct faster and more efficient at very complicated analyses, as is the

case for composite lay-up optimizations.

Another notable feature of the composite m aterial ana lysis sof tware is the ability to

define m anufacturing constraints. The engi neer can s pecify ratio s of lam inate layer

thicknesses, or group layers found to be aligne d in the sam e direction. This seam lessly

combines the “des ign for m anufacture” s tage into the optim ization stage, ensuring that th e

final product is not just optimized, but can be easily built as well.

40

With lightweight com posite m aterials be ing used m ore and m ore, it’s im portant to

develop efficient ways to design with them, and use these high- performance materials to their

maximum potential. Th e Altair Engineering OptiStruct software package is a d efinite step in

the right direction when it comes to streamlining composite design.

5.2 Conclusion

The first objective of this project was to design, manufacture and test a F ormula SAE

racecar chassis, with particu lar focus on the in tegration of com posite materials. The second

objective was to develop com posite sandwich pa nels optim ally designed for use in this

particular racecar chassis, utilizing Altair Engineering OptiStruct software.

More specifically, the key goals of ch assis design are to produce a lightweight,

torsionally stiff structure. Gains produced through the optim ization process of the 2007

chassis include an 8% increase in stiffness over the previous 2006 chassis, as well as a 7.5 lb

reduction in weight over the Formula SAE mandated steel structure.

Both of the overa ll goa ls of this th esis were accom plished over the course of this

project through the use of com puter m odeling and analysis, calculations of structura l

equivalence, and through physical testing. It is the author’s hope that this report has given a

sufficient overview of the process of chassis design to demonstrate the need for many types of

analysis and validation in order to produce an end product that is fully optimized, but also safe

for its given application.

41

REFERENCES

[1] Lafreniere, Margaret. “University of Toronto Safety Structure Equivalency”. University

of Toronto Formula SAE Racing, 2006 [2] Pilling, John, “Effect of Orientation on Stiffness,” Michigan Technological University,

http://callisto.my.mtu.edu/MY472/class4/os0.html [3] Altair Engineering, “Efficient Composite Design Optimization Uses Free-Size

Optimization Techniques.” Altair Engineering Newsletter, March 2006, http://www.altairtorino.it/pdf/Newsletter/mar_06.pdf

[4] Milliken, Douglas; Race Car Vehicle Dynamics; Society of Automotive Engineers Inc.;

1995 [5] Thom pson, Lonny; The effects of Chassis Flexibility on Roll Stiffness of a Winston Cup

Race Car; SAE Paper: 983051; Society of Automotive Engineers; 1998 [6] Photographs provided courtesy of Andrew Wong Nevey, S and L. Alvarez. “Optimize the Optimized: Weight Reduction of an F1

Composite Wing”. (2002) Altair Engineering Ltd. http://www.uk.altair.com/images/casestudies/jaguar_racing.pdf

Christensen, Richard. Mechanics of Composite Materials. Krieger Publishing

Company, 1991. Hex WebTM, “Honeycomb Sandwich Design Technology,” Hexcel Composites,

http://hexcel.com/NR/rdonlyres/80127A98-7DF2-4D06-A7B3-7EFF685966D2/0/7586_HexWeb_Sand_Design.pdf

Oberg, Erik; Jones, Franklin; 27th Edition Machinery’s Handbook; Industrial Press Inc., 2004

Norton, Robert L.; Machine Design – An Integrated Approach; Prentice Hall Inc., 1998

APPENDIX A:

ADDITIONAL FIGURES

a1

APPENDIX A: ADDITIONAL FIGURES Chapter 2: Method and Approach

Figure A1: FSAE standard tube structure

Figure A2: Deflection of FSAE tube structure

a2

Figure A3: UofT composite forward structure

Figure A4: Deflection of UofT composite forward structure

a3

Chapter 3: Materials and Manufacturing

Figure A5: First layers being soaked with epoxy on the jig surface

Figure A6: Uniaxial carbon cloth being Figure A7: Nomex core being added to layup placed on layup

a4

Figure A8: Beginning of symmetric layer on opposite side of panel

Figure A9: Final panel layup enclosed in vacuum-bag

a5

Figure A10: Final panel cut to shape, with material removed for bend lines

Figure A11: Bent panel being fit to steel tube frame

a6

Figure A12: All panels cut and fit into place on chassis

Figure A13: Steel chassis section Figure A14: Panel bonded into chassis

a7

Figure A15: Example of panels in chassis Figure A16: Carbon fiber wrapped around bond Chapter 4: Validation and Testing

