A Thrust Force Analysis Method for Permanent Magnet Linear Motor Using Schwarz–Christoffel Mapping and Considering Slotting Effect, End Effect, and Magnet Shape

A Schwarz-Christoffel (SC) mapping-based method is presented for accurately and efficiently predicting the thrust force of permanent magnet linear motors (PMLMs). It accounts for not only the slotting effect but also the end effect and the magnet shape. In this method, according to the magnet shape, the PMs are modeled as equivalent line currents on their surfaces. Through analyzing the invariant of the governing Poissonian field equation of line currents under a conformal mapping, the magnetic field boundary value problem in the air gap is mapped to a rectangle by the SC mapping, which is calculated with the SC Toolbox of MATLAB. Furthermore, the magnetic field solution is constructed with the line currents in a strip under the flux continuity condition. The cogging force due to the slotting effect and the end effect is obtained, respectively, by integrating the Maxwell stress tensor along the lines closely surrounding the slotted and finite-length iron core. The validity of the proposed method is examined by the finite-element method. The influences of the magnet shape on the thrust force pulsation characteristic are investigated for a PMLM equipped with rectangular PM and bread loaf PM.