Vehicle Dynamics: Theory and Application

1074 Pages·2014·11.68 MB·English

by  Reza N. Jazar (auth.)

Reza N. Jazar
Vehicle Dynamics
Theory and Application
2nd Edition
Vehicle Dynamics

Reza N. Jazar
Vehicle Dynamics
Theory and Application
Second Edition
Reza N. Jazar
School of Aerospace, Mechanical and
Manufacturing Engineering
RMIT University
Bundoora, VIC
Australia
ISBN978-1-4614-8543-8 ISBN 978-1-4614-8544-5 (eBook)
DOI10.1007/978-1-4614-8544-5
Springer New York Heidelberg Dordrecht London
Library of Congress Control Number: 2013951659
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Contents
Preface xvii
1 Tire and Rim Fundamentals 1
1.1 Tires and Sidewall Information . . . . . . . . . . . . . . . . 1
1.2 Tire Components . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3 Radial and Non-Radial Tires . . . . . . . . . . . . . . . . . 15
1.4 Tread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 Tireprint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.6 Wheel and Rim . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.7 Vehicle Classi(cid:31)cations . . . . . . . . . . . . . . . . . . . . . 26
1.7.1 ISO and FHWA Classi(cid:31)cation . . . . . . . . . . . . . 26
1.7.2 Passenger Car Classi(cid:31)cations . . . . . . . . . . . . . 29
1.7.3 Passenger Car Body Styles . . . . . . . . . . . . . . 31
1.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.9 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
I Vehicle Motion 37
2 Forward Vehicle Dynamics 39
2.1 Parked Car on a Level Road . . . . . . . . . . . . . . . . . . 39
2.2 Parked Car on an Inclined Road . . . . . . . . . . . . . . . 45
2.3 Accelerating Car on a Level Road. . . . . . . . . . . . . . . 50
2.4 Accelerating Car on an Inclined Road . . . . . . . . . . . . 55
2.5 Parked Car on a Banked Road . . . . . . . . . . . . . . . . 66
2.6 F Optimal Drive and Brake Force Distribution . . . . . . . 70
2.7 F Vehicles With More Than Two Axles . . . . . . . . . . . 76
2.8 F Vehicles on a Crest and Dip . . . . . . . . . . . . . . . . 80
2.8.1 F Vehicles on a Crest . . . . . . . . . . . . . . . . . 81
2.8.2 F Vehicles on a Dip . . . . . . . . . . . . . . . . . . 86
2.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
2.10 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3 Tire Dynamics 99
3.1 Tire Coordinate Frame and Tire Force System . . . . . . . 99
3.2 Tire Sti(cid:30)ness . . . . . . . . . . . . . . . . . . . . . . . . . . 103
v
vi Contents
3.3 E(cid:30)ective Radius . . . . . . . . . . . . . . . . . . . . . . . . 107
3.4 F Tireprint Forces of a Static Tire . . . . . . . . . . . . . . 122
3.4.1 F Static Tire, Normal Stress . . . . . . . . . . . . . 123
3.4.2 F Static Tire, Tangential Stresses . . . . . . . . . . 126
3.5 Rolling Resistance . . . . . . . . . . . . . . . . . . . . . . . 128
3.5.1 E(cid:30)ect of Speed on the Rolling Friction Coe(cid:33)cient . 131
3.5.2 E(cid:30)ect of In(cid:32)ation Pressure and Load on the Rolling
Friction Coe(cid:33)cient . . . . . . . . . . . . . . . . . . . 135
3.5.3 F E(cid:30)ect of Sideslip Angle on Rolling Resistance . . 138
3.5.4 F E(cid:30)ect of Camber Angle on Rolling Resistance . . 138
3.6 Longitudinal Force . . . . . . . . . . . . . . . . . . . . . . . 139
3.7 Lateral Force . . . . . . . . . . . . . . . . . . . . . . . . . . 148
3.8 Camber Force . . . . . . . . . . . . . . . . . . . . . . . . . . 158
3.9 Tire Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
3.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3.11 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
4 Driveline Dynamics 179
4.1 Engine Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 179
4.2 Driveline and E(cid:33)ciency . . . . . . . . . . . . . . . . . . . . 186
4.3 Gearbox and Clutch Dynamics . . . . . . . . . . . . . . . . 192
4.4 Gearbox Design . . . . . . . . . . . . . . . . . . . . . . . . . 200
4.4.1 Geometric Ratio Gearbox Design . . . . . . . . . . . 201
4.4.2 F Progressive Ratio Gearbox Design . . . . . . . . . 215
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
4.6 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
II Vehicle Kinematics 231
5 F Applied Kinematics 233
