Non-linear vibration of the rotor-housing system

Abstract

An influence of dynamical properties of a massive housing system on forward synchronous whirling motion of an unbalanced rotor with four degrees of freedom is studied. The rotor is assumed to be a rigid body with dynamical axial symmetry attached to a massless linearly elastic shaft. The case is also a dynamically symmetric body with its center of mass located on the bearings’ axes. The elastic supports of the case are isotropic with restoring forces being non-linear functions of the displacement. The Hertz and Duffing’s types of non-linearity have been considered. Rotation occurs with constant spin speed. Damping is not taken into account. Two additional non-linear resonances, which are connected with the dynamics of the massive case, have been found. Their location depends on the rotor and case’s mass ratio. The dynamic response of a symmetric hyperboloidal whirling has been obtained. The linear standard method of stability investigation has been applied for a full range of frequencies. It has been also shown that rotor’s self-centering does not take place and the massive case produces a balancing effect as the spin speed approaches infinity. Refs 10. Figs 5.

Keywords:

nonlinear rotor dynamics, whirling motion, stability of stationary revolution