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An eddy current model of pot-cored coil for testing multilayer conductors with a hole

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Języki publikacji
EN
Abstrakty
EN
Pot-cored coils are commonly used as probes in eddy current testing. In this paper, an analytical model of such a coil placed over a three-layer plate with a hole has been presented. The proposed solution enables the modelling of both magnetic and non-magnetic conductive plates that contain different types of hole, i.e. a through, a surface, an inner or a subsurface hole. The problem was solved by using the truncated region eigenfunction expansion (TREE) method. The analysis was carried out in a cylindrical coordinate system in which the solution domain was radially limited. With the employment of the filamentary coil, the expressions for the magnetic vector potential, and subsequently for the impedance of the cylindrical coil were obtained. The final formulas were presented in a closed form and then implemented in Matlab. The resistance and reactance values were compared with the results obtained in the experiment and using the finite element method in the Comsol Multiphysics package. In each of the cases, good agreement was obtained.
Rocznik
Strony
1311--1317
Opis fizyczny
Bibliogr. 35 poz., rys., tab.
Twórcy
autor
  • Institute of Electronics, The Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland
Bibliografia
  • [1] C. Maierhofer, G. Zacher, C. Kohl, and J. Wöstmann, “Evaluation of Radar and Complementary Echo Methods for NDT of Concrete Elements”, J. Nondestruct. Eval. 27, 47–57 (2008).
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  • [4] I. Altpeter, G. Dobmann, and K. Szielasko, “Electromagnetic NDT to characterize usage properties of flat steel products”, CINDE Journal 36 (4), 6–9 (2015).
  • [5] R. K ̨edra and M. Rucka, “Preload monitoring in a bolted joint using Lamb wave energy”, Bull. Pol. Ac.: Tech. 67 (6), 1161–1169 (2019).
  • [6] C.F. John et al., “Corrosion behavior of ZrC particles reinforcement with Al-12Si composites by weight loss method using acidic media”, Bull. Pol. Ac.: Tech. 66 (1), 9–16 (2018).
  • [7] I. Babic, F. Sirois, and C. Akyel, “Validity check of mutual inductance formulas for circular filaments with lateral and angular misalignments”, Prog. Electromagn. Res. M 8, 15–26 (2009).
  • [8] S. Zhang, J. Tang, and W. Wu, “Comparison the impedance calculation models of coil above conductive plates”, in IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, China, 2015.
  • [9] L. Liang, “Analysis of inductance calculation of coaxial circular filamentary coils, thin-wall solenoids, and disk coils using inverse hyperbolic functions”, IET Sci. Meas. Technol. 10, 754–760 (2016).
  • [10] G. Tytko and L. Dziczkowski, “Fast calculation of the filamentary coil impedance using the truncated region eigenfunction expansion method”, ACES Journal, 33, 1461–1466 (2018).
  • [11] Y. Zhilichev, “Analysis of eddy currents in rectangular coils by integral equation method in sub-domains”, IEEE Trans. Magn. 50, 7028110 (2014).
  • [12] S. Zhang, J. Tang, and W. Wu, “Calculation model for the induced voltage of pick-up coil excited by rectangular coil above conductive plate”, 2015 IEEE International Conference on Mechatronics and Automation (ICMA), Beijing, 2015, pp. 1805–1810, doi: 10.1109/ICMA.2015.7237760.
  • [13] P. Putek et al., “Two-level approach for solving the inverse problem of defects identification in Eddy Current Testing – type NDT”, Arch. Electr. Eng. 60, 497–518 (2011).
  • [14] V. Chudacik and M. Smetana, “Tilt-shift eddy current probe impact on information value of response signal”, Arch. Electr. Eng. 65, 133–140 (2016).
  • [15] D. Wen, M. Fan, B. Cao, Z. Xue and P. Wang, “A PEC thrice subtraction method for obtaining permeability invariance feature in conductivity measurement of ferromagnetic samples”, Appl. Sci. 9, 2745 (2019).
