Tài liệu Cam design handbook

CAM DESIGN HANDBOOK Harold A. Rothbart Editor Dean Emeritus College of Science and Engineering Fairleigh Dickinson University Teaneck, New Jersey McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2004 by The McGraw-HIll Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-143328-7 The material in this eBook also appears in the print version of this title: 0-07-137757-3. All trademarks are trademarks of their respective owners. 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If you d like more information about this book, its author, or related books and websites, please click here. To Florence, Ellen, Dan and Jane, Candice, Michael, Jessica and Justine This page intentionally left blank. For more information about this title, click here. CONTENTS Contributors Preface ix vii Chapter 1. Introduction 1 Chapter 2. Basic Curves 27 Chapter 3. Modified Cam Curves 55 Chapter 4. Polynomial and Fourier Series Cam Curves 89 Chapter 5. Cam Motion Synthesis Using Spline Functions 107 Chapter 6. Elements of Cam Profile Geometry 159 Chapter 7. Geometry of Planer Cam Profiles 175 Chapter 8. Cam Mechanism Forces 217 Chapter 9. Cam Materials and Lubrication 251 Chapter 10. Cam Manufacturing 285 Chapter 11. Cam System Modeling 315 Chapter 12. Cam System Dynamics—Analysis 357 Chapter 13. Cam System Dynamics—Response 399 Chapter 14. Special Cam Mechanisms 453 Chapter 15. Cams in Microelectromechanical Systems 505 Chapter 16. Automotive Camshaft Dynamics 529 Appendix A Appendix B Appendix C Appendix D Appendix E Appendix F Index Basic Contours 545 Basic Cam Curve Factors 551 Polynomial Coefficients 557 Cam Computer Software 561 CAD/CAM for a Medical Instrument Cam Mechanism 565 Optinal Control Theory Derivation for Two-Point Boundary 585 Value Problem 587 v Copyright 2004 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use. This page intentionally left blank. CONTRIBUTORS G.K. Ananthasuresh Assistant Professor of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania (chap. 15) Jorge Angeles (chap. 7) Professor of Mechanical Engineering, McGill University, Montreal, Canada J. Jesús Cervantes-Sánchez Professor, Departamento de Ingeniera Mecanica, Universidad de Guanajuato, Salamanca, Mexico (chap. 7) Thomas L. Dresner Demitri Elgin Consulting Engineer, Mountain View, California (chap. 13) D. Elgin Cams Co., Redwood City, California (chap. 16) J. Christian Gerdes Assistant Professor of Mechanical Engineering, Design Division, Stanford University, Palo Alto, California (chap. 11) Cecil O. Huey, Jr. Professor of Mechanical Engineering Clemson University, Clemson, South Carolina (chap. 5) Harold A. Rothbart Dean Emeritus, College of Science and Engineering, Fairleigh Dickinson University, Teaneck, New Jersey (chaps. 1, 2, 3, 4, 6, 8, 9, 10, 12, 14) Carlos Santiago Lopez-Cajún Professor de la Faculted, Departamento de Ingenieria, Universidad Autónoma de Querétaro, Querétaro, Mexico (chap. 7) Dermin Tsay Professor, Department of Mechanical Engineering, National Sun Yat Sen University, Kaohsiung, Taiwan (chap. 5) vii Copyright 2004 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use. This page intentionally left blank. PREFACE A cam is a versatile, specially shaped part of a machine that is always in contact with a member called the follower. The name cam should not be confused with the common abbreviation cam for camera or camcorder, both used in the fields of photography and video, nor with the acronym CAM applied to computer-aided manufacturing, which utilizes computational facilities for machinery fabrication of all kinds. The book is written for the designer concerned with creating or inventing a physical or mathematical function, a motion or an action, a mechanism or a machine. It would be valuable to the mechanical engineer, electrical engineer, physicist, and scientist aimed at developing cam-follower systems of all kinds, sizes, and speeds. In addition, shop machinists and toolmakers who make and assemble the machinery will find this book of value in their work. Automobile and racing car enthusiasts should find this book helpful in their aspirations. Last, the book can be an aid to students in engineering by introducing theoretical and practical applications of multifaceted ingenious mechanisms and machinery. Cam design is constantly evolving. New techniques and information are available for cam synthesis, analysis, dynamics, and performance and the production