Analysis and minimization of detent end force in linear permanent magnet synchronous machines

In this paper, the end forces caused by the longitude end effects in linear permanent magnet synchronous machines (LPMSMs) are analyzed and minimized. First, the left/right-end forces are calculated based on an analytical model and the Maxwell stress tensor, in which the optimal integration surfaces are investigated. Then, based on the spectrum analysis of the left/right-end forces, two different methods are adopted to minimize the fundamental and high-order harmonics, respectively. The optimal length of the primary iron is obtained from the phase difference of the fundamental and a two-step iteration instead of the trial-and-error with the finite element method. Furthermore, step-skewed auxiliary irons are added to the primary end to eliminate the high-order harmonics. Third, to reduce the secondary end effect when the primary moves to the secondary end, a compensation method of adding mirror permanent magnet is proposed and good results are obtained. Finally, an LPMSM prototype is manufactured and experiments are conducted. The experimental results verify the theoretical study.