On the Passive Control of Friction-Induced Instability Due to Mode Coupling

Abstract

This study investigates a passive controller for a coupled two degrees-of-freedom (DOFs) oscillator to suppress friction-induced mode-coupling instability. The primary system is acted upon by a friction force of a moving belt and static coupling of the oscillator provided with an oblique spring. The combined system, original system plus absorber, response is governed by two sets of differential equations to include contact and loss of contact between the mass and the belt. Therefore, the model accounts for two sources of nonlinearity in the system: (1) discontinuity in the friction force and (2) intermittent loss of contact. Friction coefficient and absorber orientation are used to define planar parameter space for stability analysis. For various mass ratios, the parameter space is divided into stable and unstable zones by defining stability boundaries. In general, an absorber expands the stability region and provides a significant reduction in transient response overshoot and settling time. Incorporation of the absorber also prevents mass-belt separation, thereby suppressing the belt-speed-overtake by the primary mass.