Friction Damping of Circular Motion and Its Implications to Vibration Control

When vibrating bodies are mutually constrained through friction contact they may move with respect to each other and dissipate energy at the interface. If the relative motion of the contacting surfaces follows a straight line the motion is said to be one-dimensional. This case has been examined extensively in the literature. More generally the point of contact can follow a path which is not a straight line. For the case of a periodic response the path will form a closed loop. In this paper we investigate the simplest, yet most extreme case of two dimensional motion—when the contacting point moves in a circular path. It is found that an exact solution can be derived for the problem of a frictionally constrained system when it is subjected to a circular excitation. The solution is used to determine the characteristics of the system’s response and they are compared with those for one-dimensional motion. In the case of one-dimensional motion if the contacting surfaces are compliant they will stick for at least a portion of each cycle. This is not the case for circular motion as it is found that the interface is either always stuck for small motions or always slipping if the excitation is above a certain level. This result suggests that the slip/stick transition which occurs during every cycle for the one-dimensional case may not be as important for the more general two-dimensional friction contact problem. Friction is often a major source of energy dissipation in vibrating machinery. As a result, the friction contact is sometimes used to reduce the peak response of the system by designing the contacting parts so as to have an optimum friction constraint. In order to investigate this effect expressions are derived for the peak amplitude as a function of the friction force, for the friction force that will minimize peak response, and for the amplitude of the peak response under optimum friction conditions. The results for circular motion are compared with those for straight line motion in order to assess the importance of two-dimensional effects.