2-D Exact Analytical Method for Steady-State Heat Transfer Prediction in Rotating Electrical Machines

Abstract

Actually, the heat transfer prediction and temperature distribution in electrical machines are realized by using the finite-element method (Fem) and/or thermal equivalent circuit. The analytical resolution of partial differential equations representing the temperature distribution in electrical machines does not exist. In this paper, a 2-D exact analytical calculation of steady-state temperature distribution in rotating electrical machines by solving the heat equation in homogenous and nonhomogenous regions by using Fourier’s series and the separation of variables method is presented. It is based on the new subdomain technique where the solution depends on both directions ( $r$ , $\theta $ ) and able to model different materials of the machine with different thermal conductivities. The heat sources are volumique power losses due to hysteresis, eddy-current, and Joule losses in all the regions of machine. A simplified method is used to determine the power losses in permanent-magnet motors. The main studied problem is conductive with conductive interface conditions, although convective heat transfer in the air gap is also investigated. The boundary conditions considered for solving the conduction problem is a convective heat transfer between the machine and external air and at the rotor internal air. The semi-analytical results are in very good agreement with those obtained by Fem, considering both amplitude and waveform.