Figure A17: Torsion test setup for a Formula SAE vehicle. (Note the weight basket attached to front, right wheel studs, measuring bar attached to front bulkhead, and pivot point under front axle (not

visible))

a8

Figure A18: Close up of weight basket attached to front right suspension corner to apply torque on chassis

Figure A19: Measurement of deflection of bar attached to chassis as torque is applied

APPENDIX B:

EQUIVALENCY CALCULATIONS

b1

LIST OF SYMBOLS

E = Modulus of elasticity of steel σyeild = Yeild strength of steel lAB = Length of upper SAE tube member lBC = Length of mid SAE tube member lCD = Length of lower SAE tube member dT = SAE steel tube diameter tT = SAE steel tube thickness IT = SAE tube bending moment of inertia Pyeild = Horizontal load on tubes δAB = SAE upper tube deflection δBC = SAE upper tube deflection δAB = SAE upper tube deflection δavg = Average tube deflection ψyeild = Maximum energy absorption (limiting tube yields) Pmax = Max load on SAE structure (limiting tube yields) Ecarbon = Modulus of elasticity of carbon laminate Enomex = Modulus of elasticity of nomex core λ = Poisson’s ratio for carbon panel h = Height of composite panel w = Width of composite panel tcarbon = Thickness of laminate skin tnomex = Thickness of core material tpanel = Total panel thickness lT = Length of support tubes dT = Diamater of support tubes tT = Thickness of support tubes IT = Support tube bending moment of inertia Ptube = Load applied to each tube σtube = Stress in support tube δtube = Support tube deflection ψyeild = Support tube energy absorption D = Panel bending stiffness Kp = Deflection geometry constant σpanel = Panel wall stress ψpanel = Panel energy absorption S = Safety factor in panel Ptotal = Total load carried by structure ψtotal = Total energy absorbed by structure

b2

δavg 0.19 in=δavgδAB δBC+ δCD+

3:=

δCD 0.17 in=δCDlCD

3 Pyeild⋅

48 E⋅ IT⋅:=

δBC 0.24 in=δBClBC

3 Pyeild⋅

48 E⋅ IT⋅:=

δAB 0.16 in=δABlAB

3 Pyeild⋅

48 E⋅ IT⋅:=

Deflection of Tubes

Pyeild 238.37 lbf=Pyeild4 IT⋅ σyeild⋅

lBCdT2

⋅

:=Horizontal Load on Tubes -- ascalculated for the limiting member

Loading Conditions

IT 0.021 in4=IT π

dT4 dT 2tT−( )4−⎡

⎣⎤⎦

64⋅:=

Tube ThicknesstT 0.065in:=

Tube DiametersdT 1in:=

Tube LengthslCD 27.56in:=lBC 31.10in:=lAB 27.17in:=

See Figure 2.2 for loading geometry which represents the geometric equivalent steel tube structure of the UT2007 vehicle as stated in the FSAE rules.

Geometric Properties of Tubes

Properties of 4130 Steel Tubingσyeild 44200psi:=E 2.97 107psi⋅:=

Properties of Steel

Side Impact Equivalency Calculations

SAE Standard Tube Structure

b3

Width of Panel

tnomex 0.80in:= Nomex Honeycomb Core Thickness

tcarbon 0.035in:= Carbon Facing Skin Thickness

tpanel tnomex 2tcarbon+:= tpanel 0.87 in= Overall Panel Thickness

Support Tube Geometry

lT w:= lT 27.95 in= Upper and Lower Tube Lengths

dT 0.75in:= Tube Outer Diameter

tT 0.035in:= Tube Wall Thickness

IT πdT

4 dT 2tT−( )4−⎡⎣

⎤⎦

64⋅:= IT 5.04 10 3−

× in4= Tube Bending Moment of Inertia

The maximum energy absorption of all 3 tubes with the limiting tube yielding:

ψyeild32

Pyeild⋅ δavg⋅:= ψyeild 5.63 ft lbf⋅=

The maximum load resisted by these three tubes with the limiting tube yielding:

Pmax 3 Pyeild⋅:= Pmax 715.11 lbf=

2007 University of Toronto Equivalency

Material Properties

Ecarbon 9.5 106× psi:= Carbon Modulus of Elasticity

Enomex 2.8 103× psi:= Nomex Modulus of Elasticity

λ 0.33:= Poisson Ratio

Steel strength and stiffness values are identical to above.

