1、The Shock Absorber Handbook John C. DixonThe Shock Absorber HandbookOther SAE books by John C. Dixon: Tires, Suspension and Handling, Second Edition (Order No. R-168) For more information or to order this book, contact SAE at 400 Commonwealth Drive, Warrendale, PA 15096-0001; (724) 776-4970; fax (72
2、4) 776-0790; e-mail: publicationssae.org; http:/www.sae.org/BOOKSTORE.The Shock Absorber Handbook John Dixon Society of Automotive Engineers, Inc. Warrendale, Pa. Copyright 1999 Society of Automotive Engineers, Inc. eISBN: 978-0-7680-3959-7Library of Congress Cataloging-in-Publication Data Dixon, Jo
3、hn C., 1948- Shock absorber handbook / John C. Dixon. p. cm. Includes bibliographical references and index. ISBN 0-7680-0050-5 1. AutomobilesShock absorbersDesign and construction. I Title TL257.5.D58 1999 629.243dc21 98-37276 CIP Copyright 1999 Society of Automotive Engineers, Inc. 400 Commonwealth
4、 Drive Warrendale, PA 15096-0001 U.S.A. Phone: (724)776-4841 Fax: (724)776-5760 E-mail: publicationssae.org http:/www.sae.org ISBN 0-7680-0050-5 All rights reserved. Printed in the United States of America Permission to photocopy for internal or personal use, or the internal or personal use of speci
5、fic clients, is granted by SAE for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $.50 per page is paid directly to CCC, 222 Rosewood Dr., Danvers, MA 01923. Special requests should be addressed to the SAE Publications Group. 0-7680-0050
6、-5/99-$.50. SAE Order No. R-176 Front cover photo courtesy of Jim Cutler Photography and Penske Racing Disclaimer: This book is not intended as a guide for vehicle modification, and anyone who uses it as such does so entirely at their own risk. Testing vehicle performance may be dangerous. The autho
7、r and publisher are not liable for consequential damage arising from application of any information in this book.To My FatherCONTENTS Preface xi 1 Introduction 1 1.1 History 1 1.2 Types of Friction 12 1.3 Hydraulic Damper Configurations 13 1.4 Mountings 23 1.5 Operating Speeds 26 1.6 Manufacture 32
8、1.7 Literature Review 34 2 Vibration Theory 45 2.1 Introduction 45 2.2 Undamped Free Vibration 46 2.3 Damped Free Vibration 49 2.4 Undamped Forced Vibration 55 2.5 Damped Forced Vibration 60 2.6 Coulomb Damping 64 2.7 Quadratic Damping 69 2.8 Series Stiffness 71 2.9 The Resonant Absorber 78 2.10 Dam
9、per Models in Ride and Handling 80 vii3 Ride and Handling 83 3.1 Introduction 83 3.2 Vehicle Free Vibrations 84 3.3 Damping of Free Vibrations 98 3.4 Ride 110 3.5 Time-Domain Ride Analysis 114 3.6 Frequency-Domain Ride Analysis 122 3.7 Passenger on Seat 123 3.8 Wheel Hop 124 3.9 Handling . 126 3.10
10、Axle Vibrations 128 3.11 Steering Vibrations 131 3.12 The Ride-Handling Compromise 132 4 Installation 139 4.1 Introduction 139 4.2 Motion Ratio 139 4.3 Displacement Method 143 4.4 Velocity Diagrams 144 4.5 Computer Evaluation . 144 4.6 Mechanical Displacement 144 4.7 Effect of Motion Ratio 146 4.8 E
11、valuation of Motion Ratio 150 4.9 The Rocker 151 4.10 The Rigid Arm . 160 4.11 Double Wishbones 163 4.12 Struts 167 4.13 Pushrods and Pullrods 172 4.14 Motorcycle Forks 172 4.15 Motorcycle Rear Suspensions 174 4.16 Solid Axles . 180 5 Fluid Mechanics 187 5.1 Introduction 187 5.2 Properties of Fluids
12、 190 5.3 Continuity 203 5.4 Bernoullis Equation . 204 5.5 Pipe Flow 206 viii5.6 Other Losses 212 5.7 The Orifice 219 6 Valve Design 225 6.1 Introduction 225 6.2 Valve Types 228 6.3 Valve Characteristics 232 6.4 Basic Valve Models 235 6.5 Complete Valve Models 241 7 Damper Behavior 249 7.1 Introducti
13、on 249 7.2 Piston Free Body Diagram 253 7.3 Static Forces 256 7.4 Valve Flow Rates 257 7.5 Pressure and Forces 259 7.6 Basic Damper Parameters 263 7.7 Extreme Operation 268 7.8 Cyclical Characteristics F(X) 270 7.9 Stresses and Strains 276 8 Adjustables 279 8.1 Introduction 279 8.2 The Adjustable Va
14、lve 282 8.3 Parallel Hole 287 8.4 Series Hole . 287 8.5 Maximum Area 288 8.6 Opening Pressure . 288 8.7 Area Coefficient (Stiffness) 288 8.8 Automatic Systems 290 8.9 Semi-Active Systems 291 8.10 Motion Ratio 296 9 Specifying a Damper 297 9.1 Introduction 297 9.2 End Fittings 298 9.3 Length Range 29
15、9 9.4 F(V) Curve . 299 ix9.5 Configuration 300 9.6 Diameter 300 9.7 Oil Properties 300 9.8 Life 300 9.9 Cost 301 10 Testing . 303 10.1 Introduction 303 10.2 Transient Testing 306 10.3 Electromechanical Testers . 310 10.4 Hydraulic Testers 315 10.5 Instrumentation 316 10.6 Data Processing 319 10.7 Si
16、nusoidal Test Theory 323 10.8 Test Procedure 328 10.9 Triangular Test 333 10.10 Other Laboratory Tests 336 10.11 Road Testing . 338 APPENDICES A. Nomenclature 343 B. Properties of Air 363 C. Properties of Water 369 D. Test Sheets 373 E. Solution of Algebraic Equations 377 F. Units . 385 G. SAE J6a (
17、Ride and Vibration Data Manual) 389 References 453 Index 467 About the Author 495 XPREFACE In view of the tremendous worldwide production of automotive dampers (shock absorbers), the former absence of a book devoted to this topic is surprising. During many years of damper design, research, and comme
