T.P. Theodoulidis, C.S. Antonopoulos and E.E. Kriezis
The evaluation of eddy currents in cylindrical geometries is examined analytically by using a method, which utilises the second order magnetic vector potential. As an example the…
Abstract
The evaluation of eddy currents in cylindrical geometries is examined analytically by using a method, which utilises the second order magnetic vector potential. As an example the three‐dimensional problem of the calculation of eddy currents inside a long conducting cylinder excited by a saddle shaped coil is studied.
Grzegorz Tytko and Łukasz Dawidowski
Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex…
Abstract
Purpose
Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex numbers. Their computation consists of finding complex roots of a complex function that satisfies the electromagnetic interface conditions. The purpose of this paper is to present a method of computing complex eigenvalues that are roots of such a function.
Design/methodology/approach
The proposed approach involves precise determination of regions in which the roots are found and applying sets of initial points, as well as the Cauchy argument principle to calculate them.
Findings
The elaborated algorithm was implemented in Matlab and the obtained results were verified using Newton’s method and the fsolve procedure. Both in the case of magnetic and nonmagnetic materials, such a solution was the only one that did not skip any of the eigenvalues, obtaining the results in the shortest time.
Originality/value
The paper presents a new effective method of locating complex eigenvalues for analytical solutions of eddy current problems containing a conductive material with a hole.
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Subhra Paul and Jonathan Z. Bird
A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived…
Abstract
Purpose
A 3-D analytic modeling technique for calculating the eddy current distribution, force and power loss in a conductive plate of finite width and thickness is presented. The derived equations are expressed in a general form so that any magnetic source can be utilized. The model assumes the length of the conductive plate is large and the thickness of the plate is thin but not negligible. The paper aims to discuss these issues.
Design/methodology/approach
The conducting and non-conducting regions are formulated in terms of decoupled magnetic vector potential components. In order to accurately compute the eddy current fields and forces the source field only needs to be applied on the surface of the conducting plate. The primary focus is on reducing the eddy current computational time.
Findings
The accuracy of the presented approach is verified by utilizing a magnetic rotor that has both a rotational and translational motion. The proposed method is computationally efficient and its accuracy is validated using the finite element method.
Research limitations/implications
The conducting plate thickness is assumed to be thin (but not negligible), and this enables the field interaction through the edge of the plate to be neglected. The lateral force is not calculated in the proposed approach.
Practical implications
The calculation procedure presented is computationally fast and therefore this can enable the 3-D eddy current forces to be computed in near real-time.
Originality/value
This paper presents a fully 3-D analytic based eddy current formlation for computing the eddy current fields and forces in a conducting plate of finite thickness and finite width. The modeling approach is shown to be computationally accurate and relatively fast.
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Piotr Putek, Guillaume Crevecoeur, Marian Slodička, Roger van Keer, Ben Van de Wiele and Luc Dupré
The purpose of this paper is to solve an inverse problem of structure recognition arising in eddy current testing (ECT) – type NDT. For this purpose, the space mapping (SM…
Abstract
Purpose
The purpose of this paper is to solve an inverse problem of structure recognition arising in eddy current testing (ECT) – type NDT. For this purpose, the space mapping (SM) technique with an extraction based on the Gauss‐Newton algorithm with Tikhonov regularization is applied.
Design/methodology/approach
The aim is to have a computationally fast recognition procedure of defects since the monitoring results in a large amount of data points that need to be analyzed by 3D eddy current model. According to the SM optimization, the finite element method (FEM) is used as a fine model, while the model based on an integral method such as the volume integral method (VIM) serves as a coarse model. This approach, being an example of a two‐level optimization method, allows shifting the optimization load from a time consuming and accurate model to the less precise but faster coarse surrogate.
Findings
The application of this method enables shortening of the evaluation time that is required to provide the proper parameter estimation of surface defects.
Research limitations/implications
In this work only the specific kinds of surface defects were considered. Therefore, the reconstruction of arbitrary shapes of defects when using real measurement data from ECT system can be treated in further research.
Originality/value
The paper investigated the eddy current inverse problem. According to aggressive space mapping method, a suitable coarse model is needed. In this case, for the purpose of 3D defect reconstruction, the reduced VIM approach was applied. From a practical view point, the authors demonstrated that the two‐level inversion procedures allow saving of up to 50 percent CPU time in comparison with the optimization by means of regularized Gauss‐Newton algorithm in the same FE model.
