DV-06 Analytical and Experimental Approaches to Predicting Magnetic Field Asymmetry and Electromagnetic Forces in Slotted Surface-Mounted Permanent Magnet Machines with Rotor Eccentricity
Creators: Yeon-Su Kim
Jun-Won Yang
Yong-Joo Kim
Kyung-Hun Shin and Jang-Young Choi
Publisher: name: IEEE
Year: 2025

Rotor eccentricity caused by defects in the manufacturing or operational processes of motors affects electromagnetic performance. The deviation in the air-gap flux density due to rotor eccentricity affects the back electromotive force (EMF) and cogging torque. Although rotor eccentricity can be identified using finite element analysis (FEA), the analysis is time-consuming, and understanding the direct physical relationship between eccentricity and design variables is challenging. Therefore, an analytical approach based on the electromagnetic governing equations was employed to analyze the impact of eccentricity on the design variables. Figure 1(a) shows a simplified subdomain model of surface-mounted permanent magnet synchronous motor (SPMSM), and Fig.1 (b) illustrates the coordinate system transformation of the stator and rotor. In Fig. 1(b), the coordinate systems of the stator and rotor are represented as (X-Y) and (x’-y’). Fig. 1(c) shows the experimental setup used to validate the proposed subdomain method. Fig. 1(d) depicts the FE anlysis model. Using perturbation and electromagnetic field theories, the governing equations for the air gap region were derived, and the air gap flux density was determined using the magnetic vector potential and boundary conditions, as shown in Fig. 2(a). The perturbation of the magnetic flux density due to the rotor eccentricity ratio is shown in Fig. 2(b). Fig. 2(c) shows the back-EMF. The flux density was then applied to the Maxwell stress tensor to obtain the magnetic pull-force (MPF) distribution, as shown in Fig. 2(d). The results were validated through comparisons with experimental data and FEA results, thereby confirming the asymmetry caused by rotor eccentricity. The details of the subdomain method, perturbation theory, analysis results, and design specifications of the SPMSM are provided in the full paper.References: [1] A. Rahideh, M. Mardaneh, T. Korakianitis, “Analytical 2-D Calculations of Torque, Inductance, and Back-EMF for Brushless Slotless Machines With Surface Inset Magnets,” IEEE Trans. Magn, vol. 49, no. 8, Aug, 2013. [2] T. Du, H.Geng, Y. Zhang, “Exact Analytical Method for Active Magnetic Bearings With Rotor Eccentricity,” IEEE Trans. Magn, vol. 55, no. 12, Dec, 2019. [3] A. Vahaj, A. Rahideh, T. Lubin, “General Analytical Magnetic Model for Partitioned-Stator Flux-Reversal Machines With Four Types of Magnetization Patterns,” IEEE Trans. Magn, vol. 55, no. 11, Nov, 2019. [4] V. Z. Faradonbeh, A. Rahideh, M. M. Ghahfarokhi, “Analytical Modeling of Slotted, Surface-Mounted Permanent Magnet Synchronous Motors With Different Rotor Frames and Magnet Shapes,” IEEE Trans. Magn, vol. 57, no. 1, Jan, 2021 [5] H. K. Lee, K. H. Shin, T. K. Bang, “Experimental Verification and Analytical Study of Influence of Rotor Eccentricity on Electromagnetic Characteristics of Permanent Magnet Machine,” IEEE Trans. Appl, vol. 30, no. 4, Jun, 2020.
Rotor eccentricity caused by defects in the manufacturing or operational processes of motors affects electromagnetic performance. The deviation in the air-gap flux density due to rotor eccentricity affects the back electromotive force (EMF) and cogging torque. Although rotor eccentricity can be identified using finite element analysis (FEA), the analysis is time-consuming, and understanding the direct physical relationship between eccentricity and design variables is challenging. Therefore, an analytical approach based on the electromagnetic governing equations was employed to analyze the impact of eccentricity on the design variables. Figure 1(a) shows a simplified subdomain model of surface-mounted permanent magnet synchronous motor (SPMSM), and Fig.1 (b) illustrates the coordinate system transformation of the stator and rotor. In Fig. 1(b), the coordinate systems of the stator and rotor are represented as (X-Y) and (x’-y’). Fig. 1(c) shows the experimental setup used to validate the proposed subdomain method. Fig. 1(d) depicts the FE anlysis model. Using perturbation and electromagnetic field theories, the governing equations for the air gap region were derived, and the air gap flux density was determined using the magnetic vector potential and boundary conditions, as shown in Fig. 2(a). The perturbation of the magnetic flux density due to the rotor eccentricity ratio is shown in Fig. 2(b). Fig. 2(c) shows the back-EMF. The flux density was then applied to the Maxwell stress tensor to obtain the magnetic pull-force (MPF) distribution, as shown in Fig. 2(d). The results were validated through comparisons with experimental data and FEA results, thereby confirming the asymmetry caused by rotor eccentricity. The details of the subdomain method, perturbation theory, analysis results, and design specifications of the SPMSM are provided in the full paper.References: [1] A. Rahideh, M. Mardaneh, T. Korakianitis, “Analytical 2-D Calculations of Torque, Inductance, and Back-EMF for Brushless Slotless Machines With Surface Inset Magnets,” IEEE Trans. Magn, vol. 49, no. 8, Aug, 2013. [2] T. Du, H.Geng, Y. Zhang, “Exact Analytical Method for Active Magnetic Bearings With Rotor Eccentricity,” IEEE Trans. Magn, vol. 55, no. 12, Dec, 2019. [3] A. Vahaj, A. Rahideh, T. Lubin, “General Analytical Magnetic Model for Partitioned-Stator Flux-Reversal Machines With Four Types of Magnetization Patterns,” IEEE Trans. Magn, vol. 55, no. 11, Nov, 2019. [4] V. Z. Faradonbeh, A. Rahideh, M. M. Ghahfarokhi, “Analytical Modeling of Slotted, Surface-Mounted Permanent Magnet Synchronous Motors With Different Rotor Frames and Magnet Shapes,” IEEE Trans. Magn, vol. 57, no. 1, Jan, 2021 [5] H. K. Lee, K. H. Shin, T. K. Bang, “Experimental Verification and Analytical Study of Influence of Rotor Eccentricity on Electromagnetic Characteristics of Permanent Magnet Machine,” IEEE Trans. Appl, vol. 30, no. 4, Jun, 2020.