  • [16] Z. Xue, M. Fan, B. Cao, and D. Wen, “A fast numerical method for the analytical model of pulsed eddy current for pipelines”, Insight – Non-Destructive Testing and Condition Monitoring 62, 27–33 (2020).
  • [17] O. Martens et al., “Fast precise eddy current measurement of metals”, IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Houston, USA, 2018.
  • [18] F. Jiang and S. Liu, “Calculation and analysis of an analytical model for magnetic field monitoring based on TREE in eddy current testing”, ACES Journal 33, 1489–1497 (2018).
  • [19] Y. Le Bihan, J. Pávó, and C. Marchand, “Characterization of small cracks in eddy current testing”, IET Colloquium on Reliability of Electromagnetic Systems, Paris, France, 2007.
  • [20] Y. Lu, J.R. Bowler, and T.P. Theodoulidis, “An analytical model of a ferrite-cored inductor used as an eddy current probe”, J. Appl. Phys. 111, 103907 (2012).
  • [21] G. Tytko and L. Dziczkowski, “I-cored coil probe located above a conductive plate with a surface hole”, Meas. Sci. Rev. 18, 7–12 (2018).
  • [22] Y. Zhu, B. Chen, Y. Luo, and R. Zhu, “Inductance calculations for coaxial iron-core coils shielded by cylindrical screens of high permeability”, IET Electr. Power Appl. 13 (6), 802–811 (2019), doi: 10.1049/iet-epa.2018.5667.
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  • [24] T.L. Cung, P.Y. Joubert, E. Vourch, and P. Larzabal, “Interactions of an eddy current sensor and a multilayered structure”, Electronics Letters 46, 1550–1551 (2010).
  • [25] F. Sakkaki and H. Bayani, “Solution to the problem of E-cored coil above a layered half-space using the method of truncated region eigenfunction expansion”, J. Appl. Phys. 111, 07E717 (2012).
  • [26] G. Tytko and L. Dziczkowski, “Calculation of the impedance of an E-cored coil placed above a conductive material with a surface hole”, Meas. Sci. Rev. 19, 43–47 (2019).
  • [27] T.P. Theodoulidis and J.R. Bowler, “The truncated region eigenfunction expansion method for the solution of boundary value problems in eddy current non-destructive evaluation”, Rev. Prog. Quant. Nondestruct. Eval. 24A, 403–408 (2004).
  • [28] T.P. Theodoulidis and E.E. Kriezis, Eddy Current Canonical Problems (With Applications to Nondestructive Evaluation). Tech Science Press, Duluth (Georgia), USA, 2006.
  • [29] D. Vasic, D. Ambru, V. Bilas, “Computation of the eigenvalues for bounded domain eddy-current models with coupled regions”, IEEE Trans. Magn. 52, 7004310 (2016).
  • [30] T. Theodoulidis and A. Skarlatos, “Computation of eigenvalues and eigenfunctions in the solution of eddy current problems with modal methods”, 22nd International Conference on the Computation of Electromagnetic Fields (COMPUMAG 2019), Paris, France, 2019.
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  • [32] M. Dellnitz, O. Schutze, and Q. Zheng, “Locating all the zeros of an analytic function in one complex variable”, J. Comput. Appl. Math. 138, 325–333 (2002).
  • [33] P. Kravanja, M. Barel, O. Ragos, M.N. Vrahatis, and F.A. Zafiropoulos, “ZEAL: A mathematical software package for computing zeros of analytic functions”, Comput. Phys. Commun. 124, 212–232 (2000).
  • [34] C.V. Dodd and W.E. Deeds, “Analytical solutions to eddy-current probe-coil problems”, J. Appl. Phys. 39, 2829–2838 (1968).
  • [35] G. Tytko and Ł. Dawidowski, “Locating complex eigenvalues for analytical eddy-current models used to detect flaws”, Compel-Int. J. Comp. Math. Electr. Electron. Eng. 38, 1800–1809 (2019).
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d7865de7-7e52-44c0-b586-da36adf1e126
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