Page 411 - Cam Design Handbook

THB13 9/19/03 7:56 PM Page 399

CHAPTER 13

CAM SYSTEM DYNAMICS—
RESPONSE

Thomas L. Dresner, Ph.D.
Consulting Engineer
Mountain View, California

13.1 INTRODUCTION TO RESPONSE 400 13.5.9 Optimization of Tuned Dwell-
13.2 RESPONSE IN FREQUENCY DOMAIN Rise-Return-Dwell Cams 425
401 13.5.9.1 General 425
13.3 VIBRATION MINIMIZATION 406 13.5.9.2 Formulation of Two-Point
13.3.1 Introduction to Vibration Boundary-Value Problem 425
Minimization 406 13.5.10 Conclusions 427
13.4 DYNAMIC SYNTHESIS OF CAMS 13.6 USE OF THE CONVOLUTION OPERATOR
USING FINITE TRIGONOMETRIC TO REDUCE RESIDUAL VIBRATIONS
SERIES 407 427
13.4.1 Introduction 407 13.6.1 Introduction 427
13.4.2 Symbols 408 13.6.2 Symbols 427
13.4.3 Tuned Cam Design 408 13.6.3 Basic Theory 428
13.4.4 Cam Design Based on Mean Squared 13.6.4 Fixed Convolution 430
Error Minimization 413 13.6.5 Constant Velocity Convolution 431
13.4.5 Conclusions 416 13.6.6 Conclusion 434
13.5 APPLICATION OF OPTIMAL CONTROL 13.7 POLYDYNE CAMS 434
THEORY TO THE SYNTHESIS OF 13.7.1 Introduction 434
CAM-FOLLOWER SYSTEMS 416 13.7.2 Fundamental Relationships 435
13.5.1 Introduction 416 13.7.3 Ramp Height, r a 437
13.5.2 Symbols 416 13.7.4 Spring Ratio Constant, k r 437
13.5.3 Description of Dynamic Model 417 13.7.5 Dynamic Constant, c 438
13.5.4 Development of an Optimality 13.7.6 Equivalent Weight, w 438
Criterion-1: Output Criterion 418 13.7.7 Application of Polynomials for Cam
13.5.4.1 Minimization of Rate of Change Curves 439
of Effective Follower-Spring 13.7.8 Example Using the 3-4-5 Polynomial
Force 418 End Mass Movement 440
13.5.4.2 Relative Vibration and Relative 13.7.9 4-5-6-7 and 5-6-7-8-9 Polynomials
Vibrational Energy 419 443
13.5.4.3 Problem Formulation Based on 13.7.10 Ramps or Subcams 444
the Output Criterion 419 13.7.11 D-R-R-D Cams 444
13.5.5 Development of an Optimality 13.7.12 Practical Vibration Discussion 446
Criterion-2: Cam Criterion 419 13.7.13 Summary 447
13.5.5.1 General 419 13.8 DISCUSSION 447
13.5.5.2 Contact Stress at Cam-Follower 13.8.1 Design Guidelines and Rules of
Interface 419 Thumb 448
13.5.6 Formulation of Optimization Problem 13.8.2 Conclusions and Recommendations
on the Use of the Methods Given in
420
13.5.7 Introduction to System Optimization this Chapter 449
13.8.2.1 Cam Synthesis Using
421
13.5.8 Optimization of Tuned Dwell- Trigonometric Series (Sec. 13.4)
Rise-Dwell Cams 421 449
13.5.8.1 Formulation of Two-Point 13.8.2.2 Cam Synthesis Using Optimal
Boundary-Value Problems 421 Control Theory (Sec. 13.5)
13.5.8.2 Solution of the Two-Point 449
Boundary-Value Problem 422 13.8.2.3 Cam Synthesis Using the
13.5.8.3 Minimization of Output Convolution Operator
Vibrations 423 (Sec. 13.6) 450
13.5.8.4 Minimization of Hertzian Cam 13.8.2.4 Polydyne Cams 450
Contact Stress 424 13.8.2.5 Summary of Conclusions 450
399

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