1、Road Vehicle Dynamics Rao V. Dukkipati Jian Pang Mohamad S. Qatu Gang Sheng Zuo ShuguangRoad Vehicle DynamicsOther SAE titles of interest: Fundamentals of Vehicle Dynamics By Thomas D. Gillespie (Product Code: R-114) Race Car Vehicle Dynamics By William F. Milliken and Douglas L. Milliken (Product C
2、ode: R-146) Tire and Vehicle Dynamics, Second Edition By Hans B. Pacejka (Product Code: R-372) For more information or to order a book, contact SAE International at 400 Commonwealth Drive, Warrendale, PA 15096-0001; phone (724) 776-4970; fax (724) 776-0790; e-mail CustomerServicesae.org; website htt
3、p:/store.sae.org.Road Vehicle Dynamics Rao Dukkipati Jian Pang Mohamad Qatu Gang Sheng Shuguang Zuo SAE International Warrendale, Pa. Copyright 2008 SAE International eISBN: 978-0-7680-4346-4All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmit
4、ted, in any form or by any means, electronic, mechanical, photocopy- ing, recording, or otherwise, without the prior written permission of SAE. For permission and licensing requests, contact: SAE Permissions 400 Commonwealth Drive Warrendale, PA 15096-0001 USA E-mail: permissionssae.org Tel: 724-772
5、-4028 Fax: 724-772-4891 Library of Congress Cataloging-in-Publication Data Road vehicle dynamics / Rao Dukkipati . et al. p. cm. ISBN 978-0-7680-1643-7 1. AutomobilesDynamics. I. Dukkipati, Rao V. TL243.R63 2008 629.231-dc22 2007018140 SAE International 400 Commonwealth Drive Warrendale, PA 15096-00
6、01 USA E-mail: CustomerServicesae.org Tel: 877-606-7323 (inside USA and Canada) 724-776-4970 (outside USA) Fax: 724-776-1615 Copyright 2008 SAE International ISBN 978-0-7680-1643-7 SAE Order No. R-366 Printed in the United States of America. green press I N ITI ATI VE SAE International is committed
7、to preserving ancient forests and natural resources. We elected to print this title on 30% post consumer recycled paper, processed chlorine free. As a result, for this printing, we have saved: 13 Trees (40 tall and 6-8 diameter) 4,830 Gallons of Wastewater 9 million BTUs of Total Energy 620 Pounds o
8、f Solid Waste 1,164 Pounds of Greenhouse Gases SAE International made this paper choice because our printer, Thomson-Shore, Inc., is a member of Green Press Initiative, a nonprofit program dedicated to supporting authors, publish- ers, and suppliers in their efforts to reduce their use of fiber obta
9、ined from endangered forests. For more information, visit www.greenpressinitiative.org Environmental impact estimates were made using the Environmental Defense Paper Calculator For more information visit www.papercalculator.org.Contents Foreword xvii Preface xix Chapter 1 Introduction 1 1.1 General
10、1 1.2 Vehicle System Classification 2 1.3 Dynamic System 3 1.4 Classification of Dynamic System Models 4 1.5 Constraints, Generalized Coordinates, and Degrees of Freedom 4 1.6 Discrete and Continuous Systems 10 1.7 Vibration Analysis 10 1.8 Elements of Vibrating Systems 15 1.8.1 Spring Elements 15 1
11、.8.2 Potential Energy of Linear Springs 18 1.8.3 Equivalent Springs 18 1.8.3.1 Springs in Parallel 19 1.8.3.2 Springs in Series 20 1.8.4 Mass or Inertia Elements. 25 1.8.5 Damping Elements 25 1.8.5.1 Viscous Damping 25 1.8.5.2 Coulomb Damping 27 1.8.5.3 Structural or Hysteretic Damping 29 1.8.5.4 Co
