Analytical Modeling of Wobble in Eddy Current Tube Testing with Bobbin Coils

By utilizing the second-order vector potential formulation we solve the eddy current problem of a coil inside a conductive tube and in an offset position to it. The study focuses on the derivation of a closed-form expression for the impedance change of the coil, which is used to calculate the signal produced by wobble in eddy current testing of tubes with bobbin coils.     

Analytical Modeling of Wobble in Eddy Current Tube Testing with Bobbin Coils

Abstract

By utilizing the second-order vector potential formulation we solve the eddy current problem of a coil inside a conductive tube and in an offset position to it. The study focuses on the derivation of a closed-form expression for the impedance change of the coil, which is used to calculate the signal produced by wobble in eddy current testing of tubes with bobbin coils.     

The Pulsed Eddy Current Differential Probe to Detect a Thickness Variation in an Insulated Stainless Steel

Non-destructive testing (NDT) plays an important role in the safety and integrity of the large industrial structures such as pipelines in nuclear power plants (NPPs). The pulsed eddy current (PEC) is an electromagnetic NDT approach which is principally developed for the detection of surface and sub surface flaws. In this study a differential probe for the PEC system has been fabricated to detect the wall thinning in insulated steel pipelines. The differential probe contains an excitation coil with two hall-sensors. A stainless steel test sample was prepared with a thickness that varied from 1 mm to 5 mm and was laminated by plastic insulation with uniform thickness to represent the insulated pipelines in the NPPs. Excitation coil in the probe is driven by a rectangular current pulse, the resultant PEC response which is the difference of the two hall sensors is detected. The discriminating features of the detected pulse, peak value and the time to zero were used to describe the wall thinning in the tested sample. A signal processing technique such as power spectrum density (PSD) is devised to infer the PEC response. The results shows that the differential PEC probe has the potential to detect the wall thinning in an insulated pipeline of the nuclear power plants (NPPs).     

Alternative approaches to the numerical calculation of impedance

In many practical applications of numerical analysis applied to low-frequency electromagnetic problems, the desired output is often in terms of coil impedance. The mesh variable calculated by the more commonly used numerical formulations is the magnetic vector potential from which quantities like field intensities, eddy currents and others are calculated. In nondestructive testing applications, the quantity of interest is often the impedance of a coil or an array of coils. This paper discusses the calculation of impedance as a post-processing computation and introduces a new method of calculation of impedances and inductances based on computation of energy in the finite element mesh. The results presented clearly show the advantage of using direct integration methods for 2D and axisymmetric geometries. The energy approach, while valid regardless of dimensionality, should be restricted to 3D applications. Multiple-coil configurations in 3D applications present a special problem in analysis. The total impedance or inductance can be easily calculated but not independent coil or differential impedances. A method for calculation of these quantities in 3D computations is also presented.     

Accurate probe-response calculation in eddy current NDE by finite element method

A method is presented to evaluate flaw signals in eddy current NDE using the finite element technique. The analysis of the electromagnetic field is based on a three-dimensional finite element scheme that computes directly the electromagnetic field distortions due to defects. This direct field-distortion calculation together with an accurate unflawed field calculation provides accurate total field values in general three-dimensional geometries. The paper shows that the application of the reaction concept and the reciprocity theory allows computations of the probe responses by performing integrals over the flaw region only, even if the analysis is performed by a finite element scheme. Two benchmark problems—a plate with rectangular slot scanned by a differential probe and a tube with axial and circumferential slots scanned by an absolute probe—have been solved to demonstrate the validity and the efficiency of the method. The calculated probe responses show good agreement with the measured trajectories. In order to reach better quantitative agreement, a calibration algorithm that adjusts the parameters of the cylindrical coil model and the lift-off within the range of the geometrical tolerances has been developed.     

平纹编织碳纤维增强树脂复合材料离散电导率建模方法

编织碳纤维增强树脂复合材料(CFRP)的电阻抗分布具有各向异性、异质性、几何结构复杂等特点。建立电阻抗分布模型是利用电磁涡流无损检测技术获取编织CFRP缺陷及疲劳损伤信息的关键关节。基于电阻抗张量建模理论,采用多层编织结构CFRP二维平面的分块均化电学特性表征方法,建立编织结构CFRP的简化电阻抗分布模型,从而实现编织结构CFRP电磁特性的精确、快速有限元分析。在有限元仿真基础上,通过设计双空气旋转线圈电磁传感器对平纹编织CFRP进行电磁无损检测,选用阻抗的极坐标图描述被测材料沿不同方向的阻抗变化趋势,通过实验验证有限元建模的正确性。最后利用所提出的建模方法模拟了双空气旋转线圈传感器对平纹编织CFRP的结构缺陷及循环载荷疲劳的检测效果。      

