An analytical solution to the problem of a cup-cored coil located over a conducting plate with a hole

Abstract

Pot-core coils are utilised in eddy current non-destructive testing (NDT) to detect defects in conducting materials. In this paper, an analytical solution to the problem of a cup-cored coil placed over a three-layer plate with an inner hole is obtained. Using the truncated region eigenfunction expansion (TREE) method, expressions for the magnetic vector potential of the filamentary coil, and final formulae for the impedance of the cylindrical coil, are derived. These formulae make it possible to model conducting magnetic and non-magnetic plates with an internal hole, a surface hole, a subsurface hole and a through hole. The final expressions in a closed form are implemented in MATLAB. The calculation results are verified using finite element method (FEM) models created with COMSOL Multiphysics, Finite Element Method Magnetics (FEMM) and Ansys Maxwell software packages. Very good agreement for the coil impedance components is obtained within the whole studied frequency range of 1 kHz to 100 kHz.