of the actual cam body itself. The most significant advancement of cam systems has resulted from the application of the digital computer. Computer-aided design (CAD) and computer-aided manufacturing (CAM) have been invaluably applied as software tools. CAD design is downloaded to CAM in discrete increments by computer numerical control (CNC) for actual cam production. The content of the handbook may be considered in the following categories: • Cam curves: basic trigonometric, modified or blended from basic curves, polynomial curves, Fourier series curves, and spline functions • Cam profile geometry, consisting of pressure angle, curvature, and profile analysis • Cam hardware, including materials, lubrication, and manufacturing • Cam system dynamics, containing the elastic follower and drive systems, vibratory analysis, and response This book is for use in the following fields of application: • Industrial and commercial machinery, as a critical part of production equipment for goods and services, for example, shoe making, steel mill equipment, and paper printing presses • Automotive performance and optimization, as a high-speed automotive valve operating system • Cams in microelectromechanical systems (MEMS), for micromachinery in miniature control systems • Cams as analog computers • Gadgets, mechanisms, and machinery, as inventive, ingenious devices ix Copyright 2004 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use. x PREFACE Furthermore, this book contains the latest, most important techniques and test data available. The philosophy of the book is to present diversified applications for cams to aid the reader’s understanding and design selection. This volume also contains many new examples, a listing of computer software, and an extensive list of references. It should be noted that cams, gearing, rolling-element bearings, and traction (friction) drives are of the same basic mechanical family, the study of which is generically referred to as contact mechanics. These devices have in common rolling and/or sliding action coupled with reasonably high concentrated contact (Hertz) stresses. In the field of contact mechanics the failure mechanisms among these machine elements are similar and are related to material metallurgy and heat treatment, lubricant rheology and chemistry, surface topography and geometry, and applied contact load (stress). These machine components also have commonly related manufacturing requirements. Hence, they share a similar manufacturing technology and engineering analysis. The significance of cam profile accuracy is emphasized. A surface may appear smooth to the eye and yet have poor dynamic properties. Depending on the application and loads the cam profile accuracy and its surface finish may affect the life, vibration, and noise of a cam-follower system. Poor manufacturing techniques can impede the functional ability of a mechanism or machine. Also, the choice of a lubricant and the lubrication system is pertinent on all designs. We express our respect for the inventors, designers, engineers, scientists, toolmakers, and machinists who produced cam systems in the past. Our knowledge and experience are a result of the amazing contributions and successful machines these experts handed down over the years that they toiled. This evidence of their work is our fortunate heritage. We are surrounded with evidence of the high-quality performance of these machines, which was accomplished with less mathematical guidance, poor manufacturing facilities, and crude measurement tools. All the while, nature revealed her secrets, very slowly, bit by bit. It is to be noted that the Chinese exercise for health and combat, T’ai Chi Ch’uan, has a ritual that spiritually parallels the foregoing thought. The training performance classes conclude with the loud clapping of hands, which is speculated to be in deference to all those who went before. Last, I wish to express my appreciation to Heather Tinsley, Washington, D.C., who edited and assisted in the production of this handbook. Also, grateful acknowledgment is due the elite chapter contributors whose dedication to the handbook is most noteworthy. I wish also to thank the many in academia and industry who were helpful in providing valuable guidance and information for the book, such as Samuel L. Doughty, Consulting Engineer, Mount Ephraim, New Jersey; Arthur F. Erdman, Professor of Mechanical Engineering, University of