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Fatima Barrarat, Karim Rayane, Bachir Helifa, Samir Bensaid and Iben Khaldoun Lefkaier
Detecting the orientation of cracks is a major challenge in the development of eddy current nondestructive testing probes. Eddy current-based techniques are limited in their…
Abstract
Purpose
Detecting the orientation of cracks is a major challenge in the development of eddy current nondestructive testing probes. Eddy current-based techniques are limited in their ability to detect cracks that are not perpendicular to induced current flows. This study aims to investigate the application of the rotating electromagnetic field method to detect arbitrary orientation defects in conductive nonferrous parts. This method significantly improves the detection of cracks of any orientation.
Design/methodology/approach
A new rotating uniform eddy current (RUEC) probe is presented. Two exciting pairs consisting of similar square-shaped coils are arranged orthogonally at the same lifting point, thus avoiding further adjustment of the excitation system to generate a rotating electromagnetic field, eliminating any need for mechanical rotation and focusing this field with high density. A circular detection coil serving as a receiver is mounted in the middle of the excitation system.
Findings
A simulation model of the rotating electromagnetic field system is performed to determine the rules and characteristics of the electromagnetic signal distribution in the defect area. Referring to the experimental results aimed to detect artificial cracks at arbitrary angles in underwater structures using the rotating alternating current field measurement (RACFM) system in Li et al. (2016), the model proposed in this paper is validated.
Originality/value
CEDRAT FLUX 3D simulation results showed that the proposed probe can detect cracks with any orientation, maintaining the same sensitivity, which demonstrates its effectiveness. Furthermore, the proposed RUEC probe, associated with the exploitation procedure, allows us to provide a full characterization of the crack, namely, its length, depth and orientation in a one-pass scan, by analyzing the magnetic induction signal.
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Long Thanh Cung, Nam Hoang Nguyen, Pierre Yves Joubert, Eric Vourch and Pascal Larzabal
The purpose of this paper is to propose an approach, which is easy to implement, for estimating the thickness of the air layer that may separate metallic parts in some…
Abstract
Purpose
The purpose of this paper is to propose an approach, which is easy to implement, for estimating the thickness of the air layer that may separate metallic parts in some aeronautical assemblies, by using the eddy current method.
Design/methodology/approach
Based on an experimental study of the coupling of a magnetic cup core coil sensor with a metallic layered structure (consisting of first metal layer/air layer/second metal layer), which is confirmed by finite element modelling simulations, an inversion technique relying on a polynomial forward model of the coupling is proposed to estimate the air layer thickness. The least squares and the nonnegative least squares algorithms are applied and analysed to obtain the estimation results.
Findings
The choice of an appropriate inversion technique to optimize the estimation results is dependent on the signal-to-noise ratio of measured data. The obtained estimation error is smaller than a few percent, for both simulated and experimental data. The proposed approach can be used to estimate both the air layer thickness and the second metal layer thickness simultaneously/separately.
Originality/value
This model-based approach is easy to implement and available to all types of eddy current sensors.
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Martin Koll, Daniel Wöckinger, Christoph Dobler, Gereon Goldbeck, Gerd Bramerdorfer, Stefan Schuster, Stefan Scheiblhofer, Norbert Gstöttenbauer and Johann Reisinger
This paper aims to investigate the reliable thickness, and more generally, the geometric and material parameter determination of thin electrically conductive and diamagnetic…
Abstract
Purpose
This paper aims to investigate the reliable thickness, and more generally, the geometric and material parameter determination of thin electrically conductive and diamagnetic coatings on conductive and ferromagnetic substrates, e.g. steel, using eddy current testing (ECT).
Design/methodology/approach
The analytical model of an ECT coil arrangement known from the literature is analyzed to evaluate the numerical simulation performed by a Finite Element (FE) program. The latter is used to investigate the influence of the sheet edge on the measurement result. Finally, a measurement setup is presented and the unknown geometric and material parameters are estimated from measurement data of different sample sheets at different air gaps.
Findings
Generally, valid mesh rules are found for a very accurate FE analysis of eddy current problems with large air gaps. The influence of large air gaps on the parameter estimation is emphasized. Moreover, the formulated hypotheses can be widely confirmed by measurements.
Research limitations/implications
In this paper, electrical steel sheets coated with a conductive oven-cured ink are used. This sample configuration creates a discrete transition between the substrate and the coating as present in the analytical modeling approaches. Furthermore, the ferromagnetic substrate’s nonlinear B-H curve is not considered in the analytical model so far.
