Tire and vehicle dynamics

Covers everything you need to know about pneumatic tires and their impact on vehicle performance, including mathematic modeling and its practical application Written by the acknowledged world authority on the topic and the name behind the most widely used model, Pacejka's 'Magic Formula' Updated with the latest information on new and evolving tire models to ensure you can select the right model for your needs, apply it appropriately and understand its limitations

In this well-known resource, leading tire model expert Hans Pacejka explains the relationship between operational variables, vehicle variables and tire modeling, taking you on a journey through the effective modeling of complex tire and vehicle dynamics problems.

Covering the latest developments to Pacejka's own industry-leading model as well as the widely-used models of other pioneers in the field, the book combines theory, guidance, discussion and insight in one comprehensive reference.

While the details of individual tire models are available in technical papers published by SAE, FISITA and other automotive organizations, Tire and Vehicle Dynamics remains the only reliable collection of information on the topic and the standard go-to resource for any engineer or researcher working in the area.

Author Notes

1934 Born in Rotterdam, the Netherlands

1946-1951 Highschools in Rotterdam and Bandung (Indonesia)

1959 MSc. degree in Mechanical Engineering at TU-Delft

1966 Ph.D. degree at the Delft University of Technology

Thesis on the Wheel Shimmy Phenomenon

Advisers: Prof. De Pater and Prof. Van Eldik Thieme

!966-1996 Professor of Vehicle System Engineering

Delft University of Technology

1971 Visiting professor at HSRI (UMTRI), University of Michigan

!972-1989 Editor in Chief of journal Vehicle System Dynamics

1977-1989 Secretary General of the International Association for Vehicle System Dynamics (IAVSD)

!989 Honorary Doctorate

Stockholm Royal Institute of Technology

1993-2006 Consultant TNO-Automotive, The Netherlands

1994-2000 President of IAVSD

2002- 2012 Author of book (1st, 2nd ,3d editions) 'Tire and Vehicle Dynamics'

Hans' areas of expertise include theoretical and experimental research on the dynamics of road vehicles and on the mechanical behaviour of pneumatic tires, and Bond graph modeling of dynamic systems.

