Simulating and Prototyping a Formula SAE Race Car Suspension System - - PowerPoint PPT Presentation

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Simulating and Prototyping a Formula SAE Race Car Suspension System - - PowerPoint PPT Presentation

Feb 15, 2023 266 likes •596 views

Simulating and Prototyping a Formula SAE Race Car Suspension System Mark Holveck 01, Rodolphe Poussot 00, Harris Yong 00 Progress Report January 6, 2000 MAE 339/439 Advisor: Prof. Bogdonoff Role of a Race Car Suspension System

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SLIDE 1

Simulating and Prototyping a Formula SAE Race Car Suspension System

Progress Report January 6, 2000 MAE 339/439 Advisor: Prof. Bogdonoff

Mark Holveck ’01, Rodolphe Poussot ’00, Harris Yong ’00

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SLIDE 2

Intro Kinematics Dynamics Reliability Manufacturing Summary

Role of a Race Car Suspension System

  • Transfers forces from the tire contact

patch to accelerate a car:

– Kinematics:

  • relative motion between the ground, tire/wheel

and car body

  • governs manner of force transfer
  • concerned with geometry

– Dynamics:

  • forces between the tires and the car
  • behavior of the car
  • concerned with rates

Intro Intro Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 3

Intro Kinematics Dynamics Reliability Manufacturing Summary

Assumptions

  • Sprung and unsprung masses
  • Front/rear mass distribution
  • Center of gravity height
  • Rigid frame
  • Assumed maximum accelerations:

– 1.5 G cornering – 1.2 G braking – < 1 G acceleration

Intro Intro Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 4

Intro Kinematics Dynamics Reliability Manufacturing Summary

Major Components

  • Control arms

– Rigid suspension links

  • Upright

– Interface between control arms and wheels

  • Spring and damper (shock absorber)

Intro Intro Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 5

Intro Kinematics Dynamics Reliability Manufacturing Summary

Basic Design

  • Independent double

A-arms

– Flexibility in choosing parameters – Mostly axial loading – Common race car design

  • Outboard springs

and dampers

– Reduced complexity – Sufficient adjustability

Intro Intro Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 6

Intro Kinematics Dynamics Reliability Manufacturing Summary

Suspension Kinematics

  • Bottom line:

– Maximize tire contact patch utilization – Correct geometry between tire and ground

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 7

Intro Kinematics Dynamics Reliability Manufacturing Summary

Camber

  • Affects tire’s ability to generate lateral

(cornering) forces

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 8

Intro Kinematics Dynamics Reliability Manufacturing Summary

Camber

  • Camber needs to change with wheel

travel because car rolls to the side during cornering

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 9

Intro Kinematics Dynamics Reliability Manufacturing Summary

Camber Gain

  • Different for front and rear suspension

Camber Curves

  • 6

6

  • 50

50 Wheel Displacement (Bump Positive) Camber Angle

Camber required to keep tires flat Front wheel camber Rear wheel camber

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 10

Intro Kinematics Dynamics Reliability Manufacturing Summary

Caster

  • Caster centers steered front wheels
  • Also introduces camber change on

steered front wheels

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 11

Intro Kinematics Dynamics Reliability Manufacturing Summary

Caster and Camber

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

Camber Curves

  • 6

6

  • 50

50 Wheel Displacement (Bump Positive) Camber Angle

Camber required to keep tires flat Front wheel camber Rear wheel camber

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SLIDE 12

Intro Kinematics Dynamics Reliability Manufacturing Summary

Roll Center

  • Front and rear roll centers define roll

axis of vehicle

– Determines amount of body roll and load transfer distribution – Jacking effects

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 13

Intro Kinematics Dynamics Reliability Manufacturing Summary

Jacking

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 14

Intro Kinematics Dynamics Reliability Manufacturing Summary

“Anti” Effects

  • Reduce pitching during accelerating and

braking

  • Anti-dive: 12%
  • Anti-lift: 5%
  • Anti-squat: 12%

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 15

Intro Kinematics Dynamics Reliability Manufacturing Summary

Compromises

  • Roll center and camber objectives often

conflict

  • Other parameters to optimize:

– Tire scrub – Scrub radius – Kingpin inclination – Trail – Bump steer – Many others!

