Numerical Analysis for Eddy Current Characteristics of Magnetically Saturated Ferromagnetic Tubes

Abstract

Magnetic saturation is applied to ferromagnetic tubes inspected by the encircling or inner coil because suppressing magnetic noise is important for the eddy current testing technique. Eddy current signal characteristics in magnetically saturated tubes are different from those in nonmagnetic tubes. In ferromagnetic tubes, defect signal phase angle is not useful for estimating defect depth because it does not depend on the defect depth. In this paper, numerical eddy current analysis has been done in order to explain the relationship between the defect depth and the phase angle in magnetically saturated tubes. This analysis is performed as follows: 1) The magnetic permeability near the defect is calculated as the non-linear magnetostatic problem. 2) The eddy current distribution is calculated as the linear magnetodynamic problem using the incremental permeability value calculated in step 1. The numerical analysis results reveal that the permeability around the defect remains inhomogeneous and it causes the unique eddy current characteristics. Based on these calculated results, a quantitative evaluation method of determining defect depth is proposed. After determining the defect shape by using signal characteristics obtained from the strongly magnetizing state, the defect depth can be estimated by using the signal amplitude.     

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.     

Remote field eddy current technique: Phantom exciter model calculations

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.     

Techniques for depth-selective,low-frequency eddy current analysis for SQUID-based nondestructive testing

Conventional eddy current techniques are widely used for detection of surface-breaking cracks in metal structures. These techniques have limited success in the detection of deep, nonsurface-breaking flaws that require low frequency eddy currents, for which inductive pick-up probes have drastically reduced sensitivity. High resolution, Superconducting QUantum Interference Device (SQUID) magnetometers, which are very sensitive to do or low frequency magnetic fields, have been developed for detection of subsurface flaws. We have now extended SQUID NDE by utilizing a sheet inducer to produce an extended eddy current parallel to the surface in a conducting plate. The magnitude of the induced current density inside the plate reduces with the depth; however, the current component at a certain phase angle may increase with the depth. At a particular phase angle, the current density on the surface becomes zero, while the current inside the plate is large, so that the magnetic signal at that phase angle due to the surface structures can be minimized. With this method, we have detected simulated cracks in the sides of plugged holes in a thick plate, a hidden corrosion area in a specimen which consisted of two painted aluminum plates joined with sealant, as well as crack defects adjacent to fasteners in the second layer of lap joined aluminum plates. We present a theoretical model for simulation of the phase-related magnetic signal due to a flaw, which shows the relation between the phase angle and the depth of the flaw. The theoretical phase analysis is compared with the experimental results.     

Application of ferromagnetic resonance probes to the characterization of flaws in metals

This article presents some results obtained in the characterization of surface flaws by means of probes using ferromagnetic resonance of yttrium iron garnets (FMR probes). These experiments on artificial flaws show that FMR probes operate like eddy current probes for nonmagnetic materials and like magnetic field sensors for magnetic ones. Consequently, the working distance is larger for magnetic materials (1000–1500 µm) than for nonmagnetic ones (100–300 µm). FMR probes have good sensitivity to narrow flaws, good spatial discrimination, and are sensitive to flaw width and depth. Vector analysis allows the separation of distance and flaw effect by phase analysis on nonmagnetic materials. On magnetic materials this phase separation does not exist and another procedure is suggested. These results, and in particular those obtained on ferromagnetic materials, point to the possibility of replacing some eddy current or magnetic particle inspections by tests with ferromagnetic resonance probes.     

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.     

Magnetic Nondestructive Test for Resistance Spot Welds Using Magnetic Flux Penetration and Eddy Current Methods

Resistance spot welding technologies are widely used in industry. A highly reliable monitoring method is needed to effectively weld and create a robust structure. We developed a combined technique using magnetic flux penetration and an eddy current test (ECT). The magnetic measuring system consists of a pair of magnetic probes having an induction coil and detection coil, a lock-in amplifier, a current source, and a personal computer. The magnetic flux penetration through both surfaces at the weld was measured at low frequency. The ECT was performed at each surface with multiple frequencies. The magnetic flux penetration method showed good correlation with the destructive shear test because of the change in permeability due to the formation of the nugget. The ECT method reflected the depth profile of the nugget and was effective for determining a defective product.     

