A Sequential Topology and Shape Optimization Framework for Synchronous Reluctance Motors

Abstract

Synchronous reluctance motors （SynRMs） offer the advantages of low cost and high-speed operation owing to their magnet-free, simple, and robust rotor structure; however, their electromagnetic and mechanical performance depends strongly on the rotor geometry. Because of this geometric dependence, optimal design is essential to obtain a high-performance rotor, and topology optimization has been widely employed for this purpose. The most commonly used density-based topology optimization effec tively explores the global material layout, but it inevitably produces gray-scale elements with intermediate densities that do not correspond to a clearly defined, manufacturable boundary. As a result, performance degradation occurs when the design is reconstructed into a manufacturable geometry, and boundary-sensitive metrics such as torque ripple and stress are particularly difficult to predict and control at the topology optimization stage. To address this, applying shape optimization sequentially after topology opti mization to refine the boundary geometry is effective. Since shape optimization treats the boundary as the design variable, it is well suited to improving performance metrics– i that are sensitive to local geometric variations. This thesis proposes a sequential topology and shape optimization framework for SynRM rotor design that simultaneously considers electromagnetic and structural per formance. The global metrics—average torque and compliance—are handled in the topology optimization stage, while the boundary-sensitive metrics—torque ripple and von Mises stress—are improved in the subsequent shape optimization stage, with the average torque and compliance attained in the topology optimization stage preserved. The topology optimization result is reconstructed into a manufacturable geometry us ing the Douglas–Peucker algorithm, from which a small number of boundary control points are selected as design variables. To reduce the cost of repeated finite element analyses, artificial neural network （ANN） surrogate models are trained, and shape optimization is performed on the surrogates using sequential quadratic programming （SQP）. Compared with single-step topology optimization, the proposed sequential frame work imposes a smaller computational burden at the topology optimization stage, allowing a variety of design candidates to be obtained within the same amount of time. This provides the designer with a wide range of options from which a preferred de sign can be selected by considering not only performance but also geometric aspects such as manufacturability. Furthermore, by performing shape optimization on the de sign variables sensitive to the boundary geometry, the performance degraded during reconstruction into a manufacturable geometry was effectively recovered.|동기 릴럭턴스 모터（SynRM）는 영구자석이 없는 단순하고 견고한 회전자 구조로 저비용·고속 운전의 장점을 가지지만, 전자기 및 기계적 성능이 회전자 형상에 크게 의존하는 문제를 가진다. 이러한 형상 의존성으로 인해 우수한 성능의 회전자를 얻기 위해서는최적설계가필수적이며,그방법으로위상최적화가널리활용되어왔다.가장 널리활용되는밀도기반의위상최적화는전역적인재료배치를효과적으로탐색하지만, 중간밀도의회색조요소를포함하여제작가능한경계와직접대응되지않는다.이로 인해제작가능한형상으로복원하는과정에서성능저하가발생하며,특히토크리플과 응력과같이경계형상에민감한지표는위상최적화단계에서미리예측하고제어하기 어렵다. 이를보완하기위해,위상최적화이후형상최적화를순차적으로적용하여경계 형상을정밀하게다듬는접근이효과적이다.형상최적화는경계를설계변수로다루므로, 국부적형상변화에민감한성능지표를개선하는데강점을가진다. 본논문에서는전자기및구조성능을동시에고려하는SynRM회전자설계를위한 순차적 위상 및형상최적화프레임워크를제안한다. 전역적 지표인 평균 토크와 컴플 라이언스는 위상최적화 단계에서 다루고, 경계 형상에 민감한 토크 리플과 폰미세스 응력은후속형상최적화단계에서개선하되위상최적화에서확보한성능은유지하도록– iii 하였다. 위상최적화결과는Douglas–Peucker 알고리즘으로 제작 가능한 형상으로 복원 하여소수의경계제어점을설계변수로선정하고,ANN대리모델을학습하여SQP기반 형상최적화를수행하였다. 제안하는순차적프레임워크는단일위상최적설계에비해위상최적화단계의계산 부담이 작아, 동일한 시간에 다양한 설계안을 확보할 수 있었다. 이를 통해 설계자는 성능뿐아니라제작가능성등형상까지고려하여원하는설계를선택할수있는폭넓 은선택지를제공하였다.또한경계형상에민감한설계변수를대상으로형상최적화를 수행함으로써, 제작 가능한 형상으로 복원하며 저하된 성능을 효과적으로 회복할 수 있었다.