Exercises | p. xi |

Preface | p. xiii |

Tire Characteristics and Vehicle Handling and Stability | |

Introduction | p. 2 |

Tire and Axle Characteristics | p. 3 |

Introduction to Tire Characteristics | p. 3 |

Effective Axle Cornering Characteristics | p. 7 |

Vehicle Handling and Stability | p. 16 |

Differential Equations for Plane Vehicle Motions | p. 17 |

Linear Analysis of the Two-Degree-of-Freedom Model | p. 22 |

Nonlinear Steady-State Cornering Solutions | p. 35 |

The Vehicle at Braking or Driving | p. 49 |

The Moment Method | p. 51 |

The Car-Trailer Combination | p. 53 |

Vehicle Dynamics at More Complex Tire Slip Conditions | p. 57 |

Basic Tire Modeling Considerations | |

Introduction | p. 59 |

Definition of Tire Input Quantities | p. 61 |

Assessment of Tire Input Motion Components | p. 68 |

Fundamental Differential Equations for a Rolling and Slipping Body | p. 72 |

Tire Models (Introductory Discussion) | p. 81 |

Theory of Steady-State Slip Force and Moment Generation | |

Introduction | p. 87 |

Tire Brush Model | p. 90 |

Pure Side Slip | p. 92 |

Pure Longitudinal Slip | p. 97 |

Interaction between Lateral and Longitudinal Slip (Combined Slip) | p. 100 |

Camber and Turning (Spin) | p. 112 |

The Tread Simulation Model | p. 128 |

Application: Vehicle Stability at Braking up to Wheel Lock | p. 140 |

Semi-Empirical Tire Models | |

Introduction | p. 150 |

The Similarity Method | p. 150 |

Pure Slip Conditions | p. 152 |

Combined Slip Conditions | p. 158 |

Combined Slip Conditions with F_{x} as Input Variable | p. 163 |

The Magic Formula Tire Model | p. 165 |

Model Description | p. 165 |

Full Set of Equations | p. 176 |

Extension of the Model for Turn Slip | p. 183 |

Ply-Steer and Conicity | p. 191 |

The Overturning Couple | p. 196 |

Comparison with Experimental Data for a Car, a Truck, and a Motorcycle Tire | p. 202 |

Non-Steady-State Out-of-Plane String-Based Tire Models | |

Introduction | p. 212 |

Review of Earlier Research | p. 212 |

The Stretched String Model | p. 215 |

Model Development | p. 216 |

Step and Steady-State Response of the String Model | p. 225 |

Frequency Response Functions of the String Model | p. 232 |

Approximations and Other Models | p. 240 |

Approximate Models | p. 241 |

Other Models | p. 256 |

Enhanced String Model with Tread Elements | p. 258 |

Tire Inertia Effects | p. 268 |

First Approximation of Dynamic Influence (Gyroscopic Couple) | p. 269 |

Second Approximation of Dynamic Influence (First Harmonic) | p. 271 |

Side Force Response to Time-Varying Load | p. 277 |

String Model with Tread Elements Subjected to Load Variations | p. 277 |

Adapted Bare String Model | p. 281 |

The Force and Moment Response | p. 284 |

Theory of the Wheel Shimmy Phenomenon Introduction | p. 287 |

Introduction | p. 287 |

The Simple Trailing Wheel System with Yaw Degree of Freedom | p. 288 |

Systems with Yaw and Lateral Degrees of Freedom | p. 295 |

Yaw and Lateral Degrees of Freedom with Rigid Wheel/Tire (Third Order) | p. 296 |

The Fifth-Order System | p. 297 |

Shimmy and Energy Flow | p. 311 |

Unstable Modes and the Energy Circle | p. 311 |

Transformation of Forward Motion Energy into Shimmy Energy | p. 317 |

Nonlinear Shimmy Oscillations | p. 320 |

Single-Contact-Point Transient Tire Models | |

Introduction | p. 329 |

Model Development | p. 330 |

Linear Model | p. 330 |

Semi-Non-Linear Model | p. 335 |

Fully Nonlinear Model | p. 336 |

Nonlagging Part | p. 345 |

The Gyroscopic Couple | p. 348 |

Enhanced Nonlinear Transient Tire Model | p. 349 |

Applications of Transient Tire Models | |

Vehicle Response to Steer Angle Variations | p. 356 |

Cornering on Undulated Roads | p. 356 |

Longitudinal Force Response to Tire Nonuniformity, Axle Motions, and Road Unevenness | p. 366 |

