Contents. Chapter 1 Introduction Chapter 2 Unacceptable Cam Curves Chapter 3 Double-Dwell Cam Curves... 27

Transcription

1 Contents Chapter 1 Introduction Cam-Follower Systems Fundamentals Terminology... 4 Type of Follower Motion... 4 Type of Joint Closure... 4 Type of Follower... 5 Type of Cam... 6 Type of Motion Constraints... 8 Type of Motion Program Applications Timing Diagrams Cam Design Software Units References Chapter 2 Unacceptable Cam Curves Introduction S V A J Diagrams Double-Dwell Cam Design Choosing S V A J Functions The Fundamental Law of Cam Design Simple Harmonic Motion (SHM) Constant Acceleration (Parabolic Displacement) Cubic Displacement Summary References Chapter 3 Double-Dwell Cam Curves Introduction Cycloidal Displacement for Double Dwells Combined Functions for Double Dwells Fall Functions The SCCA Family of Double-Dwell Functions Polynomial Functions The Polynomial The Polynomial Fourier Series Functions Summary References Chapter 4 Single-Dwell Cam Curves Introduction Single-Dwell Cam Design Choosing S V A J Functions Single-Dwell Applications of Polynomials Effect of Asymmetry on the Rise-Fall Polynomial Solution Summary VI

2 Chapter 5 Spline Functions Introduction Classical Splines Knots Smoothness Equations Interpolation Equations Boundary Conditions General Polynomial Splines B-splines Bezier Curves Knot Placement Periodic Splines Splines Other Than Polynomial Splines Trigonometric Splines Rational Splines Summary Bibliography Chapter 6 Critical Path Motion (CPM) Cam Curves Introduction Constant Velocity Motion Polynomials Used for Critical Path Motion Half-Period Harmonic Family Functions Combined Displacement and Velocity Constraints Summary Chapter 7 Cam Size Determination Introduction Pressure Angle Radial Cam with Translating Roller Follower Eccentricity Choosing a Prime Circle Radius Pressure Angle Barrel Cam With Translating Roller Follower Pressure Angle Barrel Cam With Oscillating Roller Follower Overturning Moment Radial Cam With Translating Flat-Faced Follower Pressure Angle Radial Cam With Oscillating Roller Follower Radius of Curvature Radial Cam With Translating Roller Follower Radius of Curvature Radial Cam With Translating Flat-Faced Follower Radius of Curvature Barrel Cam With Translating Roller Follower Radius of Curvature Barrel Cam With Oscillating Roller Follower Radius of Curvature Radial Cam With Oscillating Roller Follower Radius of Curvature Radial Cam With Oscillating Flat-Faced Follower Undercutting of Radial Cams with Oscillating Flat-Faced Followers References Chapter 8 Dynamics of Cam Systems Modeling Fundamentals Introduction Newton s Laws of Motion Dynamic Models Mass Mass Moment and Center of Gravity Mass Moment of Inertia (Second Moment of Mass) Parallel Axis Theorem (Transfer Theorem) Radius of Gyration Modeling Rotating Links Lumped Parameter Dynamic Models Spring Rate Damping VII

