SEED Unit Design - Cam Mechanisms < >

15. Force Closure

Study of the boundary conditions for good dynamic performance, equations (14), shows that the direction of follower acceleration reverses during rise and fall actions resulting in the negative loops shown in Figure 13. Consequently the inertia force due to the retardation of the follower mass acts to separate the roller from the cam profile during the latter part (u > 0.5) of the rise action. Therefore a means of force closure, such as a spring, must be provided to ensure that the resultant force always acts towards the cam to maintain continuous contact between these parts. The other components of the resultant force acting on the follower along its path are:

  1. frictional resistance (which is generally negligible in comparison with the other forces),
  2. the weight of the following system, and
  3. the external load (which is unique to that system).

The spring force resulting from pre-load plus the deflection due to follower displacement at the critical position should be about 1.2 to 2.0 times the maximum separating force, depending upon the quality of the profile and the type of loading. The spring pre-load can be between 20% and 50% of the maximum spring force: advice on spring selection is to be found in SEED Procedural Guide for the specification and selection of springs.

The variation of the forces acting along the follower path during a rise action is shown in Figure 24 for the no-load condition; why is this likely to be the worst case? The resultant is a positive quantity to maintain the contact. The loops of the inertia force due to follower acceleration and the increase of spring force with follower displacement during the lift are also shown. (The weight of the following system has been added to the spring pre-load).

The peak value of negative acceleration is not the sole criterion for determining the spring force. The follower displacement, and hence spring deflection, where the maximum inertia force acts to lift the follower from the cam is also significant. Desirably this should be near the end of the rise so, again, influencing the choice of cam law. (Modified Sinusiodal Acceleration motion is particularly good in this respect, especially as the maximum non-dimensional acceleration is relatively low, see Appendix E).

What are the consequences of excessive spring force on the cam and roller? What other requirements influence the spring pre-load and stiffness specified?