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This paper presents a 2D analytical model for predicting the magnetic flux density distribution in slotless permanent-magnet (PM) linear tubular (PMLT) motors due to armature reaction effects based on the sub-domain method. According to this method, the machine cross-section is divided into the six sub-regions and Maxwell partial differential equations (PDEs) are formed in each sub-region. Solving these PDEs leads to defining the magnetic vector potential in each sub-region and applying curl on the calculated magnetic vector potential results in determining the magnetic flux density components. Eventually, the extracted results are compared with those of the finite-element method (FEM) to confirm the accuracy of the described analytical model. The results reveal that the presented analytical model is a suitable candidate for predicting the magnetic flux density components of the slotless PMLT motors in a shorter time.

2D Analytical Model of Armature Reaction Magnetic Field Distribution in Slotless Permanent-Magnet Linear Tubular Machines