This conference paper was submitted for presentation at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Many sectors have started a transformation to electrical machines due to sustainability requirements and increased performance. Therefore, we present two non-linear multiphysics sensitivity based optimization approaches. The first optimization approach is topology optimization solution for the conceptual designing of the electrical machines and the following approach is non-parametric shape optimization for the fine tuning of electrical machines. The well-known solid isotropic material interpolation using penalization (SIMP) for the material stiffness in topology optimization is applied for the structural CAE modeling as well as for the highly non-linear constitutive material modeling for the reluctivity in the electromagnetic CAE modeling. The optimization process includes a reconstruction of the topology optimization solution which topological optimized design is then applied to shape optimization. The non-parametric shape modifications are directly performed on the CAE models where each node is displaced independently. Additionally, the CAE mesh is adapted by an automatic mesh smoothing algorithm in every optimization step. Furthermore, both in topology and shape optimization various regularization, symmetry and manufacturing constraints are enforced ensuring that the optimized designs are industrial feasible. The non-linear sensitivity based optimization does not only include the design variables for the topology or for the shape designing but also a phase angle for the injected current at a given operation point. Thereby, the design variables for the material layout of the rotor and stator are optimized simultaneously including the phase angle in each optimized iteration using a fully coupled optimization based upon sensitivities and mathematical programming. The optimization is multiphysics as both electromagnetic design responses and mechanical design responses can be optimized as objective functions and as constraints. The most common electromagnetic design responses are the average torque and torque rippling e.g., maximizing average torque and constraining the torque rippling to being below a sudden limit. The mechanical design responses are usual stiffness as objective or constraint, and strength using stress constraints. Previous published work on optimization typically applied simple mechanical modeling for the stiffness and strength, and does not include periodic boundary conditions and/or non-linear contact modeling. The present work includes these modeling features yielding accurate optimization results with respect to the mechanical properties. Additionally, another novelty of present implementation and solution compared to previous work on sensitivity-based optimization for optimization of electrical machines is that the pulsation modes of the lumped tooth forces (spatial radial / tangential components) are included as design responses. Thereby, the design responses for the lumped tooth forces for a given order can be defined as the radial, or tangential force for addressing specific NVH-properties (Noise, Vibration, and Harshness) of the electrical machine. The stator loads from the electromagnetic simulations are mapped to multi-body simulations for assessing the noise and vibration using a digital thread for the design verification where the flexible components (stator, housing, shaft, gears) for the multi-body simulations are obtained using finite element modeling. An operating point for the electrical motor is defined by the point for rotational speed and torque. Up to now the present literate has only addressed one operating point. Contrary, we address multiple operating points and thereby, multiple phase shifts (one phase shift per operating point) as design variables for rigorously improving the electric performance, since electrical motors does not always operate on one operating point. With particular operation points selection, an overall like torque ripple reduction on the whole operation range can also be expected. We will show topology optimization and non-parametric shape optimization for a PMSM (Permanent Magnet Synchronous Machine) to illustrate that the present workflow can address the numerous design requirements.