Panel Geometry

See Figure 2.3 for rectangular representation of the proposed panel geometry.

h 20.87in:= Height of Panel

w 27.95in:=

b4

Panel Energy Absorptionψpanel 25.11 ft lbf⋅=ψpanel12

Ppanel⋅ δtube⋅:=

Load Carried by PanelPpanel 3.73 103× lbf=Ppanel

δtube D⋅

Kb w3⋅

:=

Deflection Geometry ConstantKb1

192:=

Panel Bending StiffnessD 2.63 106× lbf in2

⋅=DEcarbon tcarbon⋅ tpanel

2⋅ h⋅

2:=

See attached datasheets for equations and constants used in this section.

Mechanical Response of Carbon Panel

Energy Absorption by IndividualTube

ψtube 1.14 ft lbf⋅=ψtube12δtube⋅ Ptube⋅:=

Deflection of Tubeδtube 0.162 in=δtube

5Ptube

2⋅ lT

3⋅

384 IT⋅ E⋅:=

Yield Safety FactorSF 1=SFσyeildσ tube

:=

Stress in Tubeσ tube 4.42 104× psi=σ tube

Ptube dT⋅ lT⋅

16 IT⋅:=

Mechanical Response of Support Tubes

Ptube 169.96lbf:=

Iterative Parameter

The force placed on each tube is now iterated until the point at which the deflections of the tubesand panel are equal, and one tube has just yielded. This is the maximum deflection of the entire structure before yielding, and will act in the direction normal to the panel. With this value, the load carried by the panel can be calculated.

Assumptions:1. Tubes are held rigidly at both vertical edges by front and rear roll hoops.2. The panels and tubes will deflect together in the direction normal to the plane of

the panels.3. Roll hoops, (0.095" thick steel), do not deflect significantly and will not alter the

loading mode of the panels.

Failure Load and Energy Absorption of Structure

b5

Since the total load resisted by the equivalent panels exceeds the load resisted by the equivalent steel tube structure, the panels are a suitable structure in terms of safety.

Ptotal 4.07 103× lbf=Pmax 715.11 lbf=

Conclusion

Ptotal 4.07 103× lbf=Ptotal 2 Ptube⋅ Ppanel+:=

Total Load Carried by Structure at Yield Point

ψtotal 27.39 ft lbf⋅=ψtotal 2 ψtube⋅ ψpanel+:=

Total Energy Absorption for Structure at Yield Point

Safety Factor of PanelS 9.76=Sσyeildσpanel

:=

Yield Stress of Panelσyeild 1.001 105× psi:=

Panel Wall Stressσpanel 1.03 104× psi=σpanel

Ppanel w⋅

16 tpanel⋅ tcarbon⋅ h⋅:=

b6

δavg 0.130 in=δavgδAB δBC+ δCD+

3:=

δCD 0.078 in=δCDlCD

3 Pyeild⋅

48 E⋅ IT⋅:=

δBC 0.162 in=δBClBC

3 Pyeild⋅

48 E⋅ IT⋅:=

δAB 0.148 in=δABlAB

3 Pyeild⋅

48 E⋅ IT⋅:=

Deflection of Tubes

Pyeild 229.29 lbf=Pyeild4 IT⋅ σyeild⋅

lBCdT2

⋅

:=Horizontal Load on Tubes -- ascalculated for the limiting member

Loading Conditions

IT 0.017 in4=IT π

dT4 dT 2tT−( )4−⎡

⎣⎤⎦

64⋅:=

Tube ThicknesstT 0.049in:=

Tube DiametersdT 1in:=

Tube LengthslCD 20.08in:=lBC 25.59in:=lAB 24.80in:=

See Figure 2.4 for loading geometry which represents the geometric equivalent steel tube structure of the UT2007 vehicle as stated in the FSAE rules. The tube lengths listed below make up the upper, lower and diagonal front bulkhead support tubes noted in the figure.


Properties of Mild Steel Tubingσyeild 44200psi:=E 2.97 107× psi:=

Properties of Steel


Forward Structure Calculations: Side Impact Case

b7

Height of Panel

w 24.02in:= Width of Panel




Lower Support Tube Geometry

lT w:= lT 24.02 in= Lower Tube Length

dLT 1.00in:= Lower Tube Side Length (Square)

tT 0.035in:= Tube Wall Thickness

The maximum energy absorption of all 3 tubes with the limiting tube yielding:

ψmax32

Pyeild⋅ δavg⋅:= ψmax 3.71 ft lbf⋅=

The maximum load resisted by these three tubes with the limiting tube yielding:

Pmax 3 Pyeild⋅:= Pmax 687.88 lbf=

2007 UofT Equivalent Front Bulkhead Support

Material Properties

Ecarbon 9.5 106⋅ psi:= Carbon Modulus of Elasticity

Enomex 2.8 103⋅ psi:= Nomex Modulus of Elasticity

λ 0.33:= Poisson Ratio


Panel Geometry

See Figure 2.5 for rectangular representation of the proposed panel geometry.

