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Analytical modeling of coil impedance based on truncated region eigenfunction expansion method in eddy current tube inspection

Fan Meng-Bao Yin Ya-Dan Cao Bing-Hua

Analytical modeling of coil impedance based on truncated region eigenfunction expansion method in eddy current tube inspection

Fan Meng-Bao, Yin Ya-Dan, Cao Bing-Hua
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  • In order to calculate theoretically the coil impedance, the separation of variables method and the Cheng matrix method are used to establish the analytical model by applying the magnetic insulation condition in eddy current tube detection with encircling probes inside and outside respectively. In the established model, there exists a definite integral related to modified Bessel function. Gaussian integral algorithm is proposed to accurately perform the numerical calculation. Simulations are carried out on the thinning of a copper tube wall thickness using the presented model, traditional Dodd model and finite element model. Their results are in good agreement with each other, demonstrating that the derived analytical model is correct. Compared with the Dodd and finite element models, the improved model has some advantages such as good efficiency, easy adjustment of accuracy and so on.
    • Funds: Project supported by the National High Technology Research and Development Program of China (Grant No. 2008AA062202), the China Postdoctoral Science Foundation (Grant Nos. 20090460086, 201003606), and the Natural Science Foundation for Young Scholar of China Univeristy of Mining and Technology (Grant No. 2009A018).
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    Yusa N 2009 Nondestruct. Test. Evat. 24 39

    [2]

    Huang S L, Xu C, Zhao W, Xu P 2011 J. Tsinghua Univ. ( Sci. Techn.) 51 390 (in Chinese) [黄松岭, 徐琛, 赵伟, 许鹏 2011 清华大学学报(自然科学版) 51 390]

    [3]

    Chen D Z, Huang Z H, Liao S S, Nie Y 2007 J. Huazhong Univ. Sci. Techn. (Nat. Sci. Ed.) 35 41 (in Chinese) [陈德智, 黄振华, 廖述圣, 聂勇 2007 华中科技大学学报(自然科学版) 35 41]

    [4]

    Wu X J, Huang C, Ding X, Lin S Q, Shen G T 2010 Nondestr. Test. 32 127 (in Chinese) [武新军, 黄琛, 丁旭, 林树青, 沈功田 2010 无损检测 32 127]

    [5]

    Hao K S, Huang S L, Zhao W, Wang S 2011 Acta Phys. Sin. 60 078103 (in Chinese) [郝宽胜, 黄松岭, 赵伟, 王珅 2011 物理学报 60 078103]

    [6]

    Xie L, Lei Y Z 2006 Acta Phys. Sin. 55 4397 (in Chinese) [谢莉, 雷银照 2006 物理学报 55 4397]

    [7]

    Dodd C V, Deeds W E 1968 J. Appl. Phys. 39 2829

    [8]

    Dodd C V, Cheng C C, Deeds W E 1974 J. Appl. Phys. 45 638

    [9]

    Theodoulidis T P, Kriezis E E 2005 J. Mater. Process. Technol. 161 343

    [10]

    Theodoulidis T P 2004 Int. J. Appl. Electromagn. Mech. 19 207

    [11]

    Theodoulidis T P 2008 J. Appl. Phys. 103 024905

    [12]

    Theodoulidis T P, Poulakis N 2010 NDT E Int. 43 13

    [13]

    Bowler J R, Theodoulidis T P 2005 J. Phys. D 38 2861

    [14]

    Sun H, Bowler J R, Theodoulidis T P 2005 IEEE Trans. Magn. 41 2455

    [15]

    Skarlatos A, Theodoulidis T P 2010 IEEE Trans. Magn. 46 3885

    [16]

    Fan M B, Huang P J, Ye B, Hou D B, Zhang G X, Zhou Z K 2009 Acta Phys. Sin. 58 5950 (in Chinese) [范孟豹, 黄平捷, 叶波, 侯迪波, 张光新, 周泽魁 2009 物理学报 58 5950]

    [17]

    Hu J H 2008 Numerical Method (Xuzhou: China University of Ming and Technology Press) p119 (in Chinese) [胡建华 2008 数值计算方法 (徐州: 中国矿业大学出版社) 第119页]

  • [1]

    Yusa N 2009 Nondestruct. Test. Evat. 24 39

    [2]

