Analytical Calculation of the Magnetic Field Distribution in a Linear and Rotary Machine with an Orthogonally Arrayed Permanent Magnet

In this paper, an analytical model is proposed to analyze and predict the characteristics of a double stator linear and rotary permanent magnet machine (DSLRPMM). In order to simplify the magnetic field calculation, the DSLRPMM is cut along the axial direction (z direction) and transferred into a planar one. Hence, an analytical model of the machine considered the orthogonal effect (OE) is proposed based on the combined solution of Maxwell’s equation, conformal mapping, and equivalent magnetic circuit model (EMCM). The magnetic field distributions of the DSLRPMM are calculated with and without considering the OE, and some important electromagnetic parameters, including the back electromotive force (EMF), detent force, cogging torque, and output torque and thrust, are also predicted and compared to the 3D finite element analysis (FEA). The results show that the errors between the proposed analytical model and the 3D FEA results are less than 0.2% and even less than 0.1% for certain parameters, that is, the results obtained from the proposed analytical model agree well with that of the FEA. Moreover, the analyzed and predicted results are also verified by the experimental results on the prototype of the DSLRPMM.