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.
Bibliographical noteFunding Information:
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.
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Control and Optimization