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Article

Analytical Modeling and GA-Based Optimization of Multi-Layered Segmented SPM Magnets

by
Choayeb Barchouchi
*,
Matthew Franchek
and
Yingjie Tang
Department of Mechanical and Aerospace Engineering, University of Houston, Houston, TX 77204, USA
*
Author to whom correspondence should be addressed.
Energies 2025, 18(23), 6303; https://doi.org/10.3390/en18236303 (registering DOI)
Submission received: 4 October 2025 / Revised: 26 November 2025 / Accepted: 26 November 2025 / Published: 30 November 2025

Abstract

Presented here is a 2-D analytical model for predicting the magnetic field distribution in a surface-mounted permanent magnet (SPM) rotor with multi-layered segmented permanent magnets (PMs). Each layer is treated independently, enabling the linear superposition of magnetic fields across all layers. The model employs subdomain modeling combined with the separation of variables, with the magnetic vector potential expressed as a Fourier series to derive the airgap magnetic field. The formulation is generalizable to five regions in each layer: outer airgap, optional outer inactive magnetic layer, active magnetic layer(s), optional inner inactive magnetic layer, and inner airgap. Validation against finite element analysis (FEA) shows a prediction difference of around 0.5% in airgap flux density. The model’s design utility is demonstrated through a genetic algorithm (GA) optimization, which maximizes static flux linkage and confirms performance improvements from the multi-layered configuration.
Keywords: electrical motors; surface-mounted permanent magnets; segmented permanent magnets; subdomain analytical modeling; genetic algorithm optimization electrical motors; surface-mounted permanent magnets; segmented permanent magnets; subdomain analytical modeling; genetic algorithm optimization

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MDPI and ACS Style

Barchouchi, C.; Franchek, M.; Tang, Y. Analytical Modeling and GA-Based Optimization of Multi-Layered Segmented SPM Magnets. Energies 2025, 18, 6303. https://doi.org/10.3390/en18236303

AMA Style

Barchouchi C, Franchek M, Tang Y. Analytical Modeling and GA-Based Optimization of Multi-Layered Segmented SPM Magnets. Energies. 2025; 18(23):6303. https://doi.org/10.3390/en18236303

Chicago/Turabian Style

Barchouchi, Choayeb, Matthew Franchek, and Yingjie Tang. 2025. "Analytical Modeling and GA-Based Optimization of Multi-Layered Segmented SPM Magnets" Energies 18, no. 23: 6303. https://doi.org/10.3390/en18236303

APA Style

Barchouchi, C., Franchek, M., & Tang, Y. (2025). Analytical Modeling and GA-Based Optimization of Multi-Layered Segmented SPM Magnets. Energies, 18(23), 6303. https://doi.org/10.3390/en18236303

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