Deflection Magnetic Field Analysis and Deflection Torque Calculation of a Hybrid Excitation Multi-Degree of Freedom Spherical Motor

In order to solve the problems of small torque, large torque fluctuation and small motion range in the deflection motion part of the existing multi-degree-of-freedom motor, a hybrid excitation multi-degree of freedom spherical motor was proposed. After introducing the basic structure and operation principle of the motor, this paper proposed a magnetic field analysis method based on multi-node Schwarz-Christoffel (S-C) transform to solve the problem of slow speed in the magnetic field calculation of the motor when using the three-dimensional (3D) finite element method. This method uses discrete line currents to be equivalent to the permanent magnets and windings of the motor, and converts the complex air gap region into the torus region through multi-node S-C transform and exponential transform, respectively. And it uses the analytical solution of the scalar position in the torus region to calculate the magnetic field information in the current region of a single line, and calculates the overall magnetic field information by superposition. Then, the magnetic field information of the original air gap region was calculated by using the conversion relationship of the coordinate points in each region. After calculating the radial magnetic density, the electromagnetic torque of the deflected part was calculated by Ampere's law. In addition, the analytical method and the three-dimensional finite element method were used to model and analyze the magnetic field characteristics and deflection torque characteristics of the motor. Through comparison, it is found that the magnetic field calculation results of the two methods are in good agreement, the maximum errors in amplitude of the analytical method relative to the finite element method are 7.3% and 3.92%, respectively, which verifies the accuracy of the analytical method. In order to further verify its validity, a prototype and an experimental platform were developed to test the static deflection torque of the motor. The results show that the motor has a high deflection torque, and the maximum deflection torque is 2.13 N·m. The errors between the experimental results and the calculation results of the finite element method and the analytical method are 22.62% and 20.13%, respectively, which verifies the effectiveness of the analytical method modeling.