12、mbination of Damping Elements 30 1.9 Review of Dynamics 32 1.9.1 Newtons Laws of Motion 32 1.9.2 Kinematics of Rigid Bodies 33 1.9.3 Linear Momentum 37 1.9.4 Principle of Conservation of Linear Momentum 37 1.9.5 Angular Momentum 38 1.9.6 Equations of Motion for a Rigid Body 39 1.9.7 Angular Momentum
13、 of a Rigid Body 39 1.9.8 Principle of Work and Energy 40 1.9.9 Conservation of Energy 41 1.9.10 Principle of Impulse and Momentum .42 1.9.11 Mechanical Systems 45 1.9.12 Translational Systems 46 1.9.13 Rotational Systems 47 1.9.14 Translation and Rotational Systems 48 1.9.15 Angular Momentum and Mo
14、ments of Inertia 48 1.9.16 Geared Systems 52 1.10 Lagranges Equation 59 1.10.1 Degrees of Freedom 59 1.10.2 Generalized Coordinates 60 1.10.3 Constraints 61 1.10.4 Principle of Virtual Work 63vi Road Vehicle Dynamics 1.10.5 DAlemberts Principle 68 1.10.6 Generalized Force 71 1.10.7 Lagranges Equatio
15、ns of Motion 74 1.10.8 Holonomic Systems .74 1.10.9 Nonholonomic Systems 76 1.10.10 Rayleighs Dissipation Function .78 1.11 Summary 85 1.12 References . 86 Chapter 2 Analysis of Dynamic Systems 91 2.1 Introduction .91 2.2 Classification of Vibrations 91 2.3 Classification of Deterministic Data 92 2.
16、3.1 Sinusoidal Periodic Data 93 2.3.2 Complex Periodic Data 94 2.3.3 Almost Periodic Data .95 2.3.4 Transient Nonperiodic Data 95 2.4 Linear Dynamic Systems 97 2.4.1 Linear Single-Degree-of-Freedom System 98 2.4.2 Free Vibration of a Single-Degree-of-Freedom System 98 2.4.3 Forced Vibration of a Sin
17、gle-Degree-of-Freedom System 102 2.4.4 Linear Multiple-Degrees-of-Freedom System 109 2.4.5 Eigenvalues and Eigenvectors: Undamped System .110 2.4.6 Eigenvalues and Eigenvectors: Damped System 115 2.4.7 Forced Vibration Solution of a Multiple-Degrees- of-Freedom System. 119 2.5 Nonlinear Dynamic Syst
18、ems 123 2.5.1 Exact Methods for Nonlinear Systems. 124 2.5.2 Approximate Methods for Nonlinear Systems 128 2.5.2.1 Iterative Method 128 2.5.2.2 Ritz Averaging Method 131 2.5.2.3 Perturbation Method 134 2.5.2.4 Variation of Parameter Method 140 2.5.3 Graphical Method 142 2.5.3.1 Phase Plane Represent
19、ation 142 2.5.3.2 Phase Velocity 142 2.5.3.3 Pells Method 144 2.5.4 Multiple-Degrees-of-Freedom Systems 146 2.6 Random Vibrations 147 2.6.1 Probability Density Function 149 2.6.2 Autocorrelation Function 152 2.7 Gaussian Random Process 153 2.7.1 Fourier Analysis .154 2.7.1.1 Fourier Series 154 2.7.1
20、.2 Fourier Integral 155 2.7.2 Response of a Single-Degree-of-Freedom Vibrating System157 2.7.2.1 Impulse Response Method 158 2.7.2.2 Frequency Response Method 160 2.7.3 Power Spectral Density Function 163 2.7.4 Joint Probability Density Function 165 2.7.5 Cross-Correlation Function 166Contents vii 2
21、.7.6 Application of Power Spectral Densities to Vehicle Dynamics .166 2.7.7 Response of a Single-Degree-of-Freedom System to Random Inputs 168 2.7.8 Response of Multiple-Degrees-of-Freedom Systems to Random Inputs 170 2.8 Summary 174 2.9 References. 174 Chapter 3 Tire Dynamics 177 3.1 Introduction .
