Influences of Winding MMF Harmonics on Torque Characteristics in Surface-Mounted Permanent Magnet Vernier Machines

This paper presents the influences of winding magneto-motive force (MMF) harmonics on the torque characteristics in surface-mounted permanent magnet vernier (SPMV) machines. Based on the magnetic gearing effects, the armature magnetic field of the SPMV machines is modulated by flux modulation poles (FMPs). In the modulated magnetic field, a working harmonic which corresponds to the number of the rotor pole pairs generates torque. Unlike regular PM machines, the winding MMF harmonics in the SPMV machines can produce the working harmonic by adjusting the FMP shapes. In order to investigate the effects of the winding MMF harmonics, the operating principle of the SPMV machines is elaborated by an analytical method using the winding MMF distribution and air-gap permeance function. After that, the design method of the FMP shapes that can improve the output torque by using the winding MMF harmonics is proposed. For the SPMV machine having 6 slots and 24 FMPs, the effects of the winding MMF harmonics and the validity of the proposed design method are confirmed by the finite element analysis method. It is shown that the proposed design method can improve the performances of the SPMV machine in terms of the torque density, induced electromagnetic force, and efficiency