Ramakrishnan, K., Romanazzi, P., Zarko, D., Mastinu, G. et al., "Improved Analytical Model of an Outer Rotor Surface Permanent Magnet Machine for Efficiency Calculation with Thermal Effect," SAE Int. J. Alt. Power. 6(1):34-46, 2017, doi:10.4271/2017-01-0185.
In this paper, an improved analytical model accounting for thermal effects in the electromagnetic field solution as well as efficiency map calculation of an outer rotor surface permanent magnet (SPM) machine is described. The study refers in particular to an in-wheel motor designed for automotive electric powertrain. This high torque and low speed application pushes the electric machine close to its thermal boundary, which necessitates estimates of winding and magnet temperatures to update the winding resistance and magnet remanence in the efficiency calculation. An electromagnetic model based on conformal mapping is used to compute the field solution in the air gap. The slotted air-gap geometry is mapped to a simpler slotless shape, where the field solution can be obtained by solving Laplace's equation for scalar potential. The canonical slottless domain solution is mapped back to the original domain and verified with finite element model (FEM) results. Closed form solutions of core loss and magnet loss are derived from the air-gap field solution. The copper loss is calculated by considering the proximity loss and skin effects. In order to estimate the winding and magnet temperatures, a thermal model is built using a lumped parameter thermal network with an improved discretization approach. The model has been validated experimentally using the end-winding and coolant temperatures. The energy consumption calculation with the New European Driving Cycle (NEDC) is performed and the benefit of having the thermal model is quantified in terms of percentage difference in the calculated energy consumptions.