Modeling and analysis of non-circumferential symmetric permanent magnet spherical motor using genetic algorithm-based torque map method

A permanent magnet spherical motor (PMSpM) is a typical multiple-degree-of-freedom apparatus. This paper proposes a torque map-based torque model and its counterpart using a genetic algorithm for the PMSpM with non-circumferential symmetric permanent magnets. The basic structure and operating principle of the PMSpM under study are presented. The analytic model of the 3D magnetic field is researched using the spherical harmonic method. The magnetic field model is verified via finite element method (FEM) analysis and an experiment of radial magnetic flux density. The analytic torque model is formulated using the Lorentz force method. The torque maps are established according to the principle, and the torque map-based torque model originates from the maps. FEM and the experimental results prove the correctness of the torque map-based torque model, and real-time performance of the torque model is also estimated. To solve the coil current calculation difficulty, the genetic algorithm is introduced for establishing the reversal torque model; MATLAB simulation is conducted for the convergence speed of the reversal torque model; and the real-time performance is studied on Qt 5.14/C++ upper software.