Analysis of thrust ripple harmonics on different electric loadings in PM linear synchronous machines with skewed PMs

Permanent magnet linear synchronous machines (PMLSMs) have large thrust ripple due to the longitudinal end effect caused by the finite length of the armature compared with rotary machines. The purpose of this paper is to analyze the influence of electric loading on thrust ripple performances based on a 12 slots/14 poles (12S/14P) PMLSM. Furthermore, the method of skewed PMs to reduce thrust ripple is investigated based on multi slices 2D finite element (FE) models.

The thrust ripple of PMLSM under open-circuit condition results from the slotting and the longitudinal end effects. Therefore, periodical model has been designed to clarify the effect of the longitudinal end effect. Under on-load condition, the thrust ripple increases and exhibits an effective component of thrust force. To analyze the thrust ripple under on-load condition, frozen permeability (FP) technique is employed. In addition, the method of skewed PMs is analyzed in this paper to obtain more smooth thrust force performance. The effectiveness of skewing accounting for skew angles, step skew numbers and slot/pole number combinations was highlighted.

The longitudinal end effect dominates the thrust ripple of PMLSM in both cases, i.e., open-circuit and on-load conditions. Under on-load condition, the second harmonic component of thrust ripple related to flux linkage harmonics increases significantly. Moreover, the effectiveness of skewed PMs is largely reduced with the increase of magnetic saturation. At last, a proper skew angle and step skew number are obtained for the conventional PMLSM with fractional-slot winding.

By 60 electrical degrees and two or three step skewed PMs, the thrust ripple can be decreased to a tolerable limite for conventional PMLSM. The thrust ripple harmonics contributed by longitudinal end effect and flux linkage harmonics are analyzed, respectively, which is beneficial to exploring other techniques such as adding end auxiliary teeth to obtain lower thrust force pulsation.