Abstract：Dual-stator permanent magnet motors have attracted more and more attention in electric vehicles, renewable energy sources, and flywheel energy storage systems because of their advantages of compact structure, large power density, and high output torque. Nevertheless, the noise caused by the high-frequency electromagnetic force has become a serious bottleneck issue restricting the vibration-noise analysis of motors. Usually, finite element analysis (FEA) has been widely used in the multi-physical coupling analysis of electrical machinery. However, FEA faces some prominent disadvantages, including the strong dependence on mesh quality and high computational cost. In recent years, a meshless technique has received significant attentions. But it is worth noting that the shape function of meshless method can hardly fulfill the character of the Kronecker function. Hence, it is urgent to develop a quick and accurate coupling calculation technique that can combine advantages of two methods mentioned above. Taking a dual-stator permanent magnet electric machine used in electric vehicles as an example, we proposed a multi-physical field coupling analysis technique combining FEA with an optimized meshless approach for accurate prediction of vibration-noise distribution. Firstly, a two-dimensional FEA electromagnetic model is established, then high-frequency electromagnetic forces exerted on the stators and permanent magnets under arbitrary currents are thoroughly studied. Secondly, forces are mapped into the three-dimensional structural model for harmonic response analysis employing FEA and the conventional meshless method, respectively. With the coupled multi-physics field analysis, precise boundary conditions and data transfer are keys to the precision of the proposed multi-physical modelling technology. In this research, it can be achieved by constructing a non-matching mesh data mapping matrix at the interface between FEA and meshless computational domains. Afterward, the vibration frequency response analysis results are treated as boundary conditions to calculate the radiated noise using FEA. Thirdly, the matrix of conventional meshless method suffers from the ill-conditioned defect in the process of convergence calculation. To mitigate this drawback, an optimized meshless method is proposed by modifying the local basis functions to recalculate the vibration-noise equation. Then the results of coupled simulation based on the traditional coupled FEA-meshless method, the optimized coupled FEA-meshless method, and the complete FEA coupled method are compared. Finally, the accuracy of the simulations is verified by a noise test, which indicated that the multi-physics field-coupled analytical approach was valid. The following conclusions can be drawn from the simulation analysis: (1) Electromagnetic-vibration-noise evaluation considering high-frequency current harmonics are performed. It is found that frequencies of the vibration and noise in dual-stator rotor motors are quite different from those of conventional permanent magnet motors, namely the frequency of the magnetic force is same as the frequency of the current. Besides, forces from permanent magnets should also be fully considered. (2) To accomplish the data mapping, a non-matching mesh data mapping matrix at the interface between FEA and meshless computational domains are constructed to impose the boundary conditions, which can satisfy not only the continuity of function, but also the continuity of radial and tangential derivatives. (3) This paper proposes an optimized meshless approach based on the non-singular weighted function method. Compared with FEA and experiment, it has been confirmed that the optimized meshless method proposed can not only guarantee the calculation accuracy but also reduce the calculation time significantly.
李思泽, 徐炜, 金振, 徐涛. 一种基于有限元法与改进无网格法耦合的双定子电机振动噪声分析方法[J]. 电工技术学报, 2023, 38(19): 5112-5127.
Li Size, Xu Wei, Jin Zhen, Xu Tao. A Novel Vibration-Noise Calculation Method by Coupling Finite Element Analysis and Optimized Meshless Method for Dual-Stator Electric Machine. Transactions of China Electrotechnical Society, 2023, 38(19): 5112-5127.
