Self-Excited Oscillations in Sliding With a Constant Friction Coefficient—A Simple Model

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Abstract
The sliding of two surfaces with respect to each other involves many interacting phenomena. In this paper a simple model is presented for the dynamic interaction of two sliding surfaces. This model consists of a beam on elastic foundation acted upon by a series of moving linear springs, where the springs represent the asperities on one of the surfaces. The coefficient of friction is constant. Although a nominally steady-state solution exists, an analysis of the dynamic problem indicates that the steady solution is dynamically unstable for any finite speed. Eigenvalues with positive real parts give rise to self-excited motion which continues to increase with time. These self-excited oscillations can lead either to partial loss-of-contact or to stick-slip. The mechanism responsible for the instability is a result of the interaction of certain complex modes of vibration (which result from the moving springs) with the friction force of the moving springs. It is expected that these vibrations play a role in the behavior of sliding members with dry friction.