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.