roll cage 1

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Front End RedesignReport

For:

GVSU Laker RacerCar #95

EGR 345: Dynamic System and Modeling ControlSemester ProjectProf. Hugh Jack

Written by: Matt Brower, John WitteBuilding, testing and design by: 2006 2007 Mini Baja Team

Society of Automotive EngineeringGrand Valley State Universitys Mini Baja Team

12/08/2006


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1

Table of Contents

Abstract 2

Introduction 2

Theory 2

Procedure 8

Results

Wheel deflection test 9Drop test 12Rollover test 14

FEA 15

New Design

Spindle 17Frame 20

Conclusions 22

Recommendations 23

Acknowledgements 24

References 24

Appendix A 25

Appendix B 27

Appendix C 29

Appendix D 30

Appendix E 32

Appendix F 33

Appendix G 36


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Abstract

This report describes the redesign of the front end for the 2007 Grand ValleyState Universitys entry into the Midwest Mini Baja competition sponsored by the

Society of Automotive Engineers (SAE international). It also fulfills the semesterproject requirements for EGR 345 Dynamic Systems and Modeling Control. Theprimary objective of the project described in this report is to start with the existingcar (# 55) design and modify it to not experience the fatigue failure in the spindlethat the 2006 car did. The secondary objective is to improve the vehiclesperformance by lightening it to make it faster, shortening the wheelbase to makeit more maneuverable, and improving the ergonomics of the front to eliminatedriver fatigue. These changes were derived by a consensus of the 2006 teamafter the completion of the 2006 race. To achieve these goals the frame was firsttested to verify its integrity during driving and rolling over by directly testing thestrain in the front members and then calculating the primary stresses using

Coulomb-Mohr theory. After finding the primary stresses and verifying theintegrity of the roll cage, a-arms, and chassis, the spindle was redesigned andtested using Finite Element Analysis to verify its structural integrity. The framewas then shortened to allow the wheels to be moved back. Also, unnecessarymembers were removed and a new material, 4130 chrome moly, and geometry,larger diameter but thinner wall tubing, were chosen for certain frame membersto reduce weight. Finally the front was widened to provide more legroom for thedriver because last years drivers complained of leg fatigue during the 4 hourendurance race.

Introduction

The SAE Baja team at Grand Valley State University intends to enter the 2007Rochester competition with a fully re-designed and re-manufactured vehicle,which will be based on improvements from the 2006 car. GVSU expects to returnas a strong competitor in the 2007 competition with 7 members retained from the2006 team and an additional 2 freshman and 1 junior. At last years competitionin Wisconsin the team finished 2nd place in the chain pull and earned the 20 thpole position for the endurance race. They finished 47th overall in spite of a 45-minute pit stop taken to repair a front spindle during the endurance race. Thiswas a marked improvement over the ranking of 68 th by the 2005 team. Keyimprovements for 2007 will include reducing the vehicle weight by 100 pounds,shortening the wheelbase by 12 inches to improve handling, and thedevelopment of a new, fully machined aluminum, front spindle. Testing was alsoperformed to verify the integrity of the frame during driving and a rolloverincident.


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Theory

Figure 1 shows the locations for the strain gages used in testing the framemembers. There is one gage on each member where stresses are of the mostconcern. The number before the description of the frame member corresponds

to the type of member. A designation of 1 means that the member is critical forthe safety of the driver in a crash. The members with a 1 designation arespecified by SAE in the 2007 rules to be of an equivalent bending strength andstiffness as that of 1018 steel tube, 1-inch in diameter and having a wallthickness of 0.125-inches. The members must also be at least 1-inch in diameterand have a wall thickness of 0.065-inches. The reason for these specificationsis, for example, if the top roll cage member were to fail in a rollover the drivercould be seriously injured. A member of the A-arm would be designated 2 sinceits failure would impair the drive-ability of the car but not the drivers safety.Members designated 2 are specified by SAE to have the same bending strengthand stiffness as described previously but may have a wall thickness as low as

0.035-inches. Loads were applied to the frame to simulate typical driving androllover conditions. Members in the rear of the vehicle were not analyzed for thisreport. Also, only one side of the car was tested to save strain gauges since theframe was symmetric except for two cross-braces.