18、rcial testing, I have become aware of a need for a suitable book to present the fundamentals of damper design and use, since the necessary body of knowledge is far from readily available in the research literature. This book will benefit the many designers of vehicles such as passenger cars, motorcy
19、cles, trucks, racing cars and so on. Damper designers themselves will already be familiar with most of the material here, but may find some useful items, especially with regard to installation motion ratios and behavior of the vehicle as a whole. In any case, they will probably be pleased to see the
20、 basic material collected together. As in my previous work, I have tried to present the basic core of theory and practice, so that the book will be of lasting value. I would be delighted to hear from readers who wish to suggest any improvements to presentation or coverage. I would like to express my
21、 thanks to Dr. Brian G. Warner of Truck Chassis, The Chrysler Corporation, for reading a draft and making many constructive sugges- tions for improvements. I also wish to acknowledge Anne Bullman, Karen Lemmon, and Julie Mortimer for per- forming the word processing, and David Greenway for preparing
22、 many of the diagrams. John C. Dixon The Open University Milton Keynes, England xi1 INTRODUCTION 1.1 History If all is well, the suspension dampers on a vehicle do their work quietly and without fuss. Like punctuation or acting, dampers are at their best when they are not noticed. Drivers and passen
23、gers simply want the dampers to be trouble-free. For the designer, however, there is some satisfaction in creating a good, new damper for a racing car or rally car, and perhaps making some contribution to competition success. Less exciting, but economically more important, there is also satisfaction
24、 in seeing everyday vehicles traveling safely, with comfortable occupants, at speeds that would be quite impractical without good dampers. The current worldwide production of dampers is difficult to estimate with accuracy, but it is probably around 50 to 100 million units per year with a retail valu
25、e well in excess of one billion dollars per year. The need for dampers arises because of the roll and pitch associated with vehicle maneuvering, and from the roughness of roads. In the mid-nineteenth century, road quality was generally very poor. The better horse-drawn car- riages of the period ther
26、efore had soft suspension, achieved by using long, bent leaf springs called semi-elliptics, or even by using a pair of such curved leaf springs set back-to-back on each side, forming full-elliptic suspension. No special devices were fitted to provide damping; rather this depended on inherent frictio
27、n, mainly between the leaves of the beam springs. Such a set- up was appropriate to the period, being easy to manufacture, and probably 1THE SHOCK ABSORBER HANDBOOK worked tolerably well at moderate speed, although running at high speed must have been at the least exciting, and at worst dangerous, b
28、ecause of the lack of damping control. The arrival of the so-called horseless carriage, i.e., the carriage driven by an internal combustion engine, at the end of the nineteenth century, provided a new stimulus for suspension development which continues to this day. The rapidly increasing power avail
29、able from the internal combustion engine made higher speeds routine; this, plus the technical attitude of the vehicle and com- ponent designers, coupled with a general commercial mood favoring develop- ment and change, provided an environment that led to invention and innovation. The fitting of damp
30、ing devices to vehicle suspensions followed rapidly on the heels of the arrival of the motor car itself. Since those early days, the damper has passed through a century of evolution, the basic stages of which may be considered as; (1) Dry friction (snubbers) (2) Blow-off hydraulics (3) Progressive h
31、ydraulics (4) Adjustables (manual alteration) (5) Adaptives (slow automatic alteration) (6) Semi-actives (fast automatic alteration) The Zeitgeist regarding dampers has changed considerably over the years, in roughly the following periods: (1) Up to 1910, dampers were hardly used at all. In 1913, Ro
32、lls Royce actually discontinued rear dampers on the Silver Ghost, illustrating just how different the situation was in the early years. (2) From 1910 to 1925, mostly dry snubbers were used. (3) From 1925 to 1980, there was a long period of dominance by simple hydraulics, initially simply constant fo
33、rce blow-off, then a propor- tional characteristic, then adjustables, leading to a mature product. (4) From 1980 to 1985, there was excitement about the possibilities for active suspension, which could effectively eliminate the ordinary damper; however, little has come of this in practice so far bec
