Static Bifurcation And Hopf Bifurcation Of Magnetic Liquid Double Suspension Bearing System

Magnetic liquid double suspension bearing system was composed of magnetic bearing and hydrostatic bearing system,the bearing capacity and bearing stiffness can be greatly improved in the system.Both of magnetic bearing and hydrostatic bearing system were nonlinear bearing system,the interplay and coupling of two system exacerbated the nonlinearity.So Magnetic liquid double suspension bearing system was a strong nonlinear system,nonlinear vibration problems will occur during runtime such as static bifurcation and Hopf bifurcation.Therefore,this paper mainly analyzes the mathematical model and parameter's influence on the static bifurcation and Hopf bifurcation.The main research contents of this paper are as follows:(1)First,the initial state mathematical model of Magnetic liquid double suspension bearing system was developed according to the mathematical modeling theory of Maxwell and Navier-Stokes equation.Seconnd,the work state mathematical model was developed based on initial state mathematical model according to the change of oil film thickness,air gap,flux and current.(2)The change rule of static bifurcation was analyzed according to theory of bifurcation and nonlinear mathematical model.Range of parameters for which static bifurcation occurs and the change rule of singular point were determined.The phase track,x-t diagram and basin of attraction of system were obtained by Matlab to confirm the calculation results.(3)The static bifurcation was further studied based on analysis of previous section.The change rule of the static bifurcation,range of parameters for which static bifurcation occurs and change rule of singular point when two parameters change at the same time were determined.The phase track,x-t diagram and basin of attraction of system were obtained by Matlab to confirm the calculation results.(4)Based on the nonlinear mathematical model,the Hopf bifurcation was analyzed according to the Hopf bifurcation theory,and the range of parameters for which Hopf bifurcation occurs was obtained.The phase track and x-t diagram of system were obtained by Matlab to confirm the calculation results.