Research on Torque Calculation Method of Permanent-Magnet Spherical Motor Based on the Finite-Element Method

In this paper, the finite-element method (FEM) is used to calculate the spinning torque of the permanent-magnet (PM) spherical motor. Three-dimensional (3-D) FE model of the PM spherical motor is established. Spinning torque distribution on the spherical surface and its variation curve on the equator are obtained respectively. In order to avoid the complicated torque calculation process under 3-D magnetic field and thus reduce the computational burden, the torque calculation method based on the 2-D conversion model is proposed. This method equivalently simplifies the magnetic field of the spherical PMs and the shape of cylindrical stator windings to be simulation parameters of the 2-D conversion model. With these parameters, 2-D conversion model of the PM spherical motor is established. Spinning torque variation curves obtained by the 3-D model and the 2-D conversion model respectively are compared and the results agree extremely well. By comparing the maximum static torque (MST) obtained under different configuration parameters of the PM spherical motor, it is found that the errors are within the allowable range. Therefore, the reliability of the proposed torque calculation method in the paper is verified. Finally, based on the 2-D conversion model, variation curves of the MST with the length of the air gap, the ampere turns, the length of stator windings and the outer radius of stator windings are obtained, and they are validated by those based on the 3-D model. These results can provide the basis for the optimization of the PM spherical motor.