Contents Preface .......................................................................................................................... xi Preface to Second Edition .......................................................................................... xiii Symbols........................................................................................................................ xv CHAPTER 1 Vehicle Dynamics and Control .........................................1 1.1 Definition of the Vehicle.....................................................................1 1.2 Virtual Four-Wheel Vehicle Model ....................................................1 1.3 Control of Motion...............................................................................2 CHAPTER 2 Tire Mechanics .................................................................5 2.1 Preface.................................................................................................5 2.2 Tires Producing Lateral Force ............................................................5 2.2.1 Tire and Side-Slip Angle.......................................................... 5 2.2.2 Deformation of Tire with Side Slip and Lateral Force ........... 7 2.2.3 Tire Camber and Lateral Force................................................ 8 2.3 Tire Cornering Characteristics............................................................9 2.3.1 Fiala’s Theory........................................................................... 9 2.3.2 Lateral Force........................................................................... 19 2.3.3 Self-Aligning Torque.............................................................. 25 2.3.4 Camber Thrust........................................................................ 26 2.4 Traction, Braking, and Cornering Characteristics............................28 2.4.1 Mathematical Model .............................................................. 28 2.4.2 Tire Lateral Force During Traction and Braking .................. 30 2.4.3 Self-Aligning Torque.............................................................. 35 2.5 Dynamic Characteristics...................................................................40 2.5.1 Lateral Force Dynamic Characteristics.................................. 40 2.5.2 Self-Aligning Torque Dynamic Characteristics..................... 42 Problems ...................................................................................................43 References.................................................................................................44 CHAPTER 3 Fundamentals of Vehicle Dynamics ............................... 45 3.1 Preface...............................................................................................45 3.2 Vehicle Equations of Motion............................................................45 3.2.1 Equations of Motion with Fixed Coordinates on the Vehicle .................................................................................... 45 3.2.2 Equations of Motion with Fixed Coordinates on the Ground .................................................................................... 52 v vi CONTENTS 3.3 Vehicle Steady-State Cornering........................................................56 3.3.1 Description of Steady-State Cornering .................................. 56 3.3.2 Steady-State Cornering and Steer Characteristics ................. 61 3.3.3 Steady-State Cornering and Tire Nonlinear Characteristics ........................................................................ 73 3.4 Vehicle Dynamic Characteristics......................................................79 3.4.1 Vehicle Transient Response to Steering Input....................... 79 3.4.2 Steering Response Transfer Function and Response Time History........................................................................... 88 3.4.3 Vehicle Response to Periodic Steering Input......................... 96 3.4.4 Effect of Nonlinear Tire Characteristics.............................. 103 Problems .................................................................................................107 References...............................................................................................107 CHAPTER 4 Vehicle Motion by Disturbances .................................. 109 4.1 Preface.............................................................................................109 4.2 Motion by Lateral Force Exerted on the Center of Gravity ..........109 4.2.1 Vehicle Motion to a Step Change in Lateral Force............. 109 4.2.2 Vehicle Motion to Impulse Lateral Force............................ 121 4.2.3 Vehicle Motion due to External Disturbances and Steer Characteristics ...................................................................... 123 4.3 Vehicle Motion due to a Lateral Wind Disturbance ......................127 4.3.1 Lateral Wind Disturbance Force.......................................... 127 4.3.2 Vehicle Motion to Lateral Wind with Constant Speed........ 128 4.3.3 Vehicle Motion due to a Lateral Wind Gust........................ 131 4.4 Conclusion of Vehicle Motion by Disturbances ............................136 Problems .................................................................................................136 References...............................................................................................137 CHAPTER 5 Steering System and Vehicle Dynamics ...................... 139 5.1 Preface.............................................................................................139 5.2 Steering System Model and Equations of Motion.........................139 5.3 Effects of Steering System Characteristics on Vehicle Motion.....142 5.3.1 Effects of Steering System Characteristics on Vehicle Motion with Fixed Steering Angle ...................................... 142 5.3.2 Effects of Steering System Characteristics on Vehicle Motion with Non-Fixed Steering Angle .............................. 146 5.3.3 Effects of Driver’s Hands and Arms.................................... 149 Problems .................................................................................................151 References...............................................................................................152 CONTENTS vii CHAPTER 6 Vehicle Body Roll and Vehicle Dynamics.................... 153 6.1 Preface.............................................................................................153 6.2 Roll Geometry.................................................................................153 6.2.1 Roll Center and Roll Axis.................................................... 153 6.2.2 Roll Stiffness and Load Transfer ......................................... 156 6.2.3 Camber Change and Roll Steer............................................ 158 6.3 Body Roll and Vehicle Steer Characteristics .................................161 6.3.1 Load Transfer Effect ............................................................ 161 6.3.2 Camber Change Effect ......................................................... 163 6.3.3 Roll Steer Effect................................................................... 164 6.3.4 Suspension Lateral Stiffness and Its Effect ......................... 166 6.4 Equations of Motion Inclusive of Roll...........................................167 6.4.1 Coordinate System and Dynamic Model............................. 168 6.4.2 Inertias .................................................................................. 169 6.4.3 External Force ...................................................................... 174 6.4.4 Equations of Motion............................................................. 176 6.5 Effect of Steady-State Body Roll on Vehicle Dynamics ...............178 6.6 Effects of Body Roll on Vehicle Stability......................................182 Problems .................................................................................................185 References...............................................................................................186 CHAPTER 7 Vehicle Motion with Traction and Braking .................. 187 7.1 Preface.............................................................................................187 7.2 Equations of Motion Inclusive of Longitudinal Motion................187 7.3 Vehicle Quasi-Steady-State Cornering ...........................................188 7.3.1 Expansion of the Stability Factor for Traction/Braking...... 188 7.3.2 Effect of Traction and Braking on Cornering...................... 194 7.4 Vehicle Transient Steering Response .............................................195 7.4.1 Equations of Motion............................................................. 195 7.4.2 Transient Response to Steering Input .................................. 197 References...............................................................................................200 CHAPTER 8 Vehicle Active Motion Controls.................................... 201 8.1 Preface.............................................................................................201 8.2 Vehicle Motion with Additional Rear-Wheel Steering..................201 8.2.1 Rear-Wheel Steering Proportional to Front-Wheel Steering................................................................................. 202 8.2.2 Rear-Wheel Steering Proportional to Front-Wheel Steering Force......................................................................