Parametric representation of stationary points in rotor-ball bearing system

Abstract

The frequencies of the stationary points in rotor-ball bearing system are difficult to determine due to the nonlinear and non-smooth ball supporting effects. This paper presents a linearized discriminant to calculate the frequency of the stationary points of the system. The influences of system parameters on the stationary points with the Timoshenko beam and the Bernoulli–Euler beam models are also discussed. The comparison between the linear and nonlinear results indicates that the underlying assumptions are reasonable for the range of parameters considered. With the help of linearized discriminant, the frequency values of the stationary points can be found conveniently. Taking the frequency values of stationary points into the linearized discriminant, the corresponding system parameters can also be obtained by setting the linear determinant to be zero.