Vehicle Dynamics - Theory and Application

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Contents
Preface x
1 Tire and Rim Fundamentals 1
1.1 TiresandSidewallInformation ................ 1
1.2 TireComponents........................ 11
1.3 RadialandNon-RadialTires ................. 14
1.4 Tread .............................. 17
1.5 F Hydroplaning ........................ 18
1.6 Tireprint............................. 20
1.7 WheelandRim......................... 21
1.8 Vehicle Classifications ..................... 25
1.8.1 ISO and FHWA Classification............. 25
1.8.2 Passenger Car Classifications ............. 28
1.8.3 PassengerCarBodyStyles .............. 30
1.9 Summary ............................ 31
1.10KeySymbols .......................... 33
Exercises ............................... 34
I One-Dimensional Vehicle Dynamics 37
2ForwardVehicleDynamics 39
2.1 ParkedCaronaLevelRoad.................. 39
2.2 ParkedCaronanInclinedRoad ............... 44
2.3 AcceleratingCaronaLevelRoad............... 50
2.4 AcceleratingCaronanInclinedRoad ............ 55
2.5 ParkedCaronaBankedRoad ................ 65
2.6 F OptimalDriveandBrakeForceDistribution....... 68
2.7 F VehiclesWithMoreThanTwoAxles ........... 74
2.8 F VehiclesonaCrestandDip ................ 78
2.8.1 F VehiclesonaCrest ................. 78
2.8.2 F VehiclesonaDip .................. 82
2.9 Summary ............................ 87
2.10KeySymbols .......................... 88
Exercises ............................... 90
Tire Dynamics 95
3.1 TireCoordinateFrameandTireForceSystem ....... 95
3.2 Tire Stiffness .......................... 98
3.3 TireprintForces......................... 104
3.3.1 StaticTire,NormalStress............... 104
3.3.2 StaticTire,TangentialStresses............ 108
3.4 EffectiveRadius ........................ 109
3.5 RollingResistance ....................... 114
3.5.1 F Effect of Speed on the Rolling Friction Coefficient 119
3.5.2 FEffect of Inflation Pressure and Load on the Rolling
Friction Coefficient................... 122
3.5.3 F Effect of Sideslip Angle on Rolling Resistance . . 125
3.5.4 F Effect of Camber Angle on Rolling Resistance . . 127
3.6 LongitudinalForce ....................... 127
3.7 LateralForce .......................... 135
3.8 CamberForce.......................... 145
3.9 TireForce............................ 151
3.10Summary ............................ 157
3.11KeySymbols .......................... 159
Exercises ............................... 161
Driveline Dynamics 165
4.1 EngineDynamics........................ 165
4.2 Driveline and Efficiency .................... 173
4.3 GearboxandClutchDynamics ................ 178
4.4 GearboxDesign......................... 187
4.4.1 GeometricRatioGearboxDesign........... 188
4.4.2 F ProgressiveRatioGearboxDesign......... 190
4.5 Summary ............................ 205
4.6 KeySymbols .......................... 207
Exercises ............................... 209
Vehicle Kinematics 217
Applied Kinematics 219
5.1 RotationAboutGlobalCartesianAxes............ 219
5.2 SuccessiveRotationAboutGlobalCartesianAxes ..... 223
5.3 RotationAboutLocalCartesianAxes ............ 225
5.4 SuccessiveRotationAboutLocalCartesianAxes ...... 229
5.5 F EulerAngles......................... 231
5.6 GeneralTransformation .................... 241
5.7 AngularVelocity ........................ 248
5.8 F TimeDerivativeandCoordinateFrames ......... 257
5.9 RigidBodyVelocity ...................... 267
5.10 Angular Acceleration . . . ................... 272
5.11RigidBodyAcceleration.................... 279
5.12 F Axis-angleRotation..................... 282
5.13 F ScrewMotion ........................ 288
5.14Summary ............................ 301
5.15KeySymbols .......................... 304
Exercises ............................... 305
Applied Mechanisms 309
6.1 Four-BarLinkage........................ 309
6.2 Slider-CrankMechanism.................... 332
6.3 InvertedSlider-CrankMechanism............... 339
6.4 InstantCenterofRotation................... 346
6.5 CouplerPointCurve...................... 356
6.5.1 CouplerPointCurveforFour-BarLinkages ..... 356
6.5.2 Coupler Point Curve for a Slider-Crank Mechanism . 360
6.5.3 Coupler Point Curve for Inverted Slider-Crank Mech-
anism .......................... 362
6.6 F UniversalJointDynamics ................. 363
6.7 Summary ............................ 372
6.8 KeySymbols .......................... 373
Exercises ............................... 374
Steering Dynamics 379
7.1 KinematicSteering....................... 379
7.2 VehicleswithMoreThanTwoAxles ............. 395
7.3 F VehiclewithTrailer..................... 398
7.4 SteeringMechanisms...................... 403
7.5 F Fourwheelsteering...................... 409
7.6 F SteeringMechanismOptimization............. 424
7.7 F Trailer-TruckKinematics.................. 434
7.8 Summary ............................ 447
