This study presents an analytical model for calculating the armature reaction magnetic field of outer rotor permanent magnet brushless DC motor (PMBLDCM) in stator stationary coordinate system (SSCS) and rotor rotation coordinate system (RRCS). Firstly, an expression of armature reaction magnetic field of single-phase winding is deduced, without considering slotting effect. Afterwards, analytical expressions of armature reaction magnetic field in both SSCS and RRCS regardless of slotting effect are obtained using vector addition method. Then complex relative permeances of outer rotor BLPMDCM in SSCS and RRCS are analysed, respectively. Finally, analytical solutions of the armature reaction magnetic field in both SSCS and RRCS are derived, respectively, by multiplying the slotless armature reaction magnetic field and the complex relative magnetic permeance, the self-and mutual inductance are calculated by the armature reaction magnetic field. A 46-ploes-51-slots outer rotor BLPMDCM is set as an example, the accuracy of proposed analytical model is verified by the Finite Element Method. Based on this analytical model, the pattern of slotting effect on armature reaction of both outer rotor and internal stator are analysed, respectively, as well as spatial order characteristics and frequency characteristics of armature reaction for outer rotor PMBLDCM in SSCS and in RRCS.

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As it has been widely and wrongly believed that noises at any frequency of permanent magnet synchronous motor (PMSM) are positively correlated with subjective annoyance, reducing sound pressure level or sound power level of PMSM is mostly regarded as the only optimisation goal of sound quality (SQ). This study presents a sensitive critical band (SCB) diagnostic method for SQ of PMSM for electric vehicles (EV). First, a new acquisition method of near-field noises without sound attenuation of PMSM was proposed and a neural network model for SQ evaluation was established to determine the specific operating condition with the worst SQ. Second, the band-pass filter of CB (BPFCB) and band-stop filter of CB (BSFCB) were designed to diagnose positive SCBs or negative SCBs in which noises were positively or negatively correlated with the subjective annoyance, respectively. Finally, the major excitation sources of abnormal noises in SCBs were diagnosed by using the analytical calculation. An 8-pole-48-slot PMSM was considered as a case study to testify to the effectiveness and practicability of the proposed method. It may provide a new route for the precise SQ optimisation of PMSM.

A 3-D analytical model of armature reaction field (ARF) of interior permanent magnet synchronous motor (IPMSM) with multi-segmented skewed poles (MSP) and multi-layered flat wire winding (MFWW) considering current harmonics is proposed in this paper. Firstly, based on the MFWW distribution analysis and the coil magnetic field vector superposition method, the ideal ARF functions of the MFWW considering low-order current harmonics and high-order sideband current harmonics are derived. Secondly, 3-D relative permeance functions caused by the stator slotting effect and the multi-segmented rotor magnetic barriers are presented. Thirdly, 3-D analytical expressions of ARF are obtained by multiplying the ideal ARF functions and the 3-D relative permeance functions. Additionally, the effects of low-order current harmonics, high order sideband current harmonics, MSP, and stator slotting on the spatial orders and frequencies of ARF are analyzed. Finally, the proposed model is verified by finite element method (FEM) and experiment.INDEX TERMS Analytical model, armature reaction field, current harmonic, interior permanent magnet synchronous motor.