Dynamics Of A JEFFCOTT Rotor-Magnetic Bearing System With Two Time Delays

The Jeffcott-rotor magnetic bearing, as a kind of high-tech product, is levitated at the disc by the magnetic force which is controlled by a control system. It has a far-reaching meaning and extensive application prospect and its practical value is inestimable. It is inevitable that time delay will exist in the control system of the magnetic bearing, and time delay will affect the dynamic of the system. Thus, investigating the magnetic bearing system with time delay is of great theoretical and practical significance. In connection with the characteristic of non-linear magnetic rotor-bearing system is studied in this thesis.Firstly, we introduce the Jeffcott rotor-magnetic bearing system model with two time delays. Secondly, the time delays are taken as parameters, the condition to ensure the stability of the zero solution and its stable domain are decided by analyzing the characteristic equation of the linearization. Thirdly, the existence of Hopf bifurcation is given. Then we discuss the direction and stability of the Hopf bifurcation by using the center manifold theory and normal form method introducing by Hassard and Kazarinoff. Finally, for the pitchfork bifurcation, the Normal form to third order terms is given, and we analyze the change of the orbital topical structure of the system at the critical value and near it. In the end we have done some numerical simulations by using Matlab software. And its results are equivalent to the theoretical results.