Exercises	p. xi
Preface	p. xiii
1 Tire Characteristics and Vehicle Handling and Stability
1.1 Introduction	p. 2
1.2 Tire and Axle Characteristics	p. 3
1.2.1 Introduction to Tire Characteristics	p. 3
1.2.2 Effective Axle Cornering Characteristics	p. 7
13 Vehicle Handling and Stability	p. 16
1.3.1 Differential Equations for Plane Vehicle Motions	p. 17
1.3.2 Linear Analysis of the Two-Degree-of-Freedom Model	p. 22
1.3.3 Nonlinear Steady-State Cornering Solutions	p. 35
1.3.4 The Vehicle at Braking or Driving	p. 49
1.3.5 The Moment Method	p. 51
1.3.6 The Car-Trailer Combination	p. 53
1.3.7 Vehicle Dynamics at More Complex Tire Slip Conditions	p. 57
2 Basic Tire Modeling Considerations
2.1 Introduction	p. 59
2.2 Definition of Tire Input Quantities	p. 61
23 Assessment of Tire Input Motion Components	p. 68
2.4 Fundamental Differential Equations for a Rolling and Slipping Body	p. 72
2.5 Tire Models (Introductory Discussion)	p. 81
3 Theory of Steady-State Slip Force and Moment Generation
3.1 Introduction	p. 87
3.2 Tire Brush Model	p. 90
3.2.1 Pure Side Slip	p. 92
3.2.2 Pure Longitudinal Slip	p. 97
3.2.3 Interaction between Lateral and Longitudinal Slip (Combined Slip)	p. 100
3.2.4 Camber and Turning (Spin)	p. 112
3.3 The Tread Simulation Model	p. 128
3.4 Application: Vehicle Stability at Braking up to Wheel Lock	p. 140
4 Semi-Empirical Tire Models
4.1 Introduction	p. 150
4.2 The Similarity Method	p. 150
4.2.1 Pure Slip Conditions	p. 152
4.2.2 Combined Slip Conditions	p. 158
4.2.3 Combined Slip Conditions with F x as Input Variable	p. 163
4.3 The Magic Formula Tire Model	p. 165
4.3.1 Model Description	p. 165
4.3.2 Full Set of Equations	p. 176
4.3.3 Extension of the Model for Turn Slip	p. 183
4.3.4 Ply-Steer and Conicity	p. 191
4.3.5 The Overturning Couple	p. 196
4.3.6 Comparison with Experimental Data for a Car, a Truck, and a Motorcycle Tire	p. 202
5 Non-Steady-State Out-of-Plane String-Based Tire Models
5.1 Introduction	p. 212
5.2 Review of Earlier Research	p. 212
5.3 The Stretched String Model	p. 215
5.3.1 Model Development	p. 216
5.3.2 Step and Steady-State Response of the String Model	p. 225
5.3.3 Frequency Response Functions of the String Model	p. 232
5.4 Approximations and Other Models	p. 240
5.4.1 Approximate Models	p. 241
5.4.2 Other Models	p. 256
5.4.3 Enhanced String Model with Tread Elements	p. 258
5.5 Tire Inertia Effects	p. 268
5.5.1 First Approximation of Dynamic Influence (Gyroscopic Couple)	p. 269
5.5.2 Second Approximation of Dynamic Influence (First Harmonic)	p. 271
5.6 Side Force Response to Time-Varying Load	p. 277
5.6.1 String Model with Tread Elements Subjected to Load Variations	p. 277
5.6.2 Adapted Bare String Model	p. 281
5.6.3 The Force and Moment Response	p. 284
6 Theory of the Wheel Shimmy Phenomenon Introduction	p. 287
6.1 Introduction	p. 287
6.2 The Simple Trailing Wheel System with Yaw Degree of Freedom	p. 288
6.3 Systems with Yaw and Lateral Degrees of Freedom	p. 295
6.3.1 Yaw and Lateral Degrees of Freedom with Rigid Wheel/Tire (Third Order)	p. 296
6.3.2 The Fifth-Order System	p. 297
6.4 Shimmy and Energy Flow	p. 311
6.4.1 Unstable Modes and the Energy Circle	p. 311
6.4.2 Transformation of Forward Motion Energy into Shimmy Energy	p. 317
6.5 Nonlinear Shimmy Oscillations	p. 320
7 Single-Contact-Point Transient Tire Models
7.1 Introduction	p. 329
7.2 Model Development	p. 330
7.2.1 Linear Model	p. 330
7.2.2 Semi-Non-Linear Model	p. 335
7.2.3 Fully Nonlinear Model	p. 336
7.2.4 Nonlagging Part	p. 345
7.2.5 The Gyroscopic Couple	p. 348
7.3 Enhanced Nonlinear Transient Tire Model	p. 349
8 Applications of Transient Tire Models
8.1 Vehicle Response to Steer Angle Variations	p. 356
8.2 Cornering on Undulated Roads	p. 356
