To reveal the nonlinear instability mechanism by which the three-degree-of-freedom rotor system of a magnetic-liquid double suspension bearing transforms from stable suspension to periodic vibration, a nonlinear dynamic model considering electromagnetic suspension force, hydrostatic supporting force, rotor unbalance force, and liquid film resistance is established. The equilibrium point of the system is linearized, and the Hopf bifurcation boundary is determined using the Routh–Hurwitz criterion. Numerical simulations are then carried out to investigate the effects of the initial current i0, supply flow rate q0, and different initial disturbances on the displacement time histories, phase trajectories, and spatial phase trajectories of the rotor. The results show that, under the given system parameters, the Hopf bifurcation boundary is 0.61 A for the initial current and 9.62 × 10−5 m3/s for the supply flow rate. Current variation mainly affects electromagnetic stiffness and nonlinear electromagnetic force, whereas flow rate variation primarily changes the hydrostatic load capacity and oil film damping characteristics. Under different initial disturbances, the system may exhibit amplitude attenuation, recovery to stable suspension, or finite amplitude periodic vibration. Experimental results show good agreement with numerical simulations in terms of frequency spectra, displacement time histories, and phase trajectories, thereby verifying the effectiveness of the proposed three-degree-of-freedom dynamic model and Hopf bifurcation analysis method. The results can provide theoretical guidance for parameter matching, stability evaluation, and self-excited vibration suppression of magnetic-liquid double suspension bearings.
Wang et al. (2026) studied this question.