Topology optimization for three-dimensional design of segmented permanent magnet arrays

Lee, Jaejoon; Jung, Taehoon; Yoo, Jeonghoon

doi:10.1007/s00158-020-02656-7

Cited by 5 publications

(9 citation statements)

References 39 publications

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“…It is noted that the orientation vector field ϑ( x) defined in (6) automatically satisfies the unity magnitude condition (i.e. ϑ( x) = 1) that is required for orientation representation in the Cartesian coordinate system [11]. The structural topology and magnetization direction of PM material can be designed by determining the distribution of the PM remanence B r in (1).…”

Section: A Materials Interpolation Schemementioning

confidence: 99%

“…For the design of segmented PM blocks, various approaches [7]- [16] have been proposed. Among various techniques, the present work applies a penalization scheme using the approximated minimum distance in [11].…”

Section: B Penalization Scheme For Pm Fragmentationmentioning

confidence: 99%

“…In the penalization scheme in [11], the discrete target direction vector v i is not fixed, but optimized together during a topology optimization procedure. Instead of directly using v i as design variables, the vectors…”

Section: B Penalization Scheme For Pm Fragmentationmentioning

confidence: 99%

“…In [9], segmented PMs were designed using topology optimization considering finite coercivity of PM material. In [10], [11], three-dimensional segmented PMs were designed, respectively, using the virtualmagnet approach and topology optimization with penalization scheme. Structural topology optimization for the simultaneous design of segmented PMs and back-irons has been proposed in [12]- [16].…”

Section: Introductionmentioning

confidence: 99%

“…back-iron) is included in multi-material topology optimization, which was not considered in [15], [16]. PM segmentation is carried out using an orientation penalization scheme proposed in [11]. A frame structure is next designed using a post-processing scheme proposed in the present work.…”

Section: Introductionmentioning

confidence: 99%

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Design and Fabrication of Magnetic System Using Multi-Material Topology Optimization

Jung

Lee

2021

IEEE Access

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Section: A Materials Interpolation Schemementioning

confidence: 99%

Section: B Penalization Scheme For Pm Fragmentationmentioning

confidence: 99%

Section: B Penalization Scheme For Pm Fragmentationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design and Fabrication of Magnetic System Using Multi-Material Topology Optimization

Jung

Lee

2021

IEEE Access

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

Cherrière

Laurent

Hlioui

et al. 2022

Struct Multidisc Optim

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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.

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Gradient-based optimization of permanent-magnet assemblies for any objective

Insinga,

Bjørk

2023

Phys. Rev. Applied

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We introduce a semianalytical optimization method that can be applied to find the optimal magnetization for any permanent-magnet system regarding the desired field or objective. Our approach is based on the Landau-Lifshitz equation, which is normally employed to simulate micromagnetic systems. Instead, we recognize that the same mathematical formalism is also applicable to the optimization of macroscopic magnetic assemblies. This point of view has the advantage of being easy to intuitively visualize and thus is also easy to implement. Our approach can also be seen as a special case of the adjoint method, which is a gradient-based constrained optimization method. However, most studies applying the adjoint method to magnet design adopt the point of topology optimization, where the magnetic permeability tensor field depends on the design variables, making the problem highly nonlinear. Instead, we restrict to the less general problem of optimizing the direction of the magnetization in any point of a given design region. Our strategy leads to a more robust and computationally efficient algorithm since the underlying problem is intrinsically simpler. Additionally, since the integration of the underlying magnetostatic equations is performed numerically, the method is still very flexible and versatile. Previously, an equivalent method has been considered only for solving the magnetic inverse problem. In the present work, we fully demonstrate its effectiveness by presenting several prototypical optimization problems and we discuss the strengths and limitations of the approach in relation to the existing optimization methods.

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Topology optimization for three-dimensional design of segmented permanent magnet arrays

Cited by 5 publications

References 39 publications

Design and Fabrication of Magnetic System Using Multi-Material Topology Optimization

Design and Fabrication of Magnetic System Using Multi-Material Topology Optimization

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

Gradient-based optimization of permanent-magnet assemblies for any objective

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