Some Remarks about Stick-Slip Oscillators

Abstract

The objective of this paper is to analyze the behavior of a stick-slip dry-friction oscillator in the steady-state solution. The system is composed by a block of mass m connected to a fixed support by a spring of stiffness k. 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. By numerical simulations, different imposed belt velocity and dry-friction configurations are analyzed, from a deterministic and from a stochastic viewpoint. The focus of the paper is finding the stick- and slip-mode parts of the trajectory in the steady-state through the phase diagram. In the stochastic analysis, some parameters of the dry-friction model are considered uncertain. The friction coefficient and the belt speed are modeled as random process and random field respectively. Monte Carlo simulations are employed to compute the statistics of the response of the stochastic differential equation of motion of the stick-slip dry-friction oscillator.