Cogging Force Analysis of Linear Permanent Magnet Machines Using a Hybrid Analytical Model

The aim of this paper is, first, to extend the application of the hybrid analytical modeling (HAM) approach for the analysis of tubular linear machines (TLPM), something that has never been reported yet in the scientific literature. The HAM consists of a strong coupling between the reluctance network and the Fourier series solution of magnetic scalar potential. In order to assess the merits and capabilities of the HAM, it is applied to the study of the cogging force in linear machines and compared with finite element analyses (FEA). The cogging force is a global quantity, which is very sensitive to magnetic field computation accuracy and constitutes, therefore, a good measure of the accuracy of the HAM as compared with FEA. The HAM should require less computation time as compared with FEA, and is then more suitable for predesign stage. Three different structures are analyzed: a flat linear machine, a TLPM with internal mobile armature, and, finally, a TLPM with external mobile armature. The analyses are conducted, considering the effect of magnetic saturation.