Topology optimization with arbitrarily many materials: density versus level-set applied to a hybrid excited rotor

This work addresses the topology optimization of a rotor pole of a hybrid-flux machine with gradient methods. The main challenge is handling many different material types (non-linear magnetic steel, air, DC conductors, and magnets with several discrete orientations). Classical gradient-free topology optimization approaches are inefficient due to the high dimensionality of the optimization space, and usual density-based methods fail to provide meaningful results by falling into uninteresting local optima. Therefore, two general and distinct methodologies are proposed: an extended density approach considering hierarchical non-orthogonal as well as simplex interpolation domains, and a level-set method based on the topological derivative. Both methods result in meaningful designs that are analyzed and discussed, and recommendations are formulated.