2-Front and Rear Upper A-arms

2-Spindle

2-Front Lower A-arm

2-Front Lower Shock Mount

1-Top Roll Cage1-Front Roll Cage

1-Roll Cage Support

2-Lower Roll CageSupport

2-Front Upper Shock

1-Side Impact Member

1-Bottom Roll Cage

Pedal Brace

Speedometer Brace

Top Cross Brace

Figure 1: Location and Description of 15 Strain Gages Used in Frame Testing

And 3 Members that were Removed for Testing Purposes


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Figure 2 shows a schematic of a strain rosette used in testing. Each Rosettecontains 3 strain gages that can measure compressive or tensile strain. SolvingEqs. (1-3) for strain in thex, y, and zdirection and entering these strain valuesinto the Maple worksheet in Appendix D yielded the principle stresses acting on

the plane that the rosette was mounted to as shown in Figure 3.

Figure 2: Geometric Arrangement of Strain Gage Rosette

aaxyayaxa cossinsincos22 ++= (1)

bbxybybxb cossinsincos22 ++= (2)

ccxycycxc cossinsincos22 ++= (3)

Figure 3: Plane Stresses Correlating to the Strains from Rosette

Three tests were performed to determine the integrity of the frame. The first wasthe wheel displacement test. For this test, one front wheel was raised up tosimulate the stresses acting on the frame due to the wheel being displaced as ifgoing over a bump. Figure 4 shows the range of motion the wheel and a-armsexperienced during this test. The force transmitted to the car was done via the

xy

a

b

b

ca

45o

-45o


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shock that was mounted to the front lower a-arm and the front upper shockmembers. Since this test was static and did not account for the force exerted bythe damper an equivalent load had to be calculated. This load was applied via atesting apparatus to simulate the car going over a bump or coming down off of a

jump and had to account for inertia, the damper, and the spring rate of the tire, as

well as the spring in the shock. This test was referred to as the drop test. Figure5 shows the free body diagram for the dynamic loading to simulate a landingfrom a height of 2 feet on only 2 wheels. The final test performed on the framewas the rollover test. For this test the testing apparatus was attached to the topof the roll cage and a downward force was applied to the frame while the framewas set on blocks instead of the wheels to bypass the shocks, which would nottransmit the force in a rollover crash.

Figure 4: Wheel Deflection Test Zero vs. 12 inch Wheel Displacement

Figure 5: Spring Damper System and Corresponding Free body diagram

X2

Mc X2

Mw X1

X1

MwMw

KdKs

Mc

Kw

Kd (x1- x2)Ks (x1- x2)

Mc

Kw(x2)


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The state equations show below as Eqs. (4-7) were derived from theFBD(Gillespie, 147) in Figure 5 and numerically integrated using the Scilabprogram in Appendix B. The force due to the spring and damper acting on thebody was plotted against time and is shown in Figure 6. For a more extremescenario, the force experienced by the frame due to a drop was estimated for a

landing on only two wheels. Therefore the weight of the car shown in Figure 5 asthe variable Mcand used in numerical integration was one-half the total weight ofthe car and rider, or approximately 350 lbf.

11 vx =

(4)

22 vx =

(5)

21211 x

M

Kx

M

Kv

M

Kv

M

Kv

c

s

c

s

c

d

c

d

+

+

+

=

(6)

12222 1 xM

Kx

M

KKv

M

Kv

M

Kv

c

s

w

ws

w

d

w

d

+

+

+

=

(7)

Time (sec)

Force

(lbf)

Figure 6:Force as a Function of Time Acting on Car

At Each Front Shock Mount Due to a Drop of 2.5 Feet

Figure 6 shows that there would be a force of 1,100-lbf acting on the vehicleframe at each shock mount for a period of approximately 0.01 seconds.


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Therefore a load of 2,200 lbf was applied to the front end to simulate a landing onthe front wheels from a drop of 2 feet. This value was used because it alsocorresponds to the estimation that the force exerted by a falling weight from ashort distance is approximately 2 to 3 times the static weight. Figure 7 shows theapproximate directions of the forces applied to the frame in the drop test.

4-reaction forcestransmitted via shocks

Force applied for

dynamic test

Figure 7: Location and Direction of Forces Applied to the Frame for Drop Test

Figure 8 shows the approximate direction of forces applied to the frame for therollover test, with the 4 reaction forces being applied by simple blocks in order tobypass the shocks and suspension arms.

4 reaction forces

Forces applied forrollover test

Members removed for

new frame simulation

Figure 8: Location and Description of Forces Applied to Frame for Rollover Test


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Procedure

Figure 9 shows the testing apparatus used in the drop and rollover test. To applya force on the vehicle frame, an engine hoist was used to pull up on a chain thatran under a pulley mounted to the bedplate that the vehicle sat on. To measure

the load being applied to the car, an aluminum bar was mounted in between twosections of the chain with a strain gage mounted to the bar. Using the knowngeometry of the bar and the properties of aluminum, the strain required for a loadof 2,200 lbf was calculated and applied via the hydraulic on the engine hoist.

