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Magnetic flux leakage (MFL) has been widely applied to the nondestructive testing (NDT) of ferromagnetic materials due to its simple operation, low cost, and steady signal. Its defects are evaluated based on the relationship between MFL signal and the geometrical characteristic of defect. In this paper, a three-dimensional (3D) mathematical model is developed for the magnetic leakage field of surface-breaking defects that are arbitrarily oriented inside ferromagnetic material. Firstly, a finite-length rectangular slot is used as a simplified and convenient representation of a surface-breaking defect. Then, the magnetic charge densities of slot walls in different surface-breaking orientations are analyzed theoretically. The distribution of the magnetic leakage field can ultimately be derived by vector synthesis. Both simulations and experiments are conducted to analyze the magnetic leakage field distributions in different magnetization orientations. The results show that with increasing the angle between the defect orientation and the magnetic field, the horizontal component of the leakage magnetic field increases as demonstrated by increasing the prominence of its single peak. At the same time, however, the vertical component shows a bimodal distribution. The proposed model can effectively describe the influence of defect orientation on MFL signals, which can offer practical guidelines for optimizing MFL detectors and improving defect assessment.
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Keywords:
- magnetic flux leakage /
- magnetic dipole /
- crack /
- surface-breaking orientation
[1] Wu D H, Huang S L, Zhao W, Xin J J 2009 Acta Petrol Sin. 30 136 (in Chinese)[吴德会, 黄松岭, 赵伟, 辛君君 2009 石油学报 30 136]
[2] Zatsepin N N, Shcherbinin V E 1966 Defektoskopiya5 50
[3] Wu J, Sun Y, Kang Y, Yang Y 2015 MAG IEEE Trans. Mechatron. 51 1
[4] Wang C X, Zhang W M, Song J G, Li W C, Chen K 2007 J. Beijing Inst. Technol. 27 395 (in Chinese)[王朝霞, 张卫民, 宋金刚, 李文春, 陈克 2007 北京理工 大学学报 27 395]
[5] Wang B B, Liao C R, Han L, Xie Y S, Shi X C 2011 Chin. J. Sens. Actuat. 24 238 (in Chinese)[汪滨波, 廖昌荣, 韩亮, 谢 云山, 石祥聪 2011 传感器技术学报 24 238]
[6] Yong L, Wilson J, Gui Y T 2007 NDT & E Int. 40 357
[7] Wu B, Wang Y J, Liu X C, C F He 2015 Smart. Mater. Struct. 24 075007
[8] Liu B Y, Qi Y G 2010 J. Shenyang Univ. Technol. 32 187 (in Chinese)[刘保余, 綦耀光 2010 沈阳工业大学学报 32 187]
[9] Du Z Y, Ruan J J, Yu S F, Liu B 2007 Proc. Chin. Soc. Electr. Eng. 27 108 (in Chinese)[杜志叶, 阮江军, 余世峰, 刘兵 2007 中国电机工程学报 27 108]
[10] Zhang Y, Ye Z F, Wang C 2009 NDT & E Int. 42 369
[11] Mandache C, Clapham L 2003 J. Phys. D:Appl. 36 24
[12] Liao C R, Liao Z, Han L, Wang B B, Shi X C, Xie Y S 2012 J. Chongqing Univ. 35 76 (in Chinese)[廖昌荣, 廖峥, 韩亮, 汪滨波, 石祥聪, 谢云山 2012 重庆大学学报 35 76]
