Research On Bifurcation Of A Rotor Supported By Electromagnetic Bearing

The electromagnetic bearing is a kind of energy conversion device which can convert electrical energy into kinetic energy,providing powerful guarantee for advance of the science technology and development of the society. So it is widely used in various fields, such as aerospace engineering and industrial fields. But researchers find that the movement of the rotor is very unstable in the process of using. And in the modern industry, real systems mostly contain nonlinear factors, which tend to cause instability of the system and various faults. In the large mechanical rotor system, nonlinear factors make the rotor a relatively large vibration in the field of certain parameters, so it is important to analyze the nonlinear dynamics and stability of such systems.In this article, we devote to considering a class of electromagnetic bearing rigid rotor system. The Hopf bifurcation and global bifurcation of magnetic levitation bearing rotor system in some parameter areas are studied. The problem considered in the paper and the obtained results can be regarded as the beneficial supplement of the electromagnetic bearing. The main research work and results are as following:(1) This paper introduces the development status of electromagnetic bearing rotor system, the research background and significance. And the paper describes the dynamical model of a class of two degrees of freedom electromagnetic bearing rotor, by which we give the equivalent dimensionless equation. This work is the foundation to study the bifurcation of the bearing rotor system.(2) We use the methods of qualitation and quantization to study the dynamical characteristics of the rotor system. Two dimensional reduction system is obtained by using center manifold theorem. We can obtain the rotor system occurring super critical Hopf bifurcation by analyzing the reduction system. Some numerical simulation results of the bifurcation diagram are presented to verify the theoretical analysis.(3) The global dynamical characteristic is considered by combing theoretical analysis and numerical analysis. The 1:2 internal resonance is studied by adopting the method of Multiple Scales; We obtain the average equation of the four-dimensional system, and get the normal form by simplifying the average equation; The global bifurcation behavior is studied using the global perturbation method. Using numerical algorithm we respectively do numerical simulation on the original system and the average equation, and we can obtain the phase diagram of the original system and the average equation, so the correctness of the theory analysis is verified.(4) Numerical simulation method is used to analyze the influence of various single parameter on the dynamical characteristic of the rotor system. By observing the bifurcation diagram, Lyapunov exponents diagram, phase diagram, Poincare maps, the better operating intervals of the system with the corresponding parameters are obtained. And we discuss the influence of two parameters on the dynamical characteristic of the rotor system through the double parameter bifurcation diagram, eventually we find the optimization range under control of the two-dimensional parameter of the rotor system.