Intelligent sensing for non-destructive testing using eddy currents

When a metallic surface is tested by the eddy-current technique, defects produce events on the electrical signal coming from the sensor whose particular signature is a function of different factors such as the shape, size and position of any defects. Thanks to the introduction of modern digital signal processing methods, the quality of detection of events in the signal may be appreciably improved. The reliability of the decision mechanism, entrusted with reducing non-detection and limiting false alarms, is then increased and allows consideration of automatic testing. The work presented here was done jointly by the Institut de Recherches de la Sidérurgie Française (IRSID) of the Usinor-Sacilor group and the aboratoire d' Automatique et de Recherche Appliquée (LARA) of the Centre de Recherche en Automatique de Nancy (CRAN).     

The electric characteristics of HTS double-pancake coil with AC pulse over currents

A double pancake coil was designed and manufactured with a 36-m long Bi-2223/Ag tape. The tape was insulated by 25 μm thick Kapton tapes, which can stand a voltage of 400 V_rms in liquid nitrogen. The whole double pancake was impregnated with epoxy resin. AC over-current experiments of the coil were performed by applying constant AC voltages to the two terminals of the coil and lasted for 3 s. The experiment began first at a lower voltage of 33.6 V_rms, and then the voltage stepped up till the coil was burned out at the pulse voltage of 202.7 V_rms. All of the experiments were carried out with the coil dipped in liquid nitrogen. The current waveforms were measured. The impedance and resistance characters of the HTS coil with its over pulse currents were analyzed from the experiment results. At the end of this paper, some conclusions derived from the experiment results and their analyses are given, which are helpful for the safety operating of the HTS coils in power applications.     

Steady-state finite-element solver for rotor eddy currents in permanent-magnet machines using a shooting-Newton/GMRES approach

This paper presents a two-dimensional steady-state finite-element solver, incorporating mechanical motion, that calculates eddy-current losses in the rotors of permanent-magnet machines. A shooting-Newton method is used to determine the periodic solution of the electromagnetics. Computation of the shooting-Newton Jacobian is avoided by using a generalized minimum residual (GMRES) linear solver. This method is more computationally efficient than performing transient analysis until convergence. The solver can be used to compare the rotor losses of different design choices for a high-speed permanent-magnet machine. Results show that rotor losses can be reduced significantly by laminating the rotor backiron, segmenting the permanent-magnet poles, increasing the number of stator slots, and closing the stator slots.     

Analytic model for a nonlaminated cylindrical magnetic actuator including eddy currents

The eddy currents induced within a nonlaminated cylindrical magnetic actuator by a changing field have a fundamental influence on the actuator's performance. Understanding of these dynamics is essential in designing high-performance actuators and developing control algorithms for them. This paper presents an analytical approach to modeling the relationship between applied magnetomotive force and mechanical force. The approach is based on dividing the actuator into elements according to the flux distribution inside the actuator and finding the frequency-dependent reluctance of the flux paths of each element. An analytic model and its half-order simplification are derived, both of which are explicitly dependent on actuator material and geometric properties. Performance predictions from both analytic models are compared with finite-element analysis, demonstrating the accuracy of the models.     

A simple dynamic model for eddy currents in a magnetic actuator

This paper presents a simple dynamic model of eddy currents in a magnetic actuator. The model is based on the application of Maxwell's equations to a homogeneous ferromagnetic conductive material. The resulting diffusion equation is solved in two dimensions for a cross-sectional cut through a rectangular bar; boundary conditions are imposed by a sinusoidally varying actuator coil current. The utility of the new modeling approach is illustrated by predicting the dynamic performance of a magnetic bearing actuator. The predictions are found to be in good agreement with measured values. The model provides a new and convenient method of modeling the relationships among voltage, current, force, and flux in magnetic circuits containing eddy currents     

Dependence of the magnetic field of eddy currents on the parameters of a crack in aluminum alloys

On the basis of rigorous solutions of diffraction problems, we calculate the dependences of the magnetic field strength of eddy currents on changes in the length of an extended undersurface crack, the depth of its occurrence, and inclination to the surface as well as on a local change in the specific conductance of the base material. We determine the structural features of the field induced by a defect of the type of an arbitrarily oriented crack for the solution of defectometry problems. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 2, pp. 99–103, March–April, 2008.     

Meshless method for numerical modeling of pulsed eddy currents

Meshless methods have attracted great attention due to their advantage in geometric representation. In this paper, a meshless element-free Galerkin method is applied for the first time to solve pulsed eddy-current problems. Detailed mathematical derivations and the numerical implementation are discussed. The model is validated against analytic solutions for two canonical cases.     

Eddy currents in a transverse MRI gradient coil

A transverse gradient coil (x- or y-coil) of an MRI-scanner is modeled as a network of curved circular strips placed at the surface of a cylinder. The current in this network is driven by a time-harmonic source current. The low frequency applied allows for an electro-quasi-static approach. The strips are thin and the current is assumed to be uniformly distributed in the thickness direction. For the current distribution in the width direction of the strips, an integral equation is derived. Its logarithmically singular kernel represents inductive effects related to the occurrence of eddy currents. For curved circular strips of width much smaller than the radius of the cylinder one may locally replace the curved circular strip by a tangent plane circular strip. This plane geometry preserves the main characteristics of the transverse current distribution through the strips. The current distribution depends strongly on the in-plane curvature of the strips. The Petrov–Galerkin method, using Legendre polynomials, is applied to solve the integral equation and shows fast convergence. Explicit results are presented for two examples: a set of 1 strip and one of 10 strips. The results show that the current distributions are concentrated near the inner edges and that resulting edge-effects, both local and global, are non-symmetric. This behavior is more apparent for higher frequencies and larger in-plane curvatures. Results have been verified by comparison with finite-element results.     

