Abstract
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 P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> air-gap magnetomotive force (MMF) harmonic having the same pole-pair of PM, the Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> 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 P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic produces positive torque, while Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic produces negative torque. With the increase of pole ratio, the proportion of Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF 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.
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