Modeling and analysis of Halbach magnet array with pyramidal magnet in planar motor

Abstract

In this paper, the changing of magnet shape in Halbach magnet array of planar motor is analyzed for the magnetic flux density. It is the rectangular magnets that are replaced by pyramidal magnets. The magnetic flux density of Halbach magnet array with rectangular magnets is derived by Fourier series and scalar potential. The magnetic flux density of pyramidal magnet array is obtained through superposition and dividing the magnet array in several layers. Then the harmonic model has good agreement with the finite element model (FEM) by comparing the $z$ -component of magnetic flux density. The division layer $p$ is decided by analyzing the amplitude error of $z$ -component of magnetic flux density between harmonic and FEM. The pyramidal magnet array is analyzed from the items such as the waveform, peak value and total harmonic distortion (THD) of $z$ -component of magnetic flux density. Above all, the smaller the rotation angle is, the bigger the peak value of $z$ -component of magnetic flux density will be obtained and the smaller the total harmonic distortion will be simultaneously achieved.