The sizing and location of small cracks in holes using eddy currents

An eddy current method for detecting, positioning and sizing small cracks in holes is described. For NDT applications, a record of crack damage in a hole can be obtained and for mechanical testing, fatigue crack nucleation and growth data from cracks in holes can be determined. Preliminary results are presented.     

Finite element scheme for transient 3D eddy currents

A transient 3-D finite-element model is presented. The method is based on the solution of the magnetic scalar potential in nonconducting regions and the magnetic vector potential and an electric scalar potential in eddy-current regions. Multiply connected regions of magnetic scalar can be avoided by extending the region modeled by the magnetic vector potential to fill any holes in the conducting regions. The model was used to simulate the FELIX brick experiment     

Transient 3D eddy currents using modified magnetic vectorpotentials and magnetic scalar potentials

A package named VECTOR for solving 3-D eddy current problems is presented. The package is a developmental version of the commercial package CARMEN and in the same way solves the vector diffusion equation, involving a modified vector potential, within conductors and the scalar Poisson equation, using a magnetic scalar potential, in non-eddy-current regions. It has been shown that this set of equations yields a unique solution for both the magnetic vector potential (and hence the currents) and the fields (which are derived from the magnetic potentials by differentiation). This package has recently been extended to solve transient problems, using simple time-stepping techniques. Some results using the package for problems with analytic solutions are given     

Methods for magnetically nonlinear problems involving significanthysteresis and eddy currents

The authors consider the modelling of magnetic saturation and hysteresis within finite-element eddy-current calculation procedures. Specific attention is given to time-stepping methods which deal with both saturation and hysteresis and to single-harmonic time-periodic approximations for cycle problems. It is shown that time stepping results are very close to measured losses in cases where there are significant saturation, hysteresis, and eddy currents. It is also shown that periodic approximations can produce solutions which also agree well on loss but rather less well on other parameters, particularly stored energy. Rotation field components are shown to be a major modelling problem     

Measurement of crack-profiles using AC field measurement method

The alternating current field measurement technique has been employed in the present study to predict cracks of different profiles. Profiles used included surface thumb-nail cracks of semi-circular, semi-elliptical, asymmetrical and rectangular shape with aspect ratios ranging from 2 to 10. From the potential ratios measured experimentally, a numerical approach was employed to compute the crack profiles. Crack profiles were also computed from theoretical potential profiles obtained using boundary element method. The present study shows that with high aspect ratios, the crack profiles predicted using theoretical data bore great resemblance to that of the actual. The underpredictions at the centre-line position of the cracks were small. Using experimentally measured potentials with 1-dimensional interpretation, all predicted profiles showed an under estimation of the actual. The errors appeared generally lower for the narrower plate and decreased with increase in aspect ratio. Pseudo-random errors were introduced to the theoretical potentials to simulate measurement errors that may occur in practice, to improve the error handling capability of the computer programme designed for the study. In addition, a smoothing technique was also applied to improve the accuracy of the crack profile prediction. By freezing some of the distant potential field, a significant computer processing time reduction of 25–35% has been achieved.     

A boundary integral equation method for high frequency eddy currents

The authors present a new method to compute the current distribution at the surface of a conducting piece in a high frequency varying field. This method uses boundary integral equation techniques and allows at a very low computing cost to define in three dimensions the hot and cold parts of such a piece before case hardening. The integral equations have to be solved only on the boundary, so the number of dimensions of the mathematical problem is reduced from three to two. Results of current distribution on the surface of a complicated shape piece as a toothed gear are given as an example.     

Analysis of adaptive shell structures using a refined laminated model

This work presents the development of a shell conical panel finite element model, which has the possibility of having embedded piezoelectric actuators and/or sensors patches. A mixed laminated theory is used, which combines an equivalent single layer higher order shear deformation approach for the mechanical behavior with a layerwise representation in the thickness direction to describe the distribution of the electric potential in each of the piezoelectric layers of the finite element. The electrical potential function is represented through a linear variation across the thickness with two electric potential nodes for each piezoelectric layer. Based in this model an active damping scheme applied to laminated shell structures is presented and discussed.     

Finite element analysis of 3-D eddy currents

The authors review formulations of three-dimensional (3-D) eddy current problems in terms of various magnetic and electric potentials. The differential equations and boundary conditions are formulated to include the necessary gauging conditions and thus to ensure the uniqueness of the potentials. Different sets of potentials can be used in distinct subregions, thus facilitating an economic treatment of various types of problems. A novel technique for interfacing conducting regions with an electric vector and a magnetic scalar potential to eddy-current-free regions with a magnetic vector potential is described. Finite-element solutions to several large eddy-current problems are presented     

Numerical modeling of composite laminated cylinders in compression using a novel imperfections modeling method

The present study presents the finite element modeling procedure of two composite laminated cylinders exhibiting initial geometric imperfections. Using as input a set of experimental measurements of the cylinder geometry, the application of the skinning method leads to the analytical representation of the cylinder imperfect internal, external and middle surfaces. A finite element mesh is then easily constructed over these surfaces. The results of the analysis are in very good agreement with the experimental strains and buckling load measurements and are used to estimate the knockdown effect of the imperfections on the cylinder buckling behaviour. They are also compared to results obtained by other simpler finite element models, in an effort to evaluate the accuracy of various modeling simplifications.     

Analysis of laminated composite plates using a higher-order shear deformation theory

A higher-order shear deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, Vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three-dimensional elasticity theory.     

Calculation of the magnetic field of a coil

An approximate method is given for calculating the magnetic field of a coil of circular cross section with continuous coil windings.