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Topology optimization of IPM motors with V-shaped permanent magnets using a grayscale free phase-field-based level set method.

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Title: Topology optimization of IPM motors with V-shaped permanent magnets using a grayscale free phase-field-based level set method.
Authors: Onishi, Kosei1 (AUTHOR) koseionishi8@gmail.com, Hiruma, Shingo2 (AUTHOR) hiruma@ist.hokudai.ac.jp, Mifune, Takeshi1 (AUTHOR) mifune.takeshi.3v@kyoto-u.ac.jp, Matsuo, Tetsuji1 (AUTHOR) matsuo.tetsuji.5u@kyoto-u.ac.jp
Source: COMPEL. 2026, Vol. 45 Issue 4, p690-701. 12p.
Subjects: Level set methods, Brushless electric motors, Torque, Structural optimization, Numerical grid generation (Numerical analysis), Sensitivity analysis, Iterative methods (Mathematics)
Abstract: Purpose: This study aims to optimize the internal structure of an interior permanent magnet synchronous motor (IPMSM) with V-shaped magnets to maximize torque. Specifically, it addresses the issue of grayscale (intermediate density) regions that appear near material interfaces in conventional phase-field-based level set methods. The primary objective is to eliminate these intermediate regions to prevent inaccuracies in finite element analysis and to resolve ambiguities in practical manufacturing. Design/methodology/approach: The proposed method employs a phase-field-based level set framework combined with a dynamic remeshing technique. Unlike conventional approaches that rely on fixed meshes, the computational mesh is regenerated after each update of the level set function so that the mesh explicitly conforms to material boundaries. The optimization problem is formulated to maximize instantaneous torque, and sensitivity analysis is conducted using the adjoint variable method. In addition, the sensitivity of the optimization algorithm to different initial shapes and interface parameters is systematically investigated. Findings: The proposed remeshing strategy successfully suppresses the formation of grayscale regions, resulting in optimal structures that are completely free of intermediate density regions and exhibit improved structural clarity and manufacturability. The method also demonstrates low sensitivity to variations in the initial shape, yielding stable optimization results. However, the final geometry and torque performance depend strongly on the appropriate selection of the interface propagation speed and diffusion coefficient. Ultimately, the optimized design achieves a 146.2% increase in torque compared with the initial configuration. Originality/value: This research provides significant value by addressing the persistent issue of grayscale regions near material interfaces in phase-field-based topology optimization for electric machines. While prior studies typically relied on fixed meshes, this work integrates a dynamic remeshing strategy tailored for IPMSM design to achieve strictly grayscale-free optimal structures. Furthermore, the study contributes original insights by systematically investigating the sensitivity of the optimization algorithm to initial conditions, an aspect that has received limited attention in electromagnetic topology optimization literature. [ABSTRACT FROM AUTHOR]
Copyright of COMPEL is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 194579686
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Topology optimization of IPM motors with V-shaped permanent magnets using a grayscale free phase-field-based level set method.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Onishi%2C+Kosei%22">Onishi, Kosei</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> koseionishi8@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Hiruma%2C+Shingo%22">Hiruma, Shingo</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hiruma@ist.hokudai.ac.jp</i><br /><searchLink fieldCode="AR" term="%22Mifune%2C+Takeshi%22">Mifune, Takeshi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mifune.takeshi.3v@kyoto-u.ac.jp</i><br /><searchLink fieldCode="AR" term="%22Matsuo%2C+Tetsuji%22">Matsuo, Tetsuji</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> matsuo.tetsuji.5u@kyoto-u.ac.jp</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22COMPEL%22">COMPEL</searchLink>. 2026, Vol. 45 Issue 4, p690-701. 12p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Level+set+methods%22">Level set methods</searchLink><br /><searchLink fieldCode="DE" term="%22Brushless+electric+motors%22">Brushless electric motors</searchLink><br /><searchLink fieldCode="DE" term="%22Torque%22">Torque</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+grid+generation+%28Numerical+analysis%29%22">Numerical grid generation (Numerical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Sensitivity+analysis%22">Sensitivity analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Purpose: This study aims to optimize the internal structure of an interior permanent magnet synchronous motor (IPMSM) with V-shaped magnets to maximize torque. Specifically, it addresses the issue of grayscale (intermediate density) regions that appear near material interfaces in conventional phase-field-based level set methods. The primary objective is to eliminate these intermediate regions to prevent inaccuracies in finite element analysis and to resolve ambiguities in practical manufacturing. Design/methodology/approach: The proposed method employs a phase-field-based level set framework combined with a dynamic remeshing technique. Unlike conventional approaches that rely on fixed meshes, the computational mesh is regenerated after each update of the level set function so that the mesh explicitly conforms to material boundaries. The optimization problem is formulated to maximize instantaneous torque, and sensitivity analysis is conducted using the adjoint variable method. In addition, the sensitivity of the optimization algorithm to different initial shapes and interface parameters is systematically investigated. Findings: The proposed remeshing strategy successfully suppresses the formation of grayscale regions, resulting in optimal structures that are completely free of intermediate density regions and exhibit improved structural clarity and manufacturability. The method also demonstrates low sensitivity to variations in the initial shape, yielding stable optimization results. However, the final geometry and torque performance depend strongly on the appropriate selection of the interface propagation speed and diffusion coefficient. Ultimately, the optimized design achieves a 146.2% increase in torque compared with the initial configuration. Originality/value: This research provides significant value by addressing the persistent issue of grayscale regions near material interfaces in phase-field-based topology optimization for electric machines. While prior studies typically relied on fixed meshes, this work integrates a dynamic remeshing strategy tailored for IPMSM design to achieve strictly grayscale-free optimal structures. Furthermore, the study contributes original insights by systematically investigating the sensitivity of the optimization algorithm to initial conditions, an aspect that has received limited attention in electromagnetic topology optimization literature. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of COMPEL is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 12
        StartPage: 690
    Subjects:
      – SubjectFull: Level set methods
        Type: general
      – SubjectFull: Brushless electric motors
        Type: general
      – SubjectFull: Torque
        Type: general
      – SubjectFull: Structural optimization
        Type: general
      – SubjectFull: Numerical grid generation (Numerical analysis)
        Type: general
      – SubjectFull: Sensitivity analysis
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
    Titles:
      – TitleFull: Topology optimization of IPM motors with V-shaped permanent magnets using a grayscale free phase-field-based level set method.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Onishi, Kosei
      – PersonEntity:
          Name:
            NameFull: Hiruma, Shingo
      – PersonEntity:
          Name:
            NameFull: Mifune, Takeshi
      – PersonEntity:
          Name:
            NameFull: Matsuo, Tetsuji
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 07
              Text: 2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 03321649
          Numbering:
            – Type: volume
              Value: 45
            – Type: issue
              Value: 4
          Titles:
            – TitleFull: COMPEL
              Type: main
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