**
EXAMPLE 9-4
**

Comparison
of Kinetostatic Torques and Forces Among Three Alternate Designs of the Same Cam.

**
Given:
**
A
translating roller follower as shown in Figure 9-1a (p. 214) is driven by a
force-closed radial plate cam that has the following program:

**
**

**
Design 1
**

Segment
1: Rise 1 inch in 90
°
double harmonic displacement

Segment
2: Fall 1 inch in 90
°
double harmonic displacement

Segment
3: Dwell for 180
°

**
**

**
Design 2
**

Segment
1: Rise 1 inch in 90
°
cycloidal displacement

Segment
2: Fall 1 inch in 90
°
cycloidal displacement

Segment
3: Dwell for 180
°

**
**

**
Design 3
**

Segment
1: Rise 1 inch in 90
°
and fall 1 inch in 90
°
with
polynomial displacement

Segment
2: Dwell for 180
°

Camshaft
velocity is 15 rad/sec (143.24 rpm); Follower effective mass is

0.0738
lb-sec2/in (blobs); Damping is 10% of critical (
æ
= 0.10)

**
**

**
Problem:
**
**
**
Find the
dynamic force and torque functions for the cam. Compare their peak magnitudes
for the same prime circle radius.

**
**

**
Solution:
**

1
Calculate the kinematic data (follower displacement, velocity, acceleration,
and jerk) for each of the specified cam designs. See Chapter 8 to review this
procedure.

2
Calculate the radius of curvature and pressure angle for trial values of prime
circle radius, and size the cam to control these values. A prime circle radius
of 3 in gives acceptable pressure angles and radii of curvature. See Chapter 7
to review these calculations.

3
With the kinematics of the cam defined, we can address its dynamics. To solve
equation 9.1a (p. 215) for the cam force, we will assume a value of 50 lb/in
for the spring constant
*
k
*
and adjust the preload
*
Fpl
*
for
each design to obtain a minimum dynamic force of about 10 lb. For design 1,
this requires a spring preload of 28 lb; for design 2, 13 lb; and for design 3,
10 lb.

4
The value of damping
*
c
*
is calculated from equation 9.2i (p. 218). The
kinematic parameters
*
x
*
,
*
v,
*
and
*
a
*
are
known from the prior analysis.

5
Program DYNACAM will do these computations for you. The dynamic forces that
result from each design are shown in Figure 9-18 and the torques in Figure
9-19. Note that the force is largest for design 1 at 82 lb peak and least for
design 3 at 53 lb peak. The same ranking holds for the torques, which range
from 96 lb-in for design 1 to 52 lb-in for design 3. These represent reductions
of 35% and 46% in the dynamic loading due to a change in the kinematic design.
Not surprisingly, the sixth-degree polynomial design, which had the lowest
acceleration, also has the lowest forces and torques and is the clear winner.
Open the files E09-04a.cam, E09-04b.cam, and E09-04c.cam in program DYNACAM to
see these results.

Copyright 2004, Industrial
Press, Inc., New York, NY