The Shock Absorber Handbook Second Edition

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1 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.

2 Preface Acknowledgements xiii xv ffistory Types of Friction Damper Configurations Ride-Levelling Dampers Position-Dependent Dampers General Form of the Telescopic Damper Mountings Operating Speeds and Strokes Manufacture Literature Review 54 2 Vibration Theory Free Vibration Undamped (1-dof) Free Vibration Damped (l-dof) Forced Vibration Undamped (1-dof) Forced Vibration Damped (1-dof) Coulomb Damping Quadratic Damping Series Stiffness Free Vibration Undamped (2-dof) Free Vibration Damped (2-dof) The Resonant Absorber Damper Models in Ride and Handling End Frequencies Heave and Pitch Undamped 1-dof Heave and Pitch Damped 1 -dof Roll Vibration Undamped 93

3 viii Contents Roll Vibration Damped Heave-and-Pitch Undamped 2-dof Heave-and-Pitch Damped 2-dof Simplified Heave-and-Pitch Damped 2-dof Füll Analysis Ride and Handling Installation 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 Properties of Fluids Chemical Properties Density Thermal Expansion

4 ix 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 Valve Design 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

5 Head Valves Multi-Stage Valves Damper Characteristics Adjustables 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 ER and MR Dampers ER-MR History ER Materials ER Dampers ER Controlled Valve MR Materials MR Dampers Specifying a Damper

6 XI End Fittings Length Range F(V) Curve Configuration Diameter Oil Properties Life Cost 11 Testing Transient Testing Electromechanical Testers Hydraulic Testers Instrumentation Data Processing Sinusoidal Test Theory Test Procedure Triangulär Test Other Laboratory Tests On-Road Testing 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

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