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
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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.
i
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.
ii
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
iii
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
iv
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
v
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
vi
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
1
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.
2
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
3
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.
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
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
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
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.
Geometric Properties of Tubes
Properties of Mild Steel Tubingσyeild 44200psi:=E 2.97 107× psi:=
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.
Failure Load and Energy Absorption of Structure
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
See Figure 2.5 for rectangular representation of the proposed panel and tube geometry.
Panel Geometry
Steel strength and stiffness values are identical to above.
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
Failure Load and Energy Absorption of Structure
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.
Mechanical Response of Support Tubes
Geometric Properties of Tubes
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.
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
Panel Bending StiffnessD 1.78 106× lbf in2
⋅=DEcarbon tcarbon⋅ tpanel
2⋅ h⋅
2:=
See attached datasheets for equations and constants used in this section.
Mechanical Response of Carbon Panel
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.
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.
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
Uniform Load Distribution
Simple SupportP
Central Load
Both Ends FixedP
Central Load
One End Fixed(Cantilever)
P = q l b
Uniform Load Distribution
One End Fixed(Cantilever)
P
Load One End
P = q l b2
Triangular Load Distribution
One End Fixed(Cantilever)
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]