Page 450 - Cam Design Handbook

THB13 9/19/03 7:56 PM Page 438

438 CAM DESIGN HANDBOOK

approach for determining k f is by calculation of above items (a) through (e). This method
is subject to error since broad assumptions must be made in the deflection formulae.
The compression spring rigidity k s may easily be found by the design calculations if
fabrication accuracy is maintained. In the automotive and aircraft fields, typical values are
k = between 20,000 and 60,000 lb in
f
k = between100 and 600 lb in
s
These values depend on engine size and speed.

13.7.5 Dynamic Constant, c
The dynamic constant
m
c = 36 N 2
k
f
which can be rewritten as
w
2
.
c = 0093 N . (13.84)
k
f
13.7.6 Equivalent Weight, w
This weight w may or may not be the total weight of the members, depending upon (1)
the effect of the flexible members, (2) levers, and (3) gears. The following are suggestions
for finding the equivalent weight w.

13.7.6.1 Springs. For both long thin rods that act as springs and actual compression
springs, we do not use their weights directly. Theory and experience have shown that about
one-third of their actual weight is effective. This is because flexibility prevents all the mass
from being accelerated at the same rate. Thus, the acceleration above does not affect the
other two-thirds of the weight.

13.7.6.2 Levers and Gears. A lever (Fig. 13.20) with unequal arms has its effective
weight w inversely related to the square of its lever arm ratio. In this figure, we have a
lever with arms d 1 and d 2, follower velocities v 1 and v 2, and a weight w 1 to be referred to
the follower end.

The kinetic energy of weight w 1
w
K.E. = 1 v .
2
2 g 1
This must equal the kinetic energy of the equivalent weight on the follower end
w
K.E. = v 2 2
2 g
equating gives
2
Ê v ˆ
w = w Á 1 ˜ = wU 2 (13.85)
1
1
Ë v ¯
2