Finite-element calculations of remote field eddy current interactions with slit defects

Remote field eddy current (RFEC) excitation is a promising approach for detection of the very fine axial cracks typical of stress corrosion cracking (SCC) in pipelines. Interactions between adjacent cracks or slits can enhance responses in some cases. Detailed finite-element modeling was undertaken to establish the behavior and interactions of multiple slits such as those occurring in SCC. Three different field/slit configurations are considered, with anomalous source models used to aid interpretation of the results. The study noted that magnetic perturbations generated by ferromagnetic material tend to be vanishingly small, and that the interactions between multiple cracks give minimal enhancement, indicating that eddy current rather than magnetic field excitation is best for the detection of SCC. With eddy current excitation, field perturbations are generated by even very fine slits, and are larger in non-ferromagnetic material. For nonferromagnetic pipes, the perturbations tend to merge as a circumferential separation between parallel axial cracks decreases, resulting in significant interaction and signal enhancement.     

Electromagnetic field formulation for eddy current calculations in nondestructive testing systems

The authors present the most practical configuration for detecting cracks in material, by applying an electromagnetic field along the largest dimension of the crack. An electromagnetic field formulation of the system equation is proposed using Maxwell's relations and separating the magnetic field into externally applied field and reaction field. The system equation is solved by using two classical methods : finite element technic for spatial problem and finite difference for time discretisation. So two dimensional eddy currents can be calculated immediately and related to the excitation characteristics for impedance calculation. Eddy currents lines in material for different cracks and sensor positions are presented. Theoretical results show important impedance changes.     

Geometrically anisotropic probes: an improved eddy current technique

Geometrically anisotropic eddy current probes are a type of separate function probes especially fit to the detection of defects showing a preferential direction. This kind of flaw induces a coupling between the transmitter and the receiver by guiding eddy currents from the one to the other. On the other hand, this coupling will be almost non-existent in the presence of defects or spurious effects not displaying this geometrical particularity. Basic studies on an elementary two-coil set-up allow the acknowledgment of the intrinsic qualities of such probes: good signal-to-noise ratio, influence field practically constant on the whole defect length, ability to detect bridged defects, insensitivity to lift off. These results can be improved by achieving multicoils probes adapted to different kinds of problems. An application to continuous casting slabs testing yields very interesting results in the detection of cracks, while getting rid of the effect of oscillation marks with no need of any signal processing. These achievements are promising for the improvement of eddy current testing, in terms of detection sensitivity as well as of rapidity to obtain information.     

3-D eddy current calculations using the magnetic vector potential

Two methods for using the magnetic vector potential for 3-D eddy current calculation are treated. One method uses the magnetic vector potential that is continuous over the entire region and generally accompanies the electric scalar potential. It has the advantage that no cutting is necessary for the multiply-connected-region problem. The other method uses the magnetic vector potential that is discontinuous across the interface surface between different media. This magnetic vector potential can be arranged so that the electric scalar potential does not appear in the equations when the conductivity is constant. It has the disadvantage that cutting is necessary for the multiply-connected-region problem. New boundary value problem formulations are given for both methods, precisely defining the interface and boundary conditions     

地铁垂向减震器座铆钉气隙的远场涡流检测研究

针对在役铆钉气隙受铆钉或者工件遮挡造成难以有效检测与定量评估的问题,建立ANSYS有限元仿真三维模型,开展垂向减震器座铆钉气隙的远场涡流检测仿真与试验研究。研究结果表明:有效电磁场可渗入铆钉孔约10 mm深处,具有检测深度深,灵敏度高的优点;提出定量表征气隙的最优特征量,在检测信号的幅值、相位、实部、虚部这4个特征量中,信号虚部分量与铆钉气隙的线性相关系数高达0.999,最能表征气隙。试验测试结果与仿真结论相吻合,规律一致,证明研究成果的可信性。     

An eddy current transducer model for image restoration

We describe in this short paper a new imaging model for the spatial magnitude response of an absolute eddy current transducer to a flaw. This model is appropriate for image restoration purposes in that it captures the transducer response with sufficient accuracy for image restoration, yet is simple enough to be computationally practical. The model described in this paper is based on a simple resistive loop approximation to the transducer impedance changes induced by a flaw, and is efficiently implemented as layers of linear blurring functions and nonlinear point operations. The model is shown to accurately reflect the magnitude response of an absolute transducer to an EDM slot in a non-ferrous alloy. Furthermore, the model is shown to produce good restoration results for both synthetic and real images of flaws. The model may be adapted to a particular combination of absolute transducer and surface flaw type by optimizing the model parameters, either by forming the partial derivatives with respect to the parameters and minimizing by gradient descent, or by a straightforward implementation of a neural net back-propagation algorithm. Other types of eddy current transducers may be modeled by simply modifying the spatial layers to combine the local terms appropriately for the geometry of the transducer.     

