Page 244 - Cam Design Handbook

THB8 9/19/03 7:25 PM Page 232

232 CAM DESIGN HANDBOOK

F
T = n ( ˙ y + m V ). (8.8)
s
w
From the velocity diagram, Fig. 8.10b, it is seen that the sliding component velocity
w
+
V = ( y r ). (8.9)
s b
Substituting Eq. (8.9) into Eq. (8.8) gives
È y ˙ ˘
+
T = F n Í Îw + ( m yr ) . (8.10)
˙
b
˚
Equation 8.10 shows that the torque is a variable function of the displacement of the
˙ y
follower and the converted velocity (or the slope of the cam surface) and is also
w
dependent on the coefficient of friction and on the base circle radius of the cam.
In Eq. 8.10 the total load F n is variable: it is the result of the weight and the
loading of the follower and the resistance, the inertia, and the spring forces. If the rela-
tionship between F n and the displacement of the follower is known, the cam-driving torque
at each instant, its maximum and minimum values, and the average torque can easily be
found.

8.11.3 Torque-Controlled Cams
In many slow-speed cam-activated mechanisms, we can design the cam profile to the
desired input force and output torque relationships for a finite range of operation. We
will use a radial cam with a roller follower to illustrate this; see Chen (1982) and Garrett
(1962).
From Fig. 8.11 we see that pressure angle
dr
tana =
p
rd q
where r = distance from cam center to roller follower center, in.
Substituting this into Eq. (8.5) gives torque
Ldr
T = . (8.11)
dq
If a design requires that the output torque T be proportional to the angle of rotation q while
the input force be proportional to the follower displacement, then
T = T + q (8.12)
C
i 1
(
L = L + C r r ) (8.13)
-
i
2
i
where T i, L i, and r i, are initial values of torque (lb-in), force (lb), and radial distance (in),
respectively. C 1 and C 2 are constants of proportionality.
Substituting Eqs. (8.12) and (8.13) into Eq. (8.11) and integrating we obtain
Cq 2 C
2
Tq + i = Lr + 2 ( rr ) + C .
-
i i i 3
2 2