Multi-material topology optimization using Wachspress interpolations for designing a 3-phase electrical machine stator

Density methods; Electrical machine; Multimaterial topology optimization; Nonlinear magnetostatics; Wachspress’ shape functions; Multi materials; Permanent magnets synchronous machines; Polytopes; Shape functions; Topology optimisation; Wachspress’ shape function; Software; Control and Systems Engineering; Computer Science Applications; Control and Optimization; Computer Graphics and Computer-Aided Design

Abstract :

[en] This work uses multi-material topology optimization (MMTO) to maximize the average torque of a 3-phase permanent magnet synchronous machine (PMSM). Eight materials are considered in the stator: air, soft magnetic steel, three electric phases, and their three returns. To address the challenge of designing a 3-phase PMSM stator, a generalized density-based framework is used. The proposed methodology places the prescribed material candidates on the vertices of a convex polytope, interpolates material properties using Wachspress shape functions, and defines Cartesian coordinates inside polytopes as design variables. A rational function is used as penalization to ensure convergence towards meaningful structures, without the use of a filtering process. The influences of different polytopes and penalization parameters are investigated. The results indicate that a hexagonal-based diamond polytope is a better choice than the classical orthogonal domains for this MMTO problem. In addition, the proposed methodology yields high-performance designs for 3-phase PMSM stators by implementing a continuation method on the electric load angle.

Disciplines :

Computer science

Author, co-author :

Cherrière, Théodore ; SATIE laboratory, ENS Paris-Saclay, CNRS, Université Paris-Saclay, Gif-sur-Yvette, France

Laurent, Luc ; Laboratoire de Mécanique des Structures et des Systèmes Couplés, Paris, France ; HESAM University, Paris, France

Hlioui, Sami ; SATIE Laboratory, CY Cergy Paris University, CNRS, Paris-Saclay University, Cergy, France

Louf, François ; LMPS - Laboratoire de Mécanique Paris-Saclay, Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, Gif-sur-Yvette, France

Duysinx, Pierre ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Ingénierie des véhicules terrestres

Geuzaine, Christophe ; Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Applied and Computational Electromagnetics (ACE)

Ben Ahmed, Hamid ; SATIE Laboratory, ENS Rennes, CNRS, Bruz, France

Gabsi, Mohamed; SATIE laboratory, ENS Paris-Saclay, CNRS, Université Paris-Saclay, Gif-sur-Yvette, France

Fernandez Sanchez, Eduardo Felipe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire

Language :

English

Title :

Multi-material topology optimization using Wachspress interpolations for designing a 3-phase electrical machine stator

Publication date :

December 2022

Journal title :

Structural and Multidisciplinary Optimization

ISSN :

1615-147X

eISSN :

1615-1488

Publisher :

Springer Science and Business Media Deutschland GmbH

Volume :

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.springer.com/content/pdf/10.1007/s00158-022-03460-1.pdf

Available on ORBi :

since 15 December 2022

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