Analysis of Back EMF Harmonics Influenced by Slot–Pole Combinations in Permanent Magnet Vernier In-Wheel Motors

In this article, we analyze the back electromotive force (EMF) harmonic characteristics influenced by the slot–pole combinations in permanent magnet vernier motors for in-wheel drive applications. First, the feasible matches among the slot–pole combinations, stator tooth types, as well as winding topologies are given. Second, the expressions of fundamental and harmonic back EMF are then derived, where the equivalent winding factor considering the air-gap permeance harmonics is introduced to evaluate the back EMF fundamental amplitude. Next, the contribution of each air-gap magnetic-field harmonic on the back EMF harmonic is investigated, which has proven that the air-gap odd-order ineffective magnetic-field harmonics are responsible for unexpected back EMF harmonics. Based on this, the feasible principle of the number of permanent magnet (PM) poles, armature poles, and flux modulation poles aiming at the low ineffective back EMF harmonics is established. Finally, extensive finite-element analysis (FEA) is conducted, and two prototypes are manufactured and tested, where the experimental results have good agreement with the FEA and theoretical results.