Topology Optimization Method Based on the Maxwell Stress Tensor for the Design of Ferromagnetic Parts in Electromagnetic Actuators

Topology optimization methods suffer from a lack of convexity for the design of electromagnetic devices. Local minimizers indeed prevent deterministic methods from attaining the optimal solution. The optimization result may then vary according to the initial conditions. This paper proposes a convexity-oriented method focusing on the maximization of the forces exerted on ferromagnetic parts in electromagnetic actuators. The method is based on a simultaneous optimization of two topologies by a gradient-based algorithm, the forces being computed by combining their magnetic fields within the Maxwell stress tensor. During the optimization, the two topologies converge towards a unique design using constraints whose shape is progressively modified. The method benefits from a fast convergence and produces consistent and efficient results, which is highlighted on a test problem. The method is eventually applied to a realistic problem related to the design of a switched reluctance actuator.