Simultaneous Magnetic and Structural Topology Optimization of Synchronous Reluctance Machine Rotors

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This article presents the simultaneous magnetic and structural topology optimization of a transverse laminated synchronous reluctance machine rotor using a solid isotropic with material penalization (SIMP)-based approach with the globally convergent method of moving asymptotes (GCMMA) optimization algorithm. Magneto-structural single and multi-objective optimization formulations are presented. The single objective formulation maximizes the average torque subject to constraints on torque ripple, Von Mises stress, and compliance. The multiobjective formulation simultaneously maximizes average torque and minimizes compliance subject to constraints on torque ripple and Von Mises stress. In both optimization formulations, the electrical steel densities in the rotor mesh elements are the control variables. Including stress and compliance in the optimization formulation ensures a structurally feasible design. The design-dependent centripetal force contributed by each element in the rotor mesh is considered dependent on its density and mass. An intermediate density material issue is observed where the density of the material in a mesh element does not converge fully to air or electrical steel. This issue is addressed through the use of a thresholding mass function which forces the convergence of the mass but not the density. The two optimization formulations are compared for rotors operating at 4000 and 12 000 r/min. An initial magnetic only topology optimization is used to seed the magneto-structural topology optimization to decrease the computational time. The impact of the magnetic only seed and rotor mesh density on the optimization outcomes is also examined.