[13] Liu M Q, Xu Z S, Wang J B 2005 Chin. Mech. Eng. 16 952 (in Chinese)[刘美全, 徐章遂, 王建斌 2005 中国机械工程 16 952]
[14] Xu Z S, Xu Y, Wang J B 2005 Quantitative Detection Principle and Application of Crack in MFL Method (Vol. 1) (Beijing:National Defend Industry Press) p124 (in Chinese)[徐章遂, 徐英, 王建斌 2005 裂纹漏磁定量检测原理与应用(上卷)(北京:国防工业 出版社) 第124页]
[15] Edwards C, Palmer S B 1986 J. Phys. D:Appl. Phys. 19 657
[16] Liu J J, Sun J J, Hu H Y, Xing X S 2005 Acta Phys. Sin. 54 2414 (in Chinese)[刘晶晶, 孙俊君, 胡海云, 邢修三 2005 54 2414]
[17] Wu D H, Liu Z L, Zhang Z Y, Xia X H 2013 J. Basic Sci. Eng. 21 1188 (in Chinese)[吴德会, 柳振凉, 张忠远, 夏晓昊 2013 应用基础与工程科学学报 21 1188]
[18] He Y Z 2013 Acta Phys. Sin. 62 084105 (in Chinese)[何永周 2013 62 084105]
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[1] Wu D H, Huang S L, Zhao W, Xin J J 2009 Acta Petrol Sin. 30 136 (in Chinese)[吴德会, 黄松岭, 赵伟, 辛君君 2009 石油学报 30 136]
[2] Zatsepin N N, Shcherbinin V E 1966 Defektoskopiya5 50
[3] Wu J, Sun Y, Kang Y, Yang Y 2015 MAG IEEE Trans. Mechatron. 51 1
[4] Wang C X, Zhang W M, Song J G, Li W C, Chen K 2007 J. Beijing Inst. Technol. 27 395 (in Chinese)[王朝霞, 张卫民, 宋金刚, 李文春, 陈克 2007 北京理工 大学学报 27 395]
[5] Wang B B, Liao C R, Han L, Xie Y S, Shi X C 2011 Chin. J. Sens. Actuat. 24 238 (in Chinese)[汪滨波, 廖昌荣, 韩亮, 谢 云山, 石祥聪 2011 传感器技术学报 24 238]
[6] Yong L, Wilson J, Gui Y T 2007 NDT & E Int. 40 357
[7] Wu B, Wang Y J, Liu X C, C F He 2015 Smart. Mater. Struct. 24 075007
[8] Liu B Y, Qi Y G 2010 J. Shenyang Univ. Technol. 32 187 (in Chinese)[刘保余, 綦耀光 2010 沈阳工业大学学报 32 187]
[9] Du Z Y, Ruan J J, Yu S F, Liu B 2007 Proc. Chin. Soc. Electr. Eng. 27 108 (in Chinese)[杜志叶, 阮江军, 余世峰, 刘兵 2007 中国电机工程学报 27 108]
[10] Zhang Y, Ye Z F, Wang C 2009 NDT & E Int. 42 369
[11] Mandache C, Clapham L 2003 J. Phys. D:Appl. 36 24
[12] Liao C R, Liao Z, Han L, Wang B B, Shi X C, Xie Y S 2012 J. Chongqing Univ. 35 76 (in Chinese)[廖昌荣, 廖峥, 韩亮, 汪滨波, 石祥聪, 谢云山 2012 重庆大学学报 35 76]
[13] Liu M Q, Xu Z S, Wang J B 2005 Chin. Mech. Eng. 16 952 (in Chinese)[刘美全, 徐章遂, 王建斌 2005 中国机械工程 16 952]
[14] Xu Z S, Xu Y, Wang J B 2005 Quantitative Detection Principle and Application of Crack in MFL Method (Vol. 1) (Beijing:National Defend Industry Press) p124 (in Chinese)[徐章遂, 徐英, 王建斌 2005 裂纹漏磁定量检测原理与应用(上卷)(北京:国防工业 出版社) 第124页]
[15] Edwards C, Palmer S B 1986 J. Phys. D:Appl. Phys. 19 657
[16] Liu J J, Sun J J, Hu H Y, Xing X S 2005 Acta Phys. Sin. 54 2414 (in Chinese)[刘晶晶, 孙俊君, 胡海云, 邢修三 2005 54 2414]
[17] Wu D H, Liu Z L, Zhang Z Y, Xia X H 2013 J. Basic Sci. Eng. 21 1188 (in Chinese)[吴德会, 柳振凉, 张忠远, 夏晓昊 2013 应用基础与工程科学学报 21 1188]
[18] He Y Z 2013 Acta Phys. Sin. 62 084105 (in Chinese)[何永周 2013 62 084105]
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