The Shock Absorber Handbook Second Edition John C. Dixon, Ph.D, F.I.Mech.E., F.R.Ae.S. Senior Lecturer in Engineering Mechanics The Open University, Great Britain IICIUTIHHIIL BICINTINNIIM. John Wiley & Sons, Ltd Professional Engineering Publishing This Work is a co-publication between Professional Engineering Publishing Ltd and John Wiley and Sons, Ltd.
Preface Acknowledgements xiii xv 1 1 1.1 ffistory 1 1.2 Types of Friction 15 1.3 Damper Configurations 17 1.4 Ride-Levelling Dampers 33 1.5 Position-Dependent Dampers 35 1.6 General Form of the Telescopic Damper 37 1.7 Mountings 42 1.8 Operating Speeds and Strokes 47 1.9 Manufacture 53 1.10 Literature Review 54 2 Vibration Theory 61 2.1 61 2.2 Free Vibration Undamped (1-dof) 61 2.3 Free Vibration Damped (l-dof) 63 2.4 Forced Vibration Undamped (1-dof) 68 2.5 Forced Vibration Damped (1-dof) 71 2.6 Coulomb Damping 74 2.7 Quadratic Damping 77 2.8 Series Stiffness 79 2.9 Free Vibration Undamped (2-dof) 85 2.10 Free Vibration Damped (2-dof) 85 2.11 The Resonant Absorber 86 2.12 Damper Models in Ride and Handling 87 2.13 End Frequencies 88 2.14 Heave and Pitch Undamped 1-dof 90 2.15 Heave and Pitch Damped 1 -dof 91 2.16 Roll Vibration Undamped 93
viii Contents 2.17 2.18 2.19 2.20 Roll Vibration Damped Heave-and-Pitch Undamped 2-dof Heave-and-Pitch Damped 2-dof Simplified Heave-and-Pitch Damped 2-dof Füll Analysis 94 95 100 102 Ride and Handling 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 Installation 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 Modelling the Road Ride Time-Domain Ride Analysis Frequency-Domain Ride Analysis Passenger on Seat Wheel Hop Handling Axle Vibrations Steering Vibrations The Ride-Handling Compromise Damper Optimisation Damper Asymmetry Motion Ratio Displacement Method Velocity Diagrams Computer Evaluation Mechanical Displacement Effect of Motion Ratio Evaluation of Motion Ratio The Rocker The Rigid Arm Double Wishbones Struts Pushrods and Pullrods Motorcycle Front Suspensions Motorcycle Rear Suspensions Solid Axles Dry Scissor Dampers Fluid Mechanics 5.1 5.2 5.3 5.4 5.5 Properties of Fluids Chemical Properties Density Thermal Expansion 105 105 105 111 113 117 118 119 120 122 124 124 129 131 135 135 135 137 138 138 138 139 142 142 148 150 153 155 156 160 165 168 169 169 170 171 171 172
ix 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 Compressibility Viscosity Thermal Capacity Thermal Conductivity Vapour Pressure Gas Density Gas Viscosity Gas Compressibility Gas Absorbability Emulsincation Continuity Bernoulli's Equation Fluid Momentum Pipe Flow Velocity Profiles Other Losses The Orifice Combined Orifices Vortices Bingham Flow Liquid-Solid Suspensions ER and MR Fluids 172 173 175 176 176 176 177 177 177 179 188 188 189 191 196 199 203 207 209 212 212 214 Valve Design 6.1 6.2 Valve Types 6.3 Disc Valves 6.4 Rod Valves 6.5 Spool Valves 6.6 Shim Valves 6.7 Valve Characteristics 6.8 Basic Valve Models 6.9 Complete Valve Models 6.10 Solution of Valve Flow 6.11 Temperature Compensation 6.12 Position-Sensitive Valves 6.13 Acceleration-Sensitive Valves 6.14 Pressure-Rate Valves 6.15 Frequency-Sensitive Valves 6.16 Stroke-Sensitive Valves 6.17 Piezoelectric Valves 6.18 Double-Acting Shim Valves 6.19 Rotary Adjustables 6.20 Bellows Valves 6.21 Simple Tube Valves 217 217 219 220 221 222 223 225 227 230 235 237 240 240 243 245 245 249 249 250 252 252
6.22 6.23 Head Valves Multi-Stage Valves 257 257 7 Damper Characteristics 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 8 Adjustables 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 Basic Damper Parameters Mechanical Friction Static Forces Piston Free Body Diagram Valve Flow Rates Pressures and Forces Linear Valve Analysis Cavitation Temperature Compressibility Cyclical Characteristics, F(X) Extreme Cyclic Operation Stresses and Strains Damper Jacking Noise The Adjustable Valve Parallel Hole Series Hole Maximum Area Opening Pressure Area Coefficient (Stiffness) Automatic Systems Fast Adaptive Systems Motion Ratio 259 259 263 265 268 269 271 272 273 274 276 276 278 282 283 286 287 289 289 290 295 295 299 301 9 ER and MR Dampers 303 9.1 9.2 9.3 9.4 9.5 9.6 9.7 ER-MR History ER Materials ER Dampers ER Controlled Valve MR Materials MR Dampers 303 303 309 314 319 321 324 10 Specifying a Damper 10.1 333 333
XI 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 End Fittings Length Range F(V) Curve Configuration Diameter Oil Properties Life Cost 11 Testing 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 Transient Testing Electromechanical Testers Hydraulic Testers Instrumentation Data Processing Sinusoidal Test Theory Test Procedure Triangulär Test Other Laboratory Tests On-Road Testing 337 337 338 342 344 345 346 348 352 354 356 357 Appendix A: Nomenclature 361 Appendix B: Properties of Air 375 Appendix C: Properties of Water 379 Appendix D: Test Sheets 381 Appendix E: Solution of Algebraic Equations 385 Appendix F: Units 393 Appendix G: Bingham Flow 397 References 401 Index 409