Thomas Industrial Library

EXAMPLE 9-3

Dynamic Force Analysis of a Form-Closed (Desmodromic) Cam-Follower

System.

Given: A translating roller follower as shown in Figure 9-15a is driven by a formclosed radial plate cam which has the following program:

Segment 1: Rise 1 inch in 50 ° with modified sine acceleration

Segment 2: Dwell for 40 °

Segment 3: Fall 1 inch in 50 ° with cycloidal displacement

Segment 4: Dwell for 40 °

Segment 5: Rise 1 inch in 50 ° with 3-4-5 polynomial displacement

Segment 6: Dwell for 40 °

Segment 7: Fall 1 inch in 50 ° with 4-5-6-7 polynomial displacement

Segment 8: Dwell for 40 °

Camshaft angular velocity is 18.85 rad/sec

Follower effective mass is 0.0738 in-lb-sec2 (blobs)

Damping is 10% of critical ( = 0.10)

Problem: Compute the dynamic force function for the cam. Keep the pressure angle under 30 ° .

Solution:

1 Calculate the kinematic data (follower displacement, velocity, acceleration, and jerk) for the specified cam functions. The acceleration for this cam is shown in Figure 9-11 (p. 235) and has a maximum value of 3504 in/sec2.

2 Calculate radius of curvature and pressure angle for trial values of prime circle radius, and size the cam to control these values. Figure 9-12 shows the pressure angle function and Figure 9-13 the radii of curvature for this cam with a prime circle radius of 4 in and zero eccentricity. The maximum pressure angle is 29.2 ° and the minimum radius of curvature is 1.7 in.

3 With the kinematics of the cam defined, we can address its dynamics. To solve equation 9.10 (p. 233) for the cam force, we assume zero values for the spring constant k and the preload Fpl . The value of c is assumed to be 1.153, the same as in the previous example. The kinematic parameters are known.

4 Program DYNACAM does this computation for you. The dynamic force that results is shown in Figure 9-16. Note that the force is now more nearly symmetric about the axis and its peak absolute value is 289 lb. Crossover shock will occur each time the follower force changes sign. Open the file EX_09-03.cam in DYNACAM to see this example

Compare the dynamic force plots for the force-closed system (Figure 9-14b, p. 237) and the form-closed system (Figure 9-16). The absolute peak force magnitude on either side of the track in the form-closed cam is less than that on the spring-loaded one. This shows the penalty that the spring imposes on the system in order to keep the joint closed. Thus, either side of the cam groove will experience lower stresses than will the open cam, except for the areas of crossover shock mentioned on p. 238.