    Huang S L, Xu C, Zhao W, Xu P 2011 J. Tsinghua Univ. ( Sci. Techn.) 51 390 (in Chinese) [黄松岭, 徐琛, 赵伟, 许鹏 2011 清华大学学报(自然科学版) 51 390]

    [3]

    Chen D Z, Huang Z H, Liao S S, Nie Y 2007 J. Huazhong Univ. Sci. Techn. (Nat. Sci. Ed.) 35 41 (in Chinese) [陈德智, 黄振华, 廖述圣, 聂勇 2007 华中科技大学学报(自然科学版) 35 41]

    [4]

    Wu X J, Huang C, Ding X, Lin S Q, Shen G T 2010 Nondestr. Test. 32 127 (in Chinese) [武新军, 黄琛, 丁旭, 林树青, 沈功田 2010 无损检测 32 127]

    [5]

    Hao K S, Huang S L, Zhao W, Wang S 2011 Acta Phys. Sin. 60 078103 (in Chinese) [郝宽胜, 黄松岭, 赵伟, 王珅 2011 物理学报 60 078103]

    [6]

    Xie L, Lei Y Z 2006 Acta Phys. Sin. 55 4397 (in Chinese) [谢莉, 雷银照 2006 物理学报 55 4397]

    [7]

    Dodd C V, Deeds W E 1968 J. Appl. Phys. 39 2829

    [8]

    Dodd C V, Cheng C C, Deeds W E 1974 J. Appl. Phys. 45 638

    [9]

    Theodoulidis T P, Kriezis E E 2005 J. Mater. Process. Technol. 161 343

    [10]

    Theodoulidis T P 2004 Int. J. Appl. Electromagn. Mech. 19 207

    [11]

    Theodoulidis T P 2008 J. Appl. Phys. 103 024905

    [12]

    Theodoulidis T P, Poulakis N 2010 NDT E Int. 43 13

    [13]

    Bowler J R, Theodoulidis T P 2005 J. Phys. D 38 2861

    [14]

    Sun H, Bowler J R, Theodoulidis T P 2005 IEEE Trans. Magn. 41 2455

    [15]

    Skarlatos A, Theodoulidis T P 2010 IEEE Trans. Magn. 46 3885

    [16]

    Fan M B, Huang P J, Ye B, Hou D B, Zhang G X, Zhou Z K 2009 Acta Phys. Sin. 58 5950 (in Chinese) [范孟豹, 黄平捷, 叶波, 侯迪波, 张光新, 周泽魁 2009 物理学报 58 5950]

    [17]

    Hu J H 2008 Numerical Method (Xuzhou: China University of Ming and Technology Press) p119 (in Chinese) [胡建华 2008 数值计算方法 (徐州: 中国矿业大学出版社) 第119页]

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    [9] LI MING-XIAN. MEASUREMENT OF THE DETECTION IMPEDANCE AND A DESIGN FOR INCREASING THE SENSITIVITY OF THE DETECTOR IN THE ACOUSTIC IMPEDANCE METHOD. Acta Physica Sinica, 1974, 137(3): 3-12. doi: 10.7498/aps.23.3
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  • Received Date:  26 June 2011
  • Accepted Date:  28 April 2012
  • Published Online:  20 April 2012

Analytical modeling of coil impedance based on truncated region eigenfunction expansion method in eddy current tube inspection

  • 1. College of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China;
  • 2. College of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China
Fund Project:  Project supported by the National High Technology Research and Development Program of China (Grant No. 2008AA062202), the China Postdoctoral Science Foundation (Grant Nos. 20090460086, 201003606), and the Natural Science Foundation for Young Scholar of China Univeristy of Mining and Technology (Grant No. 2009A018).

Abstract: In order to calculate theoretically the coil impedance, the separation of variables method and the Cheng matrix method are used to establish the analytical model by applying the magnetic insulation condition in eddy current tube detection with encircling probes inside and outside respectively. In the established model, there exists a definite integral related to modified Bessel function. Gaussian integral algorithm is proposed to accurately perform the numerical calculation. Simulations are carried out on the thinning of a copper tube wall thickness using the presented model, traditional Dodd model and finite element model. Their results are in good agreement with each other, demonstrating that the derived analytical model is correct. Compared with the Dodd and finite element models, the improved model has some advantages such as good efficiency, easy adjustment of accuracy and so on.

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