Page 327 - Cam Design Handbook

THB11 9/19/03 7:33 PM Page 315

CHAPTER 11

CAM SYSTEM MODELING

J. Christian Gerdes, Ph.D.
Assistant Professor of Mechanical Engineering, Design Division
Stanford University
Palo Alto, California

11.1 INTRODUCTION 316 11.4.1 Coil Springs 334
11.2DYNAMIC SYSTEM MODELING AND 11.4.2 Compliance of Other Mechanical
REDUCTION 317 Elements 335
11.2.1 Natural Frequencies and Modes of 11.4.3 Combinations of Springs 338
Vibration 317 11.4.4 Equivalent Springs and Mechanical
11.2.2 Model Sufficiency and Model Advantage 340
Reduction 321 11.4.5 Massive Springs 341
11.3MASS, INERTIA, AND KINETIC 11.5DAMPERS AND DISSIPATION 342
ENERGY 324 11.5.1 Viscous or Speed-Dependent
11.3.1 Finding Mass and Moment of Damping 343
Inertia 327 11.5.2 Coulomb or Dry Friction 344
11.3.2 Moving Moments of Inertia to Other 11.5.3 Mechanical Efficiency 345
Points 329 11.5.4 Combinations and Equivalent
11.3.3 Equivalent Mass or Inertia 329 Dampers 346
11.4SPRINGS AND POTENTIAL 11.6EXAMPLE: MODELING AN AUTOMOTIVE
ENERGY 332 VALVE-GEAR SYSTEM 348

SYMBOLS

b Damping coefficient lbf/(in/s) (N/(m/s))
b r Rotary damping coefficient ft-lbf/(rad/s) (Nm/(rad/s))
2
Mass moment of inertia about O lbm-in 2 (kgm )
J o
(or moment of inertia of body O)
K or k Stiffness or spring rate lbf/in (N/m)
Rotary stiffness or spring rate ft-lbf/rad (Nm/rad)
K r
Free length of spring in (m)
L f
M or m Mass lbm (kg)
N Number active coils
Velocity vector at point P in/s (m/s)
v p
Magnitude of velocity at point P in/s (m/s)
v p
Vector from O to given point in (m)
r o
d . Deflection or relative displacement in (m)
d Relative velocity in/s (m/s)
Dq Angular deflection or displacement rad (rad)
h Mechanical efficiency % —
w Angular velocity vector rad/s (rad/s)
Natural frequency rad/s or Hz (rad/s or Hz)
w n

315

Copyright 2004 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.