Use of magnetically-saturated regions in remote field eddy current tools

The remote field eddy current (RFEC) technique is of potential interest for inspecting pipelines for stress corrosion cracking. Magnetic saturation techniques would allow higher operating frequencies and scanning speeds to be used. The use of selectively-saturated regions (windows) near the exciter and detector offers additional advantages. Finite element, analytic, and experimental measurements are presented in this paper. They show that, while saturation techniques are helpful, the effects are less than initially estimated from simple skin depth approximations.     

Comparison of conventional,through-wall and remote field eddy current techniques

A through-wall eddy current system produces similar signals for defects of equal size, independent of the location of the defects in the sample being tested. The remote field eddy current technique is also reported to generate similar signals for equal defects, independent of the location of the defects in the wall of the tube which is being inspected. A theoretical study of an ideal conventional through-wall eddy current system is presented, and the results are compared with the results of a remote field eddy current system. It is shown that while the remote field system does not always obey the one-dimensional skin effect equation, it detects external material loss with nearly equal sensitivity to internal material loss. Experimental results are presented which show that the complex plane displays of similar ID and OD defects are similar in shape, size and orientation.     

Prediction of in-service microstructural degradation of A106 steel using eddy current technique

In-service microstructural degradation of ASTM A106 steel occurs by the spheroidising and coarsening of pearlite. The specimens of the A106 have been exposed at 710 °C for different durations to simulate service conditions. The resultant pearlite coarsening was evaluated by measuring eddy current inductive reactance and resistance; phase angles were measured using these values and compared with results of optical microscopy, image analysis and resistivity measurements. It was observed that the eddy current phase angle has a linear relation with pearlite variations. It can further be used for in-situ eddy current evaluation of microstructural degradation of pipes or steel vessels. A mathematical model has been proposed to assist such field investigations.     

MRI梯度磁场下人体心脏感应涡流仿真研究

通过MRI中梯度磁场对人体心脏影响的模型仿真,运用FDTD方法计算出心脏部分感应涡流,并与心脏刺激阈值进行比较.结果表明,心脏感应涡流的峰值离推荐阈值尚有一定距离,因此不会诱发心室颤动,但是提高梯度场的切换频率可能会引发心室颤动.     

Remote Field Eddy Current Technique: Phantom Exciter Model Calculations

Abstract

High resolution results of finite element calculations for remote field eddy current “phantom exciter” simulations of slit defect interactions using single through wall transit are presented. These show that fine circumferential slits cause almost no field perturbations in the case of nonferromagnetic tubes but big perturbations in ferromagnetic tubes where high magnetic H fields occur in the slits. Defect-induced magnetic field perturbations must therefore be considered in addition to eddy current perturbations when ferromagnetic materials are inspected, particularly in the case of fine slits orthogonal to the magnetic field direction. Additional details seen are the funnelling of energy into slits in ferromagnetic pipes and precursor disturbances of fields approaching defects. It is suggested that these are due to the reflection of the electromagnetic waves dictates by boundary conditions at the near side defect boundary.     

Parametric eddy current defect depth model and its application to graphite epoxy

An empirical eddy current model of defect depth has been developed. The model applies to idealized defects (notches and flat bottom holes) both in metals and in electrically conductive composite materials. The phase angle of the response of a ferrite pot core probe to a subsurface defect, normalized with respect to the lift-off angle, was found to depend on the ratio of the product of the depth of the defect and the mean core radius to the square of the skin depth. This relationship between the phase angle difference and this product provided estimates of defect depth to within 10% independent of the defect geometries considered.     

Computational methods for solving static field and eddy current problems via Fredholm integral equations

Two-dimensional static field problems can be solved by a method based on Fredholm integral equations (equations of the second kind). This has numerical advantages over the mote commonly used integral equation of the first kind. The method is applicable to both magnetostatic and electrostatic problems formulated in terms of either vector or scalar potentials. It has been extended to the solution of eddy current problems with sinusoidal driving functions. The application of the classical Fredholm equation has been extended to problems containing boundary conditions: 1) potential value, 2) normal derivative value, and 3) an interface condition, all in the same problem. The solutions to the Fredholm equations are single or double (dipole) layers of sources on the problem boundaries and interfaces. This method has been developed into computer codes which use piecewise quadratic approximations to the solutions to the integral equations. Exact integrations are used to replace the integral equations by a matrix equation. The solution to this matrix equation can then be used to directly calculate the field anywhere.     

