Dynamic Instability of an Elastic Disk Under the Action of a Rotating Friction Couple

Abstract

This paper investigates the instability of the transverse vibration of a disk excited by two corotating sliders on either side of the disk. Each slider is a mass-spring-damper system traveling at the same constant speed around the disk. There are friction forces acting in the plane of the disk at the contact interfaces between the disk and each of the two sliders. The equation of motion of the disk is established by taking into account the bending couple acting in the circumferential direction produced by the different friction forces on the two sides of the disk. The normal forces and the friction couples produced by the rotating sliders are moving loads and are seen to bring about dynamic instability. Regions of instability for parameters of interest are obtained by the method of state space. It is found that the moving loads produced by the sliders are a mechanism for generating unstable parametric resonances in the subcritical speed range. The existence of stable regions in the parameter space of the simulated example suggests that the disk vibration can be suppressed by suitable assignment of the parameter values of the sliders.