13.3.1 Introduction to Vibration Minimization

Many investigators have studied optimization criteria for cam profile design. Their methods minimized many important response parameters, particularly vibration of the cam follower. One of the first presentations of a form of vibration optimization was by Hussmann (1938). He established specific harmonics near the follower natural frequency equal to zero to minimize vibrations. Chew and Chuang (1990) applied Lagrange multipliers and polynomial lift curves to minimize the integral of the end of the rise residual vibrations over the desired speed range. They developed a direct procedure for minimizing residual vibrations when designing cam motions. They concluded (as did Wiederrich and Roth, 1978) that for high-speed applications, specification of vanishing cam boundary conditions for derivatives higher than the velocity is inappropriate when using an optimization procedure that accounts for the dynamic response. Perhaps the most important feature of these optimization methods in cam design is that they can readily be applied to design the entire cam motion rather than just a segment of the motion. Cams designed in this way have been found to work well in practice. Optimization methods can also be applied to optimize the geometry of the cam and follower mechanism.

For many years much research has been directed toward identifying and tabulating suitable functions to define cam motion segments which produce good dynamic response. Neklutin (1952) contributed much in this area.

Freudenstein (1960) observed that cam dynamics could be improved by minimizing the harmonic content of the motion and...