Influence of Coil Current and Oil Film Thickness on Hopf Bifurcation of MLDSB

Abstract

Magnetic-liquid double-suspension bearing (MLDSB) is composed of an electromagnetic supporting system and a hydrostatic supporting system. Due to its greater supporting capacity and stiffness, it is appropriate for middle-speed applications, overloading, and frequent starting. However, because it contains two sets of systems, its structure and rotor support system are more complex. It contains strong nonlinear links. When the parameters of the system change, the bearing rotor may feature Hopf bifurcation, resulting in system flutter and reducing the operational stability of the magnetic fluid double-suspension bearing rotor, which has become one of the key problems restricting its development and application. As key parameters of MLDSB, the coil current and oil film thickness exert a major impact on Hopf bifurcation. Therefore, the mathematical model of MLDSB is established in this paper, and the border and direction of Hopf bifurcation, period, and amplitude of limit cycle are analyzed. The calculation, simulation, and experimental results show that when the coil current and oil film thickness of the bearing system are greater than the boundary value of the Hopf bifurcation, Hopf bifurcation will occur, resulting in the vibration of the bearing rotor and affecting the stability of the system. In addition, when analyzing the combined effects of coil current and oil film thickness on the Hopf bifurcation of the system, it was found that the boundary value of Hopf bifurcation in the system is reduced compared with when it is are affected solely due to the coupling of the two parameters. The period, amplitude and vibration speed of limit cycle increase with increases in the coil current and oil film thickness. Hopf bifurcation experiment was conducted on MLDSB testing system. The results show that Hopf bifurcation does not occur when i0 < 0.5 A, the bearing rotor operates stably in the balanced position, i0 > 1.0 A, Hopf bifurcation occurs in the system, and the bearing rotor vibrates with equal amplitude, which reduces the stability of operation. The research in this paper can provide a theoretical reference for the Hopf bifurcation analysis of MLDSB.