Magnetic Field Analysis of Surface-Mounted Permanent Magnet Motors Based on an Improved Conformal Mapping Method

In this article, an improved conformal mapping (ICM) method based on a complex potential function is proposed. It can improve the calculation speed and accuracy of magnetic fields for surface-mounted permanent magnet synchronous motors (SPMSMs). The eccentric-shaped poles are replaced by equivalent currents, and the improved conformal mapping method is adopted to transform an actual slotted motor air gap to an equivalent rectangular regular slotless air gap. The ICM method improves the speed of calculation because its number of mapping times is less than the traditional conformal mapping (TCM) method. By solving the complex potential generated by the equivalent current in the rectangular regular air-gap region, the air-gap magnetic field of the SPMSM under no-load, armature reaction and loaded conditions can be solved. Then, the no-load back-EMF and loaded torque performance under different load conditions are calculated. The accuracy of the ICM method is verified by finite-element simulation. In addition, the fast speed and high accuracy of the proposed ICM method incorporating the complex potential function for solving the air-gap magnetic field has been demonstrated in comparison to the TCM method with the Hague equation. An eccentric-shaped-pole permanent magnet motor prototype is also built and tested in experiment and the results agree with those calculated by the proposed ICM method.