Page 346 - Cam Design Handbook

THB11 9/19/03 7:33 PM Page 334

334 CAM DESIGN HANDBOOK

T

Dq
FIGURE 11.10. A Torsional Spring.

known amount and measuring force) but can also be determined analytically for a number
of simple geometries.
Torsional springs (Fig. 11.10) are completely analogous to the linear springs described
above but relate torque and angular deflection instead of torque and linear deflection. The
corresponding expressions for torsional springs are:
T = K Dq (11.44)
r
where K r is the torsional spring rate (in units of torque/angle such as in-lbf/rad or
Nm/rad) T is the torque exerted by the spring and Dq is angle through which the
spring is turned, relative to its equilibrium position. The potential energy in the spring is
given by:

D q 1
D
PE = Ú K d = K q . (11.45)
hh
2
r
r
0 2
11.4.1 Coil Springs
While many types of manufactured springs exist, coil springs are one of the most
commonly used springs in cam systems. Coil springs may be used in either extension or
compression, depending upon the design of their ends. Figure 11.11 illustrates a typical
compression coil spring such as the type used in automotive suspensions. The spring rate
for a coil spring in axial tension or compression is given by

Gd 4
K = (11.46)
8 DN
3
where d is the diameter of the spring wire, D is the diameter of the spring coil (measured
from the center of the spring wire), G is the shear modulus of the material, and N is the
number of active coils. N does not need to be an integer and does not include ground ends
that are pressed against the mating surface at either end of the spring since these do not
participate in the compression or extension of the spring. Values of G for various spring
materials may be found in engineering handbooks: a typical value used for steel springs
6
when no additional information is available is 11.0 ¥ 10 psi. Coil springs may be designed
in such a way that the diameters d and D change over the length of the spring. As a first
order approximation, spring rates in such cases can be estimated by using the average
values of these parameters.