Aluminum Bar with Strain

Gage to Measure Load

Pulley Mounted to

Bed Plate for Chain to

Run Through

5,000 lb Engine Hoist

Used to Apply load

Strain Indicator to Display

Microstrain

Figure 9: Vehicle Testing Apparatus

To further compare stress in the spindle, since it is such a crucial part of theredesign a testing fixture was built to put the old spindle in the Instron tensiletester to precisely measure the relationship between applied force and stress inthe complex geometry of the spindle. Also FEA was run on the old and newspindle design to verify results and integrity of new design. Figure 14 in the

results section shows the Instron tensile tester with the testing apparatus and oldspindle design mounted to it.


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Results

Wheel displacement

The plots in Figures 10a-f show the principle stresses in the membersexperiencing the most stress as wheel deflection increased.

-5000

-4000

-3000

-2000

-1000

0

1000

2000

0 5 10 15

Wheel Travel (inches)

Principle

Stress(psi)

Principle Stress 1 (psi)


Figure 10a: Plot of Principle Stresses in Rear Upper A-arm for

Varying Wheel Deflections

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

0 5 10 15


Principle

Stress(psi)



Figure 10b: Plot of Principle Stresses in Rear Lower A-arm for



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-4000

-2000

0

2000

4000

6000

8000

10000

12000

4 8 12


Principle

Stress

(psi)

Principle Stress 1(psi)


Figure 10c: Plot of Principle Stresses in Front Upper Shock forVarying Wheel Deflections

-4000

-2000

0

2000

4000

6000

8000

10000

4 8 12


Principle

Stress(psi)



Figure 10d: Plot of Principle Stresses in Front Lower A-arm for



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-4000

-3000

-2000

-1000

0

1000

2000

0 5 10 15


Principle

Stress(psi)



Figure 10e: Plot of Principle Stresses in Lower Roll Cage SupportFor Varying Wheel Deflections

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

4 8 12


PrincipleS

tress(psi)



Figure 10f: Plot of Principle Stresses in the Spindle

For Varying Wheel Deflections

The principle stresses in four of the six members shown in Figures 8a-f are allincreasing as the wheel deflection increases. This was expected sinceincreasing the wheel deflection compresses the shock further and thus increasesthe force being applied to the frame, thereby increasing the stress. Theexception to this was the rear upper and lower a-arm members. This could beexplained by observing the angle of the a-arms with respect to a vertical plane as


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shown in Figure 4. When the wheel was displaced 12-inches, the a-arms formedan angle of approximately 90 degrees to the vertical plane formed by theadjoining frame members. This may have caused the a-arm members toexperience a different direction of bending since they form a triangular shape,thereby putting the stress on the member in a different plane that was not being

measured. The shock mounted to the lower a-arm is likely what caused thatmember to experience increased stress in the same direction while the upperfront a-arm experienced such small stress it was not even analyzed. Also, sincethe shock is mounted at an angle that goes from the front lower arm towards therear upper a-arm on the front upper shock member, the greater compression ofthe shock during the 12-inch wheel displacement test could have also contributedto the change in direction of the bending of the rear a-arm members since theywere being pushed away from their mounting points. It should be noted thatnone of the stresses in the wheel deflection test came close to the 60,000-psiyield strength of the 2026 steel used in the 2006 frame. The lowest safety factorof the frame members in the wheel displacement test was between 5 to 6. These

were the safety factors of the upper shock mount, the front lower a-arm (both ofwhich have the shock mounted to them) and the spindle. The stress of 11,000 psiexperienced by the spindle was probably not enough to cause fatiguing since it iswell below the 30,000-psi, or 50% of yield, that is generally required for fatiguefailure.

Drop test

Figures 11a and 11b show the stresses measured during the drop test. Onlythree members are shown because they were the only ones experiencingsignificant stress.

