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.     

基于COMSOL连铸坯壳测厚横波EMAT优化

为了研究电磁超声传感器(Electromagnetic Acoustic Transducer,EMAT)横波测量连铸坯壳厚度的机理及横波在连铸坯中的传播情况,选取坯壳厚度为10~50 mm的Q235小方坯为研究对象,利用有限元软件COMSOL建立脉冲电磁铁和螺旋线圈的电磁超声模型,分析在不同EMAT结构参数下,连铸坯中电磁场、力场、声场的分布规律。研究结果表明:脉冲电磁铁和螺旋线圈组成的EMAT能够在连铸坯壳集肤层激发出超声波横波。脉冲电磁铁空心螺线管线圈匝数、内半径、线圈导线半径对换能效率的影响依次减小,且当脉冲电磁铁内半径尺寸大于螺旋线圈尺寸时,产生横波的效率最高。坯壳厚度越小,螺旋线圈最优激励频率越大,测量精度越高,信号衰减越快。因此,坯壳厚度为10~50 mm的Q235小方坯选择1.1 MHz为最佳激励频率。     

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.     

吸波材料优化匹配的理论分析

为了研究电磁参数和涂层的厚度对单/双层吸波材料的吸收性能的影响,以期制备出具有良好的电磁匹配特征的吸波材料,利用通过单/双层吸波涂层内电磁波传播的理论机制,计算机模拟技术,分析了涂层厚度、电磁参数及频率变化对材料的电磁波吸收性能影响的规律.同时提出了双层吸波材料设计中厚度匹配和阻抗匹配等基本原则.结果显示,随着厚度的增加,吸波材料对电磁波的吸收峰向低频移动,并且相继出现多个吸收峰.当电磁匹配常数M=0.25时,涂层材料展现了很好的吸波性能.对于双层吸波材料,阻抗渐变原则和厚度匹配规律直接影响到其吸收性能.     

Reconstructing electrical conductivity profiles from variable-frequency eddy current measurements

A method for reconstructing radially varying conductivity profiles in cylindrical conductors is described. Solenoidal driving and sensing coils surround the cylindrical sample and an AC magnetic field applied by the driving solenoid induces axisymmetric eddy currents in the sample. It is shown how a radially varying conductivity profile can be recovered from measurements of the complex impedance recorded as a function of frequency, where impedance here is defined as the ratio of the induced electromotive force (EMF) in the sensing coil to the current in the driving coil. An iterative nonlinear least-squares algorithm is employed to reconstruct the profiles. Demonstrations of the reconstruction method are presented based on both simulated and experimentally recorded impedance data.     

Rapid inversion of eddy current data for conductivity and thickness of metal coatings

A feature-based method that determines the thickness and electrical conductivity of a coating on a metal plate from the change in the frequency-dependent impedance of an eddy-current probe coil is presented. Recently a least-squares solution of this problem was presented, which, however, requires approximately 20 CPU minutes on a DEC 5000 work station for the analysis of each set of measurements. We show that a feature-based approach can reduce the time to a few seconds on the same processor. We start by showing that a three-parameter scaling of the resistive component of the impedance change vs. frequency leads to a simple and nearly universal curve. Consequently these parameters provide a simple and compact way of expressing the data. Next, we show that the three scaling parameters can be used to construct a look-up table that determines the conductivity and thickness of the coating. Finally, we test the method using experimental data.     

Impedance of the eddy-current displacement probe: the transformer model

A new approach to calculation of the impedance of the eddy-current displacement probe is presented. It is based on the transformer model of the probe-to-target coupling. The usual method of calculating the impedance by solving for the electromagnetic field distribution in the probe and the conductive target involves solution of integral equations. Instead, a simpler approach is possible by modeling the probe-to-target coupling as a loaded transformer, involving only linear ac circuit analysis and elliptic integrals (readily available in MATHCAD, MATLAB, etc.). The model transformer has single primary and multiple secondary windings. The primary winding models the probe coil, while the distributed Eddy current's circulation paths are modeled by multiple secondary windings. The target active area (the eddy current's carrying area) is divided into concentric rings. Each ring is modeled as a single-turn secondary loaded with the ring impedance. Simulation shows that division of the target active area into a moderate number of rings (16) is sufficient for very good accuracy of the model. Accuracy was checked by comparison of the simulated transfer curve of the displacement transducer to the measured transfer curve of the actual transducer. The agreement between the model and the measurement is very good. The model can be used to investigate the influence of various coil shapes and target materials on linearity and sensitivity of the eddy-current displacement transducer.     

