3D Analytical Modeling of Slotless Axial Flux Machines under No-Load Condition and Different Magnet Shapes

Document Type : Research Paper

Authors

1 Department of Electrical Engineering, Faculty of Engineering, Lorestan University, Khorramabad, Iran

2 Department of Civil Engineering, Faculty of Engineering, Lorestan University, Khorramabad, Iran

Abstract

This paper presents a new 3D analytical model based on Fourier-Bessel series for electromagnetic modeling the performance of slotless Axial Flux Permanent Magnet (AFPM) machines under no-load condition. The machine geometry is divided into different domains including Permanent Magnet (PM) domain, air-gap domain and so on. The Laplace equation in terms of scalar magnetic potential is solved in each domain, and their solutions is expressed based on Fourier-Bessel series to accurately consider the radial variation of air-gap magnetic field. A 2D geometry function based on Fourier-Bessel series is introduced to accurately consider the different PM shaping in magnet domain. The boundary condition is then used to determine the unknown constants in general solutions. This 3D analytical model is prepared to calculate the no-load flux-linkage of stator phases while considering different PM shapes and skewing effect. Two indexes including the amplitude of fundamental component and the total harmonic distortion (THD) of no-load phase flux-linkage are considered to investigate the effect of skewed PMs and other PM shapes. The capability of proposed 3D analytical model is also presented to calculate the air-gap magnetic field due to stator phases for determining the inductance matrix. In final, the accuracy of proposed 3D analytical model is verified by comparing with the corresponding results obtained through finite element method (FEM) and experiment set-up.

