Abstract：As to ironless long-stroke planar motor with moving permanent magnet, the distortion of the magnetic field at the end of Halbach permanent magnet array will cause the end-effect, and the positioning and moving precision will be influenced by the thrust ripple caused by end-effect. Therefore, establishing an accurate three dimensional analytical model containing the magnetic field at the end of Halbach permanent magnet array is an important foundation for force modeling, avoiding the thrust ripple, improving the utilization rate of the end magnetic field, and reducing the energy- consuming of each coil. Take ironless synchronous planar motor with moving permanent magnet for study, the magnetic field properties at the sine-like and end-distorted area are analyzed. The mechanical pseudo cycle is defined by the distance between zero magnetic field characteristic boundaries, and then a completed three dimensional analytical magnetic field model of Halbach permanent magnet array is derived by the new Fourier series and spatial integral technology. Finally, the accuracy and effectiveness of the magnetic field modeling method proposed in this paper are verified by comparing with the finite element and the existing analytical calculation approach.
宋玉晶,张鸣,朱煜,李鑫. 基于伪周期的Halbach永磁阵列三维磁场端部效应建模研究[J]. 电工技术学报, 2015, 30(12): 162-170.
Song Yujing,Zhang Ming,Zhu Yu,Li Xin. Three Dimensional Magnetic Field End-effect Modeling for Halbach Permanent Magnet Array Based on Pseudo Periodic. Transactions of China Electrotechnical Society, 2015, 30(12): 162-170.
[1] W. J. Kim, High-Precision Planar Magnetic Levitation, Ph. D. thesis, Massachusetts Inst. Technol., Cambridge, Jun. 1997. [2] J. W. Jansen, Magnetically levitated planar actuator with moving magnets: Electromechanical analysis and design, Ph. D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, Nov. 2007. [3] Lee, M. G., S. Q. Lee, and D. -G. Gweon, Analysis of Halbach magnet array and its application to linear motor[J]. Mechatronics, 2004. 14(1): 115-128 [4] Silva-Rivas J C, Kim W. Multivariable control and optimization of a compact 6-DOF precision positioner with hybrid and digital filtering[J]. Transactions on Control Systems Technology, 2013, 21(5): 1641-1651. [5] . 周赣, 黄学良, 蒋浩, 等. Halbach 型磁悬浮平面电动机电流控制方法[J]. 电工技术学报, 2010 (5): 69-75. [6] Rovers J M M, Jansen J W, Lomonova E A. Novel force ripple eduction method for a moving-magnet linear synchronous motor with a segmented stator[C]. Electrical Machines and Systems, 2008. ICEMS 2008. International Conference on. IEEE, 2008: 2942-2947. [7] Jin, P, et al. General Analytical Method for Magnetic Field Analysis of Halbach Magnet Arrays Based on Magnetic Scalar Potential[J]. Journal of Magnetics, 2013. 18(2): 95-104. [8] Taniguchi, T., L. Eciolaza, and M. Sugeno. Look- Up-Table controller design for nonlinear servo systems with piecewise bilinear models. in Fuzzy Systems (FUZZ), 2013 IEEE International Conference on. 2013. IEEE. [9] Jeroen de Boeij, Multi-Level Contactless Motion System, Ph. D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2009. [10] Achterberg, J, et al. Model based commutation contai- ning edge coils for a moving magnet planar actuator [J]. IEEE Transactions on Industry Applications, 2010, 130: 1147-1152. [11] Ham, C., et al., Study of a Hybrid Magnet Array for an Electrodynamic Maglev Control[J]. Journal of Magnetics, 2013. 18(3): p. 370-374. [12] Furlani E P. Permanent magnet and electromechanical devices[electronic resource]: materials, analysis, and applications[J/OL]. Access Online via Elsevier, 2001. [13] 黄学良, 张前, 周赣. 一种无铁 Halbach 型永磁直线电机[J]. 电工技术学报, 2010(6): 1-6. [14] C. M. M. van Lierop,Magnetically levitated planar actuator with moving magnets: Electromechanical analysis and design, Ph. D. thesis, Eindhoven University of Technology, Eindhoven, Netherlands, 2008. [15] Liu, Y, et al. Optimization of voice coil motor to enhance dynamic response based on an improved magnetic equivalent circuit model. Magnetics, IEEE Transactions on, 2011. 47(9): 2247-2251. [16] Amrhein, M. and P. T. Krein. Magnetic equivalent circuit simulations of electrical machines for design purposes. in Electric Ship Technologies Symposium, 2007. ESTS'07. IEEE. [17] Freschi, F. and M. Repetto, Natural Choice of Integra- tion Surface for Maxwell Stress Tensor Computation. IEEE Transactions on Magnetics, 2013. 49(5): 1717-1722. [18] Meessen, K., J. Paulides, and E. Lomonova, Force Calculations in 3D Cylindrical Structures Using Fourier Analysis and the Maxwell Stress Tensor, 2013. [19] 宋玉晶, 张鸣, 朱煜. Halbach永磁阵列磁场解析求解及推力建模研究[J]. 电工技术学报, 2014, 29(11): 61-67. [20] 杜怿, 程明, 邹国棠. 初级永磁型游标直线电机设计与静态特性分析[J]. 电工技术学报, 2013, 27(11): 22-30.
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