The Science of Vehicle Dynamics: Handling, Braking, and Ride of Road and Race Cars

364 Pages·2014·7.42 MB·English

by  Massimo Guiggiani (auth.)

The Science of Vehicle Dynamics
Massimo Guiggiani
The Science of Vehicle
Dynamics
Handling, Braking, and Ride of Road
and Race Cars
MassimoGuiggiani
Dip.diIngegneriaCivileeIndustriale
UniversitàdiPisa
Pisa,Italy
ISBN978-94-017-8532-7 ISBN978-94-017-8533-4(eBook)
DOI10.1007/978-94-017-8533-4
SpringerDordrechtHeidelbergNewYorkLondon
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Preface
VehicledynamicsshouldbeabranchofDynamics,but,inmyopinion,toooftenit
doesnotlooklikethat.Dynamicsisbasedonterseconceptsandrigorousreasoning,
whereasthetypicalapproachtovehicledynamicsismuchmoreintuitive.Qualita-
tivereasoningandintuitionarecertainlyveryvaluable,buttheyshouldbesupported
andconfirmedbyscientificandquantitativeresults.
Iunderstandthatvehicledynamicsis,perhaps,themostpopularbranchofDy-
namics.Almosteverybodyhasbeeninvolvedindiscussionsaboutsomeaspectsof
thedynamicalbehaviorofavehicle(howtobrake,howtonegotiateabendathigh
speed, which tires give best performance, etc.). At this level, we cannot expect a
deepknowledgeofthedynamicalbehaviorofavehicle.
But there are people who could greatly benefit from mastering vehicle dynam-
ics.Fromhavingclearconceptsinmind.Fromhavingadeepunderstandingofthe
main phenomena. This book is intended for those people who want to build their
knowledge on sound explanations, who believe equations are the best way to for-
mulateand,hopefully,solveproblems.Ofcoursealongwithphysicalreasoningand
intuition.
Ihavebeenconstantlyalertnottogiveanythingforgranted.Thisattitudehasled
tocriticizesomeclassicalconcepts,suchasself-aligningtorque,rollaxis,understeer
gradient,handlingdiagram.Ihopethatevenveryexperiencedpeoplewillfindthe
bookinteresting.Atthesametime,lessexperiencedreadersshouldfindthematter
explainedinawayeasytoabsorb,yetprofound.Quickly,Iwish,theywillfeelnot
solessexperiencedanymore.
Acknowledgments OverthelastfewyearsIhavehadinteractionsanddiscussions
withseveralengineersfromFerrariFormula1.Theproblemstheyconstantlyhave
tofacehavebeenamongthemotivationsforwritingthisbook.Moreover,theirdeep
knowledge of vehicle dynamics has been a source of inspiration. I would like to
express my gratitude to Maurizio Bocchi, Giacomo Tortora, Carlo Miano, Marco
Fainello,TitoAmato(presentlyatMercedes),andGabrielePieraccini(presentlyat
Bosch).
IwishtothankDallaraAutomobiliand,inparticular,AndreaToso,Alessandro
Moroni,andLucaBergianti.Theyhavehelpedmeinmanyways.
v
vi Preface
AttheUniversitàdiPisathereareanM.S.degreecourseinVehicleEngineering
(whereIteachVehicleDynamics)andaPh.D.programinVehicleEngineeringand
Transportation Systems. This very lively environment has played a crucial role in
the development of some of the most innovative topics in this book. In particular,
IwishtoacknowledgethecontributionofmycolleagueFrancescoFrendo,andof
myformerPh.D.studentsAntonioSponziello,RiccardoBartolozzi,andFrancesco
Bucchi.FrancescoFrendoandRiccardoBartolozzihavealsoreviewedpartofthis
book.
DuringthelastsixyearsIhavebeentheFacultyAdvisorofE-Team,theFormula
StudentteamoftheUniversitàdiPisa.Ithankalltheteammembers.Ithasbeena
veryinterestingandrewardingexperience,bothprofessionallyandpersonally.
Testingrealvehiclesisessentialtounderstandvehicledynamics.Iwishtothank
Danilo Tonani, director of FormulaGuidaSicura,for having given me the opportu-
nityofbecomingasafedrivinginstructor.Everyyear,heorganizesanexcellentsafe
drivingcoursefortheM.S.studentsinVehicleEngineeringoftheUniversitàdiPisa.