0

5000

10000

15000

20000

25000

30000

35000

40000

Front LowerShock Mount

Front UpperShock Mount

Lower RollCage

Support

PrincipleStress(psi)

Original Frame

Pedal Brace Removed

Speedometer BraceRemoved

Figure 11a: Principle Stress (Sigma 1) for Select Members

In Drop Test with Reinforcing Members Removed


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-16000

-14000

-12000

-10000

-8000

-6000

-4000

-2000

0

Front Lower

Shock Mount

Front Upper

Shock Mount

Lower Roll

CageSupport

PrincipleStress(ps

i)

Original Frame

Pedal Brace Removed

Speedometer BraceRemoved

Figure 11b: Principle Stress (Sigma 2) for Select MembersIn Drop Test with Reinforcing Members Removed

The stresses experienced by the members depicted in Figures 11a and 11b areall well below the 60,000 psi yield strength. When the pedal brace was removedand the members retested, the upper shock mount experienced over 30,000 psiof tensile stress. This is equal to 50% of the yield and could therefore causefatigue failure under repeated loading that could occur while driving over largebumps for a long period of time. This result is not surprising since the pedalbrace was located directly between the upper shock mounts on either side of theframe. Therefore, when the shock is compressed and pushes against the uppershock mount member, it takes on much of that stress, thereby relieving the uppershock mount member. It was observed by the graphs that the increase of stressin the upper shock mount, when the pedal brace was removed, resulted in adecrease in stress in the front lower a-arm, which the shock was mounted to atthe other end. Removing the speedometer brace made negligible increase in thestress of the other primary members. This was probably due to the distance thatit was located from the areas of high stress, the distance from the point ofloading, and the direction of bending of the members experiencing high stress.The lowest safety factor in this test was 1.8 for the front upper shock mount after

the pedal brace had been removed. If the pedal brace were left in, the lowestsafety factor would be approximately 3.


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Rollover Test

Figures 12a and 12b show the results of the rollover test for the 6 membersexperiencing the greatest stress.

0

10002000300040005000600070008000

AllMembers

Intact

Top BraceRemoved

Upper RollCage

SupportRemoved

Testing Condition

Sigma1Stress(psi) Side Impact

Member

Top Roll Cage

Bottom RollCage

Front Roll

CageLower RollCage Support

Figure 12a: Principle Stress (Sigma 1) in Select Frame Members

From Rollover Test

-14000

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

AllMembers

Intact

Top BraceRemoved

Upper RollCage

SupportRemoved

Testing Condition

S

igma2Stress(psi)

Side ImpactMember

Top RollCage

bottom RollCage

Front RollCage

Lower RollCage Support

Figure 12b: Principle Stress (Sigma 2) in Select Frame Members

From Rollover Test


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The results of the drop test showed that the side impact member experienced thegreatest amount of tensile stress. This is the desired result since the frame actsas a truss with members located far from the point of application of the forcetaking on stress, thereby dissipating it away from closer members. The top rollcage member experienced the greatest amount of compressive stress, which is

not surprising since it was the closest member to the point of application of theforce. Removal of the top cross brace did not significantly increase or decreasestress in any of the members. The upper roll cage support member did causesignificant changes though. The bottom roll cage member decreasedsignificantly in stress with the removal of the upper roll cage reinforcement. Thiswas because the upper roll cage support would have been pushing directly downon the lower roll cage member during the rollover simulation. Removing theupper roll cage support caused the front roll cage and lower roll cage support tobend significantly outwards. This was especially evident in the front roll cagemember that experienced the greatest amount of increased tensile stress. Sincethe gage was mounted on the front of the member, tensile stress means the

member was bending outwards. The lowest safety factor seen by any singlemember was 5. This was in the top roll cage after the upper roll cage supporthad been removed.

FEA

The solid model of the 2006 spindle indicating the region of failure isshown in Figure 13. The 2006 spindle was tested in the Instron tensile testerapplying sequentially increasing loads to a maximum force of 1500 pounds(Figure 14). A strain rosette was located on the spindle near the point of failureduring the 2006 race. These measurements were then compared with ANSYS toverify that the FEA model was properly constrained (Figure 15). The FEA modelindicated that a 1500-pound load would greatly exceed the ultimate strength ofthe 1026 spindle material.

Point of Failure

Figure 13: Old Spindle Design Showing Point of Failure


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Figure 14: Testing 2006 spindle in Instron

Figure 15: FEA Indicating that the 2006 Spindle Failed Due to Exceeding the UltimateStress of Material (1026 UTS is 62 ksi)


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New Design

Spindle

Figure 13 shows the first solid model of the new spindle design strengthened in

the region in which the 2006 spindle had failed. The new spindle will be CNCmachined from 6061 aluminum to keep the weight to a minimum.

Figure 16: 2007 spindle design phase 1

ANSYS was used to determine whether the new design would handle the 1500-pound load that would occur during a severe front-end landing (Figures 17a and17b). ANSYS indicated that the new spindle design was not strong enoughwhere the steel axle would be press fit into the spindle, so a boss was added.The model was then re-analyzed with ANSYS, and the results indicated that theimprovements would reduce the stress from 43 to 22 ksi near the axle.