22、177 3.2 Vertical Dynamics of Tires 180 3.2.1 Vertical Stiffness and Damping Characteristics of Tires 180 3.2.2 Vertical Vibration Mechanics Models of Tires 181 3.2.2.1 Point Contact Model of Tires 181 3.2.2.2 Fixed Contact Patch Model of Tires 182 3.2.2.3 Time-Varying Contact Patch Model of Tires 18
23、3 3.2.3 Enveloping Characteristics of Tires 185 3.3 Tire Longitudinal Dynamics 186 3.3.1 Tire Rolling Resistance 187 3.3.2 Rolling Resistance of the Tire with Toe-In 188 3.3.3 Rolling Resistance of the Turning Wheel 189 3.3.4 Longitudinal Adhesion Coefficient 191 3.3.5 Theoretical Model of Tire Long
24、itudinal Force Under Driving and Braking 194 3.4 Tire Lateral Dynamics 196 3.4.1 Tire Cornering Characteristics 196 3.4.2 Mathematical Model of the Tire Cornering Characteristic 198 3.4.2.1 Simplified Mathematical Model of the Tire Cornering Characteristic 199 3.4.2.2 Cornering Characteristic with L
25、ateral Bending Deformation of the Tire Case 204 3.4.3 Rolling Properties of Tires 208 3.4.3.1 Cambered Tire Models 209 3.4.3.2 Cambered Tire Model with Roll Elastic Deformation of the Tire Carcass 211 3.5 Tire Mechanics Model Considering Longitudinal Slip and Cornering Characteristics .211 3.5.1 C.G
26、. Gim Theoretical Model 212 3.5.2 K.H. Guo Tire Model 214 3.5.2.1 Steady-State Simplified Theoretical Tire Model 214 3.5.2.2 Nonsteady-State Semi-Empirical Tire Mechanics Model. 219 3.5.3 H.B. Pacejka Magic Formula Model 224 3.6 References 228 Chapter 4 Ride Dynamics 231 4.1 Introduction .231 4.2 Vi
27、bration Environment in Road Vehicles 233 4.2.1 Vibration Sources from the Road 233 4.2.1.1 Power Spectral Density in Spatial Frequency .233viii Road Vehicle Dynamics 4.2.1.2 Power Spectral Density in Temporal Frequency.237 4.2.2 Vehicle Internal Vibration Sources 239 4.2.2.1 Vibration Sources from t
28、he Powerplant 239 4.2.2.1.1 Coordinates and Powerplant Modes 239 4.2.2.1.2 Vibration Sources from Engine Firing Pulsation 242 4.2.2.1.3 Vibration Sources from Powerplant Inertia Forces and Moments 244 4.2.2.1.4 Powerplant Isolation Design 244 4.2.2.2 Vibration Sources from the Driveline. 252 4.2.2.2
29、.1 Driveline Imbalance 253 4.2.2.2.2 Gear Transmission Error 255 4.2.2.2.3 Second Order Excitation .256 4.2.2.2.4 Driveshaft Modes and Driveline Modes .257 4.2.2.3 Vibration Sources from the Exhaust System 257 4.3 Vehicle Ride Models .261 4.3.1 Quarter Car Model 262 4.3.1.1 Modeling for the Quarter
30、Car Model 262 4.3.1.2 Modal Analysis for the Quarter Car Model .264 4.3.1.3 Dynamic Analysis for the Quarter Car Model 266 4.3.1.3.1 Transmissibility Between the Body Response and Road Excitation 266 4.3.1.3.2 Transmissibility Between the Body Response and Vehicle Excitation 271 4.3.1.3.3 Dynamic Re
31、sponse at Random Input.272 4.3.2 Bounce-Pitch Model. 274 4.3.3 Other Modeling 281 4.4 Seat Evaluation and Modeling .282 4.4.1 Introduction 282 4.4.2 SEAT Value 283 4.4.3 Seat Velocity. .285 4.4.4 Linear Seat Modeling and Transmissibility 286 4.4.5 Nonlinear Seat Modeling and Transmissibility 286 4.5
