Effects of Flux Modulation Poles on the Radial Magnetic Forces in Surface-Mounted Permanent-Magnet Vernier Machines

This paper investigates the characteristics of the radial force density according to the shapes of the flux modulation poles (FMP) in a surface-mounted vernier machine (SPMVM). The air-gap flux density harmonics obtained from the finite-element analysis method are analyzed using the analytical equations derived from the magnetomotive force and the air-gap permeance distributions. Then, in order to find the radial force density harmonics that generate the exciting force on the stator, the spatial orders and the angular frequencies of the radial force density harmonics are calculated by using the Maxwell stress tensor method. The analysis results show that the permeance harmonics generate the radial force density harmonics, but the resulting harmonics of the radial force density are time-invariant in the spatial domain. Consequently, the variation of the FMP shape can improve the torque characteristics of the SPMVM without the increase of the exciting force on the stator core.

I. Introduction

Recently, a surface-mounted permanent-magnet vernier machine (SPMVM) has been gaining more attention due to the features of high torque density and low torque ripple. In the SPMVM, the lower spatial harmonic of the armature magnetic field is modulated into the higher spatial harmonic by flux modulation poles (FMPs), which are formed on the stator [1]. Then, the resulting higher spatial harmonic produces the torque by synchronizing with the rotor PM magnetic field of the same spatial order. Thus, many researchers of the SPMSM have focused on improving the torque density based on the magnetic-field modulation.