The spindle was then analyzed for steering loads assuming a 150-pound force

could be applied through a tie rod during hard cornering conditions (Figure 17c).ANSYS indicated that the original revision would allow stresses approaching the25 ksi yield strength of 6061 aluminum. The high stress area on the spindle tierod attachment was strengthened and re-analyzed with ANSYS (Figure 17d and17e). ANSYS indicated that the problem had been alleviated, with stressesreduced to 6 7 ksi.


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Figure 17a: New front spindle design (before boss)

Figure 17b: New front spindle design (with boss added)


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Figure 17c: Front Spindle Loaded During Hard Cornering

Figure 17d: Front Spindle Loaded During Hard CorneringAfter Revising Tie Rod Connection


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Figure 17e: Second View of Front Spindle Loaded During

Hard Cornering After Revising Tie Rod

Frame

The new requirements of the frame called for it to be shortened to lessen theamount of material used, thereby making it lighter, and also so the a-arms, andtherefore the wheels, could be moved back to shorten the wheel base for bettermaneuverability. Secondly, the front had to be made wider to allow for moreroom for the drivers legs. The most important thing to consider when designingthe frame is the SAE rules. Since last years frame passed inspections withoutany issues raised by the judges, an attempt was made to deviate as little aspossible from the old design while still incorporating the new requirements.Figure 18 shows an example provided by the SAE rules for the minimummembers required for the roll cage. The members labeled RHH, RHO, and FBMare all specified to be at least 1 inch in diameter and a minimum wall thickness of0.065-inches. The remaining members can have a wall thickness of 0.035-inches. All members must have equivalent bending stiffness and strength of1018 steel tubing that is 1 inch in diameter and has a wall thickness of at least0.125-inches. Appendix F shows two tables with the first showing the possibleweight reduction for last years vehicle design had the primary members (labeled1 in Figure 1) been made of either 1026 or 4130 alloy steel of varying dimensionsand the second showing the same comparison for the remaining members(labeled 2 in Figure 1).


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Figure 18: Frame Depiction from SAE Baja Rules for 2007.

Make this corner sharp

and add cross brace

between corners!

Figure 19: 3-D Partial Model of New Frame and SpindleDesigned in Pro-Engineer Wildfire


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Figure 19 shows a solid model of the new front-end design. The key elements ofthis new frame design was that the front end was shortened by a foot andwidened by 2 inches at the bottom and 4 inches at the top. In addition, a

member was removed from the front roll cage that, all together, will allow for aweight reduction of over 37 lbf as shown in Table 1. To save weight for the 2007car, 4130 (chrome moly) was chosen for its higher yield stress, which resulted ingreater bending stiffness. This allowed for the use of 1.5 diameter 0.035 wallthickness tubing to be used for the non-primary members, thereby contributingthe greatest amount of weight reduction. An important note is that since theupper roll cage support was removed, the front upper corner of the roll cage thatpreviously had a 5-inch radius must now be sharp. This is so that the lengths ofthe members dont exceed the limit set out in the SAE rules.

Table 1: Weight and Strength Comparison for1026 and 4130 Steel Tubing

TubingType

TubingDiameter

(inch)

WallThickness

(inch)Weight

(lbf/foot)

BendingStrength

(lb in2

x 103)

BendingStiffness

Feetused

Weight(lbf)

Car #55 1026 1.25 0.065 0.826 1265 4.10 125 103.25

4130 1.25 0.065 0.823 1265 5.11 30 24.69

Car #95 4130 1.5 0.035 0.548 1284 4.32 75 41.1

WeightSavings (lbf) 37.46

Conclusions

The wheel deflection test illustrated that the a-arms are strong enough. Itrevealed that the front upper arm acts as a follower with very little stress whilethe front lower experiences the greatest amount since it has the shock mountedto it. The lowest measured safety factor in the a-arms was12 in the rear upper a-arm at 12-inches deflection.

The old spindle experienced enough stress to fail under fatigue during the droptest and enough to fail under yielding if a load of 1500 lbf was applied to it.

Applying this same load to the new spindle design should not cause failure basedon the FEA analysis that was performed. FEA on the steering mount also provedthe new design sound up to 150 lbf.

The new frame design met all of the required revisions and achieved a weightloss of over 37 lbf. The only area of concern was the top roll cage member sinceit experienced such a large spike in force due to removal of the upper roll cagesupport.


