Optimal Pole Ratio of Spoke-type Permanent Magnet Vernier Machines for Direct-drive Applications

Due to magnetic gearing effects, spoke-type permanent magnet vernier machines (ST-PMVMs) have the merit of high torque density, where an extra torque amplification coefficient, i.e., pole ratio (the pole-pair ratio of PMs to armature windings) is introduced. However, different from surface-mounted PMVM, the variation of torque against pole ratio in ST-PMVMs is non-linear, which is increased at first and then decreased. This article is devoted to identify the optimal pole ratio of ST-PMVMs by equivalent magnetic circuit model. It is found that except the Pr-th air-gap magnetomotive force (MMF) harmonic having the same pole-pair of PM, the Pa(th)air-gap MMF harmonic having the same pole-pair of armature winding is also induced due to the modulation of doubly salient air-gap structure. The Pr-th MMF harmonic produces positive torque, while (PaMMF)-M-th harmonic produces negative torque. With the increase of pole ratio, the proportion of (PaMMF)-M-th harmonic as well as negative torque is increased, which reduces the advantages of high pole ratio coefficient. Further, the influence of dimension parameters on the performance of ST-PMVMs under different pole ratio are investigated. Results show that ST-PMVMs with pole ratio 2.6 have high torque density, low cogging torque and high power factor simultaneously. Finally, a prototype is manufactured to validate the analysis.