h 14.17in:=

b8

Deflection Geometry ConstantKb1

192:=



2⋅ h⋅

2:=



Energy Absorption by IndividualLower Tube

ψLT 2.30 ft lbf⋅=ψLT12δLT⋅ Ptube⋅:=

Deflection of Lower TubeδLT 0.089 in=δLT

5Ptube

2⋅ lT

3⋅

384 ILT⋅ E⋅:=

Yield Safety Factor (Calculated withLower Tube Yielding)

SF 1=SFσyeildσLT

:=

Stress in Lower TubeσLT 4.42 104× psi=σLT

Ptube dLT⋅ lT⋅

16 ILT⋅:=


Ptube 618.23lbf:=

Iterative Parameter

The force placed on each tube is now iterated until the point at which the deflections of the tubesand panel are equal, and one tube has just yielded. This is the maximum deflection of the entire structure before yielding, and will act in the direction normal to the panel. With this value, the load carried by the panel can be calculated.

Assumptions:1. The panels and tubes will deflect together in the direction normal to the plane of

the panels.2. Roll hoop, and bulkhead (0.095" and 0.065" thick steel, respectively), do not deflect significantly and will not alter the loading mode of the panels.


Lower Tube Bending Moment of InertiaILT 0.021 in4=ILT

dLT( )4 dLT 2tT−( )4−

12:=

b9

Since the total load resisted by the equivalent panels exceeds the load resisted by the equivalent steel tube structure, the bonded-in panels are a suitable structure in terms of safety.

Ptotal 2.83 103× lbf=Pmax 687.88 lbf=

ψtotal 10.54 ft lbf⋅=ψmax 3.71 ft lbf⋅=

Conclusion

Ptotal 2.83 103× lbf=Ptotal Ptube Ppanel+:=

Total Load Carried by Structure at Yield Point

ψtotal 10.54 ft lbf⋅=ψtotal ψLT ψpanel+:=

Total Energy Absorption for Structure at Yield Point

Safety Factor of PanelS 11.97=Sσyeildσpanel

:=

Yield Stress of Panelσyeild 1.001 105× psi:=

Panel Wall Stressσpanel 8.36 103× psi=σpanel

Ppanel w⋅

16 tnomex⋅ tcarbon⋅ h⋅:=

Panel Energy Absorptionψpanel 8.24 ft lbf⋅=ψpanel12

Ppanel⋅ δLT⋅:=

Load Carried by PanelPpanel 2.21 103× lbf=Ppanel

δLT D⋅

Kb w3⋅

:=

b10

AT 0.146 in2= Tube Cross-sectional Area

rITAT

:= r 0.34 in= Radius of Gyration

LAB 0.7 lAB⋅:= LAB 17.36 in= Effective Tube Lengths

LBC 0.7 lBC⋅:= LBC 17.91 in=

LCD 0.7 lCD⋅:= LCD 14.06 in=

SABLAB

r:= SAB 51.56= Slenderness Ratio: (All tubes fall into the intermediate

range, 30<Le<100. Therefore, the Johnson method was used to account for both compression and buckling. Reference (2). SBC

LBCr

:= SBC 53.21=

SCDLCD

r:= SCD 41.75=

Forward Structure Calculations: Frontal Impact Case


Properties of Steel

E 2.97 107psi⋅:= σyeild 44200psi:= Properties of 4130 Steel Tubing



lAB 24.80in:= lBC 25.59in:= lCD 20.08in:= Tube Lengths

dT 1.0in:= Tube Diameters

tT 0.049in:= Tube Thickness

IT πdT

4 dT 2tT−( )4−⎡⎣

⎤⎦

64⋅:= IT 0.0166 in4

= Tube Moment of Inertia

AT πdT2

⎛⎜⎝

⎞

⎠

2 dT2

tT−⎛⎜⎝

⎞

⎠

2

−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

b11

Width of Panelw 24.02in:=

Height of Panelh 14.17in:=

See Figure 2.5 for rectangular representation of the proposed panel and tube geometry.

Panel Geometry


Poisson Ratioλ 0.33:=

Nomex Modulus of ElasticityEnomex 2.8 103⋅ psi:=

Carbon Modulus of ElasticityEcarbon 9.5 106⋅ psi:=

Material Properties

The purpose of this section is to check all end load conditions and ensure that in the frontal impact scenario, the bonded-in panel and steel structure will not fail under less load than the equivalent steel structure defined in the rules.

