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The book takes the subject from an introductory level through advanced topics needed to properly design, model, analyze, specify, and manufacture cam-follower systems.
Cam Design and Manufacturing Handbook
(Kinetostatic Force Analysis of the Force-Closed Cam-Follower)

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   by Robert L. Norton
Published By:
Industrial Press Inc.
Up-to-date cam design technology, correct design and manufacturing procedures, and recent cam research. SALE! Use Promotion Code TNET11 on book link to save 25% and shipping.
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9.4 KINETOSTATICFORCE ANALYSIS OF THE FORCE-CLOSED CAMFOLLOWER

 

The previous sections introduced forward dynamic analysis and the solution to the system differential equation of motion (9.2b). The applied force Fc ( t ) is presumed to be known, and the system equation is solved for the resulting displacement x from which its derivatives can also be determined. The inverse dynamics , or kinetostatics , approach provides a quick way to determine how much spring force is needed to keep the follower in contact with the cam at a chosen design speed. The displacement and its derivatives are defined from the kinematic design of the cam based on an assumed constant angular velocity ù of the cam. Equation 9.2b can be solved algebraically for the force Fc ( t ) provided that values for mass m , spring constant k, preload Fpl , and damping factor c are known in addition to the kinematic displacement, velocity, and acceleration functions.

 

Figure 9-1a (p. 214) shows a simple plate or disk cam driving a spring-loaded, roller follower. This is a force-closed system which depends on the spring force to keep the cam and follower in contact at all times. Figure 9-1b shows a lumped parameter model of this system in which all the mass that moves with the follower train is lumped together as m , all the springiness in the system is lumped within the spring constant k , and all the damping or resistance to movement is lumped together as a damper with coefficient c .

 

The designer has a large degree of control over the system spring constant keff as it tends to be dominated by the ks of the physical return spring in this model. The elasticities of the follower parts also contribute to the overall system keff but are usually much stiffer than the physical spring. If the follower stiffness is in series with the return spring, as it often is, equation 8.15c (p. 191) shows that the softest spring in series will dominate the effective spring constant. Thus, the return spring will virtually determine the overall k unless some parts of the follower train have similarly low stiffness.

 

The designer will choose or design the return spring and thus can specify both its k and the amount of preload to be introduced at assembly. Preload of a spring occurs when it is compressed (or extended if an extension spring) from its free length to its initial assembled length. This is a necessary and desirable situation as we want some residual force on the follower even when the cam is at its lowest displacement. This will help maintain good contact between the cam and follower at all times. This spring preload Fpl adds a constant term to equation 9.2b which becomes:

 

 

or :

 

 

The value of m is determined from the effective mass of the system as lumped in the single- DOF model of Figure 9-1. The value of c for most cam-follower systems can be estimated for a first approximation to be about 0.06 of the critical damping cc as defined in equation 9.2i (p. 218).

 

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