VP3-10 Magnetic Field and Torque Analysis of Coaxial Magnetic Gear Considering Permeability Nonlinear in Harmonic Modeling Method
Creators: Manh-Dung Nguyen
Duy-Tinh Hoang
Kyung-Hun Shin
Yong-Joo Kim
Anh-Tuan Phung
and Jang-Young Choi
Publisher: name: IEEE
Year: 2025

Magnetic gears (MGs) transfer power between high-torque, low-speed, and low-torque, high-speed rotations by leveraging magnetic field interactions rather than the physical interlocking of teeth found in traditional mechanical gears. The concept of coaxial magnetic gears was first introduced in [1]. To obtain MGs characteristic, the analytical method provides faster processing times to compare with FEM simulations. Two main analytical methods are commonly explored. The first, subdomain modeling, involves directly solving Maxwell’s equations and boundary/interface conditions using Fourier series expansion. This method was applied to magnetically geared machines in [2]. The second method, harmonic modeling, solves permeability issues using the complex Fourier series and Cauchy product, which enables the consideration of nonlinear core characteristics. Harmonic modeling was initially introduced in a straightforward configuration with a single stator and one air gap [3]. A convergence algorithm is proposed to consider the nonlinear aspect of the iron used in the machine’s stator [4]. The prototype is illustrated in the 2-D polar coordinate system and divided into eight regions, as shown in Fig. 1. Each area is described by a vector potential which will be derived in the following section. The authors separated the steel material regions (I, IV, VII) into sub-regions that have corresponding permeability. A 3/16/19 specification given in Fig.1 was simulated in 2-D FEM. Fig. 2 depicts a good agreement between harmonic modeling and FEM simulation not only in linear analysis but also in saturation cases. It can be seen that flux densities are generally diminished due to saturation in the outer rotor yoke. It leads to an output torque decrease. A prototype shown in Fig.1(a-d) was validated for torque measurement. Further results will be presented in a full paper.References: [1] T. Martin, Magnetic transmission., U.S. Patent 3 378 710, Apr. 16, 1968. [2] Manh-Dung Nguyen, Su-Min Kim, Hyo-Seob, AIP Advances., 1 February 2024; 14 (2). [3] R. L. J. Sprangers, J. J. H. Paulides, B. L. J. Gysen, IEEE Trans. Magn., vol. 52, no. 2, pp. 1-10, Feb. 2016. [4] D. C. Teles, C. Chillet, L. Garbuio, 2022 International Conference on Electrical Machines (ICEM), Valencia, Spain, 2022, pp. 178-184.
Magnetic gears (MGs) transfer power between high-torque, low-speed, and low-torque, high-speed rotations by leveraging magnetic field interactions rather than the physical interlocking of teeth found in traditional mechanical gears. The concept of coaxial magnetic gears was first introduced in [1]. To obtain MGs characteristic, the analytical method provides faster processing times to compare with FEM simulations. Two main analytical methods are commonly explored. The first, subdomain modeling, involves directly solving Maxwell’s equations and boundary/interface conditions using Fourier series expansion. This method was applied to magnetically geared machines in [2]. The second method, harmonic modeling, solves permeability issues using the complex Fourier series and Cauchy product, which enables the consideration of nonlinear core characteristics. Harmonic modeling was initially introduced in a straightforward configuration with a single stator and one air gap [3]. A convergence algorithm is proposed to consider the nonlinear aspect of the iron used in the machine’s stator [4]. The prototype is illustrated in the 2-D polar coordinate system and divided into eight regions, as shown in Fig. 1. Each area is described by a vector potential which will be derived in the following section. The authors separated the steel material regions (I, IV, VII) into sub-regions that have corresponding permeability. A 3/16/19 specification given in Fig.1 was simulated in 2-D FEM. Fig. 2 depicts a good agreement between harmonic modeling and FEM simulation not only in linear analysis but also in saturation cases. It can be seen that flux densities are generally diminished due to saturation in the outer rotor yoke. It leads to an output torque decrease. A prototype shown in Fig.1(a-d) was validated for torque measurement. Further results will be presented in a full paper.References: [1] T. Martin, Magnetic transmission., U.S. Patent 3 378 710, Apr. 16, 1968. [2] Manh-Dung Nguyen, Su-Min Kim, Hyo-Seob, AIP Advances., 1 February 2024; 14 (2). [3] R. L. J. Sprangers, J. J. H. Paulides, B. L. J. Gysen, IEEE Trans. Magn., vol. 52, no. 2, pp. 1-10, Feb. 2016. [4] D. C. Teles, C. Chillet, L. Garbuio, 2022 International Conference on Electrical Machines (ICEM), Valencia, Spain, 2022, pp. 178-184.