2007 UofT Equivalent Front Bulkhead Support

Pcr 3.44 104× lbf=Pcr 2 PAB⋅ cos 0.094( )⋅ 2PBC cos 0.384( )⋅+ 2PCD+:=

Based on the geometry, the maximum load that may be applied to the equivalent structure is:

PCD 6.05 103× lbf=PCD AT Sy

1E

Sy SCD⋅

2 π⋅

⎛⎜⎝

⎞

⎠

2

−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

PBC 5.78 103× lbf=PBC AT Sy

1E

Sy SBC⋅

2 π⋅

⎛⎜⎝

⎞

⎠

2

−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

Critical Load Values for each TubePAB 5.82 103× lbf=PAB AT Sy

1E

Sy SAB⋅

2 π⋅

⎛⎜⎝

⎞

⎠

2

−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

Since SAB, SBC, and SCD are all less than SJ, the

following equation will be used, accounting for failure by both compression and buckling.

SJ 115.17=SJ π2 E⋅Sy

⋅:=

Compressive Yeild StrengthSy 44200psi:=

b12

IUT πdUT

4 dUT 2tT−( )4−⎡⎣

⎤⎦

64⋅:= IUT 1.39 10 3−

× in4= Upper Tube Bending Moment of

Inertia

ILTdLT( )4 dLT 2tT−( )4−

12:= ILT 0.021 in4

= Lower Tube Bending Moment of Inertia


Assumptions:1. It is assumed the the frontal impact is applied evenly to the front bulkhead and distributed to the steel support structure based on the given geometry.2. The front bulkhead, (1" O.D., 0.065" thick), will not deform significantly enough to change the loading condition of the foreward tubes. This is due to the thickness and outer diameter of the front bulkhead, as well as the energy absourbed by the impact attenuator in a frontal impact scenario.




lGH 24.02in:= Lower Tube Length

dGH 1.0in:= Tube Diameters

t 0.035in:= Tube Thickness




Support Tube Geometry

lT w:= lT 24.02 in= Lower Tube Length

dUT 0.5in:= Upper Tube Outer Diameter

dLT 1.00in:= Lower Tube Side Length (Square)

tT 0.035in:= Upper and Lower Tube Wall Thickness

b13

Total Critical LoadPtube 5.78 103× lbf=Ptube PGH:=

Based on the geometry, the total load the equivalent structure can take is:

Critical Load Values for each TubePGH 5.78 103× lbf=PGH AT Sy

1E

Sy SBC⋅

2 π⋅

⎛⎜⎝

⎞

⎠

2

−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

SGH is less than SJ, so the Johnson

equation will be used.SJ 115.17=SJ π

2 E⋅Sy

⋅:=

Compressive Yeild StrengthSy 44200psi:=

SGH 49.25=SGHLGHrGH

:=Slenderness Ratio: (The lower tube falls into the intermediate range, 30<Le<100. Therefore, the Johnson method was used to account for both compression and buckling. Reference (2).

Effective Tube LengthLGH 16.81 in=LGH 0.7 lGH⋅:=

Lower Tube Radius of GyrationrGH 0.34 in=rGHIGHAGH

:=

Lower Tube Cross-sectional Area

AGH 0.106 in2=AGH π

dGH2

⎛⎜⎝

⎞

⎠

2 dGH2

t−⎛⎜⎝

⎞

⎠

2

−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

Lower Tube Moment of InertiaIGH 0.0124 in4=IGH π

dGH4 dGH 2t−( )4−⎡

⎣⎤⎦

64⋅:=

b14

Since the load at which the SAE structure will fail is lower than the UofT composite structure, the UofT structure is shown to be equivalent.

Pcr 3.44 104× lbf=

Max Load for SAE Equivalent Steel Structure

Max Load for 2007 UofT StructurePtot 6.82 104× lbf=Ptot 2Ptube 2Ppanel+:=

Based on the combined effects of the tube structure and panels, the maximum load that may be applied to the equivalent structure before buckling is:

Buckling LoadPpanel 2.83 104× lbf=

Ppanelπ

2D⋅

w2 π2

D⋅Gc tpanel⋅ h⋅

+

:=

Gc 31900psi:=Shear Modulus



2⋅ h⋅

2:=



b15

The stress at which intracell buckling will occur is much greater than the typical skin yeild strength

of 1.02 x105 psi. Therefore, skin stress is more critical than intracell buckling.

