Subharmonic Resonance Due to Gap Between Geometric and Magnetic Centers of Rotor Supported by Superconducting Magnetic Bearing

Abstract

Superconducting magnetic bearings (SMBs) have various merits because of stable levitation without physical contact. However, the system's low damping causes vibration with a large amplitude near the critical rotational speed, and the nonlinearity of the electromagnetic force causes complicated vibrations. Moreover, if magnetization distribution of a rotor is not uniform, the rotor's dynamical behavior can be more complicated because a superconducting bulk in a superconductive state traps the nonuniform magnetic field, which has significant influence on restoring force acting on the rotor. Therefore, it is necessary to consider influence of magnetic unbalance of the rotor on the whirling of a rotor supported by a SMB. This paper deals with nonlinear dynamics of a rotor, which has a gap between the geometric and magnetic centers of the rotor and which is supported by a SMB. We derived the equations of motion of the rotor and discussed whether subharmonic resonances of order 1/2 and order 1/3 occur by considering nonlinear terms of the electromagnetic force. By numerical calculation based on the Rung-Kutta method, we clarified that subharmonic resonances of order 1/2 can occur without disturbance, whereas subharmonic resonances of order 1/3 can occur only with disturbance. Moreover, we performed nonlinear analysis by means of the harmonic balance method. We also carried out experiments, which verified the analytical and numerical predictions of occurrence of subharmonic resonances.