MycollaboratorsanddearfriendsAlessioArtoniandMarcoGabiccinihavecare-
fullyreviewedthisbook.Iammostgratefultothemfortheirvaluablesuggestions
tocorrectandimprovethetext.
Pisa,Italy MassimoGuiggiani
October2013
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 VehicleDefinition . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 VehicleBasicScheme . . . . . . . . . . . . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 MechanicsoftheWheelwithTire . . . . . . . . . . . . . . . . . . . 7
2.1 TheTireasaVehicleComponent . . . . . . . . . . . . . . . . . 8
2.2 RimPositionandMotion . . . . . . . . . . . . . . . . . . . . . 9
2.3 CarcassFeatures . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 ContactPatch . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 FootprintForce . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5.1 PerfectlyFlatRoadSurface . . . . . . . . . . . . . . . . 16
2.6 TireGlobalMechanicalBehavior. . . . . . . . . . . . . . . . . 17
2.6.1 TireTransientBehavior . . . . . . . . . . . . . . . . . . 17
2.6.2 TireSteady-StateBehavior . . . . . . . . . . . . . . . . 18
2.6.3 RollingResistance . . . . . . . . . . . . . . . . . . . . 20
2.6.4 SpeedIndependence(Almost) . . . . . . . . . . . . . . 21
2.6.5 PureRolling(notFreeRolling) . . . . . . . . . . . . . . 21
2.7 TireSlips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.7.1 RollingVelocity . . . . . . . . . . . . . . . . . . . . . . 27
2.7.2 DefinitionofTireSlips . . . . . . . . . . . . . . . . . . 27
2.7.3 SlipAngle . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.8 GripForcesandTireSlips . . . . . . . . . . . . . . . . . . . . 31
2.9 TireTesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.9.1 PureLongitudinalSlip . . . . . . . . . . . . . . . . . . 34
2.9.2 PureLateralSlip . . . . . . . . . . . . . . . . . . . . . 35
2.10 MagicFormula . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.11 MechanicsofWheelswithTire . . . . . . . . . . . . . . . . . . 39
2.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.13 ListofSomeRelevantConcepts . . . . . . . . . . . . . . . . . 44
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
vii
viii Contents
3 VehicleModelforHandlingandPerformance . . . . . . . . . . . . 47
3.1 MathematicalFramework . . . . . . . . . . . . . . . . . . . . . 48
3.2 VehicleCongruence(Kinematic)Equations . . . . . . . . . . . 48
3.2.1 Velocities . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.2 YawAngleandTrajectory . . . . . . . . . . . . . . . . 49
3.2.3 VelocityCenter . . . . . . . . . . . . . . . . . . . . . . 51
3.2.4 FundamentalRatios . . . . . . . . . . . . . . . . . . . . 52
3.2.5 AccelerationsandRadiiofCurvature . . . . . . . . . . 53
3.2.6 AccelerationCenter . . . . . . . . . . . . . . . . . . . . 54
3.2.7 TireKinematics(TireSlips) . . . . . . . . . . . . . . . 56
3.3 VehicleConstitutive(Tire)Equations . . . . . . . . . . . . . . . 58
3.4 VehicleEquilibriumEquations . . . . . . . . . . . . . . . . . . 59
3.5 ForcesActingontheVehicle . . . . . . . . . . . . . . . . . . . 59
3.5.1 Weight. . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.5.2 AerodynamicForce . . . . . . . . . . . . . . . . . . . . 60
3.5.3 Road-TireFrictionForces. . . . . . . . . . . . . . . . . 61
3.5.4 Road-TireVerticalForces . . . . . . . . . . . . . . . . . 63
3.6 VehicleEquilibriumEquations(moreExplicitForm) . . . . . . 63
3.7 LoadTransfers . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.7.1 LongitudinalLoadTransfer . . . . . . . . . . . . . . . . 65
3.7.2 LateralLoadTransfers . . . . . . . . . . . . . . . . . . 66
3.7.3 VerticalLoadsonEachTire . . . . . . . . . . . . . . . 66