Intracell Bucklingσcell 1.49 106× psi=σcell 2 Ecarbon⋅

tcarboncell

⎛⎜⎝

⎞

⎠

2

⋅:=

Cell Size of Nomex Corecell 0.125in:=

Failure by Intracell Buckling

The maximum calculated facing stress is lower than the stress at which skin wrinkling will occur. Therefore, skin wrinkling is not a concern for this situation.

Skin Wrinklingσwrink 4.73 104× psi=σwrink 0.5 Gc Ecarbon⋅ Enomex⋅( )

13⎛⎜⎝⎞⎠⋅:=

Failure by Skin Wrinkling

The load at which shear crimping will occur is considerably higher than the maximum end load that would be applied to the sandwich panel.

Shear CrimpingPcrimp 3.62 105× lbf=Pcrimp tnomex Gc⋅ h⋅:=

Failure by Shear Crimping

The maximum calculated facing stress is significantly lower than the typical woven carbon skin

yeild strength of 1.02 x105 psi.

Facing Stressσf 2.85 104× psi=σf

Ppanel2 tcarbon⋅ h⋅

:=

Tensile Failure of Facing Material

Maximum End Load for a Single Panel and Tube Assembly

Ppanel 2.83 104× lbf=

Other End Load Failures (of Sandwich Panel)

11HEXCEL COMPOSITES

MAXIMUM MAXIMUM BENDING SHEARBEAM TYPE SHEAR BENDING DEFLECTION DEFLECTION

FORCE MOMENT COEFFICIENT COEFFICIENTF M kb kS

P Pl 5 12 8 384 8

P Pl 1 12 12 384 8

P Pl 1 12 4 48 4

P Pl 1 12 8 192 4

P Pl 1 12 8 2

P Pl 1 13

P Pl 1 13 15 3

Summary of beam coefficients

Simple SupportP = q l b

Uniform Load Distribution

Both Ends FixedP = q l b


Simple SupportP

Central Load

Both Ends FixedP

Central Load

One End Fixed(Cantilever)

P = q l b



P

Load One End

P = q l b2

Triangular Load Distribution


HEXCEL COMPOSITES 12

HexWebTM HONEYCOMB SANDWICH DESIGN TECHNOLOGY

Beam

SAMPLE PROBLEMS BASED ON A STANDARD HEXLITE 220 PANEL

Simply Supported Beam

- taking a beam as being defined as having width (b) lessthan 1/3 of span (l)

Bending Stiffness

D = Ef tf h2 b

2

Where h = tf + tC

Shear Stiffness

S = b h GC

D = (70 x 109) (0.5 x 10-3) (25.9 x 10-3)2 (0.5)2

D = 5869.6 Nm2

Configuration and Data:

Facing Skins Aluminium 5251 H24

Thickness t1 and t2 = 0.50mm

and from Appendix II

Yield Strength = 150 MPa

Ef Modulus = 70 GPa

Poissins Ratio m = 0.33

Core 5.2 - 1/4 - 3003

Thickness tC = 25.4 mm

and from Appendix I

EC Modulus = 1000 MPa

Longitudinal shear = 2.4 MPa

GL Modulus = 440 MPa

Transverse shear = 1.5 MPa

GW Modulus = 220 MPa

Stabilized Compression = 4.6 MPa

As the core shear here will be taken by the weaker transversedirection - take GC = GW shear modulus

S = (0.5) (25.9 x 10-3) (220 x 106)

S = 2849 x 103 N

Considering a centre point loaded beamwith b = 0.5m and l = 2m and P = 1500N

13HEXCEL COMPOSITES

Deflection

Bending plus Shear

ddddd = kb Pl3 + kS PlD S

Where kb and kS are deflection coefficients from page 11.

If doing preliminary calculations, just work out the bendingdeflection.

If optimising design, calculate for both bending and shearcomponents (as shown opposite).

Facing Stress

sssssf ===== Mh tf b

Where M is Maximum Bending Moment expression from page 11

and h = tf + tC

Core Stress

tttttCCCCC ===== Fhb

Where F is Maximum Shear Force expression from page 11

Beam continued

Bending plus Shear

ddddd = 1 x 1500 x 23 + 1 x 1500 x 248 5869.6 4 2849 x 103

ddddd = 0.04259m + 0.000263m

Total = approx 43mm

If excessive, then the most efficient way to reduce deflection isto increase core thickness, and thus increase the skinseparation and the value of h.

M = Pl = 1500 x 2 = 750 Nm4 4

sssssf = 750(25.9 x 10-3) (0.5 x 10-3) (0.5)

sssssfffff ===== 115.8 MPa

So calculated stress is less than face material typical yieldstrength of 150 MPa, thus giving a factor of safety.

