Analytical 2-D Model of Slotted Brushless Machines With Cubic Spoke-Type Permanent Magnets

Brushless machines with interior permanent magnets (PMs) are mostly made with PM geometries inconsistent with the polar coordinates of the rotor cross section. Therefore, without any subdomain transformation, the analytical approaches cannot precisely model the interior PM machines in a single coordinate. This paper presents an accurate two-dimensional (2-D) analytical model for electromagnetic analysis of slotted brushless machines with rectangular spokePMs assisted by hub magnets. The slotting effect is modeled via subdomain technique. However, the spoke PM is not consistent enough with polar coordinates to be approximated by one subdomain. In order to map the spoke PMs in polar coordinates, herein, the rectangular geometry is approximated by a combination of arc shaped subdomains. On this basis, the 2-D analytic model is developed for M-fraction spoke PM. To verify the accuracy of the proposed 2-D approach, analytic results are compared with numeric results of finite elements method. It is revealed that by dividing the spoke PM into arc subdomains, the 2-D model achieves higher accuracy in calculation of electromagnetic quantities such as PM and armature reaction fields, electromagnetic torque, and back electromotive force.