Magnetic Field Analysis of 3-DOF Permanent Magnetic Spherical Motor Using Magnetic Equivalent Circuit Method

The paper studies the magnetic field distribution of three degree-of-freedom (3-DOF) permanent magnet (PM) spherical motor adopting the 3-D magnetic equivalent circuits (MEC) method. Compared with the analytical method and finite element analysis (FEA) method, the MEC has such desirable attributes as moderate computational effort and reasonable accuracy. The model of PM spherical motor is evenly meshed into elements in spherical coordinates, and the expressions of reluctances and magnetomotive force (MMF) sources in the element have been deduced. Given that magnetic field of the PM spherical motor distributes in the whole space, to reduce the number of elements and increase the solving speed, an approximate equipotential surface is adopted based on the simplified magnetic circuit, and the different magnetic boundary conditions are represented by the corresponding states of nodes and branches of the elements. Finally, the MEC network, which represents half of the magnetic pole and the corresponding air region of the motor, is built. Flux density distribution is calculated by means of the proposed model and verified by the FEA method.