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In order to determine the currents required in different attitudes and torque target conditions, this paper proposes a calculation method for drive currents of permanent magnet spherical motors based on three-dimensional magnetic field, torque analytical model and optimization algorithm. Firstly, an electromagnetic torque analytical model base on equivalent surface currents of a permanent magnet and Lorentz force is proposed. The feasibility and accuracy are verified by comparing results with those by the finite element method. Then, an inverse calculation model of the motor drive current is built by combining the torque analytical model with the Particle Swarm Optimization (PSO) algorithm. At last, using the proposed drive current calculation model, the driving current characteristics of spherical motors under different energization strategies are compared and analyzed. INDEX TERMS Permanent magnet spherical motor, analytical model, electromagnetic torque, drive current, particle swarm optimization.

The magnetic field and torque of permanent-magnetic spherical motor (PMSpM) are difficult to analyze due to the complicated structure, and therefore are often analyzed by the finite-element method (FEM) or Lorentz force method, with large amount of calculation and time consumption. This paper first establishes a three-dimensional (3-D) magnetic field analytical model of a spherical motor with permanent magnets (PMs) by the equivalent surface current method. Secondly, through the Lorentz force spatial integration of energized stator coil, a torque analytical model is established. Thirdly, in order to avoid repeated integration operation, a torque interpolation model based on torque Map is established. Both magnetic field and torque analytical models are verified by comparing with FEM and the experiment respectively. It is shown that the method proposed not only ensures the modeling accuracy but also significantly speeds up the analysis.

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