An Analytical Model of a New T-cored Coil Used for Eddy Current Nondestructive Evaluation
Keywords:
Analytical model, coil impedance, eddy current testing, non-destructive evaluation, T-core coil, truncated region eigenfunction expansionAbstract
A model of an axisymmetric probe with a new T-core coil that can be used in eddy current testing is developed. The truncated region eigenfunction expansion (TREE) method is used to analyze the coil impedance problem of the T-core coil located above a multi-layer conductive material. First, the magnetic vector potential expressions of each region are formulated, then the coefficients of the magnetic vector potential are derived by using the boundary conditions, finally, the closed form expression of the coil impedance is obtained. The normalized impedance changes of the T-core coil caused by the presence or absence of the multi-layer conductor are calculated using Mathematica. The presented T-core coil is compared with I-core coil and air-core coil. The effects of the T-core parameter a2, relative permeability μf and the thickness of the top section on the change in the coil impedance are discussed respectively. The analytical calculation results are compared with the results of finite element method, and the two agree very well, which verifies the correctness of the proposed T-core coil model.
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References
T. P. Theodoulidis, “Model of ferrite-cored probes for eddy current nondestructive evaluation,” J. Appl. Phys., vol. 93, no. 5, pp. 3071-3078, 2003.
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., vol. 111, no. 10, pp. 103907-10, 2012.
G. Tytko and L. Dziczkowski, “I-cored coil probe located above a conductive plate with a surface hole,” Measurement Science Review, vol. 18, no. 1, pp. 7-12, 2018.
G. Tytko and L. Dziczkowski, “An analytical model of an I-cored coil located above a conductive material with a hole,” The European Physical Journal Applied Physics., vol. 82, no. 21001, pp.1- 7, 2018.
Y. Li, Y. Wang, Z. Liu, I. M. Z. Abidin and Z. Chen, “Characteristics regarding lift-off intersection of pulse-modulation eddy current signals for evaluation of hidden thickness loss in cladded 2 4 6 8 10 12 14 16 18 8 10 12 14 16 18 a 2 [mm] R [] TREE FEM 2 4 6 8 10 12 14 16 18 -35 -30 -25 -20 -15 -10 a 2 [mm] X [] TREE FEM 0 500 1000 1500 2000 2500 3000 12 12.5 13 13.5 14 f R [] TREE FEM 0 1 2 3 4 5 12.5 13 13.5 14 14.5 15 h 2 -h1 [mm] R [] TREE FEM ZHANG: A MODEL OF A NEW T-CORED COIL FOR EDDY CURRENT EVALUATION 1103 conductors,” Sensors., vol. 19, no. 4102, pp. 1-14, 2019.
H. Bayani, T. Theodoulidis, and I. Sasada, Application of Eigenfunction Expansions to Eddy Current NDE: A Model of Cup-Cored Probes. London, U.K.: IOP Press, pp. 57-64, 2007.
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,” Journal of Applied Physics, vol. 111, no. 7, pp. 2829-64, 2012.
G. Tytko and L. Dziczkowski, “Calculation of the impedance of an E-cored coil placed above a conductive material with a surface hole,” Measurement Science Review, vol. 19, no. 2, pp. 43-47, 2019.
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. Progr. Quant. Non-Destruct. Eval., vol. 24A, pp. 403-408, 2004.
T. P. Theodoulidis and E. E. Kriezis, Eddy Current Canonical Problems (With Applications to Nondestructive Evaluation). Tech Sci. Press, Duluth, Georgia, pp. 106-121, 2006.
F. Jiang and S. Liu, “Calculation and analysis of an analytical model for magnetic field monitoring based on TREE in eddy current testing,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 12, pp. 1489-1497, 2018.
G. Tytko and L. Dziczkowski, “Fast calculation of the filamentary coil impedance using the truncated region eigenfunction expansion method,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 12, pp. 1461-1466, 2018.
H. Zaidi, L. Santandrea, G. Krebs, Y. Le Bihan, and E. Demaldent, “FEM technique for modeling eddy-current testing of ferromagnetic media with small skin depth,” IEEE Trans. Magn., vol. 50, no. 2, pp. 129-132, 2014.
B. Helifa, M. Féliachi, I. K. Lefkaier, B. Fouad, A. Zaoui, and N. Lagraa, “Characterization of surface cracks using eddy current NDT simulation by 3DFEM and inversion by neural network,” Applied Computational Electromagnetics Society Journal, vol. 31, no. 2, pp. 187-194, 2016.
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products. New York, Academic Press, 1980.
