Stochastic dynamics of systems with friction-induced vibration

This paper presents linear and non-linear phenomenological models of interf acial forces between a rotating disc and a rigid pin in contact with the di sc. The models are developed based on experimental results which revealed t hat both normal and frictional forces were essentially random non-Gaussian processes. The characteristics of these forces are different when the disc reverses its rotation. When the disc rotates clockwise, the sprag-slip phen omenon occurs due to so-called kinematic constraint instability. Furthermor e, in view of the time variations of contact forces, the boundary condition s of the pin become time varying and its natural frequency becomes time-dep endent. The interfacial forces appear in the pin's equation of motion as mu ltiplicative and non-homogeneous terms. In the non-linear model, the normal force appears as multiplicative of velocity terms up to cubic order. The p in's dynamic behavior was studied using the method of stochastic averaging. For the non-linear model, the problem of noise-induced transition was exam ined for clockwise and counter-clockwise cases. The pin amplitude extrema w ere found to be more complex for the case of clockwise rotation than those for the counter-clockwise case. For the linear model, the complete probabil istic description of the pin's dynamic behavior is derived in a closed form in terms of disc speed and friction power spectral density level. (C) 1999 Academic Press.