基于磁偶极子模型的材料缺陷漏磁检测正演问题的单元积分计算方法
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摘要
在基于磁偶极子解析模型的漏磁检测正演问题中,已有文献关于磁荷在缺陷壁上均匀分布的假设不成立。磁化后的缺陷材料相当于磁媒质,考虑到材料的非线性,磁荷在整个缺陷材料内及缺陷壁上非均匀分布。所以,该文从磁化后整个缺陷材料区域中磁化强度的分布出发,将单位体积内的磁偶极矩的矢量和等效为一个磁偶极矩,并作为磁场源点。从磁偶极子模型出发,推导出任意单元的磁媒质在场点处产生的磁场的积分公式,将整个缺陷材料的积分问题转换为对若干单元进行积分后的叠加。对于任一单元的积分问题,采用数值积分方法求解,并将该方法扩展到整个源区单元,最终整理得到任一场点处磁场的计算方程。通过COMSOL多物理场仿真软件搭建缺陷材料的漏磁场仿真模型,将仿真结果与计算结果进行对比分析,验证该方法的有效性。
In the magnetic flux leakage probing problem, the hypothesis that the magnetic charge is evenly distributed on the defective wall is not true, which is based on the magnetic dipole analysis model. The defective material is equivalent to the magnetic medium after magnetized. Considering the non-linearity of the material, the magnetic charge is non-uniformly distributed throughout the defective material and the defective wall. Therefore, considered the distribution of the magnetization strength in the area of the entire defective material, the vector sum of the magnetic dipole moments in the unit volume is equivalent to a magnetic dipole moment, as the source of the magnetic field. Based on the magnetic dipole model, the integral formula of the magnetic field generated by the magnetic medium of any unit is deduced, and the integral problem of the whole defective material is transformed into the superposition of several units. In this paper, the numerical integration method is used to solve the integral problem of any unit. Furthermore, this method is extended to the whole source region unit, and finally the calculation equation of the magnetic field at any field is obtained. The leakage magnetic field simulation model of the defective material was constructed by COMSOL multiphysics simulation software, and finally the simulation results were compared with the calculated results to verify the correctness of the method proposed in this paper.
In the magnetic flux leakage probing problem, the hypothesis that the magnetic charge is evenly distributed on the defective wall is not true, which is based on the magnetic dipole analysis model. The defective material is equivalent to the magnetic medium after magnetized. Considering the non-linearity of the material, the magnetic charge is non-uniformly distributed throughout the defective material and the defective wall. Therefore, considered the distribution of the magnetization strength in the area of the entire defective material, the vector sum of the magnetic dipole moments in the unit volume is equivalent to a magnetic dipole moment, as the source of the magnetic field. Based on the magnetic dipole model, the integral formula of the magnetic field generated by the magnetic medium of any unit is deduced, and the integral problem of the whole defective material is transformed into the superposition of several units. In this paper, the numerical integration method is used to solve the integral problem of any unit. Furthermore, this method is extended to the whole source region unit, and finally the calculation equation of the magnetic field at any field is obtained. The leakage magnetic field simulation model of the defective material was constructed by COMSOL multiphysics simulation software, and finally the simulation results were compared with the calculated results to verify the correctness of the method proposed in this paper.
引文
[1]王长龙,陈自力,马晓琳.漏磁检测的缺陷可视化技术[M].北京:国防工业出版社,2014.
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[15]雷银照.关于电磁场解析方法的一些认识[J].电工技术学报,2016,31(19):11-25.Lei Yinzhao.Reviews of analytical methods for electromagnetic fields[J].Transactions of China Electrotechnical Society,2016,31(19):11-15.
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[17]Chen Junjie,Huang Songling,Zhao Wei.Equivalent MFL model of pipelines for 3-D defect reconstruction using simulated annealing inversion procedure[J].International Journal of Applied Electromagnetics and Mechanics,2015,47(2):551-561.
[18]Priewald R H,Magele C,Ledger P D,et al.Fast magnetic flux leakage signal inversion for the reconstruction of arbitrary defect profiles in steel using finite elements[J].IEEE Transactions on Magnetics,2013,49(1):506-516.