7.9 KeySymbols .......................... 449
Exercises ............................... 451
Suspension Mechanisms 455
8.1 SolidAxleSuspension ..................... 455
8.2 IndependentSuspension .................... 465
8.3 RollCenterandRollAxis ................... 470
8.4 F CarTireRelativeAngles.................. 478
8.4.1 F Toe.......................... 479
8.4.2 F CasterAngle..................... 482
8.4.3 F Camber ....................... 483
8.4.4 F TrustAngle ..................... 483
8.5 SuspensionRequirementsandCoordinateFrames...... 485
8.5.1 KinematicRequirements................ 485
8.5.2 DynamicRequirements ................ 486
8.5.3 Wheel, wheel-body, and tire Coordinate Frames . . . 487
8.6 F CasterTheory........................ 497
8.7 Summary ............................ 508
8.8 KeySymbols .......................... 510
Exercises ............................... 512
III Vehicle Dynamics 519
9 Applied Dynamics 521
9.1 ForceandMoment ....................... 521
9.2 RigidBodyTranslationalDynamics ............. 528
9.3 RigidBodyRotationalDynamics............... 530
9.4 MassMomentofInertiaMatrix................ 542
9.5 Lagrange’sFormofNewton’sEquationsofMotion ..... 554
9.6 LagrangianMechanics ..................... 561
9.7 Summary ............................ 571
9.8 KeySymbols .......................... 574
Exercises ............................... 575
10 Vehicle Planar Dynamics 583
10.1VehicleCoordinateFrame ................... 583
10.2RigidVehicleNewton-EulerDynamics ............ 589
10.3ForceSystemActingonaRigidVehicle ........... 597
10.3.1TireForceandBodyForceSystems ......... 597
10.3.2TireLateralForce ................... 600
10.3.3 Two-wheel Model and Body Force Components . . . 601
10.4Two-wheelRigidVehicleDynamics.............. 609
10.5Steady-StateTurning...................... 620
10.6 F LinearizedModelforaTwo-WheelVehicle........ 631
10.7 F TimeResponse ....................... 635
10.8Summary ............................ 655
10.9KeySymbols .......................... 657
Exercises ............................... 659
11 F Vehicle Roll Dynamics 665
11.1 F VehicleCoordinateandDOF................ 665
11.2 F EquationsofMotion .................... 666
11.3 F VehicleForceSystem.................... 671
11.3.1 F TireandBodyForceSystems ........... 671
11.3.2 F TireLateralForce.................. 674
11.3.3 F Body Force Components on a Two-wheel Model . 677
11.4 F Two-wheelRigidVehicleDynamics ............ 684
11.5 F Steady-StateMotion .................... 688
11.6 F TimeResponse ....................... 693
11.7Summary ............................ 710
11.8KeySymbols .......................... 712
Exercises ............................... 715
IV Vehicle Vibration 727
12 Applied Vibrations 729
12.1MechanicalVibrationElements ................ 729
12.2Newton’sMethodandVibrations............... 738
12.3FrequencyResponseofVibratingSystems .......... 744
12.3.1ForcedExcitation ................... 745
12.3.2BaseExcitation..................... 756
12.3.3 Eccentric Excitation .................. 768
12.3.4 F EccentricBaseExcitation ............. 775
12.3.5 F Classification for the Frequency Responses of One-
DOFForcedVibrationSystems............ 781
12.4TimeResponseofVibratingSystems............. 786
12.5VibrationApplicationandMeasurement........... 799
12.6 F VibrationOptimizationTheory .............. 804
12.7Summary ............................ 816
12.8KeySymbols .......................... 818
Exercises ............................... 821
13 Vehicle Vibrations 827
13.1LagrangeMethodandDissipationFunction ......... 827
13.2 F Quadratures ......................... 838
13.3NaturalFrequenciesandModeShapes ............ 845
13.4BicycleCarandBodyPitchMode .............. 853
13.5HalfCarandBodyRollMode................. 858
13.6FullCarVibratingModel ................... 864
13.7Summary ............................ 875
13.8KeySymbols .......................... 876
Exercises ............................... 878
14 Suspension Optimization 883
14.1MathematicalModel ...................... 883
14.2FrequencyResponse ...................... 890
14.3RMSOptimization....................... 894
14.4 F TimeResponseOptimization................ 918
14.5Summary ............................ 924
14.6KeySymbols .......................... 925
Exercises ............................... 927
15 F Quarter Car 931
15.1MathematicalModel ...................... 931
15.2FrequencyResponse ...................... 933
15.3 F NaturalandInvariantFrequencies............. 938
15.4 F RMSOptimization ..................... 953
15.5 F Optimization Based on Natural Frequency and Wheel
Travel .............................. 964
15.6Summary ............................ 970
15.7KeySymbols .......................... 971
Exercises ............................... 973
References 977
A Frequency Response Curves 983
B Trigonometric Formulas 989
C Unit Conversions 993
Index 997