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A multi-objective optimal design of a brushless DC electric motor for a brake system application is presented. Fifteen design variables are considered for the definition of the stator and rotor geometry, pole pieces and permanent magnets included. Target performance indices (peak torque, efficiency, rotor mass and inertia) are defined together with design constraints that refer to components stress levels and temperature thresholds, not to be surpassed after heavy duty cycles. The mathematical models used for optimization refer to electromagnetic field and related currents computation, to thermo-fluid dynamic simulation, to local stress and vibration assessment. An Artificial Neural Network model, trained with an iterative procedure, is employed for global approximation purposes. This allows to reduce the number of simulation runs needed to find the optimal configurations. Some of the Pareto-optimal solutions resulting from the optimal design process are analysed.

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.