[19]张帅,侯琬姣,张雪莹,等.基于真实乳腺模型的感应式磁声成像正问题[J].电工技术学报,2016,31(24):126-133,149.Zhang Shuai,Hou Wanjiao,Zhang Xueying,et al.Forward problem in magnetoacoustic tomography with magnetic induction based on real model of breast[J].Transactions of China Electrotechnical Society,2016,31(24):126-133,149.
[20]Wang Shunjin,Zhang Hua.Algebraic dynamics algorithm:numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm[J].Science of China(Series G),2007,50(1):53-69.
[21]王泽忠.简明电磁场数值计[M].北京:机械工业出版社,2011.
[22]吴德会,柳振凉,张忠远,等.漏磁检测中提离值影响的三维有限元仿真分析[J].应用基础与工程科学学报,2013,21(6):1188-1198.Wu Dehui,Liu Zhenliang,Zhang Zhongyuan,et al.3-D FEM simulation of lift-off effects on magnetic flux leakage testing[J].Journal of Basic Science and Engineering,2013,21(6):1188-1198.
[23]李静,胡先权.微小电流环与磁偶极子[J].重庆师范大学学报(自然科学版),2010,27(4):54-56.Li Jing,Hu Xianquan.Study on the piontlike circuit and magnetic dipole[J].Journal,of Chongqing Normal University(Natural Science).2010,27(4):54-56.
[24]刘莹,刘国松.磁偶极子远场的严格数学处理[J].长春工程学院学报(自然科学版),2014,15(2):125-128.Liu Ying,Liu Guosong.Rigorous mathematical treatment on the far field magnetic dipole[J].Changchun Institute of Technology(Natural Science Edition),2014,15(2):125-128.
[2]崔伟,黄松岭,赵伟.基于RBF网络的漏磁检测缺陷定量分析方法[J].清华大学学报(自然科学版),2006,46(7):1216-1218.Cui Wei,Huang Songling,Zhao Wei.Quantitative analysis method for MFL testing for oil and gas pipelines based on RBF neutral network[J].Journal of Tsinghua University(Science and Technology),2006,46(7):1216-1218.
[3]杜志叶,阮江军,余世峰,等.Hilbert变换在钢管漏磁检测缺陷定量化识别中的应用[J].电工技术学报,2007,22(1):17-21.Du Zhiye,Ruan Jiangjun,Yu Shifeng,et al.Quantitative analysis of magnetic flux leakage signal for steel pipe defects using Hilbert transform[J].Transactions of China Electrotechnical Society,2007,22(1):17-21.
[4]崔巍,戴光,李伟,等.基于漏磁成像的焊缝缺陷检测可视化方法研究[J].现代制造工程,2014(2):109-114.Cui Wei,Dai Guang,Li Wei,et al.The research on visualization method of the weld defect detection based on magnetic flux leakage imaging[J].Modern Manufacturing Engineering,2014(2):109-114.
[5]陈俊杰.油气管道漏磁检测缺陷三维轮廓反演方法研究[D].北京:清华大学,2015.
[6]Mukherjee D,Saha S,Mukhopadhyay S.Inverse mapping of magnetic flux leakage signal for defect characterization[J].NDT&E International,2013(54):198-208.
[7]杨理践,孙霄,高松巍.曲线拟合在管道漏磁内检测信号重构中的应用[J].沈阳工业大学学报,2012,34(6):671-676.Yang Lijian,Sun Xiao,Gao Songwei.Application of curve fitting in signal reconstruction of magnetic flux leakage innerdetection for pipeline[J].Journal of Shenyang University of Technology,2012,34(6):671-676.
[8]Priewald R H,Magele C,Ledger P D,et al.Fast magnetic flux leakage signal inversion for the reconstruction of arbitrary defect profiles in steel using finite elements[J].IEEE Transactions on Magnetics,2012,49(1):506-516.