3.8 SuspensionFirst-OrderAnalysis . . . . . . . . . . . . . . . . . 67
3.8.1 SuspensionReferenceConfiguration . . . . . . . . . . . 67
3.8.2 SuspensionInternalCoordinates . . . . . . . . . . . . . 68
3.8.3 CamberVariation . . . . . . . . . . . . . . . . . . . . . 69
3.8.4 VehicleInternalCoordinates . . . . . . . . . . . . . . . 70
3.8.5 RollandVerticalStiffnesses . . . . . . . . . . . . . . . 71
3.8.6 SuspensionInternalEquilibrium . . . . . . . . . . . . . 73
3.8.7 EffectsofaLateralForce . . . . . . . . . . . . . . . . . 74
3.8.8 No-rollCentersandNo-rollAxis . . . . . . . . . . . . . 75
3.8.9 ForcesattheNo-rollCenters . . . . . . . . . . . . . . . 77
3.8.10 SuspensionJacking . . . . . . . . . . . . . . . . . . . . 78
3.8.11 RollAngleandLateralLoadTransfers . . . . . . . . . . 79
3.8.12 ExplicitExpressionsofLateralLoadTransfers . . . . . 81
3.8.13 LateralLoadTransferswithRigidTires . . . . . . . . . 82
3.9 DependentSuspensions . . . . . . . . . . . . . . . . . . . . . . 82
3.10 SprungandUnsprungMasses . . . . . . . . . . . . . . . . . . 85
3.11 VehicleModelforHandlingandPerformance . . . . . . . . . . 86
3.11.1 EquilibriumEquations . . . . . . . . . . . . . . . . . . 86
3.11.2 Constitutive(Tire)Equations . . . . . . . . . . . . . . . 88
3.11.3 Congruence(Kinematic)Equations . . . . . . . . . . . 88
3.11.4 PrinciplesofAnyDifferentialMechanism . . . . . . . . 90
3.12 TheStructureofThisVehicleModel . . . . . . . . . . . . . . . 94
3.13 Three-AxleVehicles . . . . . . . . . . . . . . . . . . . . . . . 95
Contents ix
3.14 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.15 ListofSomeRelevantConcepts . . . . . . . . . . . . . . . . . 97
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4 BrakingPerformance . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.1 PureBraking . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2 VehicleModelforBrakingPerformance . . . . . . . . . . . . . 100
4.3 EquilibriumEquations . . . . . . . . . . . . . . . . . . . . . . 101
4.4 LongitudinalLoadTransfer . . . . . . . . . . . . . . . . . . . . 101
4.5 MaximumDeceleration . . . . . . . . . . . . . . . . . . . . . . 102
4.6 BrakeBalance . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.7 AllPossibleBrakingCombinations. . . . . . . . . . . . . . . . 103
4.8 ChangingtheGrip. . . . . . . . . . . . . . . . . . . . . . . . . 105
4.9 ChangingtheWeightDistribution . . . . . . . . . . . . . . . . 106
4.10 ANumericalExample . . . . . . . . . . . . . . . . . . . . . . 106
4.11 BrakingPerformanceofFormulaCars . . . . . . . . . . . . . . 107
4.11.1 EquilibriumEquations . . . . . . . . . . . . . . . . . . 107
4.11.2 LongitudinalLoadTransfer . . . . . . . . . . . . . . . . 108
4.11.3 MaximumDeceleration . . . . . . . . . . . . . . . . . . 108
4.11.4 BrakingBalance . . . . . . . . . . . . . . . . . . . . . 109
4.11.5 TypicalFormula1BrakingPerformance . . . . . . . . . 109
4.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.13 ListofSomeRelevantConcepts . . . . . . . . . . . . . . . . . 110
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5 TheKinematicsofCornering . . . . . . . . . . . . . . . . . . . . . 113
5.1 PlanarKinematicsofaRigidBody . . . . . . . . . . . . . . . . 113
5.1.1 VelocityFieldandVelocityCenter . . . . . . . . . . . . 113
5.1.2 AccelerationField,InflectionCircleandAcceleration
Center . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.2 TheKinematicsofaTurningVehicle . . . . . . . . . . . . . . . 119
5.2.1 FixedandMovingCentrodesofaTurningVehicle. . . . 119
5.2.2 InflectionCircle . . . . . . . . . . . . . . . . . . . . . . 123
5.2.3 VariableCurvatures . . . . . . . . . . . . . . . . . . . . 126