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 16

Intro Kinematics Dynamics Reliability Manufacturing Summary

Reynard Kinematics

  • Free evaluation software from Reynard

Motorsport

  • Parametric kinematics

Intro Kinematics Kinematics Dynamics Reliability Manufacturing Summary

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SLIDE 17

Intro Kinematics Dynamics Reliability Manufacturing Summary

Suspension Dynamics

  • Behavior of the car undergoing

accelerations

  • Bottom line:

– Choose spring, damper, and other rates to

  • ptimize among a set of compromises

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

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SLIDE 18

Intro Kinematics Dynamics Reliability Manufacturing Summary

Reduce Body Roll

  • Especially important for tight Formula

SAE courses

– Body roll slows transient response

  • Shorten distance between roll center and

center of gravity

– Results in high roll center and jacking effect

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

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SLIDE 19

Intro Kinematics Dynamics Reliability Manufacturing Summary

Reduce Load Transfer

  • Tire coefficient of friction decreases with

vertical load

– Different from elementary physics

  • Net grip is best when tires share the total

vertical load evenly

– Minimize load transfer from one tire to another

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

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SLIDE 20

Intro Kinematics Dynamics Reliability Manufacturing Summary

Reducing Load Transfer

  • Widen track, wheelbase
  • Lower center of gravity

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

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SLIDE 21

Intro Kinematics Dynamics Reliability Manufacturing Summary

Cornering Behavior

  • Understeer

– Turning radius larger than intended

  • car “plows”

– Stable – Too much load (transfer) on front tires

  • Oversteer

– Turning radius smaller than intended

  • car “spins out”

– Unstable – Too much load (transfer) on rear tires

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

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SLIDE 22

Intro Kinematics Dynamics Reliability Manufacturing Summary

Cornering Behavior

  • Neutral steer

– Car stays on track – Unlimited cornering capability – Requires fine balance of load distribution