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References

[1] Liu, Ye, Zhuoran Zhang, Chen Wang, Weiwei Geng, and Tao Yang. "Design and analysis of oil-immersed cooling stator with nonoverlapping concentrated winding for high-power ironless stator axial-flux permanent magnet machines." IEEE Transactions on Indusrial Electronics 68, no. 4 (2021): 2876-2886.
[2] Taran, Narges, Vandana Rallabandi, Greg Heins, and Dan M. Ionel. "Coreless and conventional axial flux permanent magnet motors for solar cars." IEEE Transactions on Industry Applications 54, no. 6 (2018): 5907-5917.
[3] Chan, T. F., Weimin Wang, and L. L. Lai. "Performance of an axial-flux permanent magnet synchronous generator from 3-D finite-element analysis." IEEE Transactions on Energy Conversion 25, no. 3 (2010): 669-676.
[4] Talebi, Dorsa,  Matthew C. Gardner, Sri Vignesh Sankarraman, Ahmad Daniar, and Hamid A. Toliyat. "Electromagnetic design characterization of a dual rotor Axial Flux Motor for electric aircraft." IEEE Transactions on Industry Applications 58, no. 6 (2022): 7088-7098.
[5] Ajily, Ehsan, Karim Abbaszadeh, and Mohammad Ardebili. "Three-dimensional field reconstruction method for modeling axial flux permanent magnet machines." IEEE Transactions on Energy Conversion 30, no. 1 (2015): 199-207.
[6] Cheng, Wenjie, Guangdong Cao, Zhikai Deng, and Ling Xiao. "Torque comparison between slotless and slotted ultra-high speed AFPM motors using analytical method." IEEE Transactions on Magnetics 58, no. 2 (2022).
[7] Parviainen, A., M. Niemelä, and J. Pyrhönen. "Modeling of axial flux permanent-magnet machines." IEEE Transactions on Industry Applications 40, no. 5 (2004): 1333-1340.
[8] Zhao, Hang, K. T. Chau, Tengbo Yang, Zaixin Song, and Chunhua Liu. "A novel quasi-3D analytical model for axial flux motors considering magnetic saturation." IEEE Transactions on Energy Conversion 37, no. 2 (2022): 1358-1368.
[9] Lubin, Thierry, and Abderrezak Rezzoug. "3-D Analytical model for axial-flux eddy-current couplings and brakes under steady-state conditions.'' IEEE Transactions on Magnetics 51, no. 10 (2015).
[10] Taghipour Boroujeni, Samad, Abdolmajid Abedini Mohammadi, Ashknaz Oraee, and Hashem Oraee, "Approach for analytical modelling of axial-flux PM machines."  IET Electric Power Applications 10, no. 6 (2016): 441-450.
[11] Si, Jikai, Meng Huang, Rui Nie, Chun Gan, and Yaofei Han. "Inductance calculation and analysis of axial-flux slotless surface-mounted permanent magnet machine with equidirectional toroidal winding." IEEE Transactions on Energy Conversion 39, no. 3 (2024): 1509-1519.
[12] Tong, Wenming, Deyi Cai, and Shengnan Wu. "An improved subdomain model for optimizing electromagnetic performance of AFPM machines." IEEE Transactions on Industry Applications 60, no. 6 (2024): 8745-8754.
[13] Guo, Baocheng, Zakarya Djelloul-Khedda, and Frédéric Dubas. "Nonlinear analytical solution in axial flux permanent magnet machines using scalar potential." IEEE Transactions on Indusrial Electronics 71, no. 4 (2024): 3383-3393.
[14] Kano, Yoshiaki, Takashi Kosaka, and Nobuyuki Matsui. "A simple nonlinear magnetic analysis for axial-flux permanent-magnet machines." IEEE Transactions on Indusrial Electronics 57, no. 6 (2010): 2124-2133.
[15] Hemeida, Ahmed, Antti Lehikoinen, Pavvo Rasilo, Hendrik Vansompel, Anouar Belahcen, Antero Arkkio, and Peter Sergeant. "A simple and efficient quasi-3D magnetic equivalent circuit for surface axial flux permanent magnet synchronous machines." IEEE Transactions on Indusrial Electronics 66, no. 11 (2019): 8318-8333.
[16] Taqavi, Omolbanin, and Nasim Taghavi. "Development of a mixed solution of maxwell’s equations and magnetic equivalent circuit for double-sided axial-flux permanent magnet machines." IEEE Transactions on Magnetics 57, no. 4 (2021).
[17] Sung, So-Young, Jae-Hoon Jeong, Yu-Seop Park, Jang-Young Choi, and Seok-Myeong Jang. "Improved analytical modeling of axial flux machine with a double-sided permanent magnet rotor and slotless stator based on an analytical method." IEEE Transactions on Magnetics 48, no. 11 (2012): 2945-2948.
[18] Deng, Wenzhe, and Shuguang Zuo. "Analytical modeling of the electromagnetic vibration and noise for an external rotor axial flux in-wheel motor." IEEE Transactions on Indusrial Electronics 65, no. 3 (2018): 1991-2000.
[19] Alipour-Sarabi, Ramin, Zahra Nasiri-Gheidari, and Hashem Oraee. "Development of a three-dimensional magnetic equivalent circuit model for axial flux machines." IEEE Transactions on Indusrial Electronics 67, no. 7 (2020): 5758–5767.
[20] Okita, Taishi, and Hisako Harada. "3-D analytical model of axial-flux permanent magnet machine with segmented multipole-halbach array." IEEE Access 11 (2023): 2078-2091.
[21] Diao, Chengwu, Wenliang Zhao, Longxuan Li, Sunil Kumar, and Byung-II Kwon. "Analytical calculation of slotless axial flux permanent magnet motor with sinusoidal magnets for torque ripple reduction." IEEE Transactions on Magnetics 60, no. 12 (2024).
[22] Alatawneh, Natheer, and P. Pillay. "Rotational Core Loss and Permeability Measurements in Machine Laminations with Reference to Permeability Asymmetry." IEEE Transactions on Magnetics 48, no. 4 (2012): 1445-1448. 
[23] Frank, Zdenek and Jan Laksar. "Analytical design of coreless Axial-Flux Permanent Magnet machine with planar coils." IEEE Transactions on Energy Conversion 36, no. 3 (2021): 2348-2357.
[24] Min, Seun Guy. "Analytical design and optimization of Axial Flux Permanent Magnet machines with slotless structure." IEEE Transactions on Transportation Electrification 8, no. 2 (2022): 1994–2004.
Journal of Modeling in Engineering
Volume 23, Issue 83
December 2025
Pages 11-25

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History

  • Receive Date: 09 October 2024
  • Revise Date: 02 February 2025
  • Accept Date: 05 February 2025

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