3 VIII THE CAM DESIGN AND MANUFACTURING HANDBOOK 8.10 Equivalent Systems Combining Dampers Combining Springs Combining Masses Lever and Gear Ratios Modeling Nonlinear Springs Determining the Effective Spring Rate of an Air Cylinder Modeling an Industrial Cam-Follower System References Chapter 9 Dynamics of Cam Systems Force, Torque, Vibration Introduction Dynamic Force Analysis of the Force-Closed Cam-Follower Undamped Response Damped Response Resonance Follower Rise Time Estimating Damping Logarithmic Decrement Kinetostatic Force Analysis of the Force-Closed Cam-Follower Kinetostatic Force Analysis of the Form-Closed Cam-Follower Kinetostatic Camshaft Torque Controlling Cam Speed Motors Electric Motors Controlling Cam Speed Flywheels Torque Compensation Cams References Chapter 10 Modeling Cam-Follower Systems Introduction Degrees of Freedom Single-Mass SDOF Linear Dynamic Models Force-Closed Models Form-Closed Model Two-Mass, One- or Two-DOF, Nonlinear Dynamic Model of a Valve Train Multi-DOF Dynamic Model of a Valve Train One-Mass Model of an Industrial Cam-Follower System Two-Mass Model of an Industrial Cam-Follower System Solving System Differential Equations Block Diagram Solution Simulink/MatLab Ordinary Differential Equation Solution Using Mathcad State Space Solutions Polydyne Cam Functions Double-Dwell Polydyne Curves Splinedyne Cam Functions References Chapter 11 Residual Vibrations in Cam-Follower Systems Introduction Residual Vibration Residual Vibration of Double-Dwell Functions Double-Dwell Functions for Low Residual Vibration Freudenstein 1-3 Fourier Series (Harmonic) Function Gutman F-3 Fourier Series (Harmonic) Function Berzak-Freudenstein Polynomials Residual Vibration Spectra for "Low Vibration" Functions Actual Cam Performance Compared to Theoretical Performance References

4 CONTENTS IX Chapter 12 Failure of Cam Systems Stress, Wear, Corrosion Introduction Surface Geometry Mating Surfaces Adhesive Wear Abrasive Wear Abrasion-Resistant Materials Corrosion Wear Corrosion Fatigue Fretting Corrosion Stress Strain Principal Stresses Plane Stress and Plane Strain Plane Stress Plane Strain Applied Versus Principal Stresses Surface Fatigue Spherical Contact Contact Pressure and Contact Patch in Spherical Contact Static Stress Distributions in Spherical Contact Cylindrical Contact Contact Pressure and Contact Patch in Parallel Cylindrical Contact Static Stress Distributions in Parallel Cylindrical Contact General Contact Contact Pressure and Contact Patch in General Contact Stress Distributions in General Contact Dynamic Contact Stresses Effect of a Sliding Component on Contact Stresses Surface Fatigue Failure Models Dynamic Contact Surface Fatigue Strength Roller Followers Types of Rolling-Element Bearings Failure of Rolling-Element bearings Selection of Rolling-Element Bearings Basic Dynamic Load Rating C Basic Static Load Rating C Calculation Procedures References Chapter 13 Cam Profile Determination Introduction Inversion Digitization Increment Radial Cams With Roller Followers Offset Translating Roller Follower Oscillating Roller Follower Radial Cams With Flat-Faced Followers Radial Cams with Translating Flat-Faced Followers Radial Cams with Oscillating Flat-Faced Followers Barrel Cams With Roller Followers Barrel Cam With Translating Roller Follower Barrel Cam With Oscillating Roller Follower Linear Cams With Roller Followers Conjugate Cams Designing Conjugate Cams Conjugate Radial Cams With Translating Followers Conjugate Radial Cams With Oscillating Followers Conjugate Axial Ribbed Cams With Oscillating Followers Indexing Cams Cam-Linkage Combinations Modifying the Cam Contour for Follower Linkage Geometry

5 X THE CAM DESIGN AND MANUFACTURING HANDBOOK 13.7 Shifting the Cam Contour to Machine Zero References Chapter 14 Cam Materials and Manufacturing Introduction Cam Materials Cast Irons Wrought Steels Forged Steel Sintered Metals Steel Numbering Systems Hardness Heat Treatment Surface (Case) Hardening Cam Manufacturing Methods Geometric Generation Manual or NC Machining to Cam Coordinates (Plunge-Cutting) Continuous Numerical Control with Linear Interpolation Continuous Numerical Control with Circular Interpolation Analog Duplication Cutting the Cam Interpolation Method Digitization Increment Resampling the Data Pythagorean Hodographs Manufacturing Methods Finishing Processes Polishing Processes Surface Coatings Measuring the Cam References Bibliography Chapter 15 Lubrication of Cam Systems Introduction Lubricants Viscosity Types of Lubrication Full-Film Lubrication Boundary Lubrication Material Combinations in Cam-Follower Joints Hydrodynamic Lubrication Theory Petroff s Equation for No-Load Torque Reynolds Equation for Eccentric Journal Bearings Nonconforming Contacts Cam Lubrication References Chapter 16 Measuring Cam-Follower Performance Introduction Transducers Angular Position Transducers Displacement Transducers Velocity Transducers Strain Transducers Force Transducers Acceleration Transducers Vibration Measurement Experimental Cam-Follower Measurements Data Analysis