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Recommendations

Further testing could be performed on the rear a-arms by mounting another gage90 degrees to the existing one to see if the members change the direction they

bend after 12 inches of wheel deflection.

It is recommended that FEA be performed on the new frame design with a non-student version of ANSYS software because the student version cannot modelenough elements to provide accurate results. It is also recommended that thepedal brace be retained to keep the upper shock mount from fatiguing. However,the speedometer mount could be removed or replaced with a much weakermember. Also the top cross brace was deemed unnecessary although furthertesting might be required if non-symmetric loading were to occur.

Also, the reduced room in the length of the front end may require that a linkage

be used for the brake pedal to keep the master cylinder in the front of the vehicleas it was in the previous years design.


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Acknowledgements

Members of the 2006 2007 Baja Team: Matt Brower, Brian Buchanan, NickHayhoe, Ryan Lush, Dan Morris, Hieu Nguyen, Michael Olson, Dan Polanic,Brandon Redeker, John Witte (Captain).

Faculty Advisors: Dr. Hugh Jack, Dr. Jeff Ray, and Dr. Bill Waldron

Also: Bob Bero, and Ron Grew

References

Thomas D. Gillespie; Fundamentals of Vehicle Dynamics, Society of AutomotiveEngineers, 1992.

Edmund F. Gaffney III and Anthony R. Salinas; Introduction to Formula SAE

Suspension and Frame Design, University of Missouri Rolla, 1997.

Jonathan Hastie; Mini Baja Vehicle Design Optimization, College of EngineeringNortheastern University, Boston, MA, 2005.

Dr. Hugh Jack; Dynamic Systems and Modeling Control, Version 2.7, August 7,2006.

2006 Mini Baja team; GVSU Laker Racer Technical Design Report (car #55),Grand Valley State University Padnos College of Engineering, 2006.

SAE International; 2007 Baja SAE Competition Rules.

http://www.mech.uwa.edu.au/DANotes/SSS/safety/safety.html


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Appendix A: Tables of Results

Table 1: Results of Wheel Deflection Test

Strain Gage DescriptionPrinciple

Stress 1 (psi)Principle

Stress 2 (psi)Wheel

Deflection (in)

855 -2162 4

-16 -4068 8Rear Top A-Arm

494 -4416 12

153 -275 4

-825 -2034 8Rear Bottom A-Arm-374 -3188 12

3800 -655 4

7605 -1151 8Front Upper Shock

10958 -2503 12

1991 -440 4

4577 -1391 8Front Lower A-Arm

8557 -2307 12

33 -3055 4

-24 -5408 8Spindle

740 -11073 12

735 -1102 4

1145 -2003 8Frame Between Rear A-Arm

Connection1625 -2973 12

Table 2: Results of Drop Test

Description Original FramePedal Brace

Removed

SpeedometerBrace

Removed

Frame

Member

Sigma

1

Sigma

2

%

Error

Sigma

1

Sigma

2

Sigma

1

Sigma

2

Spindle -2711 -41728 15.99

Front LowerShock Mount 21471 -6562 20.77 17250 -4016 17607 -3884

Front UpperShock Mount 1718 -9847 22.15 35958 -15128 35159 -15063

Lower RollCage Support 1038 -2631 29.03 2997 -7081 2871 -6301


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Table 3: Results of Rollover Test

Member Condition Sigma 1 Sigma 2

All Members Intact 4562 0

Top Brace Removed 5211 0Side Impact Member Upper Roll Cage Support Removed 6802 -1572

All Members Intact 596 -3946

Top Brace Removed 1688 -3322

Top Roll Cage Upper Roll Cage Support Removed 0 -11608 All Members Intact 4250 -1145


Bottom Roll Cage Upper Roll Cage Support Removed 0 -1638



Front Roll Cage Upper Roll Cage Support Removed 4210 -84



Lower Roll Cage Support Upper Roll Cage Support Removed 3232 -577


Top Brace Removed 0 -3365Upper Roll Cage Support Upper Roll Cage Support Removed


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Appendix B: Scilab Program to calculate force.