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6 HandlingofRoadCars . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.1 OpenDifferential . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2 FundamentalEquationsofVehicleHandling . . . . . . . . . . . 132
6.3 DoubleTrackModel . . . . . . . . . . . . . . . . . . . . . . . 136
6.4 SingleTrackModel . . . . . . . . . . . . . . . . . . . . . . . . 137
6.4.1 GoverningEquationsoftheSingleTrackModel . . . . . 138
6.4.2 AxleCharacteristics. . . . . . . . . . . . . . . . . . . . 140
6.5 AlternativeStateVariables . . . . . . . . . . . . . . . . . . . . 144
6.5.1 β andρ asStateVariables . . . . . . . . . . . . . . . . 145
6.5.2 β andβ asStateVariables . . . . . . . . . . . . . . . 147
1 2
6.5.3 S andRasStateVariables . . . . . . . . . . . . . . . . 149
x Contents
6.6 InverseCongruenceEquations . . . . . . . . . . . . . . . . . . 149
6.7 VehicleinSteady-StateConditions . . . . . . . . . . . . . . . . 150
6.7.1 TheRoleoftheSteady-StateLateralAcceleration . . . . 151
6.7.2 Steady-StateAnalysis . . . . . . . . . . . . . . . . . . . 153
6.8 HandlingDiagram—TheClassicalApproach . . . . . . . . . . 154
6.9 WeakConceptsinClassicalVehicleDynamics. . . . . . . . . . 158
6.9.1 PopularDefinitionsofUndersteer/Oversteer . . . . . . . 159
6.10 MapofAchievablePerformance(MAP)—ANewGlobal
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.10.1 MAPCurvatureρ vsSteerAngleδ . . . . . . . . . . . . 161
6.10.2 MAP:VehicleSlipAngleβ vsCurvatureρ . . . . . . . 165
6.11 VehicleinTransientConditions(StabilityandControlDerivatives) 169
6.11.1 Steady-StateConditions(EquilibriumPoints) . . . . . . 170
6.11.2 LinearizationoftheEquationsofMotion . . . . . . . . 171
6.11.3 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.11.4 ForcedOscillations(DriverAction) . . . . . . . . . . . 173
6.12 RelationshipBetweenSteadyStateDataandTransientBehavior 175
6.13 NewUndersteerGradient . . . . . . . . . . . . . . . . . . . . . 179
6.14 Stability(Again) . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.15 TheSingleTrackModelRevisited . . . . . . . . . . . . . . . . 180
6.15.1 DifferentVehicleswithAlmostIdenticalHandling . . . 184
6.16 RoadVehicleswithLockedorLimitedSlipDifferential . . . . . 186
6.17 LinearSingleTrackModel . . . . . . . . . . . . . . . . . . . . 186
6.17.1 GoverningEquations . . . . . . . . . . . . . . . . . . . 187
6.17.2 SolutionforConstantForwardSpeed . . . . . . . . . . 188
6.17.3 CriticalSpeed . . . . . . . . . . . . . . . . . . . . . . . 190
6.17.4 TransientVehicleBehavior . . . . . . . . . . . . . . . . 191
6.17.5 Steady-StateBehavior:SteeringPad . . . . . . . . . . . 193
6.17.6 LateralWindGust . . . . . . . . . . . . . . . . . . . . 194
6.17.7 BankedRoad . . . . . . . . . . . . . . . . . . . . . . . 198
6.18 CompliantSteeringSystem . . . . . . . . . . . . . . . . . . . . 198
6.18.1 GoverningEquations . . . . . . . . . . . . . . . . . . . 199
6.18.2 EffectsofCompliance . . . . . . . . . . . . . . . . . . 200
6.19 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.20 ListofSomeRelevantConcepts . . . . . . . . . . . . . . . . . 201
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
7 HandlingofRaceCars . . . . . . . . . . . . . . . . . . . . . . . . . 203
7.1 LockedandLimitedSlipDifferentials . . . . . . . . . . . . . . 203
7.2 FundamentalEquationsofRaceCarHandling . . . . . . . . . . 205
7.3 DoubleTrackRaceCarModel . . . . . . . . . . . . . . . . . . 208
7.4 ToolsforHandlingAnalysis . . . . . . . . . . . . . . . . . . . 209
7.5 TheHandlingDiagramBecomestheHandlingSurface . . . . . 210
7.5.1 HandlingwithLockedDifferential(noWings). . . . . . 210
7.6 HandlingofFormulaCars . . . . . . . . . . . . . . . . . . . . 221