Minnesota, Minneapolis; Ralph Fusco, Consulting Engineer, Commack, New York; Grigor Kerdanyan, Consulting Engineer, Van Nuys, California; James A. Kurth, Senior Analytical Engineer, Commercial Cam Company, Inc., Wheeling, Illinois; Bernard Roth, Professor of Mechanical Engineering, Stanford University, Palo Alto, California; Michael Savage, Professor Emeritus of Mechanical Engineering, University of Akron, Akron, Ohio; and James L. Wiederrich, Manager, Modeling and Simulation, United Defense L.P., Santa Clara, California. Special recognition goes to Erwin V. Zaretsky, Branch Chief of Mechanical Components Branch, NASA Lewis Research Center, Cleveland, Ohio, for the many inspirational hours we spent discussing the subject of cams. Harold A. Rothbart CHAPTER 1 INTRODUCTION Harold A. Rothbart, D.Eng. 1.1 1.2 1.3 1.4 1.5 INTRODUCTION 1 CAM-FOLLOWER SYSTEM CRITERIA FOLLOWER TYPES 4 CAM CLASSIFICATIONS 5 CAMS IN TERMS OF FOLLOWER MOTION 15 1.6 1.7 1.8 1.9 2 CAM PROFILE GRAPHICAL LAYOUT 15 CAM DEFINITIONS 17 OTHER METHODS THAN CAMS 20 DESIGN CONSIDERATIONS 21 1.1 INTRODUCTION A cam is an element of the cam-follower mechanical system that compels the movement of the follower by direct contact. The motion of the follower is the result of a program. Just as a computer is programmed, so is a cam. Thus, the system can be thought of as a mechanical information device. Accordingly, the goal of the designers is to build a program, establish the locus of the contact points between the cam and follower, produce the cam profile coordinates system, and fabricate the cam within an acceptable accuracy. After all the parts are assembled the performance of the cam-follower system is observed. No one is sure where and how cams got their start. The Sanskrit (Indo-Iranian) term Jambha (“cog,” “peg,” or “tooth”) may indicate the geographic area in which they had their beginnings, and so may the Teutonic “Kambr” (toothed instrument), which refers to cam mechanisms that have their origin in the wedge (a linear cam) and have been found in Paleolithic Age relics of about 10,000 years ago. The later construction of the great pyramids of Egypt also involved the use of the wedge. However, it was the genius of Leonardo da Vinci that produced a modern design cam applied to a machine for pumping water. Cam-follower mechanisms are found in almost all mechanical devices and machines (i.e., agriculture, transportation equipment, textiles, packaging, machine tools, printing presses, automobile internal combustion engines, food processing machines, switches, ejection molds, and control systems, and more recently in micromachines such as microelectromechanical systems [MEMS]). Figure 1.1 shows an automobile cam-driven overhead valve train linkage. More recently, computer resources, known as CAD/CAM for cams, offer significant simplification in the design and fabrication of assembled cam and follower systems. CAD/CAM refers to computer-aided design and computer-aided manufacturing. Graphic workstations enable the design engineer to optimize the motion and geometry of a cam mechanism and also to incorporate the kinematic and dynamic performance requirements necessary over the entire range of operating speeds. In the manufacturing proccess, networked numerically controlled (NC) machines receive digitized geometric data from a CAD system. The downloaded file of cam coordinate data is forwarded directly to the machine tool controller, which eliminates the potential human error inherent in older techniques of manufacturing. The accuracy of the cam produced is frequently improved, and the costs are lowered. 1 Copyright 2004 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use. 2 CAM DESIGN HANDBOOK Valve spring Valve linkage Camshaft FIGURE 1.1. Automobile cam-driven overhead valve train linkage. 