5.1 Rotation About Global Cartesian Axes . . . . . . . . . . . . 233
5.2 Successive Rotation About Global Cartesian Axes . . . . . 238
5.3 Rotation About Local Cartesian Axes . . . . . . . . . . . . 239
5.4 Successive Rotation About Local Cartesian Axes . . . . . . 243
5.5 General Transformation . . . . . . . . . . . . . . . . . . . . 251
5.6 Local and Global Rotations . . . . . . . . . . . . . . . . . . 258
5.7 Axis-angle Rotation . . . . . . . . . . . . . . . . . . . . . . 259
5.8 Rigid Body Motion . . . . . . . . . . . . . . . . . . . . . . . 264
5.9 Angular Velocity . . . . . . . . . . . . . . . . . . . . . . . . 267
5.10 F Time Derivative and Coordinate Frames . . . . . . . . . 275
5.11 Rigid Body Velocity . . . . . . . . . . . . . . . . . . . . . . 284
5.12 Angular Acceleration . . . . . . . . . . . . . . . . . . . . . . 288
Contents vii
5.13 Rigid Body Acceleration . . . . . . . . . . . . . . . . . . . . 293
5.14 F Screw Motion . . . . . . . . . . . . . . . . . . . . . . . . 296
5.15 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
5.16 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
6 Applied Mechanisms 319
6.1 Four-Bar Linkage . . . . . . . . . . . . . . . . . . . . . . . . 319
6.2 Slider-Crank Mechanism . . . . . . . . . . . . . . . . . . . . 339
6.3 Inverted Slider-Crank Mechanism . . . . . . . . . . . . . . . 346
6.4 Instant Center of Rotation . . . . . . . . . . . . . . . . . . . 352
6.5 Coupler Point Curve . . . . . . . . . . . . . . . . . . . . . . 364
6.5.1 Coupler Point Curve for Four-Bar Linkages . . . . . 364
6.5.2 Coupler Point Curve for a Slider-Crank Mechanism. 366
6.5.3 CouplerPointCurveforInvertedSlider-CrankMech-
anism . . . . . . . . . . . . . . . . . . . . . . . . . . 370
6.6 F Universal Joint . . . . . . . . . . . . . . . . . . . . . . . 371
6.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
6.8 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
7 Steering Dynamics 387
7.1 Kinematic Steering . . . . . . . . . . . . . . . . . . . . . . . 387
7.2 Vehicles with More Than Two Axles . . . . . . . . . . . . . 404
7.3 F Vehicle with Trailer . . . . . . . . . . . . . . . . . . . . . 407
7.4 Steering Mechanisms . . . . . . . . . . . . . . . . . . . . . . 411
7.5 F Four wheel steering. . . . . . . . . . . . . . . . . . . . . . 417
7.6 F Road Design . . . . . . . . . . . . . . . . . . . . . . . . . 434
7.7 F Steering Mechanism Optimization . . . . . . . . . . . . . 461
7.8 F Trailer-Truck Kinematics . . . . . . . . . . . . . . . . . . 469
7.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
7.10 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 484
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
8 Suspension Mechanisms 497
8.1 Solid Axle Suspension . . . . . . . . . . . . . . . . . . . . . 497
8.2 Independent Suspension . . . . . . . . . . . . . . . . . . . . 508
8.3 Roll Center and Roll Axis . . . . . . . . . . . . . . . . . . . 513
8.4 F Car Tire Relative Angles . . . . . . . . . . . . . . . . . . 524
8.4.1 F Toe . . . . . . . . . . . . . . . . . . . . . . . . . . 527
8.4.2 F Caster Angle. . . . . . . . . . . . . . . . . . . . . 529
8.4.3 F Camber . . . . . . . . . . . . . . . . . . . . . . . 530
8.4.4 F Thrust Angle . . . . . . . . . . . . . . . . . . . . 532
8.5 F Suspension Requirements and Coordinate Frames . . . . 533
8.5.1 Kinematic Requirements . . . . . . . . . . . . . . . . 533
viii Contents
8.5.2 Dynamic Requirements . . . . . . . . . . . . . . . . 534
8.5.3 Wheel, wheel-body, and tire Coordinate Frames. . . 534
8.6 F Caster Theory . . . . . . . . . . . . . . . . . . . . . . . . 544
8.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
8.8 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 557
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
III Vehicle Dynamics 567
9 F Applied Dynamics 569
9.1 Elements of Dynamics . . . . . . . . . . . . . . . . . . . . . 569
9.1.1 Force and Moment . . . . . . . . . . . . . . . . . . . 569
9.1.2 Momentum . . . . . . . . . . . . . . . . . . . . . . . 570
9.1.3 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 571
9.1.4 Equation of Motion . . . . . . . . . . . . . . . . . . 573