8.3 Longitudinal Force Response to Tire Nonuniformity, Axle Motions, and Road Unevenness	p. 366
8.3.1 Effective Rolling Radius Variations at Free Rolling	p. 367
8.3.2 Computation of the Horizontal Longitudinal Force Response	p. 371
8.3.3 Frequency Response to Vertical Axle Motions	p. 374
8.3.4 Frequency Response to Radial Run-out	p. 376
8.4 Forced Steering Vibrations	p. 379
8.4.1 Dynamics of the Unloaded System Excited by Wheel Unbalance	p. 380
8.4.2 Dynamics of the Loaded System with Tire Properties Included	p. 382
8.5 ABS Braking on Undulated Road	p. 385
8.5.1 In-Plane Model of Suspension and Wheel/Tire Assembly	p. 386
8.5.2 Antilock Braking Algorithm and Simulation	p. 390
8.6 Starting from Standstill	p. 394
9 Short Wavelength Intermediate Frequency Tire Model
9.1 Introduction	p. 404
9.2 The Contact Patch Slip Model	p. 406
9.2.1 Brush Model Non-Steady-State Behavior	p. 406
9.2.2 The Model Adapted to the Use of the Magic Formula	p. 426
9.2.3 Parking Maneuvers	p. 436
9.3 Tire Dynamics	p. 444
9.3.1 Dynamic Equations	p. 444
9.3.2 Constitutive Relations	p. 453
9.4 Dynamic Tire Model Performance	p. 462
9.4.1 Dedicated Dynamic Test Facilities	p. 463
9.4.2 Dynamic Tire Simulation and Experimental Results	p. 466
10 Dynamic Tire Response to Short Road Unevennesses
10.1 Model Development	p. 475
10.1.1 Tire Envelopment Properties	p. 476
10.1.2 The Effective Road Plane Using Basic Functions	p. 478
10.1.3 The Effective Road Plane Using the 'Cam' Road Feeler Concept	p. 485
10.1.4 The Effective Rolling Radius When Rolling Over a Cleat	p. 487
10.1.5 The Location of the Effective Road Plane	p. 493
10.2 SWIFT on Road Unevennesses (Simulation and Experiment)	p. 497
10.2.1 Two-Dimensional Unevennesses	p. 497
10.2.2 Three-Dimensional Unevennesses	p. 504
11 Motorcycle Dynamics
11.1 Introduction	p. 506
11.2 Model Description	p. 508
11.2.1 Geometry and Inertia	p. 509
11.2.2 The Steer, Camber, and Slip Angles	p. 511
11.2.3 Air Drag, Driving or Braking, and Fore-and-Aft Load Transfer	p. 514
11.2.4 Tire Force and Moment Response	p. 515
11.3 Linear Equations of Motion	p. 520
11.3.1 The Kinetic Energy	p. 521
11.3.2 The Potential Energy and the Dissipation Function	p. 523
11.3.3 The Virtual Work	p. 524
11.3.4 Complete Set of Linear Differential Equations	p. 525
11.4 Stability Analysis and Step Responses	p. 529
11.4.1 Free Uncontrolled Motion	p. 529
11.4.2 Step Responses of Controlled Motion	p. 536
11.5 Analysis of Steady-State Cornering	p. 539
11.5.1 Linear Steady-State Theory	p. 540
11.5.2 Non-Linear Analysis of Steady-State Cornering	p. 555
11.5.3 Modes of Vibration at Large Lateral Accelerations	p. 563
11.6 The Magic Formula Tire Model	p. 565
12 Tire Steady-State and Dynamic Test Facilities	p. 567
13 Outlines of Three Advanced Dynamic Tire Models
Introduction	p. 577
13.1 The RMOD-K Tire Model (Christian Oertel)	p. 578
13.1.1 The Nonlinear FEM Model	p. 578
13.1.2 The Flexible Belt Model	p. 579
13.1.3 Comparison of Various RMOD-K Models	p. 581
13.2 The FTire Tire Model (Michael Gipser)	p. 582
13.2.1 Introduction	p. 582
13.2.2 Structure Model	p. 583
13.2.3 Tread Model	p. 584
13.2.4 Model Data and Parametrization	p. 586
13.3 The MF-Swift Tire Model (Igo Besselink)	p. 586
13.3.1 Introduction	p. 586
13.3.2 Model Overview	p. 587
13.3.3 MF-Tire/MF-Swift	p. 588
13.3.4 Parameter Identification	p. 589
13.3.5 Test and Model Comparison	p. 589
References	p. 593
List of Symbols	p. 603
Appendix 1 Sign Conventions for Force and Moment and Wheel Slip	p. 609
Appendix 2 Online Information	p. 611
Appendix 3 MF-Tire/MF-Swift Parameters and Estimation Methods	p. 613
Index	p. 627

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Author Notes

Table of Contents