Page 231 - Cam Design Handbook

THB8 9/19/03 7:25 PM Page 219

CAM MECHANISM FORCES 219

The static force analysis (gradually applied) was presented in Chapter 7 where the cam
pressure angle and its forces were investigated. Suddenly applied loads may be consid-
ered during a slow impact on the system with a load amplification factor of up to two
times the static force value. Bear in mind that discontinuity of the cam acceleration curve
yields the same amplification factor as suddenly applied loads. This is discussed in the
cam action descriptions of Chap. 10.

8.3 IMPACT FORCES

Impact is often called mechanical shock, referring to an extreme abruptly applied force.
It is a velocity shock transient force. Impact phenomena are especially important to the
designer since in all machines the highest forces and stresses arise as a consequence of
impact. In cam-follower systems the impact forcing functions are not precisely known.
Thus, the design for these forces requires an approximation of the idealized functions of
velocity changes on impact. As stated, practical design data for impact calculation are not
directly available, necessitating a larger design safety factor in considering its effects.
Impact or velocity shock factors have a load amplification factor of two to four times the
static force values. This is discussed in the cam action discussion of Chap. 10 in which a
“bump” on the cam profile is a discontinuity in the velocity curve, producing an impact
in the follower. For more on impact see Barkan (1996) and Zuleas (1982).
For more precise data on impact the designer could resort to experimental measurement
employing such powerful tools as strain gauges, high-speed photography, and velocity and
motion transducers. The sources of impact in cam-follower mechanisms could be the result
of: (a) backlash in a positive-drive cam and roller follower, (b) high-speed systems which
are nonlinearly elastic so that abrupt changes occur with results similar to impact, and (c)
the working load action as a cam-driven punching mechanism. To minimize impact, the
following is suggested, if possible: (a) minimize the velocity of impact, (b) minimize the
mass of impacting bodies, and (c) minimize sensitivity to local stress concentrations by
employing a ductile material with some capacity for plastic deformation.

8.4 INERTIA FORCES

Inertia forces in most cam-follower systems are the most important of all the forces
analyzed, especially at high speeds. Inertia forces are caused by the necessity of moving
the follower masses linearly or rotationally. The inertia force on a linearly moving fol-
lower is
w
F = A lb (8.1)
a
g
where A = acceleration, in/sec 2
w = equivalent follower weight, lb.
The inertia force, passing through the center of gravity of the body, has a direction
opposite to that of the acceleration. By D’Alembert’s principle, we may make a free-body
diagram of all forces and analyze the dynamic condition as a static problem, Fig. 8.1a.
For rotating bodies, the analysis is similar. If the body has an unbalanced torque, it will
have an angular acceleration which will be resisted by a torque reaction. The direction of
this torque will be opposite to the direction of acceleration (Fig. 8.1b). The torque is: