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

Abstract

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.