Analytical Model of Permanent Magnet Linear Synchronous Machines Considering End Effect and Slotting Effect

An effective analytical model of permanent magnet linear synchronous machine (PMLSM) is proposed in this paper, which considers the end effect by adding virtual slots and the slotting effect by adopting relative air-gap permeance. To employ this model, the open-circuit air-gap flux density of a slotless PMLSM with virtual slots is firstly predicted by Subdomain (SD) method, and then the complex relative air-gap permeance is introduced based on conformal mapping. By multiplying these two quantities, the open-circuit air-gap flux density of actual slotted PMLSM can be obtained. The phase flux linkage, back-EMF and detent force can be predicted accordingly. Moreover, the detent force is more easily depressed by optimizing the end teeth and slots via the proposed method. The predicted results are validated by 2-D nonlinear finite-element (FE) and prototype measurements.