THE DYNAMIC ANALYSIS OF STICK-SLIP MOTION

The most widely accepted cause of stick-slip motion is that the static (mu(s)) exceeds the kinetic friction coefficient (mu(k)), or that mu(k) drops rapidly at small speeds. Using a dynamic analysis it is shown that the rate of increase of mu(s)(t) with sticking time is a crucial parameter in addition to the condition of mu(s) > mu(k), and that stick-slip may occur even if mu(k) increases with speed V. A general equation is derived which describes the stick-slip amplitude (x(s)) in terms of substrate speed V0, spring stiffness K and damping gamma, for an arbitrary mu(s)(t) and a linearized mu(k)(V), in contrast to a set of previous equations derived by Brockley et al. for an exponential mu(s)(t) and a linearized mu(k)(V) [1]. Additional equations are developed for the ''saturation'' speed (V(ss)), below which x(s) is independent of V0, and also for a critical substrate speed V(c) above which the stick-slip amplitude vanishes. At speeds between V(ss) and V(c) the stick-slip amplitude generally decreases with increasing V0, K and gamma. Depending on the detailed conditions, different sliding modes including smooth sliding, near-harmonic oscillation or stick-slip can result. Equations developed in this paper suggest practical methods of reducing or eliminating stick-slip for a general system.