A stochastic analysis of the trajectories of a dry-friction oscillator in a belt: how much sticked and slipping?

Abstract

his paper investigates the dynamics a simple dry-friction oscillator which is composed of a block, modeled as a particle, connected to a fixed support by a spring. The block moves over a continuous belt that is driven by rollers. The frictional force between the block and the belt is modeled as a Coulomb friction. Due to this friction model, the resulting motion of the block can be characterized into two qualitatively different modes, the stickand slip-modes, with a non-smooth transition between them. The focus of the paper is to quantify the percent of time in which the block stays in the stick-mode for a non-constant belt velocity and for different values of the friction coefficient from a deterministic and from a stochastic view point.