1.2 CAM-FOLLOWER SYSTEM CRITERIA The cam-follower system may be designed for path, motion, or function generation. This book treats the cam and the follower almost totally as a function generator in which the output of the follower is a function of the cam input. Erdman and Sandor (1997) illustrate the three types of cam design functions in Figure 1.2. Figure 1.2a shows a function generator in which the cam drives a four-bar linkage to a type slug bar of an electric typewriter. The cam moves the linkage to impact the type slug to a platem roller (not shown). Figure 1.2b shows a path generator cam that uses a double cam to produce a line that is desired. Figure 1.2c shows a motion-generator cam in which a drift meter operates to define the aircraft direction of motion relative to the ground. The sight wire is aligned to follow an object on the earth that passes through the center. The instrument rotates about point 0 by two fixed guiding pins in a circular arc-shaped cam slot about its center. Without this design a physical pivot needed of point 0 would hinder the vision. As stated previously, a cam is a mechanical member which transmits a desired action to a follower by direct contact. The driver is the cam (usually at constant speed), and the driven member is the follower. The cam may remain stationary, translate, oscillate, or rotate, whereas the follower may translate, oscillate, or index. In its general form a cam mechanism (Fig. 1.3a) consists of two shaped bodies, 1 and 2, connected by a fixed third body, 3. Either body 1 or body 2 may be the driver with the other the follower. We may at each instant replace these shaped bodies by an equivalent mechanism having members as shown in Fig. 1.3b. These members are pin-jointed at the 3 INTRODUCTION Type slug Type bar Cam Cam follower (a) Function generator (cam-driven typewriter mechanism). Line produced Sight wire Roller Sight center, 0 Cams Airplane Roller (b) Path generator (double cam line generator). FIGURE 1.2. (c) Motion generator (aircraft drift meter). Cam design functions. Body 2 Body 1 b b a a Fixed body 3 (a) Mechanism (two shaped bodies in contact). FIGURE 1.3. of contact.) (b) Equivalent mechanism. General cam mechanism. (Points a and b are the centers of curvature of point 4 CAM DESIGN HANDBOOK instantaneous centers of curvature, a and b, of the contacting surfaces. At any other instant, the points a and b are shifted and the links of the equivalent mechanism have different lengths. Grodinski (1947) and Jones (1967) have excellent compilations of practical cam mechanisms. 1.3 FOLLOWER TYPES Cam follower systems are classified by referring to the follower or the cam or both. Let us consider the follower first. The follower movement is translation, oscillation, or indexing. The follower surface is knife-edge, flat, curved, or roller. The follower restraint to the cam is positive-driven by the use of rollers in the cam groove or multiple conjugate cams, is spring-loaded, or occurs by gravity. Also, the translating follower line of motion with reference to the cam center may be radial or offset. The radial translating follower shown in Figure 1.4 will be used as an example. The popular oscillating follower and the rotating follower are discussed later. The knife-edge, or point, follower (Fig. 1.4a), is, as the name implies, a sharp edge in contact with the cam. Although simple in construction, this type of follower is not practical because it results in excessive wear of the contact point. It is employed in design as the center of the roller follower. For proper performance the follower is constrained to the cam at all speeds. The roller follower, Fig. 1.4b, is the most popular design for accomplishing this criterion. Commercially available roller followers use ball or needle bearings supported by a stem. Positive drive action is accomplished by a roller follower internally in a cam groove or track (Fig. 1.8), by followers on the opposite side of a single cam (yoke cam, Fig. 1.10), or by conjugate dual disk cams (Fig. 1.11). The roller follower has a low coefficient of friction when compared to the other followers and is most frequently used in production machinery and some automotive engines. In contact with the cam surface the follower roller action at low speeds can be that of pure rolling; however, at higher speeds significant sliding is evident. In groove cams the fluctuation in roller speeds is the result of the driven rotational acceleration of the roller as it rides on different radial surfaces of the cam. Experience has shown that the grooved cam roller follower does not provide exact positive-driven action because of the necesLoad Load (a) Knife-edge follower. FIGURE 1.4. (b) Roller follower. Types of follower contact surfaces. Load (c) Flat-faced follower. Load (d ) Spherical-faced follower. INTRODUCTION (a) Radial cam FIGURE 1.5. 