// A program that uses Runge-Kutta method of numerical integration to// estimate the force acting on the body of a vehicle via the suspension system.//// Matt Brower// EGR 345 Semester project//

//// System component valuesMc = 160; // kg (approx. 700/2 lbf car and driver)Mw = 9; // kg (approx. 30 lbf wheel, rim, wheel hub, spindle, and rotor)F = [0]; // N (vector to store the force acting on the car)Ks = 20000; // N/m spring coefficient of shock before bottoming out// (approx. 117 lb/in)Kw = 2 * 10^5; // N/m spring coefficient of wheelKd = 1000; // Ns/m damper coefficient of shockshock_compression = 0;

x1 = 0; // initial conditionsx2 = 0;v1 = 3.46; // meters/second (speed of car falling from 2 feet)v2 = 0;X=[x1, x2, v1, v2];

// define the state matrix function// the values returned are [x1, x2, v1, v2]function foo=f(state,t)

foo = [state($, 3), state($, 4), (-Ks/Mc)*state($, 1) + (Ks/Mc)*state($, 2) + (-Kd/Mc)*state($, 3) + (Kd/Mc)*state($, 4), (Ks/Mw)*state($, 1) + ((-Ks-Kw)/Mw)*state($, 2) + (Kd/Mw)*state($, 3) + (-Kd/Mw)*state($, 4)];endfunction

// Set the time length and step size for the integrationsteps = 1000;t_start = 0.001;t_end = 1;


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h = (t_end - t_start) / steps;t = [t_start];

// Loop for integration

for i=1:steps,t = [t ; t($,:) + h];F1 = h * f(X($,:), t($,:));F2 = h * f(X($,:) + F1/2.0, t($,:) + h/2.0);F3 = h * f(X($,:) + F2/2.0, t($,:) + h/2.0);F4 = h * f(X($,:) + F3, t($,:) + h);X = [X ; X($,:) + (F1 + 2.0*F2 + 2.0*F3 + F4)/6.0];

// Store value of force acting on car (in lbf)

F = [F ; 0.224089*(Kd*(X($,3) - X($,4)) + Ks*(X($,1) - X($,2)))];

// change value of spring coefficient after shock bottoms out

shock_compression = (X(i,1) - X(i,2)); // distance in meters of shock travel

if(shock_compression >= 0.1524) // if statement to account for shockbottoming out after 6 inches

Ks = 20000; // N/m spring coefficient after bottoming (effectively infinite)Kd = 1500; // Ns/m (effectively zero)

else Ks = 20000; Kd = 1500;end

// if statement to account for wheel bottoming out after 4 inchesif(X(i,2) >= 0.1016)

Kw = 2 * 10^10; // N/m spring coefficient after bottoming (effectivelyinfinite)

else Kw = 2 * 10^5;end

end

// Plot graph of position and velocity of two mass bodies//plot2d(t, X, [-2, -5, -7, -9],leg="position_car@position_wheel@velocity_car@velocity_wheel");//xtitle('Position and Velocity of Car and Wheel after Drop');

// Plot graph of Force acting on mass of carplot2d(t, F);//xtitle('Force (lbf) as a function of time (s) acting on car mass at each front shockmount due to a drop of 2 feet');


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29

Appendix C: Sample Spreadsheet of Collected Strain Data.

Gage Location Channel Position ZeroGageReading

ActualMeasurement

Sigma P 1(psi)

Sigma P 2(psi)

Gage ZeroRe-check Off b

1A -45 0

2A 0 621 609 -12 609

7Front Top A-

Arm 3A 45 0

4A -45 150 19 -131 117

5A 0 1455 1336 -119 1427

8Rear Top A-

Arm 6A 45 -105 -70 35 494 -4416 -110

7A -45 -79 -145 -66 -109 8A 0 962 862 -100 940

9Rear Bottom

A-Arm 9A 45 73 53 -20 -374 -3138 67

1B -45 -183 183

2B 0 763 -763

10Rear Top

Swing Arm 3B 45 320 -320

4B -45 370 -370

5B 0 1570 -1570

11Rear SideSwing Arm 6B 45 3 -3

7B -45 357 242 -115 357

8B 0 860 816 -44 862

12

FrameBetween

Rear A-ArmConnection 9B 45 394 476 82 1625 -2973 401


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30

Appendix D: Maple Worksheet to Calculate Principle Stresses

SECTION 1This section calculates the strain in the x and y directions as well as the shear strain as

defined by:

Rossete angles: e1 = -45, e2 = 0, e3= 45, ex is along 0 degree rosette pointing towardswire connections

> e1:=176;:=e1 176

> e2:=394;:=e2 394

> e3:=31;:=e3 31

> eqns1 := {ex*(cos(-Pi/4))^2+ey*(sin(-Pi/4))^2+gxy*cos(-Pi/4)*sin(-Pi/4)=e1,ex*(cos(0))^2+ey*(sin(0))^2+gxy*cos(0)*sin(0)=e2,ex*(cos(Pi/4))^2+ey*(sin(Pi/4))^2+gxy*cos(Pi/4)*sin(Pi/4)=e3};

:=eqns1 { }, ,=+

ex

2

ey

2

gxy

2 176 =ex 394 =+ +

ex

2

ey

2

gxy

2 31

> sols1 := solve( eqns1 );:=sols1 { }, ,=ex 394 =gxy -145 =ey -187

> evalf( [%] );[ ]{ }, ,=ex 394. =gxy -145. =ey -187.