Anomalous magnetic source defect modelling

Defect-induced field perturbations occurring during electromagnetic testing of ferromagnetic material can be modelled as combinations of anomalous eddy current and missing magnetization sources. At low frequencies, such as are used in Remote Field Eddy Current (RFEC) inspection of steel tubes, the anomalous magnetization defect sources dominate and give strong responses to circumferential slits orthogonal to the axial magnetic field. Here we present the results of finite element calculations and computer animations of the time-varying fields from a missing magnetization model of a slit defect. These are compared with the defect-induced anomalous field patterns obtained by phasor vector subtraction of calculations for slit defect and defect-free problems. It is noted that the ferromagnetic material in which the defect is located must be included in the missing magnetization model.Research supported by Natural Sciences and Engineering Research Council of Canada, Pipetronix Ltd., Province of Ontario, Gas Research Institute and Infolytica Corp.     

Nonlinear eddy current effects in ferromagnetic materials in the presence of DC magnetic fields

Eddy current effects in nonlinear ferromagnetic materials in the presence of a supplementary DC magnetic field are analyzed. The analysis is for a one-dimensional configuration, a semi-infinite plate magnetized homogeneously in a direction parallel to its surface. The nonlinear magnetization characteristic of the ferromagnetic plate material is assumed to be of a step-function form. Solutions of the electric field intensity on the plate surface, the penetration depth of eddy currents in the plate, the eddy current losses, and surface impedance in the presence of a DC magnetic field are obtained. A connection is found between the values obtained in simultaneous DC and AC magnetization conditions and the values obtained in the case of only AC magnetic field excitation.<>     

Magnetic order in thet-J andt-t′-J models

The magnetic structure of thet-J andt-t′-J models are investigated. Assuming that the ground state has magnetic long-range order, we calculated the energy of some magnetically ordered states using a simple transformation of the models and theS→∞ approximation. The result shows that the Néel state is destroyed by doped holes unless the next-nearest neighbor hoppingt′ is finite, and that the ferromagnetic phase appears at moderate doping. Mean field analysis shows that the intermediate phase between the Néel and ferromagnetic phase has spiral spin order, although the spiral phase is shown to be unstable against density fluctuations.     

A Permeability-Measuring Magnetic Flux Leakage Method for Inner Surface Crack in Thick-Walled Steel Pipe

It is difficult for traditional magnetic flux leakage (MFL) methods to detect inner surface cracks of thick-walled steel pipe or plate due to magnetic shielding of the wall and strong magnetic background noise, and for eddy current testing (ECT) as well due to its skin effect. On the basis of the nonlinear magnetic permeability of ferromagnetic materials, a new non-destructive testing method (NDT) permeability-measuring magnetic flux leakage (P-MFL) is proposed, in which the magnetization is perpendicular to the inner surface crack, and the surface layer permeability distortion caused by magnetic field distortion is measured by differential pick-up coils. Afterwards, its detection mechanism is presented and analyzed, and its feasibility is verified by simulations and experiments. Finally, some application cases for steel pipe are also realized effectively. Meanwhile, its testing characteristics for cracks are given and effects of crack size, specimen thickness, scanning paths to testing signal amplitude are briefly analyzed. Finally, the proposed P-MFL method compared to traditional MFL method is discussed in detail.     

Transient Eddy Current NDE System Based on Fluxgate Sensor for the Detection of Defects in Multilayered Conducting Material

This paper describes a novel transient eddy current non destructive evaluation (NDE) system for the detection of defects in a multilayered conducting material by using fluxgate magnetometer as a sensor. In conventional eddy current NDE, the depth of defect detection is restricted due to the excitation frequency and its associated skin depth. Similarly, in conventional pulsed eddy current testing the time derivative of the secondary magnetic field, which decays much faster than the magnetic field itself, is measured by the induction coil. However, in this work we use fluxgate magnetometer which measures magnetic field directly and double “D” differential excitation coil in order to enhance the depth of investigation. In addition to this, the other instruments such as transmitter, transmitter controller and data acquisition system used for this work are the same one used for TEM based geophysical applications. The system has been used for the detection of an artificially engineered defect in an aluminum plate at a depth of 2 mm as well as 20 mm below the surface.     

