Analytical Model of Magnetic Field of a Permanent Magnet Synchronous Motor With a Trapezoidal Halbach Permanent Magnet Array

This paper presents an analytical model of magnetic field of a permanent magnet synchronous motor (PMSM) with a trapezoidal Halbach permanent magnet array (THPMA). Compared with conventional Halbach array, the shape of each magnet in THPMA is transformed from rectangle to trapezium in polar coordinates. The THPMA is delaminated indefinitely radially and each layer is approximately considered to be a conventional Halbach array. The air-gap magnetic field of each layer is analyzed with the scalar magnetic potential. Then, the air-gap magnetic field of the THPMA is obtained by superposing magnetic fields of all layers. The validity of the analytical model is verified by a finite-element model (FEM). The air-gap flux density is optimized by adjusting the center angle coefficients of the THPMA, and a no-load phase back electromotive force (EMF) with the harmonic distortion rate (THD) of 0.75% is obtained by FEM. The back EMF is basically consistent with the measured result of a prototype motor.