Stick–slip vibration of an oscillator with damping

Abstract

This paper proposes a new criterion for the occurrence of stick–slip vibration in an oscillator excited by a moving belt. Equations of motion were derived for a single-degree-of-freedom oscillator excited by the friction between the oscillator mass and a moving belt, considering two types of velocity-dependent friction models: exponential and polynomial. Based on the derived equations, dynamic responses were analyzed for various damping values, and it was found that the damping value determines the classification of oscillator motion among stick–slip, pure slip, and damped slip motions. Furthermore, a criterion for the occurrence of stick–slip motion, expressed in an integral form, was derived in terms of friction and damping forces. Using the least squares method, closed forms for the damping values to determine the occurrence of stick–slip vibration were obtained as functions of normal force, relative speed between contact surfaces, and friction parameters. In addition, the effects of the belt speed and of friction parameters on the occurrence of stick–slip vibration were also investigated.