Page 429 - Cam Design Handbook

THB13 9/19/03 7:56 PM Page 417

CAM SYSTEM DYNAMICS—RESPONSE 417

f f = compressive force exerted by follower spring on output mass
f fe = effective follower spring force = f f - s p
h c, h = cam rise and corresponding (total) output rise
k s, k f = stiffness of return and follower spring
m 0, m f = mass of output and of follower
p(t) = costate vector
s p = preload force of closing spring
t 0 = natural period of vibration of system
t 1, t 2 = rise, return time
t = time
x(t) = state variable vector
y, y c = displacement of follower output and cam, respectively
h = distance between axis of rotation of cam and center of roller, measured in direction
of follower motion
s c = Hertzian contact stress at cam-follower interface
s ce = effective cam contact stress
q 1, q 2 = cam rotation during rise, return
w = angular frequency of cam rotation
w 0 = angular frequency of vibration = 2p/t 0
( )¢= derivative with respect to time, t
Normalized parameters
C F = nonlinear factor relating cam contact stress s c to cam contact force F c
F c = f c/(k fh)
F ce = f ce/(k fh)
F f = f f /(k fh)
F fe = f fe /(k f h)
J = optimality criterion
K k = (k s + k f) /k f
N F = nonlinear factor relating cam contact stress s c to Follower force F f
r 0 = (2pl) 2
r 1 = 2z (2pl)
R p = r p /h c
R v = Y c - Y = relative vibration
S F = factor allowing for follower guide friction, follower pressure angle, and follower mass
acceleration to relate roller contact force F c to follower force F f
S p = s p /(k f h)
T = (t 1 + t 2) /t 1
V i = weight functions for i = 1, 2
W i = weight factors for i = 1, 2, 3
Y = y/h
Y c = y c/h c
2
h ¯ = h/h c = R -e 2
p
t = t/t 1
l = t 1/t 0
z = c/(2m 0 w 0 ) damping ratio
·
( ) = first derivative with respective to t
(n)
( ) = n - th derivative with respect to t
13.5.3 Description of Dynamic Model
Figure 13.11 shows a lumped-parameter model of a cam-follower system. This is a
single degree-of-freedom model with two masses, two springs, and a dashpot. The model