Electro-thermal topology optimization of an electric machine by the topological derivative considering drive cycles

We consider a 2d permanent magnet synchronous machine operating in a sequence of static operating points coming from a drive cycle. We aim to find a rotor design which maximizes the efficiency defined as the quotient of input and output energy considering Joule losses in the stator and eddy current losses in the permanent magnets. A coupled electromagnetic-thermal analysis of the rotor considers the eddy current losses as heat source and adds a temperature constraint to avoid damage of the permanent magnets. Additionally we impose Von-Mises stress constraints to maintain the mechanical integrity of the design. To solve the resulting free form topology optimization problem we use a level set description of the design and the topological derivative as sensitivity information. We show the effect of this constraint at very high speeds which is a trend in recent machine development.