Two-dimensional steady-state thermal analytical model of permanent magnet linear motor in Cartesian coordinates

Compared with the time-consuming numerical method and the complex lumped parameter thermal network method to solve the steady-state heat distribution of the permanent magnet (PM) linear motor, there is no analytical method based on the thermal partial differential equations. This paper aims to propose a two-dimensional (2-D) analytical model for predicting the steady-state temperature distribution of PM linear motors to improve the prediction accuracy and speed up the calculation.

Based on the complex Fourier series theory and Cauchy’s product theorem, this paper presents for the first time a general analytical solution for 2-D temperature field in Cartesian coordinates. Then, by combining the electromagnetic field finite element model (FEM), the copper loss, iron loss and PM eddy current loss are used as the heat sources of the thermal analytical model. Finally, the solution to the temperature field is obtained by solving the system equations under boundary and interface conditions.

The analytical results are in good agreement with those from the thermal FEM, and the calculation speed is significantly faster than that of the thermal FEM.

The multilayer model proposed in this paper can consider heat conduction, convection and radiation. It is not only suitable for PM linear motors but also has significant application value for the thermal analysis of electromagnetic devices modeled in 2-D Cartesian coordinates.