Analytical Model of Slotless Brushless PM Linear Motors Considering Different Magnetization Patterns

This paper presents a two-dimensional (2-D) analytical model for plannar linear permanent-magnet (PM) synchronous motors. The general and particular solutions are presented for a slotless single-sided linear PM synchronous motor as a case study. The governing partial differential equations of the motor are formulated for seven regions: Mover side exterior, mover back iron, PMs, air-gap, winding, stator back-iron, and stator-side exterior. Four different magnetization patterns, i.e., parallel, ideal Halbach, 2-segment Halbach, and bar magnets in shifting directions magnetization patterns are considered to calculate the tangential and normal components of the open-circuit magnetic flux density and armature reaction of the motor under the study. The winding-induced voltage, flux linkage, self- and mutual inductances, and normal and tangential components of forces are computed. The validity of the proposed technique is confirmed by comparing the analytical results with the results obtained from a 2-D finite-element analysis.