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

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Abstract

This paper proposes a topology optimization formulation for the three-dimensional (3-D) design of segmented permanent magnet (PM) arrays. Specifically, the proposed formulation aims to find an optimal 3-D structural topology of PM segments and their discrete magnetization directions. To achieve this, a design variable is defined in the vector form of a Cartesian coordinate system. The magnitude of the design variable vector determines a PM density, and the directional cosines of the vector determine PM magnetization directions. To acquire a segmented PM design with discrete magnetization directions, a PM strength penalization scheme is proposed. In this scheme, a PM strength is controlled using a minimum distance function between a magnetization direction and target discrete directions. Here, the minimum distance function is approximated using the p-norm for sensitivity calculation. To validate the effectiveness of the proposed formulation, three design examples are provided. In the first example, a two-dimensional (2-D) dipole Halbach cylinder is designed to confirm that the proposed formulation can be applied for a 2-D design problem. The second example aims to design 3-D dipole PM arrays with a cuboid cavity. In the third example, a 3-D PM arrays are designed for maximizing the magnetic force acting on a soft ferromagnetic material.

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Funding

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) (NRF-2019R1A2C1002808), and GIST Research Institute(GRI) grant funded by the GIST in 2020.

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Authors and Affiliations

  1. School of Mechanical Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju, 61005, South Korea

    Jaejoon Lee, Jaewook Lee & Taehoon Jung

  2. School of Mechanical Engineering, Yonsei University, Seoul, 03722, South Korea

    Jeonghoon Yoo

Authors
  1. Jaejoon Lee
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  2. Jaewook Lee
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  3. Taehoon Jung
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  4. Jeonghoon Yoo
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Correspondence to Jaewook Lee.

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The authors declare that they have no conflict of interest.

Replication of results

The proposed topology optimization formulation is based on well-known three-field SIMP method with Helmholtz filtering and relaxed Heaviside function. The implementation for this known method have been provided in the relevant references cited in this paper. The extension of the three-field SIMP for the proposed design variable vector field is described in detail in Section 2.2. Additionally, the enough information to implement the proposed penalization scheme is provided in Section 2.3. Parameters required to reproduce the numerical examples are summarized in Table 1. Additional details that is necessary for the replication of the numerical examples such as initial setting of design variables are described in each subsection of Section 4.

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Responsible Editor: Somanath Nagendra

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Lee, J., Lee, J., Jung, T. et al. Topology optimization for three-dimensional design of segmented permanent magnet arrays. Struct Multidisc Optim 62, 3089–3104 (2020). https://doi.org/10.1007/s00158-020-02656-7

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  • DOI: https://doi.org/10.1007/s00158-020-02656-7

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