Dynamic Behavior Analysis Of Magnetic Bearing System Under The Influence Of Compound Random Factors

With the development of industrial technology,higher requirements have been put forward for advanced rotating machinery and equipment manufacturing,especially bearings.Traditional mechanical bearings are difficult to meet the requirements of high-performance applications,and the birth of magnetic bearings has changed this pattern.Compared with traditional bearings,magnetic bearings have high speed,low energy consumption,less wear,long life and other distinctive features,this is a new type of bearing with great potential for development,and has therefore become a research hotspot in the field of engineering in recent years.With further research on magnetic bearings found that the magnetic bearings in the operation process by a variety of random noise is not negligible.The dynamics of magnetic bearing systems under the action of noise has been seen in the literature,but the noise composition is relatively single,the study of magnetic bearing systems under the action of composite random is still relatively rare.In order to be more relevant to the actual situation,it is of great theoretical significance and application value to investigate the dynamical behaviour of magnetic bearings under the combined effect of internal parameter random and external random excitation and its control.The main elements are as follows.1.The Hopf bifurcation control problem for a class of randomly perturbed systems with bounded parameters under magnetic force as a sinusoidal carrier and Gaussian white noise excitation is explored.Firstly,the composite stochastic magnetic bearing system is reduced to an equivalent extended-order deterministic nonlinear system by means of the sequential orthogonal decomposition method,using orthogonal approximation and Karhunen-Loeve decomposition theory,and the critical conditions for the occurrence of Hopf bifurcation in the system are derived by means of the Lemma.Secondly,the effects of external noise strength,internal parameter random strength and magnetic strength on the system before and after Hopf bifurcation are investigated.Finally,a composite non-linear feedback controller is designed to improve the stability of the magnetic bearing system in operation.The relative optimality of the composite non-linear controller is illustrated by comparing the effect plots of the three controllers-linear,non-linear and composite.2.A model of a magnetic bearing-rigid rotor system under the combined influence of multiplicative and additive noise is investigated.The system is first transformed into a Markov diffusion process using the amplitude wrap random averaging method,then the Ito differential rule is used to find the Ito equation for the corresponding amplitude,and then the drift and diffusion terms are time-averaged to obtain the smooth Ito equation for the amplitude.The corresponding Fokker Planck Kolmogorov equation is integrated to obtain the smooth response probability density function of the system.The factors affecting the dynamics of the magnetic bearing-rigid rotor system are analysed using the smooth response probability density function plot and the cross-sectional plot at zero velocity,and it is concluded that internal random factors are the main factors affecting the stability of the magnetic bearing system.Finally,the system was numerically simulated and Proportional Integral Derivative(PID)controlled.