Effective Rolling Radius Variations at Free Rolling | p. 367 |

Computation of the Horizontal Longitudinal Force Response | p. 371 |

Frequency Response to Vertical Axle Motions | p. 374 |

Frequency Response to Radial Run-out | p. 376 |

Forced Steering Vibrations | p. 379 |

Dynamics of the Unloaded System Excited by Wheel Unbalance | p. 380 |

Dynamics of the Loaded System with Tire Properties Included | p. 382 |

ABS Braking on Undulated Road | p. 385 |

In-Plane Model of Suspension and Wheel/Tire Assembly | p. 386 |

Antilock Braking Algorithm and Simulation | p. 390 |

Starting from Standstill | p. 394 |

Short Wavelength Intermediate Frequency Tire Model | |

Introduction | p. 404 |

The Contact Patch Slip Model | p. 406 |

Brush Model Non-Steady-State Behavior | p. 406 |

The Model Adapted to the Use of the Magic Formula | p. 426 |

Parking Maneuvers | p. 436 |

Tire Dynamics | p. 444 |

Dynamic Equations | p. 444 |

Constitutive Relations | p. 453 |

Dynamic Tire Model Performance | p. 462 |

Dedicated Dynamic Test Facilities | p. 463 |

Dynamic Tire Simulation and Experimental Results | p. 466 |

Dynamic Tire Response to Short Road Unevennesses | |

Model Development | p. 475 |

Tire Envelopment Properties | p. 476 |

The Effective Road Plane Using Basic Functions | p. 478 |

The Effective Road Plane Using the 'Cam' Road Feeler Concept | p. 485 |

The Effective Rolling Radius When Rolling Over a Cleat | p. 487 |

The Location of the Effective Road Plane | p. 493 |

SWIFT on Road Unevennesses (Simulation and Experiment) | p. 497 |

Two-Dimensional Unevennesses | p. 497 |

Three-Dimensional Unevennesses | p. 504 |

Motorcycle Dynamics | |

Introduction | p. 506 |

Model Description | p. 508 |

Geometry and Inertia | p. 509 |

The Steer, Camber, and Slip Angles | p. 511 |

Air Drag, Driving or Braking, and Fore-and-Aft Load Transfer | p. 514 |

Tire Force and Moment Response | p. 515 |

Linear Equations of Motion | p. 520 |

The Kinetic Energy | p. 521 |

The Potential Energy and the Dissipation Function | p. 523 |

The Virtual Work | p. 524 |

Complete Set of Linear Differential Equations | p. 525 |

Stability Analysis and Step Responses | p. 529 |

Free Uncontrolled Motion | p. 529 |

Step Responses of Controlled Motion | p. 536 |

Analysis of Steady-State Cornering | p. 539 |

Linear Steady-State Theory | p. 540 |

Non-Linear Analysis of Steady-State Cornering | p. 555 |

Modes of Vibration at Large Lateral Accelerations | p. 563 |

The Magic Formula Tire Model | p. 565 |

Tire Steady-State and Dynamic Test Facilities | p. 567 |

Outlines of Three Advanced Dynamic Tire Models | |

Introduction | p. 577 |

The RMOD-K Tire Model (Christian Oertel) | p. 578 |

The Nonlinear FEM Model | p. 578 |

The Flexible Belt Model | p. 579 |

Comparison of Various RMOD-K Models | p. 581 |

The FTire Tire Model (Michael Gipser) | p. 582 |

Introduction | p. 582 |

Structure Model | p. 583 |

Tread Model | p. 584 |

Model Data and Parametrization | p. 586 |

The MF-Swift Tire Model (Igo Besselink) | p. 586 |

Introduction | p. 586 |

Model Overview | p. 587 |

MF-Tire/MF-Swift | p. 588 |

Parameter Identification | p. 589 |

Test and Model Comparison | p. 589 |

References | p. 593 |

List of Symbols | p. 603 |

Sign Conventions for Force and Moment and Wheel Slip | p. 609 |

Online Information | p. 611 |

MF-Tire/MF-Swift Parameters and Estimation Methods | p. 613 |

Index | p. 627 |

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