Revealing suspension geometry design methods in unique detail, John Dixon shows how suspension properties such as bump steer, roll steer, bump camber, compliance steer and roll centres are analysed and controlled by the professional engineer. He emphasizes the physical understanding of suspension parameters in three dimensions and methods of their calculation, using examples, programs and discussion of computational problems. The analytical and design approach taken is a combination of qualitative explanation, for physical understanding, with algebraic analysis of linear and non-linear coefficients, and detailed discussion of computer simulations and related programming methods.
- Includes a detailed and comprehensive history of suspension and steering system design, fully illustrated with a wealth of diagrams
- Explains suspension characteristics and suspension geometry coefficients, providing a unique and in-depth understanding of suspension design not found elsewhere.
- Describes how to obtain desired coefficients and the limitations of particular suspension types, with essential information for suspension designers, chassis technicians and anyone else with an interest in suspension characteristics and vehicle dynamics.
- Discusses the use of computers in suspension geometry analysis, with programming techniques and examples of suspension solution, including advanced discussion of three-dimensional computational geometry applied to suspension design.
- Explains in detail the direct and iterative solutions of suspension geometry.
Author(s): John Dixon
Publisher: Wiley
Year: 2009
Language: English
Pages: 436
Suspension Geometry and Computation......Page 5
Contents......Page 9
Preface......Page 17
1.2 Early Steering History......Page 19
1.3 Leaf-Spring Axles......Page 21
1.4 Transverse Leaf Springs......Page 26
1.5 Early Independent Fronts......Page 28
1.6 Independent Front Suspension......Page 31
1.7 Driven Rigid Axles......Page 38
1.9 Undriven Rigid Axles......Page 42
1.10 Independent Rear Driven......Page 44
1.11 Independent Rear Undriven......Page 50
1.12 Trailing-Twist Axles......Page 52
1.13 Some Unusual Suspensions......Page 53
References......Page 60
2.1 Introduction......Page 61
2.2 The Road......Page 63
2.3 Road Curvatures......Page 66
2.4 Pitch Gradient and Curvature......Page 67
2.5 Road Bank Angle......Page 69
2.7 Path Analysis......Page 71
2.8 Particle-Vehicle Analysis......Page 73
2.9 Two-Axle-Vehicle Analysis......Page 75
2.10 Road Cross-Sectional Shape......Page 77
2.12 Logger Data Analysis......Page 79
References......Page 81
3.2 Isolated Ramps......Page 83
3.3 Isolated Bumps......Page 85
3.4 Sinusoidal Single Paths......Page 87
3.5 Sinusoidal Roads......Page 89
3.6 Fixed Waveform......Page 92
3.7 Fourier Analysis......Page 93
3.9 Stochastic Roads......Page 95
References......Page 100
4.2 Wheel and Tyre Geometry......Page 101
4.4 Ride Positions......Page 106
4.6 Roll......Page 108
4.7 Ride Height......Page 110
4.8 Time-Domain Ride Analysis......Page 113
4.9 Frequency-Domain Ride Analysis......Page 114
4.10 Workspace......Page 115
5.1 Introduction......Page 117
5.2 Turning Geometry – Single Track......Page 118
5.3 Ackermann Factor......Page 121
5.4 Turning Geometry – Large Vehicles......Page 126
5.5 Steering Ratio......Page 129
5.6 Steering Systems......Page 130
5.7 Wheel Spin Axis......Page 131
5.8 Wheel Bottom Point......Page 134
5.10 Caster Angle......Page 136
5.11 Camber Angle......Page 137
5.12 Kingpin Angle Analysis......Page 138
5.13 Kingpin Axis Steered......Page 141
5.14 Steer Jacking......Page 142
References......Page 143
6.2 Wheel Bump Steer......Page 145
6.3 Axle Steer Angles......Page 149
6.4 Roll Steer and Understeer......Page 150
6.5 Axle Linear Bump Steer and Roll Steer......Page 151
6.6 Axle Non-Linear Bump Steer and Roll Steer......Page 152
6.8 Vehicle Roll Steer......Page 154
6.10 Vehicle Pitch Steer......Page 155
6.12 Rigid Axles with Link Location......Page 156
6.14 Rigid Axles with Steering......Page 158
References......Page 159
7.2 Wheel Inclination and Camber......Page 161
7.3 Axle Inclination and Camber......Page 163
7.4 Linear Bump and Roll......Page 165
7.5 Non-Linear Bump and Roll......Page 167
7.6 The Swing Arm......Page 168
7.8 Roll Camber Coefficients......Page 170
7.9 Bump Scrub......Page 171
References......Page 174
8.1 Introduction......Page 175
8.2 The Swing Arm......Page 176
8.3 The Kinematic Roll Centre......Page 178
8.4 The Force Roll Centre......Page 180
8.5 The Geometric Roll Centre......Page 182
8.6 Symmetrical Double Bump......Page 183
8.7 Linear Single Bump......Page 185
8.8 Asymmetrical Double Bump......Page 187
8.9 Roll of a Symmetrical Vehicle......Page 189
8.10 Linear Symmetrical Vehicle Summary......Page 191
8.11 Roll of an Asymmetrical Vehicle......Page 192
