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Using the second-order vector potential and Lorentz reciprocity theorem, the non-axisymmetric eddy current field induced by a probe coil outside a conducting ferromagnetic pipe is obtained analytically, where the probe coil is differently oriented: its axis being along the pipe radial direction, parallel to the pipe axis, along the pipe circumferential direction. Then, the time-domain expressions of induced voltage and eddy current density in the pipe are obtained through the Laplace inverse transformation, by calculating the residues of poles. Furthermore, the diffusion process of pulsed eddy current in the pipe, and the detection sensitivity of the time-domain induced voltage signal to the wall thickness are studied. Finally, the analytical solutions are verified through the experimental results of a steel pipe. It is found that when the probe coil is positioned such that its axis is perpendicular to the pipe axis, the strongest and the most sensitive induction voltage signal for detecting the wall thickness of a ferromagnetic pipe is obtained.
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Keywords:
- pulsed eddy current electromagnetic field /
- second-order vector potential /
- ferromagnetic pipe /
- time-domain analytical solutions
[1] Cheng W 2012 J. Nondestr. Eval. 31 215
[2] Dodd C V, Deeds W E 1968 J. Appl. Phys. 39 2829
[3] Lei Y Z 2000 Analytical Methods for Tme-Harmonic Electromagnetic Fields (Beijing: Science Press) p178 (in Chinese) [雷银照 2000 时谐电磁场解析方法 (北京: 科学出版社) 第178页]
[4] Theodoulidis T P 2002 Res. Nondestruct. Eval. 14 111
[5] Theodoulidis T P 2004 Int. J. Appl. Electromagne Mech. 19 207
[6] Skarlatos A, Theodoulidis T P 2010 IEEE Trans. Magn. 46 3885
[7] Burke S K, Theodoulidis T P 2004 J. Phys. D 37 485
[8] Theodoulidis T P, Burke S K 2004 Electromagn. Nondestr. Eval. VIII 24 11
[9] Theodoulidis T, Skarlatos A 2012 IEEE Trans. Magn. 48 2392
[10] Chen X L, Lei Y Z 2012 Proc. CSEE 32 176 (in Chinese) [陈兴乐, 雷银照 2012 中国电机工程学报 32 176]
[11] Mao X F, Lei Y Z 2013 NDT & E Int. 54 69
[12] Mao X F, Lei Y Z 2013 NDT & E Int. 60 121
[13] Xie L, Lei Y Z 2006 Acta Phys. Sin. 55 4397 (in Chinese) [谢莉, 雷银照 2006 55 4397]
[14] Xie L, Lei Y Z 2007 Chin. Phys. 16 2523
[15] Jaeger J C 1940 Philos. Mag. Ser. 29 18
[16] Theodoulidis T 2008 IEEE Trans. Magn. 44 1894
[17] Fan M B, Cao B H, Yang X F 2010 Acta Phys. Sin. 59 7570 (in Chinese) [范孟豹, 曹丙花, 杨雪峰 2010 59 7570]
[18] Xiao C Y, Zhang J 2010 Chin. Phys. B 19 120302
[19] Chen X L, Lei Y Z 2013 Trans. China Electrotech. Soc. 28 1 (in Chinese) [陈兴乐, 雷银照 2013 电工技术学报 28 1]
[20] Smythe W R 1950 Static and Dynamic Electricity (2nd Ed.) (New York: McGraw-Hill)
[21] Bronshtein I N, Semendyayev K A, Musiol G, Muehlig H 2007 Handbook of Mathematics (5th Ed.) (Berlin: Springer) p718
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[1] Cheng W 2012 J. Nondestr. Eval. 31 215
[2] Dodd C V, Deeds W E 1968 J. Appl. Phys. 39 2829
[3] Lei Y Z 2000 Analytical Methods for Tme-Harmonic Electromagnetic Fields (Beijing: Science Press) p178 (in Chinese) [雷银照 2000 时谐电磁场解析方法 (北京: 科学出版社) 第178页]
[4] Theodoulidis T P 2002 Res. Nondestruct. Eval. 14 111
[5] Theodoulidis T P 2004 Int. J. Appl. Electromagne Mech. 19 207
[6] Skarlatos A, Theodoulidis T P 2010 IEEE Trans. Magn. 46 3885
[7] Burke S K, Theodoulidis T P 2004 J. Phys. D 37 485
[8] Theodoulidis T P, Burke S K 2004 Electromagn. Nondestr. Eval. VIII 24 11
[9] Theodoulidis T, Skarlatos A 2012 IEEE Trans. Magn. 48 2392
[10] Chen X L, Lei Y Z 2012 Proc. CSEE 32 176 (in Chinese) [陈兴乐, 雷银照 2012 中国电机工程学报 32 176]
[11] Mao X F, Lei Y Z 2013 NDT & E Int. 54 69
[12] Mao X F, Lei Y Z 2013 NDT & E Int. 60 121
[13] Xie L, Lei Y Z 2006 Acta Phys. Sin. 55 4397 (in Chinese) [谢莉, 雷银照 2006 55 4397]
[14] Xie L, Lei Y Z 2007 Chin. Phys. 16 2523
[15] Jaeger J C 1940 Philos. Mag. Ser. 29 18
[16] Theodoulidis T 2008 IEEE Trans. Magn. 44 1894
[17] Fan M B, Cao B H, Yang X F 2010 Acta Phys. Sin. 59 7570 (in Chinese) [范孟豹, 曹丙花, 杨雪峰 2010 59 7570]
[18] Xiao C Y, Zhang J 2010 Chin. Phys. B 19 120302
[19] Chen X L, Lei Y Z 2013 Trans. China Electrotech. Soc. 28 1 (in Chinese) [陈兴乐, 雷银照 2013 电工技术学报 28 1]
[20] Smythe W R 1950 Static and Dynamic Electricity (2nd Ed.) (New York: McGraw-Hill)
[21] Bronshtein I N, Semendyayev K A, Musiol G, Muehlig H 2007 Handbook of Mathematics (5th Ed.) (Berlin: Springer) p718
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