Broadband holography applied to eddy current imaging by using signals with multiplied phases

In this paper an eddy current imaging method for nondestructive testing purposes is presented which utilizes the concept of broadband holography. An eddy current coil which is used simultaneously as an antenna for eddy current generation and as a probe for detection of response of interaction between eddy currents and flaws, respectively, is moved along a synthetic aperture during the imaging procedure generating synthetic eddy current pulses by scanning a certain frequency range. In terms of wave propagation phenomena the penetration depth (range) of eddy currents in conducting media is small compared to the equivalent wavelength of this type of fields. Therefore, adequate resolution can only be obtained in the reconstructed cross-sectional images by phase multiplication of received multifrequency signals, which is equivalent to a fictitious reduction of wavelengths. Experimental results verify the imaging capability of this method with improved resolution compared to conventional eddy current testing methods.     

Eddy current inversion for layered conductors

By making multifrequency eddy current measurements on a layered conductor, it is possible to acquire information on the depth dependence of the conductivity. We consider an inversion problem in which coil impedance data are used to determine either the layer thicknesses or layer conductivities. The algorithm is based on a well known forward model which gives the impedance of an air cored coil above a stratified conductor from a closed form expression. In the forward calculation, estimates of the unknown material parameters are used to get tentative predictions of the measurements. Differences between these predictions and measured impedances are expressed in terms of a global error that is minimized iteratively with the aid of a descent algorithm by varying the parameters of the structure. Examples of minimization searches for layer parameters are given.This article is dedicated to Professor Bertram A. Auld on the occasion of his 70th birthday and his retirement from Stanford University.     

Analytical solution for impedance change due to flaws in eddy current testing

Green's function is used in order to derive the analytical solution for the change in impedance due to a presence of the flaws in a conductor. This solution is applied to a cylindrical flaw and a spherical flaw whose radii are much smaller than the radius of the test coil. For both cases, the change in impedance is obtained within Born's limit.     

Approximate model of eddy-current probe impedance for surface-breaking flaws

A theoretical model is derived for the prediction of eddy-current probe impedance changes caused by three-dimensional, surface-breaking flaws. Magnetic scalar potential theory and the surface impedance approximation are used to calculate fields on the flaw surface for arbitrary probe position and flaw geometry. Impedance changes are determined by a first-order perturbation calculation, with skin depth being the perturbation parameter. The end result is a relatively simple, three-dimensional model for simulating an eddy-current inspection. Numerical results for rectangular slots include maps of the impedance signals obtained in raster scan patterns and studies of skin-depth effects as a function of probe size, lift-off, and flaw dimensions.     

Thermal characteristics of conduction cooled 600 kJ HTS SMES system

A 600 kJ HTS SMES is developed and tested in Korea. The HTS SMES consists of 22 double pancake coils wound on each aluminum alloy bobbin. It is cooled by two GM cryocoolers down to around 6 K and current is charged through HTS current leads up to 275 A. Beside the heat penetration from room temperature structures, heat generation in the HTS coil is inevitable because of the joint resistances and the intrinsic property of the HTS tape such as index loss. Moreover, during the charging and discharging operation, AC loss of the HTS conductor and eddy current loss in the coil bobbin and metallic structures are generated. Therefore, the heat generation should be effectively removed by the cryocooler to ensure the stable operation of the coil. In the HTS SMES, aluminum alloy conduction plates outside the each coil are used as thermal paths to the cryocoolers. This paper describes the thermal characteristics of the HTS SMES for the charging and discharge operation.     

A finite-element–alternating technique for evaluating mixed mode stress intensity factors for part-elliptical surface flaws

An alternating method, in conjunction with the finite element method and an analytical solution for an elliptical flaw in an infinite solid, is used to determine the mixed mode stress intensity factors for surface flaws. This finite element alternating method leads to an inexpensive procedure for routine evaluation of accurate stress intensity factors in complex structural components containing surface flaws and subject to mixed-mode loading. A variety of numerical examples is presented.     

