Numerical Verification of Amplitude Reduction of a Rotor Supported by a Superconducting Magnetic Bearing Utilizing Internal Resonance

Superconducting magnetic bearings (SMBs) have some advantages compared with mechanical bearings. However, whirling amplitude of a rotor supported by SMB tends to be large near the critical rotational speed because of their low damping. Furthermore, complicated phenomena of dynamics can be generated due to nonlinearity of the levitation force. Therefore it is necessary to reduce the amplitude by considering the effect of the nonlinearity on dynamics during passing through the critical speed in applications. In this paper, we investigated resonant amplitude reduction of a rotor supported by two movable superconducting bulks (SCs). For this purpose, we first introduced an analytical model consisting of a rotating permanent magnet and the unfixed SCs that can move around the rotor and are connected with springs. We evaluated electromagnetic force by the advanced mirror image method and derived governing equations of the rotor at an arbitrary rotational speed. From the nondimensionalized equations of motion, we predicted that internal resonance between whirling of the rotor and swinging of the SCs can occur if the ratio among the natural frequencies of those motions is an integer ratio. We also performed numerical calculation of equations of motion. The numerical results show that internal resonance can occur at around the critical speed and that as a result reduction of the resonant whirling amplitude can be achieved by the swinging SCs at around the critical speed.