Influence of Controller’s Parameters on Static Bifurcation of Magnetic-Liquid Double Suspension Bearing

Magnetic-Liquid Double Suspension Bearing (MLDSB) is composed of an electromagnetic supporting and a hydrostatic supporting system. Due to greater supporting capacity and static stiffness, it is appropriate for occasions of middle speed, overloading, and frequent starting. Because of the complicated structure of the supporting system, the probability and degree of static bifurcation of MLDSB can be increased by the coupling of hydrostatic force and electromagnetism force, and then the supporting capacity and operation stability are reduced. As the key part of MLDSB, the controller makes an important impact on its supporting capacity, operation stability, and reliability. Firstly, the mathematical model of MLDSB is established in the paper. Secondly, the static bifurcation point of MLDSB is determined, and the influence of parameters of the controller on singular point characteristics is analyzed. Finally, the influence of parameters of the controller on phase trajectories and basin of attraction is analyzed. The result showed that the pitchfork bifurcation will occur as proportional feedback coefficient K p increases, and the static bifurcation point is K p = −60.55. When K p < −60.55, the supporting system only has one stable node (0, 0). When K p > −60.55, the supporting system has one unstable saddle (0, 0) and two stable non-null focuses or nodes. The shape of the basin of attraction changed greatly as K p increases from −60.55 to 30, while the outline of the basin of attraction is basically fixed as K p increases from 30 to 80. Differential feedback coefficient K d has no effect on the static bifurcation of MLDSB. The rotor phase trajectory obtained from theoretical simulation and experimental tests are basically consistent, and the error is due to the leakage and damping effect of the hydrostatic system within the allowable range of the engineering. The research in the paper can provide theoretical reference for static bifurcation analysis of MLDSB.