Combination Resonance of a Rotor Supported by a High-T_c Superconducting Bearing

This research deals with nonlinear dynamics of a rotating rigid magnet levitated above a high T_c superconducting (HTSC) bulk. Motion of the rotating magnet in the radial and axial directions were investigated theoretically by using analytical expression of electromagnetic force obtained by “the advanced mirror image method”. Analytical and numerical results show existence of combination resonance due to nonlinear coupling between whirling and vertical motion of the magnet. The resonant frequency of rotation is given as the sum of the natural frequency in the horizontal and vertical directions. At this resonance, the whirling motion becomes quasi-periodic, having the harmonics with both the driving and natural frequencies, while periodic motion at the natural frequency appears in the vertical direction. Stability analysis shows that this resonance occurs if the eccentricity of the magnet is larger than a certain critical value. Experiments for spinning motion of the magnet were carried out, and combination resonance predicted in the theory was clearly observed. Nonlinearity in forces can thus have significant effects on dynamics in application of HTSC bearings.