Convexity-Oriented Method for the Topology Optimization of Ferromagnetic Moving Parts in Electromagnetic Actuators Using Magnetic Energy

When applied to the topology optimization of electromagnetic devices, gradient-based algorithms suffer from a lack of convexity. They usually converge to local minimizers and the obtained designs depend on the initial material distributions. This paper focuses on avoiding these local minimizers for the optimization of ferromagnetic moving parts in electromagnetic actuators. The proposed method intends to maximize the average reluctant force computed from the difference of magnetic energy between two positions of the ferromagnetic part. It relies on a problem relaxation: distinct design variables are defined to describe the ferromagnetic part in each position. Thanks to convexity-oriented constraints, the differences between the two obtained topologies are progressively reduced in order to converge towards the optimal design. The paper besides highlights sensitivity issues related to the high permeability of iron and recommends using a geometric mapping to guarantee a fast convergence. The efficiency of the method is underlined for the design of the rotor of a switched reluctant actuator. The method succeeds in avoiding local minimizers and producing efficient topologies. The method is then combined with another method dedicated to the design of parts composed of iron and coils in order to realize the global optimization of the actuator.