Change in impedance of a single-turn coil due to a flaw in a conducting half space

The problem of detection and characterization of a flaw in a conducting half-space using an eddy-current coil oriented parallel to the interface is examined. An expression is derived for a first order approximation for the change in complex impedance due to a flaw located within the conducting medium. The overall impedance is a function of the radius and lift-off distance of the test coil and the conductivity of the material. An analytical expression is derived for the change in impedance as a function of the electric fields at the position of the flaw. It is found to be an integral over the volume of the flaw of the electric fields found with and without the flaw being present. The limiting case of a degenerate point flaw may be examined in greater detail by allowing the field in the presence of the flaw to be approximated by the unperturbed field. For flaws small enough that the field does not vary much over its volume, the field may be even further approximated by using just the value of the field at the position of the centroid of the flaw. Plots are shown to illustrate the behavior of the change in impedance as a function of the radial range of the flaw and the depth of the flaw centroid, using previously derived expressions for the fields for the unflawed case.     

铁磁材料硬度电磁检测模型

针对铁磁材料硬度无损检测问题，借助近代电磁理论，推导出含有复宗量贝塞耳函数的差动探头散射阻抗解析模型。将阻抗解析与铁磁材料硬度检测试验相结合，建立了用于钢轨硬度无损检测的电磁场数学模型，检测系统不确定度在1HRC范围内。     

Electromagnetic Analysis of the ITER Upper VS Coil

In order to control the plasma vertical stability of ITER, a novel magnet is developed, that is the vertical stability coil. The coil is located in the vacuum vessel and its safe operation is very important for ITER’s reliable working. During the normal operation, the coil should bear the electromagnetic force caused by the external superconducting magnet and plasma current. The electromagnetic load is one of the important factors to affect the lifetime of the VS coil. Therefore, it is necessary to calculate the magnetic field and evaluate the structural reliability under the electromagnetic load. In this paper, the current at the time “end of burn” was selected to perform the electromagnetic calculation. Based on the Maxwell equation, the magnetic field on the cross section of the upper VS coil was computed and the maximum electromagnetic force corresponding to the magnetic field was also presented. In order to verify the current design model, the finite element model was created by use of ANSYS. The Tresca stress was extracted and classified based on analytical design. The peak stress was compared with the ASME criteria. The analysis has verified the physical model from the perspective of electromagnetic load, and it will offer a guidance for the future optimization.     

镀镍碳纳米管的微波吸收性能研究

用竖式炉流动法制备了碳纳米管,碳纳米管的外径40nm～70nm,内径7nm～10nm,长度50μm～1000μm,呈直线型,用化学镀法在碳纳米管表面镀上了一层均匀的金属镍。碳纳米管吸波涂层在厚度为0.97mm时,在8GHz～18GHz,最大吸收峰在11.4GHz(R=-22.89dB),R<-10dB的频宽为3.0Hz,R<-5dB的频宽为4.7GHz。镀镍碳纳米管吸波涂层在相同厚度下,最大吸收峰在14GHz(R=-11.85dB),R<-10dB的频宽为2.23Hz,R<-5dB的频宽为4.6GHz。碳纳米管表面镀镍后虽然吸收峰值变小,但吸收峰有宽化的趋势,这种趋势对提高材料的吸波性能是有利的。碳纳米管作为偶极子在电磁场的作用下,会产生耗散电流,在周围基体作用下,耗散电流被衰减,从而雷达波能量被转换为其它形式的能量。     

Boundary element analysis of the electromagnet casting mould

A coupled boundary element (BE)-impedance boundary condition (IBC) formulation is used to develop an electromagnetic mold design model, taking into consideration the problem of predicting the shape of the free boundary. The computational model of the electromagnetic mold consists of a right cylindrical conductor, representing the molten metal, coaxial with an induction coil, generally having a single turn, and a field shaping short circuited turn. The IBC is applied to the high-resistivity molten metal region, and the full BE formulation is used for the field shaping turn. An iterative procedure is developed to predict the shape of the molten metal free surface by satisfying the balance between the electromagnetic and gravitational pressures. Results showing the effects of the single turn confinement coil and shielding turn placement on the electromagnetic pressure distributions and on the shape of the free surface are presented     

放电时序对双向加载式管件电磁翻边的影响

目的 研究放电时序对翻边变形的影响规律,提高成形能力.方法 以双向加载式管件电磁翻边系统为研究对象,建立基于电路-磁场-固体力学耦合的仿真模型,针对放电时序的变化,详细分析驱动电流、电磁力和翻边变形受到的影响,揭示其作用机理.结果 与常用的同时放电相比,最佳的时序放电在保证脉冲时间一致性的同时,将径、轴向线圈电流峰值分别提高11.6％和降低12.4％,最终使径、轴向电磁力峰值分别提高18.8％和6.8％,翻边角度提升约30％,显著提升了系统的翻边能力.结论 控制放电系统开关时刻改变放电时序,可以使放电能量在线圈间发生转移,影响线圈中的驱动电流波形,从而提高电磁力大小并改善其径轴向分量的比例关系,显著增强电磁系统的成形能力.     