F = P = 1500 = 750N2 2

ttttt = 750(25.9 x 10-3) (0.5)

ttttt = 0.06 MPa

So calculated shear is considerably less than core materialtypical plate shear in the transverse (W) direction of 1.5 MPa,giving a factor of safety, which could allow core density to bereduced.

HEXCEL COMPOSITES 18

HexWebTM HONEYCOMB SANDWICH DESIGN TECHNOLOGY

END LOAD CONDITIONS

Considering a uniformly distributed end load ofq = 20kN/m length and with b = 0.5m and l = 2m.

Facing Stress

sssssf = P2 tf b

assuming end load is taken by both skins, and applied loadP = q x b

Panel Buckling

Pb = ppppp² Dl2 + ppppp² D

GC h b

Taking D from the beam calculation example.

sssssf = (20 x 103) (0.5)(2) (0.5 x 10-3) (0.5)

sssssf = 20 MPa

This is safe, as it is considerably less than skin material typicalyield strength of 150 MPa.

Considering the core shear to be in the weaker transversedirection

So GC = GW shear modulus

Then

Pb = ppppp² (5869.6)(2)2 + ppppp² (5869.6)

(220 x 106) (25.9 x 10-3) (0.5)

Pb = 14,413 N

So calculated load at which critical buckling would occur isgreater than the end load being applied (P) of 10,000 N, thusgiving a factor of safety.

End Loading

q = 20kN/m length

19HEXCEL COMPOSITES

Shear Crimping

Pb = tC GC b

Skin Wrinkling

sssssCR = 0.5 [GC EC Ef] 1/3

Intracell Buckling

sssssCR = 2 Ef tf 2

s

NB: s = cell size

Taking GC as GW

Pb = (25.4 x 10-3) (220 x 106) (0.5)

Pb = 2.79 MN

So the calculated load at which shear crimping would occur, isconsiderably greater than the end load being applied (P) of10,000 N, thus giving a factor of safety.

Taking GC as GW

sssssCR = 0.5 [(220 x 106) (1000 x 106) (70 x 109)] 1/3

sssssCR = 1244 MPa

So the stress level at which skin wrinkling would occur, is wellbeyond the skin material typical yield strength of 150 MPa; soskin stress is more critical than skin wrinkling.

sssssCR = 2 (70 x 109) (0.5 x 10-3) 2

(6.4 x 10-3)

sssssCR = 854 MPa

So stress level at which intracell buckling would occur is wellbeyond the skin material typical yield strength of 150 MPa; soskin stress is more critical than intracell buckling.

End Loading continued

APPENDIX C:

FEA OPTIMIZATION STUDY OF CHASSIS

CHASSIS: Finite Element Analysis

Date: 27-Sep-06Car: 2007 Chassis

Variables: L Distance to measurement point Mz Moment applied to frameθ Chassis twist in degrees S Torsional stiffness

Mz [ft-lb] L [in] θ [rad] θ [deg] S [ft-lb/deg] Run # % Inc. Notes167 8.36 0.00431 0.247 676.52 19167 8.36 0.00254 0.145 1148.80 20 69.8167 8.36 0.00215 0.123 1353.03 21 17.8 add in small sections as tubes on front roll hoop167 8.36 0.00187 0.107 1561.19 22 15.4 missing engine mount tube167 8.36 0.00188 0.108 1551.25 24 -0.6 mesh refinement needed167 8.36 0.00161 0.093 1804.04 25 16.3167 8.36 0.00179 0.103 1623.64 26 -10.0167 8.36 0.00179 0.103 1623.64 27 0.0167 8.36 0.00262 0.150 1112.08 28 -31.5167 8.36 0.00158 0.091 1845.04 32 65.9 Run converged - good baseline167 8.36 0.00158 0.091 1845.04 33 0.0 Added bulkhead tubes in167 8.36 0.00164 0.094 1777.71 34 -3.6 Seat back tubes changed to 1", 0.035"167 8.36 0.00150 0.086 1948.36 36 9.6 Hips changed to 1", 0.035", seat back, 0.75", 0.035"167 8.36 0.00148 0.085 1964.08 36 0.8 Rear box diagonals moved to meet at node167 8.36 0.00151 0.086 1932.90 37 -1.6 Lower hips at 1", 0.035", trusses at .75", 0.035"167 8.36 0.00147 0.084 1980.05 38 2.4 Rear box upper sides changed to 1", 0.049"167 8.36 0.00158 0.091 1845.04 40 -6.8 Seat belt upper tubes changed to 1", 0.065"167 8.36 0.00151 0.086 1932.90 43 4.8 Continuation of seat belt tubes changed to 1", 0.035"167 8.36 0.00151 0.086 1932.90 44 0.0 Rear lower box sides reduced to 1", 0.035"167 8.36 0.00151 0.086 1932.90 45 0.0 Rear vertical box edges changes to 0.75", 0.035"167 8.36 0.00152 0.087 1917.68 46 -0.8 Rear box diagonals made 0.75", 0.035"167 8.36 0.00141 0.081 2063.95 47 7.6 Rear box diagonals made 0.625", 0.035"167 8.36 0.00130 0.075 2234.36 48 8.3 Upper engine connecting tubes made 0.625", 0.035"167 8.36 0.00144 0.082 2029.55 49 -9.2 Very rear diagonal tube, reduced to 0.5", 0.035"167 8.36 0.00127 0.073 2297.60 50 13.2 Upper dtrain mount reduced to 0.625", 0.035"167 8.36 0.00126 0.072 2319.48 52 1.0 Rear vertical box edges changes to 0.625", 0.035"167 8.36 0.00126 0.072 2319.48 53 0.0 Rear top box tube reduced to 0.75", 0.035"167 8.36 0.00127 0.073 2297.60 53 -0.9 One of the truss tubes was still 1", 0.035"

