Two-Dimensional Steady-State Thermal Analytical Model of Dual-PM Consequent-Pole Magnetically Geared Machine Based on Harmonic Modeling

This paper presents a mathematical approach for analyzing the thermal behavior of a dual-permanent-magnet consequent-pole magnetically geared machine. The analytical method, referred to as harmonic modeling, employs a complex Fourier series and the Cauchy product to obtain solutions to the partial differential equations governing the temperature distribution in electrical machines. Unlike lumped-parameter thermal networks that provide only average quantities, the proposed approach enables the prediction of spatial temperature distributions. The machine is further investigated under various operating conditions, including different convection coefficients and loss levels. An 11-pole, 18-slot prototype was evaluated by comparison with finite element method (FEM) simulations. The results demonstrate that the proposed method agreed well with the FEM results, with errors below 10%, while requiring less than 2 s per calculation compared with approximately 20 s for FEM simulations.