Magnetic Field Model for Permanent Magnet Spherical Motor With Double Polyhedron Structure

This paper presents an analytical method for calculating the magnetic field for a permanent magnet spherical motor (PMSM) with double polyhedron structure. For the PMSM, stator coils and cylindrical permanent magnet (PM) poles locate at the fixed point of octahedron and hexahedron, respectively, and provide the uniform magnetic field. To analyze the magnetic field in the spherical coordinate, the cylindrical PM pole is approximated as a dihedral cone pole using geometrical equivalence principle. Moreover, considering the characteristics of hexahedron structure, a virtual equatorial layer is emphasized, and the corresponding periodic boundary condition can be built for solving the Laplace equation related to the virtual equator. Then, the Tait-Bryan rotation transformation is applied three times; thereby the overall magnetic field of the PM poles is obtained by the superposition principle. Both simulations and experiments are conducted to demonstrate the effectiveness of the proposed method. The results indicate that the analytical modeling can represent the magnetic field of the PMSM with a high precision.