Page 459 - Cam Design Handbook

THB13 9/19/03 7:56 PM Page 447

CAM SYSTEM DYNAMICS—RESPONSE 447

13.7.13 Summary

In this section, we used an automobile and textile cam-follower system as examples. Other
machines could be calculated in the same manner. The methods of this chapter represent
a dynamic analysis of a high-speed, high-flexibility cam design. Vibrations at the design
speed thus approach zero. We also see that any polynomial may be used, but the 5-6-7-8-
9 is suggested with a 3-4-5 polynomial or cycloidal ramp. Note that proper ramp design
is probably the most critical aspect of the investigation.
Although time-consuming, the justification of this method has been proved in the field.
To repeat the design procedure:

1. Select a polynomial
y = C + C + C q 2 + C q 3 + ◊◊◊ C q . (13.87)
n
q
0
n
1
2
3
2. Set up a cam-follower system whose characteristic is similar to
y = r + k y cy¢¢. (13.83)
+
c a r
3. Substitute values, and plot displacement curves and their derivatives.
Be sure that the compression spring is strong enough and the ramp high enough so that
cam-follower constraint is maintained. Also, the maximum cam acceleration should always
exceed the maximum follower acceleration; otherwise the system may go out of control
because it is too flexible.
Finally, a system with a rigid camshaft and a flexible follower was employed.
Sometimes, in cam-driven mechanisms such as turret or dial cams, the camshaft is
light in weight having a small inertia or flywheel effect. In addition, the follower
linkage stiffness is high compared with that of the drive and support frame. Accordingly
it is reasonable to consider the camshaft and frame in the same manner as that shown
in deriving the characteristic equations of Eq. (13.83). A flexible torsional system will
exist. Tests in the field under actual operating conditions to measure deflection and vibra-
tion (under high speeds) will verify the design.

13.8 DISCUSSION

In cam-follower systems, follower vibrations are always induced. At low speeds, they are
rarely a factor for concern, but at high speeds, they can become great enough to signifi-
cantly degrade system performance. At very high speeds the vibration may be sufficient
to destroy the system or at least stop it from functioning.
Vibrations arise from many sources:
1. Vibrations due to the shape of the follower acceleration curve (the main source
addressed in this chapter).
2. Vibrations resulting from separation of the cam and the follower. With positive-drive
cams with backlash, impact of the roller on the cam is produced as the contact force
changes direction. This is called cross-over shock. With spring-loaded followers sepa-
ration is due to the “jump” condition that occurs when the preload force is insufficient
to maintain a positive contact force.
3. Vibrations due to surface irregularities caused by deficiencies in cam and/or follower
manufacturing.