Dynamic Behaviors Analysis Of Stochastic Magnetic Bearing Systems With Two Random Effects

The advantages and disadvantages of advanced equipment manufacturing determine the development of society.Magnetic bearings play an important role in advanced equipment manufacturing.Only through scientific understanding and monitoring can we ensure the equipment work normally.In general situations,magnetic bearings will be affected by physical random characteristics and external random excitation inevitably.Therefore,in order to ensure the magnetic bearings work normally,random factors should be considered on the model.In addition,it also provides a new perspective for the study of magnetic bearings.This paper studied stochastic dynamic behavior of magnetic bearings under random physical characteristics and external random excitation.1.The Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated.Firstly,the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established.The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic.Secondly,combining mathematical analysis tools and numerical simulations,the Hopf bifurcation of the equivalent model is analyzed.Finally,a hybrid feedback control method(linear feedback control method combined with nonlinear stochastic feedback control method)is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.2.The purpose of this paper is to investigate the vibration characteristics and motion of a class of random magnetic bearing systems with narrow band noise.Firstly,the multiple scale method is used to obtain the averaged equations.Secondly,it is found that there exist different motions with the various values of excitation forces 1)and permeability by numerical simulation method.Besides,both the bifurcation diagram and maximum Lyapunov exponent can verify the results.Finally,the influence of narrow-band excitation on magnetic bearings is verified,and the conclusion shows that the thickness of the limit cycle increases gradually as the bandwidth of narrow-band excitation changes in a small range.