A method for determining the periodic solution and its stability of non-linear bearing-rotor system based on observed states of the system

摘要

In this article, stability and bifurcation of a hydrodynamic bearing-rotor system are analysed. A numerical method is presented to find the periodic responses of the hydrodynamic bearing-rotor system with the change of the system parameter. The observed states of the system are used to solve inversely the Jacobian matrix and the obtained Jacobian matrix is used to calculate the Floquet multiplier; then the stability of periodic response can be determined by the Floquet theory. The periodic responses and their stability with the change of the system parameter can be calculated by the proposed method when steady-state and transient-state information are observed online. The proposed method is applied to a rotor system with elliptical bearing supports to determine non-linear periodic responses and their stability. The combination of the predictor-corrector mechanism and the Poincare-Newton-Floquet method is also applied to the system. Comparison of the two methods proves the proposed method to be effective. Taking rotating speed as the bifurcation parameter, the periodic, quasi-periodic, coexistent, jump, and chaotic solutions of the system are computed. The numerical results reveal the rich and complex non-linear behaviours of the system.