6 CONTENTS XI Analog to Digital Conversion Spectrum Analysis Forms of Spectra Modal Domain Frequency Response Functions (FRF) Dynamic Signal Analyzers Measuring the FRF The "Q" of a System Convolution and Deconvolution References Bibliography Chapter 17 Case Studies Introduction Analyzing Vibrations in an IC Engine Valve Train Conclusions Analyzing Vibrations in Cam-Driven Automated Assembly Machinery Conclusions References Chapter 18 Cam Design Guidelines Introduction Practical Design Considerations Translating or Oscillating Follower? Force or Form-Closed? Radial or Barrel Cam? Roller or Flat-Faced Follower? To Dwell or Not to Dwell? To Grind or Not to Grind? To Lubricate or Not to Lubricate? What Double-Dwell Cam Program to Use? What Cam Program to Use For Difficult or Complicated Motions? To Polydyne or Not to Polydyne? Camshaft Design Follower Train Design Follower Train Dynamics Natural Frequencies Backlash How Important is Theoretical Peak Acceleration? Rules of Thumb for Cam Design References Appendix A Computer Programs A.0 Introduction A.1 General information Hardware Requirements Operating System Requirements Demonstration Versions Installing the Software How to Use This Manual A.2 General Program Operation Running the Programs (All Programs) The Home Screen (All Programs) General User Actions Possible Within a Program (All Programs) Units (All Programs) Examples (All Programs) Creating New, Saving, and Opening Files (File - All Programs) Copying Screens to Clipboard or Printer (Copy - All Programs) Printing to Screen, Printer, and Exporting Disk Files (Print Button) Plotting Data (Plot Button) The About Menu (All Programs)

7 XII THE CAM DESIGN AND MANUFACTURING HANDBOOK Exiting a Program (All Programs) Support (All Programs) A.3 Program DYNACAM The DYNACAM Home Screen Input Data (DYNACAM Input Screen) Polynomial Functions Spline Functions Back to the Input Screen Continuity Check Screen Sizing the Cam Drawing the Cam Exporting Cam Contour Data (DYNACAM Only) Kinetostatic Analysis (DYNACAM Only) Dynamic Analysis (DYNACAM Only) Stress Analysis (DYNACAM Only) Fourier Transform (FFT) Other A.4 Program FOURBAR The FOURBAR Home Screen Input Data (FOURBAR Input Screen) Calculation (FOURBAR, FIVEBAR, Sixbar, and SLIDER Input Screens) Animation (FOURBAR) Dynamics (FOURBAR, FIVEBAR, SIXBAR, and SLIDER Dynamics Screen) Balancing (FOURBAR Only) Cognates (FOURBAR Only) Synthesis (FOURBAR Only) Other A.5 Program SIXBAR The SIXBAR Home Screen Input Data (SIXBAR Input Screen) Animation (SIXBAR) Dynamics (SIXBAR Dynamics Screen) Other A.6 Program SLIDER The SLIDER Home Screen Input Data (SLIDER Input Screen) Calculation (SLIDER Input Screen) Animation (SLIDER Animation Screen) Dynamics (SLIDER Dynamics Screen) Other Appendix B Material Properties Appendix C Geometric Properties Appendix D Spring Data Bibliography Glossary of Terms Index Index to CD-ROM Installation Instructions for CD-ROM...610