32、 Discomfort Evaluation and Human Body Model 290 4.5.1 Discomfort and Subjective Evaluation 290 4.5.2 Objective Evaluation of Ride Discomfort 292 4.5.2.1 Weighted Root-Mean-Square Method 292 4.5.2.2 Objective Evaluation by the Vibration Dose Value 293 4.5.3 Linear Human Body Modeling 294 4.5.4 Object
33、ive Evaluation by Nonlinear SeatHuman Body Modeling 295 4.6 Active and Semi-Active Control 298 4.6.1 Introduction 298 4.6.2 Basic Control Concepts. 298 4.6.3 Active Control 299 4.6.4 Semi-Active Control .302 4.7 Summary 307 4.8 References 307Contents ix Chapter 5 Vehicle Rollover Analysis. 311 5.1 I
34、ntroduction 311 5.1.1 Rollover Scenario 311 5.1.2 Importance of Rollover 314 5.1.3 Research on Rollover 314 5.1.4 Scope of This Chapter 315 5.2 Rigid Vehicle Rollover Model 316 5.2.1 Rigid Vehicle Model 316 5.2.2 Steady-State Rollover on a Flat Road .317 5.2.3 Tilt Table Ratio .318 5.2.4 Side Pull R
35、atio . 320 5.3 Suspended Vehicle Rollover Model 321 5.3.1 Steady-State Rollover Model for a Suspended Vehicle 321 5.3.2 Contribution from the Tire Deflection 323 5.3.3 Contribution from the Suspension Deflection 324 5.3.4 Parameters Influencing the Suspended Rollover Model 326 5.4 Dynamic Rollover M
36、odel 333 5.4.1 Rigid Dynamic Model 333 5.4.2 Dynamic Rollover Model for a Dependent Suspension Vehicle. 334 5.4.3 Dynamic Rollover Model for an Independent Suspension Vehicle 336 5.4.4 Rollover Simulation Tools 336 5.5 Dynamic Rollover Threshold 338 5.5.1 Dynamic Stability Index .338 5.5.2 Rollover
37、Prevention Energy Reserve 339 5.5.3 Rollover Prevention Metric 340 5.5.4 Critical Sliding Velocity 340 5.6 Occupant in Rollover 341 5.6.1 Overview of the Occupant and Rollover 341 5.6.2 Testing of an Occupant Model 342 5.6.3 Simulation of Occupant Rollover .343 5.7 Safety and Rollover Control 345 5.
38、7.1 Overview of Rollover Safety 345 5.7.2 Sensing of Rollover 349 5.7.3 Rollover Safety Control 350 5.8 Summary 352 5.9 References 353 Chapter 6 Handling Dynamics .357 6.1 Introduction 357 6.1.1 Tire Cornering Forces 358 6.1.2 Forces and Torques in the Tire Contact Area 360 6.2 The Simplest Handling
39、 ModelsTwo-Degrees-of-Freedom Yaw Plane Model 361 6.3 Steady-State Handling Characteristics 365 6.3.1 Yaw Velocity Gain and Understeer Gradient 365 6.3.1.1 Neutral Steer 367 6.3.1.2 Understeer 367 6.3.1.3 Oversteer 368 6.3.2 Difference Between Slip Angles of the Front and Rear Wheels 368X Road Vehic
40、le Dynamics 6.3.3 Ratio of Radius of Turn 370 6.4 Dynamic Characteristics of Handling .372 6.4.1 Handling Damping and Natural Frequency 372 6.4.2 Step Steer Input Response 375 6.4.3 Ramp Steer Input Response 379 6.4.4 Impulse Input Excitation Response 379 6.4.5 Frequency Response of Yaw Velocity 380
41、 6.4.6 Stability Analysis 384 6.4.7 Curvature Response 385 6.5 Chassis System Effects on Handling Characteristics 385 6.5.1 Lateral Force Transfer Effects on Cornering 386 6.5.2 Steering System 391 6.5.3 Camber Change Effect 392 6.5.4 Roll Steer Effect 395 6.5.5 Lateral Force Compliance Steer 395 6.
