Page 177 - Cam Design Handbook

THB6 8/15/03 2:40 PM Page 165

ELEMENTS OF CAM PROFILE GEOMETRY 165

Solving for the force normal to the cam

L
0
F = AB (6.7)
+
cosa - m Ê 2 ˆ sina
Ë B ¯
The normal force F is a maximum (equals infinity) which means that the follower will
jam in its guide when the denominator of Eq. (6.7) equals zero. Therefore,
+
Ê 2 AB ˆ
cosa - m sin a = 0
m Ë B ¯ m
The maximum pressure angle without locking the follower in its guide is

B
a = tan -1 . (6.8)
m
+
m (2 AB)
Let us substitute some trial values to compare the magnitude of the results. If we let
A = B and assume the values for the coefficient of friction of bronze on steel to be
(
m static) = 015
.
m kinetic) = 010 and ( .
Substituting in Eq. (6.8), we find the maximum pressure angle for each condition:
B
a = tan -1 = 73 degrees for m = . 010
m
+
( . 010 )(2 BB)
B
015
a = tan -1 = 66 degrees for m = ..
m
+
( . 015 )(2 BB)
Note that these values and the derivation of Eq. (6.8) are based on the ideal assumption
that the follower is perfectly rigid. Thus, the coefficient of friction may actually reach a
value of 0.25 or more depending on relative elasticity and backlash of the follower. A flex-
ible stem may “dig” into the lower corner of the bearing. Therefore, the suggested guide
in practice is to keep the coefficient of friction m, the follower overhang A, and the back-
lash as small as possible with the bearing length B as large as possible, in the range of
B = 2A. Generally the safe limiting pressure angle in practice is 30 degrees. However, for
light loads with accurate low-friction bearings, the author was successful using a pressure
angle as high as 48 degrees. Note that commercially available ball bushings for the linear
moving stem have provided low friction and little backlash; see Chap. 10.
We may observe that the follower jamming is of concern only when the follower moves
in the direction opposite that of the external load L. As shown in Figure 6.4, jamming
occurs during the rise period only. During the fall period, the size of the maximum pres-
sure angle is generally not limited in proper cam design. However, the author has seen
machine installations in which the follower drove the cam during the fall action. It occurred
with a chain-driven cam and a spring-loaded follower. The spring force, acting on an exces-
sive pressure angle of fall, produced detrimental shock and fluctuating action in absorb-
ing the backlash of the system.
Also, if the load L o varies according to the inertia acceleration in both the rise and fall,
the pressure angle should be considered in both. Chapter 9 discusses load fluctuations and
reflected torque curve which should be an initial point of analysis in all pressure angle
investigations.