Calculation of the Eddy-Current Flow Around a Cylindrical Through-Hole in a Finite-Thickness Plate

Abstract

A semianalytical solution to the eddy-current induction problem in a conducting, nonmagnetic plate near a cylindrical through-hole is derived by means of the second-order vector potential and the domain truncation technique. The construction of a solution, which simultaneously satisfies the field continuity across the cylindrical surface of the hole and the planar interfaces of the plate, proves to be a very challenging problem, and thus, a special superposition of partial subsolutions is proposed. The presented solution is part of a more general development aiming at the calculation of the probe interaction with material flaws located in the vicinity of the hole by means of the integral equation formalism. These tasks will be the subject of a future paper. The comparison of the semianalytical results against both finite-element simulations as well as experimental data demonstrates excellent agreement.Index Terms-Domain truncation, eddy-current testing (ECT), fastener inspection, impedance calculation, mode matching. 0018-9464

Study of the non-linear eddy-current response in a ferromagnetic plate: Theoretical analysis for the 2D case

“…We seek solution to the linear, odd-parity, eddy-current problem of a cylindrical coil over an infinite plate excited by an harmonic current. This is a typical eddy-current testing situation, whose solution is very well studied in the literature [11,12]. This section will thus serve as a reminder of the basic results, which will be presented without proof.…”

“…In the above analysis all the sums comprise infinite number of terms. In reality, the numerical evaluation of the solution requires the truncation of both the Fourier spectrum and the modal sums in (11), (12) and (19),(30). This is a common issue in modal techniques, and is exactly the point where the approximation of the method is introduced (it can be seen as the counterpart of the discussion about the mesh in numerical techniques).…”

“…The developed solution follows the approach of the polarisation technique, that is, the problem is linearised assuming a constant permeability in the ferromagnetic piece, and the unknown magnetic polarisation is determined via fixed-point iterations. The thus resulting linear problem is a multilayer eddy-current problem with a distributed magnetic source exceeding the domain of the ferromagnetic piece, which is treated by means of the truncated region eigenfunctions expansion (TREE) [11,12]. A simpler version of the proposed approach has been applied for the study of the 1D problem [13].…”

Calculation of the Impedance of an E-cored Coil Placed Above a Conductive Material with a Surface Hole

“…The probe-coil placed above the test object with a flaw was analyzed by applying the pulsed eddy current technique (PEC) [1]- [3] with the employment of the grating eddy current displacement sensor (GECDS) [4], and considered as the inverse problem [5], [6]. The analytical mathematical models of a coil brought closer to conductive material with a hole were obtained for air-cored coils [7]- [9] and I-cored coils [10], [11] using the truncated region eigenfunction expansion (TREE) method. In eddy current testing, however, the most commonly used probes are pot core probes.…”

The theory of eddy current nondestructive evaluation by using the volume integral equation method

“…Except for a few of special configurations, analytical solutions usually can only be found for unflawed canonical geometries, which are widely used in calculation of the incident field for the probe-flaw interaction modeling [24,25,26,27,9]. Although semi-analytical solutions are achievable for certain structures with ideal cracks by applying some simplifying approximations, such as TREE method [14,15] and thin-skin approximation at high frequency [16,17], it is expedient to seek numerical approximations of the probe signals and electromagnetic fields since numerical methods are more flexible to handle general probe-flaw interaction problem.…”