The quantitative relations between true and standard depth of penetration for air-cored probe coils in eddy current testing

The true depth of penetration of eddy currents generated in a conducting sample by an air-cored probe coil, besides depending on the electromagnetic wave frequency and the magnetic permeability and electrical conductivity of the sample, also depends strongly on the coil dimensions and the sample thickness. The standard depth of penetration widely used as a guide for eddy current inspection purposes is calculated for a plane electromagnetic wave incident perpendicularly on a conducting half-space and is thus a material/test parameter rather than a true measure of penetration. In this paper the quantitative relations between true depth of penetration and standard depth of penetration are presented for three configurations of eddy current probe and test material. First an air-cored coil above a conducting half-space is considered, then the same coil above a conducting sheet, and finally the true depth of penetration is calculated in a conducting half-space covered with cladding for different ratios of condictivity between cladding and base material.     

A Parametric Estimation Approach for Groove Dimensioning Using Remote Field Eddy Current Inspection

The remote field eddy current technique is used for dimensioning grooves that may occur in ferromagnetic pipes. We propose a method to estimate the depth and the length of corrosion grooves from the measurement of a pick-up coil signal phase at different positions close to the defect. Groove dimensioning needs the knowledge of the physical relation between measurements and defect dimensions; therefore, finite-element calculations are performed to obtain a parametric algebraic function of the physical phenomena. The parameters of this model function are obtained by an optimization technique. By means of this model and a previously defined general approach, an estimate of groove size may be given. In this approach, algebraic function parameters and groove dimensions are linked through a polynomial function. To validate this estimation procedure, a statistical study has been performed. The approach is proved to be suitable for real measurements.     

The Tube to Tube Through Transmission Technique for Inspecting Finned Heat Exchanger Tubes

Finned tubes are used in chemical processing and air conditioner heat exchangers. Conventional electromagnetic methods cannot be used to inspect the finned tubes for flaws because of the interference caused by the fins. We describe here tests of a recently developed method, the Tube to Tube Through Transmission (T4) technique which uses coplanar exciter and detector coils in neighboring tubes. As the method is new there is, as yet, little theoretical or experimental explanation for it. We report first, therefore, studies of the magnetic fields and the induced eddy currents. Since the coupling path between exciter and detector coils is primarily diffusive, skin effect equations can be applied to give useful approximations for signal analysis. Signals from machined full circumferential grooves in finned heat exchanger tubes were analyzed using these equations, and it was found that the depth of the grooves or general thinning could be estimated to within ±10%.     

高冲击载荷作用下平面式电涡流阻尼器特性数值模拟研究

为探究平面式电涡流阻尼器在冲击环境中的应用特点,开展了高冲击载荷作用下平面式电涡流阻尼器响应特性数值模拟研究.基于ANSYS Maxwell电磁学有限元软件建立平面式电涡流阻尼器二维数值仿真模型,分析了永磁体和磁靴结构尺寸、导电层和导磁层厚度以及气隙间距对电磁阻尼力的影响.研究结果表明:平面式电涡流阻尼器能够满足安全制...     

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测有限元仿真模型,研究不同角度、不同深度裂纹检测幅值、相位的变化规律。为验证该仿真模型的正确性,开展远场涡流检测多层金属板的试验。试验结果表明:设计开发的远场涡流探头可检测埋深13 mm的裂纹缺陷,当裂纹倾斜角度为0°时,检测灵敏度最高,当裂纹倾斜角度为90°时,检测灵敏度最低,与仿真结果保持一致,且能够对缺陷进行精准定位,可为飞机多层金属板构件隐藏裂纹的定量检测提供依据。     

焊接微缺陷磁光成像检测有限元分析

目的 研究铁磁材料焊接微缺陷的磁光成像规律.方法 运用漏磁检测原理和法拉第磁致旋光效应,建立微缺陷三维有限元模型,分析微缺陷磁光成像过程与磁场之间的关联,研究不同提离值、励磁电流、缺陷宽度、缺陷深度下的磁光成像,以及探索这些因素对磁光图像特征的影响.在此基础上,对最小宽度为0.05 mm的微缺陷进行磁光成像检测实验,并...     

Quasistatic and Dynamic Magnetic Permeabilities of Long Ferromagnetic Rods Magnetized by Coils of Arbitrary Length

An analysis is made of the current state of the problem of determining the permittivity of electrically conducting ferromagnetic materials. Expressions are obtained for the quasistatic and dynamic magnetic permeabilities of ferromagnetic rods with coils having arbitrary lengths and space factors.