APPENDIX D:

TORSION TEST PROCEDURE AND RESULTS

d1

CHASSIS Torsion Testing Procedure

SETUP:

1. Install solid shocks.

2. Attach the square wheels to both rear corners, as well as the left front corner, leaving the right front corner with no wheel.

3. Attach the steel basket to the four studs of the front right corner using wheel nuts to secure it in place. By adding weights to the basket it will be the applied load.

4. Securely attach the front and rear toe bars at their attachment points. These will act as the front and rear measuring bars.

5. Set up dial gauges at an outboard point along the length of each measuring bar.

PRE-TEST MEASUREMENTS:

6. Measure the distance from the centre of the vehicle to the load application point, (the attachment face of the basket). This value is x.

7. Measure the distances from the centre of the vehicle to the dial gauge measurement points. The front and rear values are LF and LR, respectively. If at any point one of the dial gauge moves, re-measure and record the value.

8. Select several masses. Measure the mass of each and label.

TEST PROCEDURE:

9. Zero the dial gauges.

10. Add a mass to the basket, and record the total mass under m.

11. Measure and record the front and rear deflections, dyF and dyR.

12. Remove the mass and ensure the dial gauges have returned to zero. If they have not returned to zero, check that all measurement bars are tightly secured and repeat test.

13. Repeat steps 9 – 11, increasing the mass for each test.

d2

CALCULATIONS:

14. Calculate the moment applied to the frame:

))(( mxMz = [in-lb]

15. Calculate the torsional stiffness of the frame, subtracting the front value from the rear value to remove suspension compliance:

)/(sin12/

1FLdy

MzS −= [ft-lb/deg]

CHASSIS: Torsion Testing

Date: Mar. 30, 2006Car: 2006 Chassis

Variables: x Distance to load application point dy Measured deflectionm Applied mass θ Chassis twist in degreesMz Moment applied to frame S Torsional stiffnessL Distance to measurement point

RUN x [in] m [lb] Mz [in-lb] LF [in] LR [in] dyF [in] dyR [in] θF [deg] θR [deg] S [ft-lb/deg]

1 24.77 5.00 123.85 31.20 33.00 0.0046 0.0020 0.0085 0.0035 2072.76

2 24.77 6.00 148.62 31.20 33.00 0.0050 0.0020 0.0092 0.0035 2167.41

3 24.77 7.00 173.39 31.20 33.00 0.0069 0.0030 0.0127 0.0052 1936.24

4 24.77 8.00 198.16 31.20 33.00 0.0074 0.0030 0.0136 0.0052 1970.41

5 24.77 9.00 222.93 31.20 33.00 0.0081 0.0030 0.0149 0.0052 1921.91

6 24.77 10.00 247.70 31.20 33.00 0.0096 0.0040 0.0176 0.0069 1931.92

7 24.77 12.00 297.24 31.20 33.00 0.0110 0.0045 0.0202 0.0078 1999.62

8 24.77 14.00 346.78 31.20 33.00 0.0129 0.0050 0.0237 0.0087 1925.47

9 24.77 18.00 445.86 31.20 33.00 0.0160 0.0055 0.0294 0.0095 1873.38

10 24.77 20.00 495.40 31.20 33.00 0.0170 0.0060 0.0312 0.0104 1984.64

AVG 1978.38

Theoretical Value (through FEA): 2089.00Percent error of FEA value to actual value: 5.6

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