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

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SLIDE 23

Intro Kinematics Dynamics Reliability Manufacturing Summary

Adjusting Cornering Behavior

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

  • Axle that resists roll the most usually

has less cornering ability than the other axle

  • Vary front/rear spring and damper rates

– Also reduces body roll

  • Anti-roll bar

– Couples left and right wheels together to resist opposite motion

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SLIDE 24

Intro Kinematics Dynamics Reliability Manufacturing Summary

Dynamics Calculations

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

  • Used Microsoft Excel to determine rates
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 B C F G H I J K L M N D e s c r i p t i
  • n
U n i t s D e s i g n I n t e n t ( F R ) D e s i g n I n t e n t ( R R ) W i t h W
  • r
s t C a s e R C ( F R ) W i t h W
  • r
s t C a s e R C ( R R ) W i t h 1 5 % l
  • w
e r r i d e f r e q u e n c y ( F R ) W i t h 1 5 % l
  • w
e r r i d e f r e q u e n c y ( R R ) W i t h 1 % G r e a t e r S p r u n g W e i g h t ( F R ) W i t h 1 % G r e a t e r S p r u n g W e i g h t ( F R ) W i t h S p r u n g M a s s D i s t r i b Basic V e hicle Len gths an d CG Vertical L ocation CG he i g ht in
  • 12. 0
  • 12. 0
  • 12. 0
  • 12. 0
  • 12. 0
  • 12. 0
  • 12. 0
  • 12. 0
  • 12. 0
wheelb ase mm 175 0 175 0 175 0 175 0 175 0 175 0 175 0 175 0 175 0 wheelb ase in
  • 68. 898
  • 68. 898
  • 68. 898
  • 68. 898
  • 68. 898
  • 68. 898
  • 68. 898
  • 68. 898
  • 68. 898
tra ck mm 120 0 120 0 120 0 120 0 120 0 120 0 120 0 120 0 120 0 tra ck in
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
aver age t rack in
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
  • 47. 244
aver age t rack mm 120 0 120 0 120 0 120 0 120 0 120 0 120 0 120 0 120 0 Spring and Dam per Mount i n g Orie ntation chassis t o sprin g mou nting p oint mm 154 .0 132 .0 154 .0 132 .0 154 .0 132 .0 154 .0 132 .0 154 .0 chassis t o lower b all joint mm 225 .0 261 .0 225 .0 261 .0 225 .0 261 .0 225 .0 261 .0 225 .0 linkage ratio perp endicular
  • not used
not used not used not used not used not used not used not used not used spr i n g/dam per moun ting an gle fro m pe rpen dicular deg not used not used not used not used not used not used not used not used not used spr i n g/dam per moun ting an gle fro m pe rpen dicular ra d not used not used not used not used not used not used not used not used not used mo tion ra tio (n et calculate d app roxima tion)
  • not used
not used not used not used not used not used not used not used not used mo tion ra tio (a ccording to Reynar d Kinema tics)
  • 0.4 89
0.3 83 0.4 89 0.3 83 0.4 89 0.3 83 0.4 89 0.3 83 0.4 89 Vehicle Weight s and Weig ht Distribut i
  • n
1 a xl e sprun g weight lb 225 275 225 275 225 275 247 .5 302 .5 175 2 a xl e sprun g weight lb 500 500 500 500 500 500 550 550 500 1 a xl e unspr ung weig ht lb 45 45 45 45 45 45 45 45 45 2 a xl e sprun g weight lb 90 90 90 90 90 90 90 90 90 1 a xl e total weigh t lb 270 320 270 320 270 320 292 .5 347 .5 220 2 a xl e total weigh t lb 590 590 590 590 590 590 640 640 590 spr ung m ass CG in
  • 12. 518
  • 12. 518
  • 12. 518
  • 12. 518
  • 12. 518
  • 12. 518
  • 12. 470
  • 12. 470
  • 12. 518
spr ung m ass distr i b ution %
  • 45. 0
  • 55. 0
  • 45. 0
  • 55. 0
  • 45. 0
  • 55. 0
  • 45. 0
  • 55. 0
  • 35. 0
  • ver all mass distributio n
%
  • 45. 8
  • 54. 2
  • 45. 8
  • 54. 2
  • 45. 8
  • 54. 2
  • 45. 7
  • 54. 3
  • 37. 3
Derive d Rates ride freq uency Hz 2.0 2.2 2.0 2.2 1.7 1.9 ride freq uency cpm 120 132 120 132 102 112 .2 ride freq uency r atio
  • 1.1
1.1 1.1 1.1 1.1 1.1 ride rate lb/in 46 68 46 68 33 49 46 68 46 tire rate lb/in 120 0 120 0 120 0 120 0 120 0 120 0 120 0 120 0 120 0 tire static load ed ra dius in 9.1 25 9.1 25 9.1 25 9.1 25 9.1 25 9.1 25 9.1 25 9.1 25 9.1 25 wheel ce nter rate lb/in 48 72 48 72 34 51 48 72 48 spr i n g ra te lb/in 200 491 200 491 143 349 210 556 200 Roll Geom etry and Rate s ro l l ce nter height mm
  • 24. 4
  • 52. 9
  • 1 26.8
  • 7 .4
  • 24. 4
  • 52. 9
  • 24. 4
  • 52. 9
  • 24. 4
ro l l ce nter height in 0.9 61 2.0 83
  • 4 .992
  • 0 .291
0.9 61 2.0 83 0.9 61 2.0 83 0.9 61 ro l ling mom ent leve r ar m in
  • 10. 940
  • 10. 940
  • 14. 924
  • 14. 924
  • 10. 940
  • 10. 940
  • 10. 893
  • 10. 893
  • 10. 828
ro l ling mom ent p er g l a teral a ccelera ti
  • n
lb-f t/g 456 456 622 622 456 456 499 499 451 1 a xl e spring roll ra te lb-f t/deg 75 110 75 110 54 80 75 110 75 2 a xl e spring roll ra te lb-f t/deg 185 185 185 185 134 134 185 185 185 ro l l g radien t with spr i n gs alone deg /g 2.5 2.5 3.4 3.4 3.4 3.4 2.7 2.7 2.4 Anti-Roll Bar G eomet ry ARB she ar m odulus psi 1.0 0E + 07 1.0 0E + 07 1.0 0E + 07 1.0 0E + 07 1.0 0E + 07 1.0 0E + 07 1.0 0E + 07 1.0 0E + 07 1.0 0E + 07 ARB inn er r adius in 0.1 00 0.0 00 0.1 00 0.0 00 0.1 00 0.0 00 0.1 00 0.0 00 0.1 00 ARB
  • u ter r adius
in 0.1 40 0.0 00 0.1 40 0.0 00 0.1 40 0.0 00 0.1 40 0.0 00 0.1 40 ARB ar ea m ome nt of in ertia in^4 4.4 64E-04 0.0 00E+00 4.4 64E-04 0.0 00E+00 4.4 64E-04 0.0 00E+00 4.4 64E-04 0.0 00E+00 4.4 64E-04 ARB leve r ar m leng th in 4.0 00 6.0 00 4.0 00 6.0 00 4.0 00 6.0 00 4.0 00 6.0 00 4.0 00 chassis t o AR B att achme nt poin t mm 350 .0 300 .0 350 .0 300 .0 350 .0 300 .0 350 .0 300 .0 350 .0 ARB linkag e ra tio
  • 2.2 73
2.2 73 2.2 73 2.2 73 2.2 73 2.2 73 2.2 73 2.2 73 2.2 73 ARB len gth mm 700 .0 600 .0 700 .0 600 .0 700 .0 600 .0 700 .0 600 .0 700 .0 Anti-Roll Bar Con tribut i
  • n
ARB twist r ate lb-f t/deg 2.3 6E
  • 01
0.0 0E + 00 2.3 6E
  • 01
0.0 0E + 00 2.3 6E
  • 01
0.0 0E + 00 2.3 6E
  • 01
0.0 0E + 00 2.3 6E
  • 01
ARB r ate lb-f t/deg ARB r oll rate lb-f t/deg 42 42 42 42 42 2 a xl e A RB ro l l r ate lb-f t/deg 42 42 42 42 42 42 42 42 42 Net Roll Cha racter istics axle r oll rate lb-f t/deg 117 110 117 110 96 80 117 110 117 2 a xl e roll ra te lb-f t/deg 227 227 227 227 176 176 227 227 227 White cells are for da t a entry. Gr ay c e lls are calcul at ed or dervied values A RB dim e nsions are
  • n approximat
e and are used only to gener a t e additional roll st i ffness values for balancing load distr ibut i on.
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SLIDE 25

