Design Considerations of a Permanent Magnetic Spherical Motor Using Spherical Harmonics

A design consideration of a permanent magnet spherical motor (PMSM) is presented based on spherical harmonic (SH) analysis. By analogy with fractional-slot rotary machines, the PMSM with eight electromagnets/six permanent magnets (PMs) (per layer) dual-winding structure is chosen to improve control flexibility and fault tolerance ability that has triple-layer concentrated windings and double-layer PM poles. A reference current equation is presented and an excited rotary/tilted magnetic field (MF) in space is proved via finite-element analysis (FEA), least square method, and SH theory. The spatial phase of the main harmonic component is shown to link directly with the current phase angle and amplitude ratio. Then, the harmonic distribution of several coil design schemes are compared to obtain the desirable geometric parameters, and the design principles of the layers angle are also derived. In addition, the analytical expression of the rotor MF is deduced. The coverage latitude of the dihedral PMs is determined according to the MF distribution and its influence on torque amplitude. Finally, experimental results are compared with FEA to validate the performance of rotor MF and back EMF.