Page 372 - Cam Design Handbook

THB12 9/19/03 7:34 PM Page 360

360 CAM DESIGN HANDBOOK

• As a result of the machine systems being old. Generally the older the machine is, the
more vibrations, noise, and lack of smoothness of operation occur.
• As result of periodic change in power input voltage of the electrical motor or prime
mover. This has occurred in the performance of a high-speed textile machine in which
the function had transient energy malfunction.
• Due to the inclusion of belts and chains in the torsional drive. This may produce
large backlash and high compliancy in the system, seriously reducing the effective
performance.
Note that in cases where the vibrating system cannot be modified satisfactorily, one
may avoid resonance effects by not operating the machine at excitation frequencies at
which resonances are excited. This may be accomplished by speed controls on a machine
or by prescribing limitations on use of the system, e.g., “red lines” on engine tachometers
to show operating speeds to be avoided.

12.3 CAM-FOLLOWER DYNAMICS—
RIGID CAMSHAFT

12.3.1 Single-Degree-of-Freedom System
Modeling, as discussed in Chap. 11, transforms the system into a set of tenable mathe-
matical equations that describe the system in sufficient detail for the accuracy required.
Various tools of analysis are at the disposal of the designer-analyst and range in complexity
from classical linear analysis for single-degree-of-freedom systems to complex multiple-
degree-of-freedom nonlinear computer programs.
In this section we present a single-degree-of-freedom system (DOF) with a rigid
camshaft. The cam mechanism consists of a camshaft, cam, follower train including one
or more connecting links, and springs terminating in a load mass or force. For lumped
systems, linkages and springs are divided into two or more ideal mass points intercon-
nected with weightless springs and dampers.
Springs. The spring force generally follows the law

4
F = kx ± Â a x 2 n+1
n
n=1
where terms under the S sign are nonlinear.
Dampers. Damping takes the general form
Cx ˙ () = Cx x ˙ r-1
˙
Ï0 Cx ˙˙ () is Coulomb damping
Ô
For r = Ì 1 Cx ˙ () is viscous damping
Ô
Ó2 Cx ˙ () is quadratic damping
“Stiction” is accounted for as the breakaway force, ¡, in one element i sliding along
another element j.
F = 0for ˙ x π ˙ x j
i
st
£¡ for ˙ x π ˙ x
i j
=¡ at breakaway