Intro Kinematics Dynamics Reliability Manufacturing Summary

CarSim Educational

Intro Kinematics Dynamics Dynamics Reliability Manufacturing Summary

  • Simulates vehicle behavior
  • Can help to analyze sensitivity of

parameters

– Deviations from design intent

  • Complement design with road testing
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SLIDE 26

Intro Kinematics Dynamics Reliability Manufacturing Summary

Reliability

  • Importance of completing all the

dynamic events

– Ability to engineer next iteration based on successes and failures

  • Structural strength to maintain intended

kinematics and dynamics

Intro Kinematics Dynamics Reliability Reliability Manufacturing Summary

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SLIDE 27

Intro Kinematics Dynamics Reliability Manufacturing Summary

A-arm Load Analyses

  • 1.5G cornering and 1.2G braking
  • Maximum tensile stress: 57 MPa

– under cornering

  • Maximum compressive stress: 42 MPa

– front suspension under braking

  • All loads under 650 MPa yield strength of

4130 chromoly steel

Intro Kinematics Dynamics Reliability Reliability Manufacturing Summary

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SLIDE 28

Intro Kinematics Dynamics Reliability Manufacturing Summary

Loads on Front Upright

  • A-arm loads

resolved into loads

  • n upright
  • No severe stresses

– Modeling is not representative of braking forces

  • Constrained hub

carrier and applied previous loads

– Hub carrier not yet fully designed

Intro Kinematics Dynamics Reliability Reliability Manufacturing Summary

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SLIDE 29

Intro Kinematics Dynamics Reliability Manufacturing Summary

Manufacturing

  • Upright:

– CNC machined from 6061-T6 aluminum

  • Control arms

– Welded 4130 chromoly steel tubing

  • Mounting brackets

– Welded 4130 chromoly rectangular tubing

  • Purchased items:

– Wheels – Dampers – Various hardware

Intro Kinematics Dynamics Reliability Manufacturing Manufacturing Summary

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SLIDE 30

Intro Kinematics Dynamics Reliability Manufacturing Summary

Summary

  • Analyzed suspension design in context
  • f Formula SAE requirements

– Compromised among parameters for best first year car

  • Combine with testing
  • Next semester:

– Complete suspension construction – Minor changes to suspension – Brakes – Steering

Intro Kinematics Dynamics Reliability Manufacturing Summary Summary

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SLIDE 31

Intro Kinematics Dynamics Reliability Manufacturing Summary

Questions