A comprehensive analytical subdomain model and its field solutions for surface-mounted permanent magnet machines

This paper presents a comprehensive analytical subdomain model together with its field solutions for predicting the magnetic field distributions in surface-mounted permanent magnet (PM) machines. The tooth tips and slotting effects during open-circuit, armature reaction, and on-load conditions are considered when deriving the model and developing its solutions. The model derivations and field solutions are extended from a previous model, and can be applied to PM machines with any combinations of slot and pole numbers and any magnetization patterns in the magnets. This model is initially formulated according to Laplace\u27s and Poisson\u27s equations in 2-D polar coordinates by the separation of variables technique in four subdomains, such as magnet, airgap, winding slots, and slot-openings. The field solution of each subdomain is obtained applying the appropriate boundary conditions and interface conditions between every two subdomains, respectively, which can precisely account for the mutual influence between slots. Finite element analysis (FEA) is later deployed to validate the analytical results in a surface-mounted PM machine that has nonoverlapping winding arrangement. For validation purposes, PM machines having 3-slot/2-pole with parallel magnetization and 12-slot/10-pole with either parallel or radial magnetizations are used for comparisons. Computation of global quantities for the motor which include the phase back-EMF and cogging torque is also included. The results indicate that the proposed analytical model can accurately predict the magnetic field distributions in each subdomain and the motor\u27s global quantities, which are in good agreement with those obtained from the FEA