Analysis and Minimization Design of Force Ripples Cased by Higher Harmonics in Ironless Permanent Magnet Planar Motors

Abstract

Ironless permanent magnet planar motors have significant potential for accurate positioning systems. The higher harmonics of the magnetic flux density distribution, which is ignored in the analytical model for real-time control, is usually one of the main reasons for the force ripples of the ironless permanent magnet planar motors. The force ripples cased by the higher harmonics is analyzed and minimized in this paper. An analytical model of the force ripples cased by the higher harmonics is developed first. Then it can be derived from the analytical model that the force ripples cased by some higher harmonics can cancel each other when the length of the coil is an even multiple of the pole pitch of the magnet array. Furthermore, the winding factors of the ironless permanent magnet planar motors are also derived and can be used to eliminate dominating components of the force ripples cased by the left higher harmonics. As a result, the force ripples cased by the higher harmonics can be basically eliminated with a selected coil length and winding factors. Finally, it is validated by comparison of the planar motors with finite element (FE) analysis that most of force ripples cased by higher harmonics can cancel each other when the length of the coil is an even multiple of the pole pitch of the magnet array.