Magnetic field intensity in Halbach trapezoidal magnet array of magnetically levitated planar actuators

Abstract

The effects of magnetic steel shapes on air-gap magnetic flux density in Halbach magnet array of magnetically levitated planar actuators were investigated. After rectangular magnetic steel was replaced by trapezoidal magnetic steel, we deduced the magnetic flux density in Halbach rectangular magnet array using Fourier series and magnetic scalar potential. The analytical expressions of magnetic flux density in trapezoidal magnet array were obtained using the principle of superposition and the infinitesimal analysis of magnetic steel. The higher harmonic error (root-mean-square) and the relation of each harmonic peak to the ratio of length-to-polar distance at y-direction magnetised steel were investigated in Halbach trapezoidal magnet array. After the structural parameters were optimised, we analysed the effects of rolling angle of trapezoid on the y-direction magnetic field intensity, and found out the optimal rolling angle. The structural analysis shows that the trapezoidal magnetic steel can change the air-gap magnetic flux density in a very large space.