Page 369 - Cam Design Handbook

THB12 9/19/03 7:34 PM Page 357

CHAPTER 12

CAM SYSTEM
DYNAMICS—ANALYSIS

Harold A. Rothbart, D. Eng.

12.1 INTRODUCTION 357 12.4 CAM DRIVE DYNAMICS—ELASTIC
12.2 SYSTEM VIBRATIONS 358 CAMSHAFT 374
12.3 CAM-FOLLOWER DYNAMICS—RIGID 12.4.1 Introduction to Elastic
CAMSHAFT 360 Camshaft 374
12.3.1 Single-Degree-of-Freedom 12.4.2 Single-Degree-of-Freedom
System 360 Torsional System 374
12.3.2 Single-Degree-of-Freedom 12.4.2.1 Open-Track Cam System 375
System Compliance 363 12.4.2.2 Closed-Track Cam System 378
12.3.3 Harmonic/Fourier Analysis 367 12.4.3 Two-Degree-of-Freedom
12.3.4 Two-Degree-of-Freedom System 384
System 370 12.4.4 Four-Degree-of-Freedom
12.3.5 Some Cam-System Dynamic System 386
Phenomena 372 12.4.5 Multi-Degree-of-Freedom
12.3.5.1 Balancing 372 System 389
12.3.5.2 Crossover Shock (Backlash) 373 12.5 SUMMARY 396
12.3.5.3 Spring Surge 374

12.1 INTRODUCTION

In this chapter we submit the dynamic analysis of cam-follower systems that are inher-
ently compliant. A measure of system compliance is the extent of the deviation between
the dynamic response and the intended kinematic response, which is the vibration level.
This deviation tends to increase (1) as any of the input harmonics of cam motion
approaches the fundamental frequency of the mechanism and (2) with the increase of the
maximum value of the cam function third-time derivative (jerk). Also, the deleterious
effects of vibration are well known. Vibration causes motion perturbations, excessive com-
ponent stresses, noise, chatter, wear, and cam surface fatigue. This wear and cam surface
erosion feeds back to further exacerbate the problem. For more on the subject of cam
system dynamics, the reader is referred to Freudenstein (1960), Chen (1982), Erdman
(1993), and Koster (1970).
In designing cam-follower systems, the compliancy of the system can be obtained by
(1) the application of mathematical theoretical formulas, (2) testing prototypes, or (3) con-
structing detailed models. It has been found that the stiffnesses obtained by simple models
is more than double the actual stiffness. The analytical inaccuracies are due to differences
between assumed and actual stress distributions (largely near the applied loads) and defec-
tion modes that were ignored in the analysis.
This chapter presents the analysis of two kinds of systems: (1) high-speed systems and
(2) highly compliant systems. The models are:

• models with a rigid camshaft
• models with an elastic camshaft
• coupled combinations of elastic camshaft and follower

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