改善金属基稀土永磁材料在交变场中抗涡损能力的研究

金属基稀土永磁材料具有良好导电特性，在高频交变场环境下由于涡流效应损耗会降低其磁性能，尤其是难以应用在高转数电机领域。本文通过理论建模计算解释了涡流效应在磁体内变化的原因，从微观和宏观两方面，首次揭示了稀土永磁合金成分的显微分布形态对其自身绝缘特性的影响作用，以及解释了不同频率条件下材料电阻率存在差异的原因。并通过具体实验，制备得到具有优良绝缘特性、高性能稀土永磁体。     

Numerical solution of eddy current problems in ferromagnetic bodies travelling in a transverse magnetic field

Eddy currents are investigated in a ferromagnetic bar travelling in a transverse magnetic field. Such an open boundary field problem is analysed by a hybrid approach based on Galerkin finite element formulation coupled with a separation of variables. A steady state is considered, introducing time‐periodic boundary conditions. The resultant system of non‐linear equations is solved by an iterative procedure based on Brouwer's fixed‐point theorem. Numerical results are presented for a bar of circular cross‐section made of cast steel or cast iron. Selected examples of the field distribution and characteristics of eddy‐current power losses are enclosed in graphic form. Copyright © 2003 John Wiley & Sons, Ltd.     

A comparison of the Coulomb gauge and Lorentz gauge magnetic vectorpotential formulations for 3D eddy current calculations

Formulations for the finite difference method (FDM) and BIEM using the Coulomb gauge and Lorentz gauge magnetic vector potentials are presented and numerically tested for two 3-D eddy current problems. It is conducted from the computed results that the computational accuracy is almost the same for the Coulomb gauge and Lorentz gauge for formulations, and that the Lorentz gauge formulation is superior to the Coulomb gauge formulation in terms of the computation time     

Determination of presence of undesirable carbides at surface of cast iron parts using differential eddy current technique

Abstract

Machinability of grey cast iron parts can greatly suffer from the formation of carbide at the surface, resulting in a decrease in cutting tool life and higher production costs. Therefore, detection of the hardened layer and its hardness are the key factors in quality control and inspection processes. In the present paper, a number of metallurgical parameters (surface carbide, surface hardness and hardened depth) have been investigated using the non-destructive differential eddy current technique. The results show the high potential of the proposed method as a fast and accurate technique in inspecting and in consequent separation of undesirable parts.     

轨道车辆焊缝缺陷远场涡流检测系统设计及试验研究

轨道车辆工作环境恶劣,车体焊缝区域易出现缺陷,对车体焊缝开展无损检测工作,可有效保障行车安全.该文设计并研制轨道车辆焊缝缺陷远场涡流检测系统,该系统包括激励模块、信号调理模块、信号采集模块组成的硬件电路和基于LabVIEW编制的上位机软件;基于该系统开展轨道车辆铝合金焊缝、不锈钢焊缝远场涡流检测试验研究,研究结果表明:...     

A new model of repulsive force in eddy current separation for recovering waste toner cartridges

Eddy current separation (ECS) is an efficient method for separating aluminum from plastic in crushed waste toner cartridge (TCs). However, in China, ECS quality of aluminum from plastic is rather low in production practice. Repeating separation even manual sorting is required in the production. Improving separation quality of aluminum has been the pressing problem in the recovery of waste TCs. Furthermore, improving ECS quality can reduce the secondary-pollution (furan and dioxin) brought by plastic in later smelting process for the purification of recovered aluminum. Thus, a new model of repulsive force containing impact factors (machine: B_r, k, R, S_m, B_m; material: S_p, V, γ; and operation: ω_m, v, δ) of the separation process was constructed for guiding the ECS process of waste TCs recovering in this paper. For testing whether the model of repulsive force was suitable to guide the ECS, calculation and experiment of detachment angle of aluminum flake were studied. The calculation results of the detachment angles were agreed with the testing experiment. It indicates that the model is suitable for guiding the ECS of waste TCs recovering.     

飞机多层金属板隐藏缺陷远场涡流探头设计及试验研究

由于飞机多层金属板结构厚度大、复杂等特性,现有检测方法无法发现原位内部缺陷,对于多层板金属缺陷的检测一直都是航空无损检测的难题.远场涡流检测技术因打破趋肤效应的限制,涡流能量可穿透较厚的被测试件,对金属板结构中隐藏缺陷的检测具有潜在优势.该文针对飞机多层金属板隐藏裂纹的原位检测,建立多层金属板构件隐藏裂纹平面远场涡流检...