SECTION 2

Assuming steel elastic modulus and Poissons ratio, this section sets up the equations to

solve for the stress in the x and y directions assuming planar stress (ie sigma z = 0)

> E := 29000000;

:=E 29000000

> v := 0.29;:=v .29

> G := E/(2*(1+v));

:=G .1124031008 108


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> eqns2 := {sigmax = (E/((1+v)*(1-2*v)))*((1-v)*ex + v*(ey +ez)), sigmay = (E/((1+v)*(1-2*v)))*((1-v)*ey + v*(ex +ez)), 0 = (E/((1+v)*(1-2*v)))*((1-v)*ez + v*(ex + ey))};

eqns2 =sigmax + +.3800295313 108 ex .1552233297 108 ey .1552233297 108 ez,{:=

=sigmay + +.3800295313 108 ey .1552233297 108 ex .1552233297 108 ez,

=0 + +.3800295313 108 ez .1552233297 108 ex .1552233297 108 ey }

SECTION 3

MUST Manually update strains that were solved for in SECTION 1 here

> ey:=-187*10^(-6);

:=ey-187

1000000

> ex:=394*10^(-6);

:=ex197

500000

> sols2:= solve (eqns2);:=sols2 { }, ,=sigmay -2303.155367 =sigmax 10758.08494 =ez -.00008454929579

> evalf( [%] );[ ]{ }, ,=sigmay -2303.155367 =sigmax 10758.08494 =ez -.00008454929579

SECTION 4 MUST Manually update stresses that were solved for in SECTON 2 here!!!!

> stressx := 10758.08;:=stressx 10758.08

> stressy := -2303.16;:=stressy -2303.16

> gammaxy := -145*10^(-6);

:=gammaxy-29

200000

> tauxy:= G * gammaxy;:=tauxy -1629.844962

SECTION 5 The principle stresses are solved for here

> sigmap1 := (stressx + stressy)/2 + sqrt(((stressx -stressy)/2)^2 + tauxy^2);

:=sigmap1 10958.38803

> sigmap2 := (stressx + stressy)/2 - sqrt(((stressx -stressy)/2)^2 + tauxy^2);

:=sigmap2 -2503.468033


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32

Appendix E: Cost Table

Part Name Vendor QtyMaterial

CostExtended

Material Cost

Kingpin Rod Ends (Part Numberfrom Michael) Mike Olson's Vendor 4 $25.00 $100.00

Aluminum Stock for Spindle (3.5"thick minimum 14" X 10") Piecequoted was 3.5" X 15" X 17" Shupan Aluminum Sales 1 $450.00 $450.00

20' lengths of 1.5" OD 0.035"Wall Thickness 4130 Chrome moly Taylor Supply - Grand Rapids 5 $135.00 $675.00

20' lengths of 1.25" OD 0.0625"Wall Thickness 4130 Chrome moly Taylor Supply - Grand Rapids 3 $110.00 $330.00

Mandrel for hole saw McMaster-Carr 2 $0.00

Heavey Duty bi-metal Hole Saw1.5" OD (part # 4066A27) McMaster-Carr 6 $9.81 $58.86

Heavy Duty bi-metal Hole Saw1.25" OD (part # 4066A23) McMaster-Carr 4 $9.52 $38.08

1/2" dia 2-flute Carbide cutter 4.5"

long Bob's Supply Store of Choice 2 $0.00

1 Box of ER80S-D2 Filler (TIG) Bob's Supply Store of Choice 1 $20.00 $20.00

1-1/2" x 5.5" CLR Round Tube Diefor JD2 Model 3 Bender

Alan GeetingsTrick-Tools.com877-826-7268 1 $240.00 $240.00

B46-0206W8" travel 6100 Series Coilover withSpring Hardware - TBD

DSVS Inc.Paul Kollek800-303-6211 (517-625-1884)9am-5pm ET Monday- Friday 2 $209.00 $418.00

Total $2,329.94


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Appendix F: Material Comparison Spreadsheets

roll cage 1

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