I-cored Coil Probe Located Above a Conductive Plate with a Surface Hole

Grzegorz Tytko; Leszek Dziczkowski

doi:10.1515/msr-2018-0002

Abstract

This work presents an axially symmetric mathematical model of an I-cored coil placed over a two-layered conductive material with a cylindrical surface hole. The problem was divided into regions for which the magnetic vector potential of a filamentary coil was established applying the truncated region eigenfunction expansion method. Then the final formula was developed to calculate impedance changes for a cylindrical coil with reference to both the air and to a material with no hole. The influence of a surface flaw in the conductive material on the components of coil impedance was examined. Calculations were made in Matlab for a hole with various radii and the results thereof were verified with the finite element method in COMSOL Multiphysics package. Very good consistency was achieved in all cases.

References

[1] Theodoulidis, T.P., Bowler, J.R. (2004). The truncated region eigenfunction expansion method for the solution of boundary value problems in eddy current non-destructive evaluation. Review of Progress in Quantitative Nondestructive Evaluation, 24A, 403–408.
Search in Google Scholar Back to article
[2] Kolyshkin, A. (2013). Solution of direct eddy current problems with cylindrical symmetry. In Proceedings of the International Conference on Application of Contemporary Non-destructive Testing in Engineering, 4–6 September 2013. Portoroz, Ljubljana, Slovenia: University of Ljubljana, 347–351.
Search in Google Scholar Back to article
[3] Koliskina, V. (2014). Semi-analytical solution of an eddy current problem for a conducting medium with a surface flaw. International Journal of Mathematical Models and Methods in Applied Sciences, 8, 473-480.
Search in Google Scholar Back to article
[4] Theodoulidis, T.P., Bowler, J.R. (2005). Eddy-current interaction of a long coil with a slot in a conductive plate. IEEE Transactions on Magnetics, 41 (4), 1238–1247.10.1109/TMAG.2005.844838
Open DOI Search in Google Scholar Back to article
[5] Koliskina, V., Kolyshkin, A. (2015). Mathematical model for eddy current testing of metal plates with two cylindrical flaws. In IEEE 15th International Conference on Environment and Electrical Engineering (EEEIC), 10-13 June 2015, 374-377.10.1109/EEEIC.2015.7165190
Search in Google Scholar Back to article
[6] Hao, K., Huang, S., Zhao, W., Wang, S., Dong, J. (2011). Analytical modelling and calculation of pulsed magnetic field and input impedance for EMATs with planar spiral coils. NDT&E International, 44 (3), 274–280.10.1016/j.ndteint.2011.01.001
Search in Google Scholar Back to article
[7] Theodoulidis, T.P., Kriezis, E.E. (2006). Eddy Current Canonical Problems (With Applications to Nondestructive Evaluation). Duluth (Georgia), USA: Tech Science Press.
Search in Google Scholar Back to article
[8] Lu, Y., Bowler, J.R, Theodoulidis, T.P. (2012). An analytical model of a ferrite-cored inductor used as an eddy current probe. Journal of Applied Physics, 111 (10), 103907.10.1063/1.4716189
Search in Google Scholar Back to article
[9] Tytko, G. Dziczkowski, L. (2015). E-cored coil with a circular air gap inside the core column used in eddy current testing. IEEE Transactions on Magnetics, 51 (9), 6201804.10.1109/TMAG.2015.2440420
Search in Google Scholar Back to article
[10] Chunfeng, L., Wei, T., Huaming, L., Yingying, J., Hui, Z. (2015). Analytical modeling for the grating eddy current displacement sensors. Measurement Science Review, 15 (1), 44-51.
Search in Google Scholar Back to article
[11] Tytko, G., Dziczkowski, L. (2017). An analytical model of an I-cored coil with a circular air gap. IEEE Transactions on Magnetics, 53 (4), 6201104.10.1109/TMAG.2016.2645678
Search in Google Scholar Back to article
[12] Delves, L.M., Lyness, J.N. (1967). A numerical method for locating the zeros of an analytic function. Mathematics of Computation, 21 (100), 543–560.10.1090/S0025-5718-1967-0228165-4
Search in Google Scholar Back to article
[13] Dellnitz, M., Schütze, O., Zheng, Q. (2002). Locating all the zeros of an analytic function in one complex variable. Journal of Computational and Applied Mathematics, 138 (2), 325-333.10.1016/S0377-0427(01)00371-5
Search in Google Scholar Back to article

I-cored Coil Probe Located Above a Conductive Plate with a Surface Hole

Abstract

Paradigm

My account