An investigation of horizontal axis coils for eddy current inspection

The possible use of horizontal axis eddy current coils for the inspection of fast breeder reactor primary vessels is being investigated. An approach which considers both theoretical modelling work and experimental work has been adopted. Owing to the lack of analytical theory for the horozontal coil case, the initial work has concentrated on determining the impedance change of a horizontal axis air-cored coil when it is brought close to a conducting half-space. An analytical solution (due to Burke) has been considered, along with a newly developed approximate model, for a range of different coils above various conducting media. The approximate model assumes a uniform H field at the material surface and has been extended to consider layered half-spaces such as stainless steel over liquid sodium. The trends exhibited by the impedance change values obtained from both theories compared well with the experimental data.     

Bead Coating Process Via an Excess of Crosslinking Agent

Coated beads were prepared by soaking in sodium alginate solutions spherical matrices (beads) of carboxymethylcellulose crosslinked with aluminum chloride (AlCl3) and loaded with ambroxol hydrochloride as a model drug. The residual amount of the crosslinker induced an interfacial crosslinking reaction of the sodium alginate. Therefore, an insoluble, smooth and uniform in thickness coat was formed around the beads. As the coating time increased, the coat thickness increased until1 AlCl3 was present inside the beads. The rate of drug release from the coated beads was slower than that from the uncoated beads and decreased with the increase in coating time. Moreover, a constant rate phase, subsequent a burst period for the samples obtained with the highest coating times, was achieved. The dynamic swelling analysis allowed to exclude the influence of the polymer relaxation on the release process which appeared to be controlled by the alginate coat.     

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。      

Evaluation of coating resistivity for pigmented/unpigmented epoxy coatings under marine alternating hydrostatic pressure

To realize a rapid evaluation of coating degradation under alternating hydrostatic pressure(AHP),appropriate physical models of electrochemical impedance spectroscopy(EIS)data fitting were respectively developed for epoxy coatings with and without pigments,based on their different water absorption behaviours.Power-law model was selected to evaluate the anti-permeability of epoxy varnish(EV)coating,which tends to form through pores in the coating structure.On the other hand,two-layer model based on Young theory was developed to evaluate the anti-permeability of pigmented epoxy coating.Consequently,the resistivity profile with coating thickness was calculated as a critical parameter to describe the anti-permeability of coating at different immersion time.The interpretation of water diffusion dynamics based on different coating structures was also given,which is responsible for the choice of distribution models.     

涂层-纤维增强磁电弹性材料的变分渐近细观力学模型

涂层可对纤维起到表面改性及调节界面残余应力的作用,对宏观性能有重要的影响。为准确预测多场环境下涂层-纤维增强磁电弹性（MEE）材料的有效属性和局部场分布,基于变分渐近理论建立均匀化细观力学模型。从非均匀连续介质的总电磁焓入手,利用材料细观尺度远小于宏观尺度的特征,将多物理场下细观力学建模转换为约束条件下总电磁焓的最小化问题。为分析工程应用中智能材料的涂层-纤维细观结构,采用有限元技术实现该模型的数值模拟。通过与有限元结果的对比分析表明：构建的模型可准确预测涂层-纤维增强MEE材料的多物理场行为,不同厚度和刚度的涂层对应力集中和有效属性有较大的影响,同时揭示了许多独特的电-磁交互现象,为预测和优化涂层-纤维增强MEE材料的性能提供有益的参考。     

Beitrag zur aufzeichnung und wiedergabe beim NRZ verfahren

When a tape is passing a reproduce head, the reversa of direction of the remanent magnetization induces a pulse in the head coil. In the most widely used NRZ technique, the recorded digital information is composed of a number of such pulses. In order to derive an expression for the output of a reproduce head by a finite medium thickness, we must know the profile of the reversal of magnetization throughout the oxide thickness. Tjaden and Leyten have analyzed this profile with a tape-head model with the scale 5000 to 1. If, for measurement, the total thickness is divided into several laminas by using a thin coated tape which is spaced varying distances away from the head, a comparable curve is obtained for the location of the flux reversal inside the coating. This measurement can be done under the actual dimensions of a regular tape. It can be shown, that this curve is allowed to be approximated by a straight line. Furthermore we may assume, that the value of magnetization inside the coating depth is constant. Now we can establish a general expression for the output pulse as a function of the gap length, the coating thickness, the spacing tape-head, and a suitable parameter for the slope of the magnetization profile. The next step to a complete computation is the inclusion of the reproducing head transient function.     

Method Using Bilinear Transformation for Measurement of Impedance Parameters of a Multielement Two-Terminal Network

This paper presents a method for the identification of the impedance parameters of objects, which can be modeled by two-terminal networks. The method uses the properties of bilinear transformation, which allows presentation of object impedance as a function of each parameter of the equivalent circuit of the object. Inverse bilinear transformation allows the determination of the value of each parameter on the basis of impedance measurement at a single frequency. The measurement frequency is selected for each identified element (on the basis of the minimal relative sensitivity of the identified element to changes of other elements), so the number of measurement frequencies is equal to the number of elements to be identified. This makes it possible to shorten the identification time when compared with the traditional identification method based on the impedance spectrum fitting method (complex nonlinear least squares). When the object model and the order of component values are known, the developed method fully assures conditions that allow an implementation in low-cost portable diagnostic instruments.