42、5.6 Aligning Torque Effects 396 6.5.7 Effect of Tractive Forces on Cornering. 396 6.6 Handling SafetyOverturning Limit Handling Characteristics 397 6.7 Nonlinear Models of Handling Dynamics 399 6.7.1 Multiple-Degrees-of-Freedom System Models 399 6.7.2 An Eight-Degrees-of-Freedom System Model 400 6.8
43、 Testing of Handling Characteristics .403 6.8.1 Constant Radius Turn 404 6.8.2 Constant Speed Test . 406 6.8.3 Constant Steer Angle Test 406 6.8.3.1 Dynamic Testing .406 6.8.3.2 Simulations and Testing Validation 408 6.9 Summary 413 6.10 References 413 Chapter 7 Braking 415 7.1 Introduction 415 7.1.
44、1 Types of Automotive Brakes 416 7.1.2 Braking Distance and Deceleration 417 7.2 Brake Torque Distribution 419 7.2.1 Drum Brakes .419 7.2.1.1 Mechanical Advantage 419 7.2.1.2 Torque Calculations 422 7.2.2 Disk Brakes 428 7.2.3 Consideration of Temperature. 429 7.3 Load Transfer During Braking 431 7.
45、3.1 Simple Braking on a Horizontal Road 432 7.3.2 Effect of Aerodynamic and Other Forces. 435 7.3.2.1 Rolling Resistance 436 7.3.2.2 Aerodynamic Drag 436 7.3.2.3 Powertrain Resistance 437 7.3.2.4 Load Transfer on a Horizontal Plane 437 7.3.3 Effect of Grade. 438 7.4 Optimal Braking Performance 441 7
46、.4.1 Braking of a Single Axle .441 7.4.1.1 Braking of the Front Axle 441Contents xi 7.4.1.2 Braking of the Rear Axle 441 7.4.1.3 Safety Considerations 443 7.4.2 Braking at Both Axles 444 7.4.2.1 Front Lock-Up 445 7.4.2.2 Rear Lock-Up 446 7.4.3 Achieving Optimal Braking Performance 450 7.5 Considerat
47、ions of Vehicle Safety 459 7.5.1 Skid (Slip) Condition and Braking 460 7.5.2 Anti-Lock Braking System 462 7.6 Pitch Plane Models 464 7.7 Recent Advances in Automotive Braking 464 7.8 Summary 466 7.9 References 468 Chapter 8 Acceleration 471 8.1 Introduction 471 8.2 Load Transfer During Acceleration
48、473 8.2.1 Simple Acceleration on a Horizontal Road 473 8.2.2 Effect of Aerodynamic and Other Forces. .475 8.2.3 Effect of Grade 477 8.3 Traction-Limited Acceleration 480 8.3.1 Drivetrain Configurations 480 8.3.2 Front-Wheel Drive 483 8.3.3 Rear-Wheel Drive 484 8.3.4 All-Wheel-Drive and Four-by-Four
49、Systems 486 8.3.4.1 Front Skid 486 8.3.4.2 Rear Skid .487 8.3.5 Optimal Tractive Effort 490 8.4 Power-Limited Acceleration .499 8.4.1 The Engine 501 8.4.2 Internal Combustion Engines .504 8.4.3 The Transmission 508 8.4.3.1 Manual Transmissions 509 8.4.3.2 Automatic Transmissions. 514 8.4.3.3 Continuously Variable Transmissions 519 8.4.4 Vehicle Acceleration 521 8.5 Safety Features 526 8.5.1 Limited Slip Axle 526 8.5.2 Traction Control 527 8.6 Summary 528 8.7 References 529 Chapter 9 Total Vehicle Dynamics 531 9.1 Introduction 531 9.1.1 Subjective and Objective Evaluat