Small‐sized probe for local measuring electrical properties of the tissues inside of human body: design,modelling and simulation

In this study, a new idea is suggested for designing an appropriate bio‐impedance probe in the form of a biopsy forceps to measure the electrical properties of the tissues inside the body. First, by analytically solving the Laplace equation for wedge‐shaped tissue in the mouth of the probe, the relationship between electric potential (results from excitation current) in a different point on the tissue and the electrical properties of the tissue is obtained. Then, to evaluate the designed bio‐impedance probe using the finite element method and the experimental data obtained for different tissues by Gabriel et al., modelling and simulation at different frequencies from 50 Hz to 5 MHz were done. Finally, to evaluate the performance of the designed probe in comparison to other methods, measurements were carried out using three methods for the same tissue. Nyquist curves were drawn and electrical properties extracted for all the three methods. It was found that the designed probe results are close to the actual values with an error of <2%. The main features of the designed probe are small size and non‐invasive measurement.Inspec keywords: Laplace equations, biological tissues, finite element analysis, electric impedance measurement, bioelectric potentials, biomedical measurementOther keywords: noninvasive measurement, local measuring electrical properties, human body, wedge‐shaped tissue, electric potential, finite element method, bio‐impedance probe, small‐sized probe, biopsy forceps, excitation current, Nyquist curves, frequency 50.0 Hz to 5.0 MHz     

Eddy-current interaction of a long coil with a slot in a conductive plate

We describe a truncated-domain method for calculating eddy currents in a plate with a long flaw. The plate is modeled as a conductive half-space and the flaw is a long slot with a rectangular cross section. A long two-dimensional (2-D) coil carrying an alternating current is aligned parallel to the slot. The coil impedance variation with frequency is determined for an arbitrary coil location. The electromagnetic field due to a long coil above a conductive half-space can be expressed as integrals of trigonometric functions. For a half-space with a long slot, however, additional boundary conditions must be satisfied at the slot walls. The truncated-domain method makes this possible by recasting the problem in a finite domain; as a result, the Fourier integral is replaced by a series. The domain can be made arbitrarily large, thereby yielding results that are numerically as close to the infinite domain solution as desired. We have used the truncated domain approach to study both eddy-current flaw interactions and edge effects in the limiting case of a very wide and deep slot. We confirmed the theoretical predictions by comparing them with results of a 2-D finite element calculation and of experiments.     

热金属气压成型电磁感应加热有限元模拟

应用感应加热理论,利用麦克斯韦方程组和温度微分方程,建立了电磁场与温度场耦合的有限元数学模型,使用有限元分析软件ANSYS对热金属气压成型工艺中的电磁感应加热过程进行了模拟与分析。模拟结果表明:随着电磁感应线圈电流频率的提高,在相等的加热时间内,金属钢管的升温速度不断增加,且最终达到的温度也进一步升高。随着电磁感应线圈电流密度的增加,在相等的加热时间内、相同的电磁感应线圈电流频率下,金属钢管的升温速度不断增加,加热效率得到有效提高,且最终达到的温度也逐步升高。随着金属钢管与线圈的间隔增加,金属钢管内、外表面的温度均逐渐降低;外表面温度的降低趋势越来越平缓,而内表面温度的降低趋势则不断加剧。     

An eddy-current model for three-dimensional inversion

A model is presented for the inversion of eddy-current data to be used for the detection of flaws. This model is based on rigorous electromagnetic theory and uses a multifrequency approach to make it truly three-dimensional. The resulting integral equations are discretized and solved using least squares techniques. The numerical problems involved in this algorithm are discussed, and a solution as well as examples of reconstructions of computer-generated flaws are presented.     

Eddy-current modeling and flaw reconstruction

A model is presented for the inversion of eddy-current data and the reconstruction of flaws. The model is based on rigorous electromagnetic theory, and uses a multifrequency approach to make it truly three-dimensional. Algorithms for solving the discretized equations are presented, and the numerical problems involved are discussed. The processing of laboratory data from actual flaws is presented, with the results of these reconstructions shown as grayscale images.     

Eddy Current Probe Parameters Identification Using a Genetic Algorithm and Simultaneous Perturbation Stochastic Approximation

This study tries to identify the coil parameters using numerical methods. The eddy current testing (ECT) is used for evaluation of a crack with the aid of numerical simulations by utilizing the identification of these parameters. In this study, a comparison of the performance of the GA and SPSA algorithms to identify the parameter values of the coil sensors are presented. So, the optimization probe geometry is introduced in the simulation with Three-dimensional finite element simulations (FLUX finite element code) were conducted to obtain eddy current signals resulting from a crack in a plate made of aluminium. The simulation results are compared with experimental measurements for the defect present in a plate.     

Analytical model for tilted coils in eddy-current nondestructive inspection

The electromagnetic field and impedance of a cylindrical eddy-current probe coil are calculated analytically for arbitrary coil orientation above a conductive half-space. The remarkably simple closed-form expressions are provided as a function of coil tilt angle. The effect of tilt on the impedance change produced by a long crack is also investigated by combining the analytical model with an existing thin-skin theory for surface crack inspections. Results for both cracked and uncracked conductors are expected to be useful for evaluation of movement-generated noise in eddy-current inspections.