Hybrid analytical model for air‐gap magnetic field prediction of surface‐mounted permanent magnet motors with a quasi‐regular polygon rotor

In this article, a hybrid analytical model for a quasi-regular polygon rotor (QPR) is proposed. It mainly uses the subdomain method and conformal mapping to solve a non-circular boundary in the QPR. Firstly, the subdomain method combined with an equivalent surface current method is used to calculate the air-gap magnetic field considering a slotted stator with a circular rotor. Secondly, by segmenting the non-circular boundary in the QPR, the complex relative air-gap permeance of the QPR can be calculated using the conformal mapping. Thirdly, this complex relative air-gap permeance modifies the air-gap magnetic field calculated in the first step to obtain the actual magnetic field distributions. Consequently, no-load and loaded air-gap flux densities, back-electromotive force and torque can be obtained. A 12-pole/3-phase permanent magnet motor is modelled using the proposed hybrid analytical model, which is validated by finite-element analysis and experiment. This proposed hybrid analytical model presents a new way of processing the QPR. Its calculation speed is nearly 50 times faster than the finite-element analysis, which is of great help to the initial design and optimisation of machines with QPRs.