Page 399 - Cam Design Handbook

THB12 9/19/03 7:34 PM Page 387

CAM SYSTEM DYNAMICS—ANALYSIS 387

x
m

k c

S

R (e)

y a
Cam

k q, k x, k y

Input
z
FIGURE 12.22. Coupled system of a four DOF closed-track cam-follower and flexible
driveshaft.

(1973), in which the initial effects of the follower are reflected in the elastic camshaft
and thus the torsion and two-dimensional bending modes are excited at twice the frequency
of other modes. Note, this phenomenon does not effect the open-track cam-follower
with its constraining external spring force on the follower for the complete cycle of
operation.
This model, shown in Fig. 12.22, is obtained by assuming that the equivalent mass m
of the follower is lumped in one point and constrained to move in the vertical direction
only. The elasticity of the follower corresponds to a linear spring, with stiffness k sup-
porting the mass. Damping in the follower is represented by the viscous damping coeffi-
cient c. The flexible camshaft is represented by the torsional stiffness k q and the transverse
.
(bending) stiffnesses k x and k y in the x and y directions, respectively. Also, x, x, and x¨ are
.
¨
the follower displacement velocity and acceleration, and s, s, and s are the cam displace-
ment, velocity, and acceleration, respectively. The input angular velocity is considered to
be constant. Backlash is neglected. This model has been developed by Koster (1975) and
Ardayfio (1976).
The motion of the bending of the follower roller is a function of the cam rotation q
and the elastic deflections of the camshaft in the y and x directions. The slope of the cam
can be approximated