Abstract：Magentostatic field calculation method is widely used in many areas, such as analyzing magnetic field characteristics of ferromagnetic objects. According to the magnetization property of uniformly magnetized body, an improved surface integral magentostatic field calculation method is presented in this paper. Compared with the volume integral method, the surface integral method is simpler in computation and the integral singularity is eliminated. Irregular hexahedron is used to mesh the complex ferromagnetic objects because of its flexibility. In order to eliminate the errors caused by numerical integration, the analytical formulas of the hexahedral coupling coefficient are deduced. Based on the above analysis, 3D magnetostatic field computation method with hexahedral surface integral is provided. Finally, two examples, a hollow ferromagnetic sphere and a hollow ferromagnetic cylinder in geomagnetic field, are given to verify its efficiency and accuracy. The results of the two examples are satisfying and the proposed method could be applied in the practical engineering.
周国华, 肖昌汉, 刘胜道, 高俊吉. 基于六面体单元表面磁场积分法求解三维静磁场[J]. 电工技术学报, 2009, 24(3): 1-7.
Zhou Guohua, Xiao Changhan, Liu Shengdao, Gao Junji. 3D Magnetostatic Field Computation With Hexahedral Surface Integral Equation Method. Transactions of China Electrotechnical Society, 2009, 24(3): 1-7.
[1] Froidurot B, Rouve L L, Foggia A, et al. Calculation of electrical machine magnetic stray fields[C]. IEE Proc. Sci. Meas. Technol, 2002, 149 (5):190-193. [2] Erik Jørgensen, Oleksiy S Kim, Peter Meincke, et al. Higher order hierarchical discretization scheme for surface integral equations for layered media[J]. IEEE Transactions on Geoscience and Remote Sensing, 2004, 42 (4):764-772. [3] Yun Huichu, Weng Chochew. Large-scale comput- ation for electrically small structures using surface- integral equation method[J]. Microwave and Optical Technology Letters, 2005, 47 (6):525-530. [4] Wolfgang Hafla, André Buchau, Friedemann Groh, et al. Efficient integral equation method for the solution of 3D magnetostatic problems[J]. IEEE Transactions on Magnetics, 2005, 41 (5):1408-1411. [5] Özgür Ergül, Levent Gürel. The use of curl- conforming basis functions for the magnetic-field integral equation[J]. IEEE Transactions on Antennas and Propagation, 2006, 54 (7):1917-1926. [6] Slobodan Babic, Cevdet Akyel, Minya M Gavriboric. Calculation improvement of 3D linear magnetostatic field based on fictitious magnetic surface charge[J]. IEEE Transactions on Magnetics, 2000, 36 (5): 3125-3127. [7] Olivier Chadebec, Jean Louis Coulomb, Jean Paul Bongiraud, et al. Recent improvements for solving inverse magnetostatic problem applied to thin shells[J]. IEEE Transactions on Magnetics, 2002, 38 (2): 1005-1008. [8] Olivier Chadebec, Coulomb JeanLouis, Fleur Janet. A review of magnetostatic moments method[J]. IEEE Transactions on Magnetics, 2006, 42 (4):515-520. [9] 冯之鑫, 韩朔. 非线性静磁场问题分析计算的积分方程法[J]. 电工技术学报, 1993, 8 (3): 6-9. [10] 郭成豹, 何明, 周耀忠. 积分方程法计算舰船感应磁场[J]. 海军工程大学学报, 2001, 13 (6): 71-74. [11] 吴立建, 王群京, 杜世俊, 等. 磁场积分法在永磁步进球形电动机场分析中的应用[J]. 中国电机工程学报, 2004, 24 (9): 192-197. [12] 郭成豹, 张晓锋, 肖昌汉, 等. 地磁场中空心铁磁圆柱体纵向磁化状态数值分析[J]. 哈尔滨工程大学学报, 2006, 27 (6): 886-890. [13] 樊明武, 颜威利.电磁场积分方程法[M].北京:机械工业出版社, 1988. [14] 盛剑霓. 工程电磁场数值分析[M]. 西安: 西安交通大学出版社, 1991. [15] Sawa K, Hirano T. An evaluation of the computa- tional error near the boundary with magnetostatic field calculation by B.E.M[J]. IEEE Transactions on Magnetics, 1990, 26 (2):403-406. [16] 周克定. 工程电磁场专论[M]. 武汉: 华中工学院出版社, 1986. [17] 成都地质学院, 武汉地质学院, 河北地质学院, 合肥工业大学.应用地球物理学——磁法教程[M]. 北京:地质出版社, 1980. [18] 周国华, 肖昌汉, 闫辉, 等. 基于单元表面积分和微粒群优化算法的铁磁物体感应磁场求解方法[C]. 全国电工理论与新技术2007学术会议论文集, 2007, 8: 322-326. [19] 周耀忠, 张国友. 舰船磁场分析计算[M]. 北京: 国防工业出版社, 2004.
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