[9]黄松岭,彭丽莎,赵伟,等.缺陷漏磁成像技术综述[J].电工技术学报,2016,31(20):55-63.Huang Songling,Peng Lisha,Zhao Wei,et al.Overview of defect magnetic flux leakage imaging technology[J].Transactions of China Electrotechnical Society,2016,31(20):55-63.
[10]Dutta S M,Ghorbel F H,Stanley R K.Dipole modeling of magnetic flux leakage[J].IEEE Transactions on Magnetics,2009,45(4):1959-1965.
[11]时朋朋.缺陷漏磁场磁偶极子模型的若干解析解[J].无损检测,2015,37(3):1-7.Shi Pengpeng.Analytical solutions of magnetic dipole model for defect leakage magnetic fields[J].Nondestructive Testing,2015,37(3):1-7.
[12]Leng J C,Xing H Y,Zhou G Q,et al.Dipole modelling ofmetal magnetic memory for V-notched plates[J].Insight—Non-Destructive Testing and Condition Monitoring,2013,55(9):498-503.
[13]王泽忠,金玉生,卢斌先.工程电磁场[M].北京:清华大学出版社,2011.
[14]徐超,王长龙,绳慧,等.三维磁场计算的有限元神经网络模型[J].电工技术学报,2012,27(11):125-132.Xu Chao,Wang Changlong,Sheng Hui,et al.FENN model for 3-D magnetic field calculation[J].Transactions of China Electrotechnical Society,2012,27(11):125-132.
[15]雷银照.关于电磁场解析方法的一些认识[J].电工技术学报,2016,31(19):11-25.Lei Yinzhao.Reviews of analytical methods for electromagnetic fields[J].Transactions of China Electrotechnical Society,2016,31(19):11-15.
[16]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.Wu Lijian,Wang Qunjing,Du Shijun,et al.Integral equation method for simulation of magnetic field of permanent magnetic spherical stepper[J].Proceedings of the CSEE,2004,24(9):192-197.
[17]Chen Junjie,Huang Songling,Zhao Wei.Equivalent MFL model of pipelines for 3-D defect reconstruction using simulated annealing inversion procedure[J].International Journal of Applied Electromagnetics and Mechanics,2015,47(2):551-561.
[18]Priewald R H,Magele C,Ledger P D,et al.Fast magnetic flux leakage signal inversion for the reconstruction of arbitrary defect profiles in steel using finite elements[J].IEEE Transactions on Magnetics,2013,49(1):506-516.
[19]张帅,侯琬姣,张雪莹,等.基于真实乳腺模型的感应式磁声成像正问题[J].电工技术学报,2016,31(24):126-133,149.Zhang Shuai,Hou Wanjiao,Zhang Xueying,et al.Forward problem in magnetoacoustic tomography with magnetic induction based on real model of breast[J].Transactions of China Electrotechnical Society,2016,31(24):126-133,149.
[20]Wang Shunjin,Zhang Hua.Algebraic dynamics algorithm:numerical comparison with Runge-Kutta algorithm and symplectic geometric algorithm[J].Science of China(Series G),2007,50(1):53-69.
[21]王泽忠.简明电磁场数值计[M].北京:机械工业出版社,2011.
[22]吴德会,柳振凉,张忠远,等.漏磁检测中提离值影响的三维有限元仿真分析[J].应用基础与工程科学学报,2013,21(6):1188-1198.Wu Dehui,Liu Zhenliang,Zhang Zhongyuan,et al.3-D FEM simulation of lift-off effects on magnetic flux leakage testing[J].Journal of Basic Science and Engineering,2013,21(6):1188-1198.
[23]李静,胡先权.微小电流环与磁偶极子[J].重庆师范大学学报(自然科学版),2010,27(4):54-56.Li Jing,Hu Xianquan.Study on the piontlike circuit and magnetic dipole[J].Journal,of Chongqing Normal University(Natural Science).2010,27(4):54-56.
[24]刘莹,刘国松.磁偶极子远场的严格数学处理[J].长春工程学院学报(自然科学版),2014,15(2):125-128.Liu Ying,Liu Guosong.Rigorous mathematical treatment on the far field magnetic dipole[J].Changchun Institute of Technology(Natural Science Edition),2014,15(2):125-128.