9.1.5 Work and Energy. . . . . . . . . . . . . . . . . . . . 573
9.2 Rigid Body Translational Dynamics . . . . . . . . . . . . . 579
9.3 Rigid Body Rotational Dynamics . . . . . . . . . . . . . . . 582
9.4 Mass Moment Matrix . . . . . . . . . . . . . . . . . . . . . 593
9.5 Lagrange’s Form of Newton’s Equations of Motion . . . . . 603
9.6 Lagrangian Mechanics . . . . . . . . . . . . . . . . . . . . . 610
9.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620
9.8 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624
10 Vehicle Planar Dynamics 631
10.1 Vehicle Coordinate Frame . . . . . . . . . . . . . . . . . . . 631
10.2 Rigid Vehicle Newton-Euler Dynamics . . . . . . . . . . . . 637
10.3 Force System Acting on a Rigid Vehicle . . . . . . . . . . . 644
10.3.1 Tire Force and Body Force Systems . . . . . . . . . 644
10.3.2 Tire Lateral Force . . . . . . . . . . . . . . . . . . . 648
10.3.3 Two-wheel Model and Body Force Components . . . 649
10.4 Two-wheel Rigid Vehicle Dynamics . . . . . . . . . . . . . . 659
10.5 Steady-State Turning. . . . . . . . . . . . . . . . . . . . . . 670
10.6 F Linearized Model for a Two-Wheel Vehicle . . . . . . . . 695
10.7 F Transient Response . . . . . . . . . . . . . . . . . . . . . 699
10.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727
10.9 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 729
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731
11 F Vehicle Roll Dynamics 741
11.1 F Vehicle Coordinate and DOF. . . . . . . . . . . . . . . . 741
11.2 F Equations of Motion . . . . . . . . . . . . . . . . . . . . 742
11.3 F Vehicle Force System . . . . . . . . . . . . . . . . . . . . 746
Contents ix
11.3.1 F Tire and Body Force Systems . . . . . . . . . . . 746
11.3.2 F Tire Lateral Force . . . . . . . . . . . . . . . . . . 749
11.3.3 F Body Force Components on a Two-wheel Model . 752
11.4 F Two-wheel Rigid Vehicle Dynamics . . . . . . . . . . . . 759
11.5 F Steady-State Motion . . . . . . . . . . . . . . . . . . . . 763
11.6 F Time Response . . . . . . . . . . . . . . . . . . . . . . . 767
11.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782
11.8 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 783
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786
IV Vehicle Vibration 795
12 Applied Vibrations 797
12.1 Mechanical Vibration Elements . . . . . . . . . . . . . . . . 797
12.2 Newton’s Method and Vibrations . . . . . . . . . . . . . . . 805
12.3 Frequency Response of Vibrating Systems . . . . . . . . . . 812
12.3.1 Forced Excitation . . . . . . . . . . . . . . . . . . . 813
12.3.2 Base Excitation . . . . . . . . . . . . . . . . . . . . . 823
12.3.3 Eccentric Excitation . . . . . . . . . . . . . . . . . . 835
12.3.4 F Eccentric Base Excitation . . . . . . . . . . . . . 841
12.3.5 FClassi(cid:31)cationfortheFrequencyResponsesofOne-
DOF Forced Vibration Systems . . . . . . . . . . . . 847
12.4 Time Response of Vibrating Systems . . . . . . . . . . . . . 852
12.5 Vibration Application and Measurement . . . . . . . . . . . 864
12.6 F Vibration Optimization Theory . . . . . . . . . . . . . . 869
12.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 880
12.8 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 882
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885
13 Vehicle Vibrations 891
13.1 Lagrange Method and Dissipation Function . . . . . . . . . 891
13.2 F Quadratures . . . . . . . . . . . . . . . . . . . . . . . . . 901
13.3 Natural Frequencies and Mode Shapes . . . . . . . . . . . . 908
13.4 Bicycle Car and Body Pitch Mode . . . . . . . . . . . . . . 915
13.5 Half Car and Body Roll Mode. . . . . . . . . . . . . . . . . 920
13.6 Full Car Vibrating Model . . . . . . . . . . . . . . . . . . . 925
13.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933
13.8 Key Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . 934
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936
14 Suspension Optimization 939
14.1 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . 939
14.2 Frequency Response . . . . . . . . . . . . . . . . . . . . . . 945
14.3 RMS Optimization . . . . . . . . . . . . . . . . . . . . . . . 949