[1] Wang Jiyao, Qin Ling, Xu Wei.Design of adjustable cogging torque permanent magnet machine with high contrast ratio[J]. IEEE Transactions on Transportation Electrification, 2022, 8(3): 3478-3488. [2] Zhu Z Q, Howe D.Electrical machines and drives for electric, hybrid, and fuel cell vehicles[J]. Proceedings of the IEEE, 2007, 95(4): 746-765. [3] Lin Fu, Zuo Shuguang, Deng Wenzhe, et al.Noise prediction and sound quality analysis of variable-speed permanent magnet synchronous motor[J]. IEEE Transactions on Energy Conversion, 2017, 32(2): 698-706. [4] Ye Caiyong, Yu Dezuan, Liu Kaifeng, et al.Research of a stator PM excitation solid rotor machine for flywheel energy storage system[J]. IEEE Transactions on Industrial Electronics, 2022, 69(12): 12140-12151. [5] Yin Hang, Zhang Hengliang, Hua Wei, et al.Quantitative analysis of electromagnetic forces by decoupling air-gap field modulation and force modulation in rotor-permanent-magnet machines[J]. IEEE Transactions on Industrial Electronics, 2023, 70(2): 1310-1320. [6] Yasa Y, Sozer Y, Garip M.Acoustic noise mitigation of switched reluctance machines with leaf springs[J]. IEEE Transactions on Industrial Electronics, 2023, 70(2): 1250-1260. [7] Cao Junci, Deng Xiaoqing, Li Dong, et al.Electromagnetic analysis and optimization of high-speed maglev linear synchronous motor based on field-circuit coupling[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(2): 118-123. [8] Bao Xiaohua, Ming Shuai, Chen Guowei, et al.Analysis of radial electromagnetic force characteristics of inverter drive double skewed rotor induction motor[J]. Transactions of China Electro-technical Society, 2023, 38(10): 2613-2624. [9] Hafeez M B, Krawczuk M, Nisar K S, et al.A finite element analysis of thermal energy inclination based on ternary hybrid nanoparticles influenced by induced magnetic field[J]. International Communications in Heat and Mass Transfer, 2022, 135: 106074. [10] Li Size, Xu Wei.Vibration analysis of permanent magnet synchronous motor using coupled finite element analysis and optimized meshless method[J]. Nonlinear Dynamics, 2022, 108(1): 167-189. [11] Bourantas G, Zwick B F, Joldes G R, et al.Simple and robust element-free Galerkin method with almost interpolating shape functions for finite deformation elasticity[J]. Applied Mathematical Modelling, 2021, 96: 284-303. [12] Ye Zisheng, Hu Xiaozhe, Pan Wenxiao.A multigrid preconditioner for spatially adaptive high-order meshless method on fluid-solid interaction problems[J]. Computer Methods in Applied Mechanics and Engineering, 2022, 400: 115506. [12] Cui Miao, Peng Haifeng, Xu Bingbing, et al.A new radial integration polygonal boundary element method for solving heat conduction problems[J]. International Journal of Heat and Mass Transfer, 2018, 123: 251-260. [14] Qin Xia, Shen Yajing, Chen Wei, et al. Bending and free vibration analyses of circular stiffened plates using the FSDT mesh-free method[J]. International Journal of Mechanical Sciences, 2021, 202/203: 106498. [15] Wang Lihua, Qian Zhihao.A meshfree stabilized collocation method (SCM) based on reproducing kernel approximation[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 371: 113303. [16] Zahur U, Baseer U, Wajid K, et al.Proportional topology optimisation with maximum entropy-based meshless method for minimum compliance and stress constrained problems[J]. Engineering With Computers, 2022, 38(6): 5541-5561. [17] Qu Renhao, Jiang Weikang.An analytical method for vibration characteristics analysis of motor stator core[J]. Journal of Vibration and Shock, 2021, 40(3): 82-87. [18] Wang Gepeng, Jin Wende, Zeng Xiangyang, et al.Analysis and control research on core vibration of UHV shunt reactor[J]. Transactions of China Electro-technical Society, 2022, 37(9): 2190-2198. [19] Wu Q, Liu Fengbin, Cheng Yumin.The interpolating element-free Galerkin method for three-dimensional elastoplasticity problems[J]. Engineering Analysis With Boundary Elements, 2020, 115: 156-167. [20] He Xingchuan, Yang J S, Mei G X, et al.Bending and free vibration analyses of ribbed plates with a hole based on the FSDT meshless method[J]. Engineering Structures, 2022, 272: 114914. [21] Bourantas G C, Mountris K A, Loukopoulos V C, et al.Strong-form approach to elasticity: hybrid finite difference-meshless collocation method (FDMCM)[J]. Applied Mathematical Modelling, 2018, 57: 316-338. [22] Zhu Ziyuan, Wang Gang, Xuan Zhihong, et al.Vibration analysis of the combined conical-cylindrical shells coupled with annular plates in thermal environment[J]. Thin-Walled Structures, 2023, 185: 110640. [23] Liu Gang, Zhang Hanfang, Chi Cheng, et al.research on node data mapping algorithm for the 2D coupling electromagnetic-fluid-thermal fields[J]. Transactions of China Electrotechnical Society, 2018, 33(1): 148-157. [24] Cheng Yumin.Meshless methods[M]. Beijing: Science Press, 2015. [25] Shi Fangmin, Zhu Liwei.Research on modal vibration mode of permanent magnet synchronous motor stator system[J]. Electric Machines and Control System, 2018, 233: 77-81.
2023, Vol. 38 
