The stability of the steady motions of a rotor system with a fluid using a discrete model

Abstract

A discrete model of a rotor system with a fluid is proposed. The model contains a rotating disc, which is directly and symmetrically seated on a spindle located in an isotropic, viscoelastic mounting, and a ring which slides with friction over the disc. There is a viscoelastic coupling between the centres of the disc and the ring. The disc simulates the rotor and the ring simulates the fluid mass of a filler. When the ring slides over the disc, an interactive force arises which is directed at an angle to the relative velocity. It is shown that, with a correct choice of the parameters, the model enables an approximate determination to be made of the domain of stability of steady rotation in the plane of the parameters of the viscoelastic mounting of the axis. It is established that, on leaving the domain of stability, Andropov-Hopf bifurcation occurs and a periodic motion of the type of a circular precession is generated (in a “soft” or “hard” way) from the state of steady rotation.