Self-excited oscillations in sliding with a constant friction coefficient - A simple model

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 rite 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 lend either to partial loss-of-contact or to stick-slip. The mechanism responsible for the instability is a result of the intel-action 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.