34、ause of the cost. 2INTRODUCTION (5) From 1985, it became increasingly apparent that a good deal of the benefit of active suspension could be obtained much more cheaply by fast auto-adjusting dampers, and the damper suddenly became an interesting, developing component again. Development of the adapti
35、ve damper is occurring rapidly. Although there will continue to be differences between commercial units, such systems will prob- ably be fully mature in a few years. Fully active suspension will then still offer some performance advantages, but will not be cost-effective for passenger cars. Further
36、developments can then be expected to be restricted to rather slow detail refinement of design, control strategies, and production costs. Fast- acting control, requiring extra sensors and controls, will continue to be more expensive, so simple, fixed dampers, adjustables, and slow adaptive types will
37、 only be displaced from the market slowly. The damper is commonly known as the shock absorber, although the implication that shocks are absorbed is misleading. Arguably, the shocks are “absorbed“ by the deflection of the tires and springs. The purpose of dampers is to dissipate any energy in the ver
38、tical motion of the body or wheels, such motion having arisen from control inputs, or from disturbance by rough roads or winds. As an agglomeration of masses and springs, the car with its wheels constitutes a vibrating system that needs dampers to optimize control behavior, by prevent- ing response
39、overshoots, and to minimize the influence of some unavoidable resonances. The mathematical theory of vibrating systems largely uses the concept of a linear damperwith force proportional to extension speed mainly because it gives equations for which the solutions are well under- stood and documented,
40、 and usually tolerably realistic. There is no requirement that a damper must exhibit such a characteristic; nevertheless the typical modern hydraulic damper does so approximately. This is because the vehicle and damper manufacturers consider this to be desirable for good physical behavior, not for t
41、he convenience of the theorist. This characteristic is achieved only by some effort from the manufacturer. Damper types, which are explained fully later, can be initially classified in two ways: (a) Dry friction with solid elements (b) Hydraulic with fluid elements 3THE SHOCK ABSORBER HANDBOOK Fig.
42、1.1.1(a) An advertisement from 1904 for the early Truffault-designed dry-friction scissor damper (snubber) manufactured by Hartford. The hydraulic type with fluid elements is the only type fitted in recent times. The friction type came originally as sliding discs operated by two arms, and later as a
43、 belt wrapped around blocks, the “snubber.“ The hydraulic varieties are lever-arm and telescopic. The lever-arm type uses a lever to operate a vane, now extinct, or a pair of pistons. Telescopics, now most common, are either double-tube or gas-pressurized single-tube. Truffault invented a scissor-ac
44、tion friction disc system before 1900, using bronze with oiled hide pressed together by conical disc springs and operated by two arms, with a floating body. Between 1900 and 1903, he developed a version for cars, at the instigation of Hartford in the United States, who began quantity production in 1
45、904, as in Fig. 1.1.1(a) and Fig. 1.1.1(b). Truffault, 4INTRODUCTION Fig. 1.1.1(b) Installation of the above (from Simanaitis, 1976). well aware of the commercial potential, also licensed several other manufac- turers in Europe, including Mors and Peugeot in France, who also had them in production a
46、nd use by 1904. Fig. 1.1.2 shows an exploded diagram of a more recent implementation from a motorcycle. This is adjustable by the hand screw, which controls the force pressing the discs together. A later version, the Hartford Fig. 1.1.2 The Greeves motorcycle front suspension from around 1950 had a
47、rubber-in-torsion spring, with an integral scissor-action dry-friction damper easily adjustable by hand. 5THE SHOCK ABSORBER HANDBOOK Fig. 1.1.3 The Hartford Telecontrol damper was adjustable via a Bowden cable, and hence could be adjusted easily from the driving seat with the vehicle in motion. Fig
48、. 1.1.4 Geometry of the scissor-type snubber. Telecontrol, Fig. 1.1.3, developed the theme with a convenient, remote Bowden cable adjustment (hence the name “Telecontrol“). Fig. 1.1.4 shows the geometry. The disc pack creates a friction moment MF which results in a damping force FD at the end of the
49、 arms, given by 6INTRODUCTION where LA is the arm length and A is the arm angle. The friction moment depends on the number, NF, of frictional surfaces; their effective coefficient of limiting friction, F; the pack diameter, D; the pack compression force, FPC; and the radial distribution of the consequent con- tact pressure, P. To give the best wear characteristic, a uniform pressure is preferred. In that case: Hence, the scissor-disc damper acts symmetrically with a Coulomb-type fric- tion characteristic. This is one of the main objections to it, plus the fact that it is poor a