5 (b) Translating cam Offset followers. (Movement of follower is different from shape of cam.) sary clearance (backlash) between the roller sides and its groove. Sliding, wear, noise, vibration, and shock may be induced at high speeds. Furthermore, high speeds and high load may necessitate the use of crowned or conical rollers to accommodate the potential misalignment of contacting surfaces to avoid excessive surface stresses and wear. Figures 1.4c and 1.4d show mushroom followers in which the contacting surface is either flat or spherical. The spherical face of the Figure 1.4d mushroom follower has a large radius that compensates for detrimental deflection or misalignment that may occur with the flat mushroom follower. The radial follower is one in which the follower translates along an axis passing through the cam center of rotation. This type, shown in Fig. 1.4, is the most common. The offset follower is one in which the axis of the follower movement is displaced from the cam center of rotation. Offsetting often improves action by reducing force, stress, and also the cam’s size. The eccentricity should be in the direction that improves force components tending to jam the translating follower in its bearing guide. Figure 1.5a shows a follower on a radial cam with an offset shown. Figure 1.5b shows the same relationship for a translating cam. In both cams, the follower path is not the profile displacement of the cam. 1.4 CAM CLASSIFICATIONS Cams are classified in three ways: 1. In terms of their shape, such as wedge, radial, cylindrical, globoidal, conical, spherical, or three-dimensional; 2. In terms of the follower motion, such as dwell-rise-dwell (DRD), dwell-rise-returndwell (DRRD), or rise-return-rise (RRR); or 3. In terms of the follower constraint, which is accomplished by either positive drive or spring load as mentioned previously. 6 FIGURE 1.6. CAM DESIGN HANDBOOK Various types commercial of cams. (Courtesy Commercial Cam Co., Inc., Wheeling, Ill.) The most popular industrial production cams (Fig. 1.6) are: • positive drive, radial groove cam • radial conjugate dual cams • cylindrical groove cam The most popular automotive cams are spring loaded. Figure 1.7 shows automotive camshafts. Let us discuss cams in terms of their shapes. The translating, wedge, or flat-plate cam is one that moves back and forth driving a follower. The follower may either translate or oscillate, with its position established by the cam shape and location. This is the simplest of all cams. The follower is held in contact by a spring or a positive-drive groove and roller. Figure 1.8 shows a translating cam with a translating follower. Translating cams have been built as large as 15 feet long for turning the outside profile on gun barrels for milling and profiling work. INTRODUCTION FIGURE 1.7. 7 Automobile camshaft. (Courtesy of D. Elgin Cams, Redwood City, Calif.) FIGURE 1.8. Translating cam. (Follower is a translating roller positive-drive type.) The radial, disk, or plate cam is one in which the position of the follower is determined by radial distances from the cam axis. Figure 1.9 shows a radial open groove cam with oscillating roller follower used on a hosiery-making machine. The radial cam is by far the most popular because of its simplicity and compactness. Cams of this type are the yoke cams, conjugate cams, wiper cams, roller cams, and circular-arc cams. The yoke cam is a positive-drive cam enclosed by a follower with opposite rollers or surfaces a constant distance apart. The rollers or surfaces may or may not be diametrically opposite of each other. The follower may translate or oscillate. Figure 1.10 shows a single-disk surface yoke cam with a translating follower. Control of follower action on single-disk cams is limited to 180 degrees of cam rotation. The other 180 degrees are 8 CAM DESIGN HANDBOOK FIGURE 1.9. Radial open-groove cam—employed on a hosiery machine. Heat-treated meehanite cam; turns approximately 50 rpm and drives an extended gear quadrant, which in turn activates other parts of the machine to multiplied higher speeds. (Courtesy Wildman Manufacturing Co., Norristown, Pa.) FIGURE 1.10. Yoke cam. complementary to maintain the fixed distance contact on the other side of the cam. Another shortcoming of the single-disk yoke cam is that any wear produces clearance, which results in poor action at moderate to high speeds. Two roller followers may be utilized in lieu of surfaces to reduce this wear and detrimental backlash. The yoke cam is rarely utilized. The conjugate, complementary, or double-disk cam is one having dual radial disks, each in contact with a roller on the follower. Figure 1.11 shows this type with an oscil-