A Novel Design Method for the Geometric Shapes of Flux Modulation Poles in the Surface-Mounted Permanent Magnet Vernier Machines

This paper presents a novel approach to determine geometric shapes of flux modulation poles (FMPs) by using the analytical equations for flux density distribution due to armature windings. The magnetic field by the windings is modulated by the FMPs. Then, the resulting magnetic field produces the torque by interacting with the rotor permanent magnets (PMs). Thus, to improve the output power of the machine, the FMP shape should be optimized in terms of the magnetic flux modulation. To do so, the permeance function which can consider the changes of the geometric parameters for the FMPs is defined using the Fourier series analysis method. Consequently, the working harmonic, which is the spatial harmonic of the air-gap magnetic field due to the windings and creates the torque, is given as the function of the geometric variables. The optimal set of design variables to maximize the working harmonic in the analytical equation is obtained by employing the genetic algorithm. The finite element analysis results show that the proposed method improves the output torque of the surface-mounted permanent magnet vernier (SPMV) machines up to 31%. In addition, the torque ripple can be minimized by regulating the harmonic components of the permeance in the analytical equations