/Department of Mechanical Engineering
Computational Modeling, Analysis, and Design Optimization Lab

Multi-Material Topology and Magnetization Co-Optimization of Circular Halbach Arrays

A Halbach array is a specialized arrangement of permanent magnets that generates a strong, uniform magnetic field in a designated region and suppresses it elsewhere. This configuration has been widely applied in magnetic levitation systems, electric motors, particle accelerators, and magnetic resonance imaging devices due to its high efficiency, reduced weight, and precise directional control. Linear Halbach arrays concentrate the field on one side, making them suitable for applications such as maglev trains and conveyor systems. Cylindrical Halbach arrays, with magnets arranged in a circular configuration, produce a uniform internal field while minimizing the external field, which is advantageous in brushless motors and imaging systems. The traditional design of Halbach arrays has relied heavily on engineering intuition because of the complexity of magnet placement and orientation. With advances in numerical methods, topology optimization now provides a systematic approach to determining both material distribution and magnetization directions to maximize magnetic flux in the target region. In this work, we propose a cardinal basis function (CBF)-based level set method for the design of circular Halbach arrays capable of generating an area-averaged magnetic field. The finite difference method is employed to optimize magnetization directions simultaneously with geometry, providing additional design flexibility. The CBF-based level set method reduces computational cost and accelerates convergence, improving the overall efficiency of the optimization. Furthermore, multi-material topology optimization is incorporated, enabling the addition of permanent magnets with distinct magnetization directions to achieve greater control over magnetic flux distribution.

 

3884

 

Undergraduate Senior Design Mentorship (Halbach Array-Based Permanent Magnet Electric Motor)


Spring 2026: Raymond Chen, Arash Khan, Michael Telesca, Bohua Wu, Ziwen Zhao

3860

 

 

 

 

 

 

 

 

385638573862

 

Representative publications:

Journal:

  1. Lingfeng Gao, David Torrey, Fang Luo, Jon Longtin, Shikui Chen*. "Multi-Material Topology and Magnetization Co-Optimization of Circular Halbach Arrays Via a Cardinal Basis Function-Based Level Set Method." Journal of Mechanical Design, September 2026; 148(9): 091705. https://doi.org/10.1115/1.4071075

Conference:

  1. Lingfeng Gao, David Torrey, Jon Longtin, Fang Luo, Shikui Chen*, “Shape and Topology Optimization of Circular Halbach Array Using a Cardinal Basis Function (CBF) Based Parametric Level Set Method”, the ASME 2025 International Design Engineering Technical Conferences &  Computers and Information in Engineering Conference (IDETC/CIE 2025), August 17-20, 2025, Anaheim, CA, USA.