Originality/value
The analytical model is known from the literature. However, real practical measurements have not been carried out with the discussed setup. Furthermore, well-known literature on eddy current measurements usually only considers constant and very small air gaps.
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In eddy current nondestructive testing, a probe with a ferrite core such as an E-core coil is usually used to detect and locate defects such as cracks and corrosion in conductive…
Abstract
Purpose
In eddy current nondestructive testing, a probe with a ferrite core such as an E-core coil is usually used to detect and locate defects such as cracks and corrosion in conductive material. However, the E-core coil has some disadvantages, such as large volume and difficulty in the process of winding the coils. This paper aims to present a novel T-core probe and its analytical model used for evaluating hidden holes in a multi- layer conductor.
Design/methodology/approach
By using a cylindrical coordinate system, the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived, and the expansion coefficients of the solutions are obtained by matching the boundary and interface conditions between the regions. By using the truncated region eigenfunction expansion method, the final expression in closed form for the impedance of the multi-turn coil is worked out, and the impedance calculation is performed in Mathematica. For frequencies ranging from 100 Hz to 100 kHz, both the impedance changes of the T-core coil above the multi-layer conductor without a hidden hole and in the absence of the layered conductor were calculated, and the influence of a hidden hole in the multi-layer conducting structure on the impedance change was investigated.
Findings
The correctness of the analytical model of the T-core coil was verified by the finite element method and experiments. The proposed T-core coil has higher sensitivity than an air-core coil, and similar sensitivity and smaller size than an E-core coil.
Originality/value
A new T-core coil probe and its accurate theoretical model for defect evaluation of conductor were presented; probe and analytical model can be used in probe design, detection process simulation or can be directly used in defect evaluation of multi-layer conductor.
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In eddy current nondestructive testing, ferrite-cored probes are usually used to detect and locate defects such as cracks and corrosion in conductive materials. However, the…
Abstract
Purpose
In eddy current nondestructive testing, ferrite-cored probes are usually used to detect and locate defects such as cracks and corrosion in conductive materials. However, the generic analytical model for evaluating corrosion in layered conductor using ferrite-cored probe has not yet been developed. The purpose of this paper is to propose and verify the analytical model of an E-cored probe for evaluating corrosion in layered conductive materials.
Design/methodology/approach
A cylindrical coordinate system is adopted and the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived first, and then the expansion coefficients of the solution are obtained by matching the boundary and interface conditions between the regions and the subregions. Finally the closed-form expression of the impedance of the multi-turn coil is derived by using the truncated region eigenfunction expansion (TREE) method, and the impedance calculation is carried out in Mathematica. In the frequency range of 100 Hz to 10 kHz, the impedance changes of the E-cored coil and air-cored coil due to the layered conductor containing corrosion are calculated, respectively, and the influences of corrosion on the coil impedance change are investigated.
Findings
An analytical model for the detection and evaluating of corrosion in layered conductive materials using E-cored probe is proposed. The model can quickly and accurately calculate the impedance change of E-cored coil due to corrosion in layered conductor. The correctness of the analytical model is verified by finite element method and experiments.
Originality/value
An accurate theoretical model of E-cored probe for evaluating corrosion of multilayer conductor is presented. The analytical model can be used to detect the inhomogeneity of layered conductor, design ferrite-cored probe or directly evaluate the corrosion defects of layered conductors.
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Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by…
Abstract
Purpose
Solutions for the earth return mutual impedance play an important role in analyzing couplings of multi-conductor systems. Generally, the mutual impedance is approximated by Pollaczek integrals. The purpose of this paper is devising fast algorithms for calculation of this kind of improper integrals and its applications.
Design/methodology/approach
According to singular points, the Pollaczek integral is divided into two parts: the finite integral and the infinite integral. The finite part is computed by combining an efficient Levin method, which is implemented with a Chebyshev differential matrix. By transforming the integration path, the tail integral is calculated with help of a transformed Clenshaw–Curtis quadrature rule.
Findings
Numerical tests show that this new method is robust to high oscillation and nearly singularities. Thus, it is suitable for evaluating Pollaczek integrals. Furthermore, compared with existing method, the presented algorithm gives high-order approaches for the earth return mutual impedance between conductors over a multilayered soil with wide ranges of parameters.
Originality/value
An efficient truncation strategy is proposed to accelerate numerical calculation of Pollaczek integral. Compared with existing algorithms, this method is easier to be applied to computation of similar improper integrals, such as Sommerfeld integral.