Analysis of Zero Stiffness Permanent Magnet Bearing Including Reluctance Effect

Abstract

The isolation bandwidth of zero stiffness permanent magnet bearing (ZSPMB) is limited by the stiffness variation near the zero stiffness point. This paper proposes an accurate and effective modeling technique to analyze and optimize the stiffness of ZSPMB in working range. Since the stiffness of ZSPMB is very sensitive to modeling errors, the variable current model of the permanent magnet is first derived considering magnetic permeability, the influences of which on the magnetic field and force are attributed to the reluctance effect in this paper. Then, the force exerted between permanent magnets (PMs) is equivalently decomposed into Lorentz force and reluctance force. Based on the Biot–Savart law and elliptic integral, the magnetic field of rings with axial, radial magnetizations and the equivalent Lorentz force (ELF) of typical ZSPMB topologies are calculated analytically. The equivalent reluctance force (ERF) is subsequently obtained by combining the finite element method. Compared with the ELF, the ERF is about one order of magnitude smaller and in the opposite direction and it causes the stiffness-displacement curve to drift and deflect. Finally, a Halbach ZSPMB is optimized with the ELF model, and then the ERF is suppressed by fine-tuning the structural size. The finite element analysis results show that the stiffness variation in the working range is effectively reduced, and the validity of the proposed hybrid analytical-finite element model modeling technique is verified.