8.12 Road Coordinates......Page 193
8.14 Experimental Roll Centres......Page 195
References......Page 196
9.1 Introduction......Page 197
9.2 Wheel Forces and Moments......Page 198
9.4 Independent Suspension Compliance......Page 200
9.5 Discussion of Matrix......Page 202
9.6 Independent-Suspension Summary......Page 203
9.7 Hub Centre Forces......Page 204
9.9 Rigid Axles......Page 205
References......Page 206
10.2 Acceleration and Braking......Page 207
10.3 Anti-Dive......Page 208
10.5 Anti-Lift......Page 210
10.7 Design Implications......Page 211
11.1 Introduction......Page 213
11.2 Pivot Axis Geometry......Page 214
11.3 Wheel Axis Geometry......Page 218
11.4 The Trailing Arm......Page 219
11.5 The Sloped-Axis Trailing Arm......Page 223
11.6 The Semi-Trailing Arm......Page 225
11.7 The Low-Pivot Semi-Trailing Arm......Page 227
11.8 The Transverse Arm......Page 228
11.9 The Sloped-Axis Transverse Arm......Page 230
11.10 The Semi-Transverse Arm......Page 232
11.12 General Case Numerical Solution......Page 234
11.13 Comparison of Solutions......Page 236
11.14 The Steered Single Arm......Page 240
11.15 Bump Scrub......Page 241
References......Page 244
12.1 Introduction......Page 245
12.2 Configurations......Page 246
12.3 Arm Lengths and Angles......Page 247
12.5 Equally-Angled Arms......Page 248
12.6 Converging Arms......Page 249
12.7 Arm Length Difference......Page 250
12.8 General Solution......Page 251
12.9 Design Process......Page 254
12.10 Numerical Solution in Two Dimensions......Page 255
12.11 Pitch......Page 257
12.12 Numerical Solution in Three Dimensions......Page 260
12.13 Steering......Page 261
12.14 Strut Analysis in Two Dimensions......Page 262
12.15 Strut Numerical Solution in Two Dimensions......Page 265
12.16 Strut Design Process......Page 266
12.17 Strut Numerical Solution in Three Dimensions......Page 267
12.18 Double Trailing Arms......Page 268
12.19 Five-Link Suspension......Page 269
13.3 Axle Variables......Page 271
13.4 Pivot-Point Analysis......Page 275
13.5 Link Analysis......Page 276
13.7 Numerical Solution......Page 278
13.8 The Sensitivity Matrix......Page 281
13.9 Results: Axle 1......Page 282
13.10 Results: Axle 2......Page 283
13.11 Coefficients......Page 284
14.2 Motion Ratio......Page 289
14.4 Velocity Diagrams......Page 292
14.6 Mechanical Displacement......Page 293
14.7 The Rocker......Page 294
14.8 The Rigid Arm......Page 300
14.9 Double Wishbones......Page 302
14.10 Struts......Page 304
14.11 Pushrods and Pullrods......Page 306
14.12 Solid Axles......Page 307
14.13 The Effect of Motion Ratio on Inertia......Page 308
14.14 The Effect of Motion Ratio on Springs......Page 310
14.15 The Effect of Motion Ratio on Dampers......Page 311
14.16 Velocity Diagrams in Three Dimensions......Page 313
14.17 Acceleration Diagrams......Page 315
References......Page 316
15.2 Coordinate Systems......Page 317
15.4 Direction Numbers and Cosines......Page 318
15.5 Vector Dot Product......Page 319
15.6 Vector Cross Product......Page 320
15.7 The Sine Rule......Page 321
15.8 The Cosine Rule......Page 322
15.10 Lines......Page 323
15.11 Planes......Page 324
15.12 Spheres......Page 325
15.13 Circles......Page 326
15.15 Routine PointFPLPDC......Page 327
15.16 Routine PointITinit......Page 328
15.17 Routine PointIT......Page 330
15.19 Routine Plane3P......Page 331
15.21 Routine PointFPPl3P......Page 332
15.22 Routine PointATinit......Page 333
15.24 Routine Points3S......Page 334
15.25 Routine Points2SHP......Page 336
15.26 Routine Point3Pl......Page 337
15.27 Routine ‘PointLP’......Page 338
15.29 Routine PointITV......Page 339
15.30 Routine PointATV......Page 340
15.31 Rotations......Page 341
16.2 The RASER Value......Page 343
16.3 Failure Modes Analysis......Page 344
16.4 Reliability......Page 345
16.5 Bad Conditioning......Page 346
16.6 Data Sensitivity......Page 347
16.7 Accuracy......Page 348
16.8 Speed......Page 349
16.10 The Assembly Problem......Page 350
16.11 Checksums......Page 352
17.1 Introduction......Page 353
17.2 Three Phases of Iteration......Page 354
17.3 Convergence......Page 355
17.4 Binary Search......Page 356
17.5 Linear Iterations......Page 357
17.6 Iterative Exits......Page 358
17.7 Fixed-Point Iteration......Page 361
17.8 Accelerated Convergence......Page 362
17.9 Higher Orders without Derivatives......Page 364
17.10 Newton’s Iterations......Page 366
17.11 Other Derivative Methods......Page 368
17.12 Polynomial Roots......Page 369
17.13 Testing......Page 372
References......Page 375
Appendix A: Nomenclature......Page 377
Appendix B: Units......Page 395
Appendix C: Greek Alphabet......Page 397
Appendix D: Quaternions for Engineers......Page 399
Appendix E: Frenet, Serret and Darboux......Page 411
Appendix F: The Fourier Transform......Page 413
References and Bibliography......Page 421
Index......Page 425
