Motion-induced Eddy Currents Research Articles

A composite testing method of homologous magnetic flux leakage and motion-induced eddy current for inner and outer defects

Magnetic flux leakage (MFL) testing, widely utilized for pipeline integrity assessments due to its efficiency and accuracy, is often challenged by motion-induced eddy currents (MIEC) that can distort MFL signals. Contrary to traditional perspectives that consider MIEC as detrimental, this paper introduces a novel MFL-MIEC composite testing method. This method leverages MIEC as a complementary technique while sharing the same excitation source. By exploring the generation and influence of MIEC on MFL signals, we simulate optimal probe positions and analyze the effects of defect position, angle, and detection speed on signal quality. Adjustments in the detection coils orientation are shown to enhance signal strength, demonstrating the methods effectiveness in identifying pipeline defects through practical experiments. This approach offers significant potential for widespread application in pipeline assessments.

Hybrid multi-modal NDE sensing system for in-motion detection and localization of rolling contact fatigue damage in rails

This article presents a multi-modal hybrid-probe approach to nondestructive inspection of RCF cracks and damage in rails. A combination of electromagnetic (EM) and ultrasonic testing (UT) techniques are presented, which allows for complementary physics to be utilized to enhance detection and characterization of surface and sub-surface cracks in a non-contact manner at high speeds. A novel integrated design which combines the motion-induced eddy current (MIEC) effect and ultrasonic Rayleigh surface waves generated and detected using electromagnetic acoustic transducer (EMAT) is presented. The hybrid probe was tested at low speeds to demonstrate an increased damage localization capability. This was carried out using a data registration and fusion approach between the sensing modalities. Finally, the capability of MIEC effect at high-speeds is demonstrated. The results show that the hybrid probe has a high potential for in-motion, high-speed damage detection and characterization in the future.

RCF crack direction assessment in moving ferromagnetic material by DC electromagnetic NDT technique

The rolling contact fatigue (RCF) cracks that initiate from the surface of ferromagnetic materials in aviation bearings and high-speed rails are typically inclined at varying angles, posing a serious threat to safety. Therefore, a rapid and quantitative characterization of inclined cracks is of great importance. This paper investigates the distribution of magnetic fields and motion-induced eddy current (MIEC) in direct current (DC) electromagnetic non-destructive testing (NDT), and proposes an approach for measuring the direction of RCF cracks in moving ferromagnetic materials. The magnetic field and MIEC distributions in the moving ferromagnetic material are initially investigated, followed by a numerical simulation exploring the impact of crack inclination angle and depth on detection signals. The resulting relationship between crack propagation angle, depth, and detection signal is then obtained. Furthermore, a DC electromagnetic NDT platform has been designed and a quantitative detection approach for inclined cracks has been proposed and validated through experiments. Finally, a real scenario detection is carried out. The investigation presented in this paper demonstrates that the DC electromagnetic NDT technique is applicable not only for assessment RCF crack direction in moving ferromagnetic materials, such as rotating aviation bearings, but also for characterizing inclined cracks under conditions of fast relative motion between the probe and the ferromagnetic material (e.g., high-speed rail, pipeline, etc.).

Speed Measurement Method for Moving Conductors Based on Motion-Induced Eddy Current

Speed measurement plays an important role in many measurement and control systems in industry. A simple and efficient speed measurement method for smooth conductive specimens based on motion-induced eddy currents is studied in this paper. The speed sensor consists of a magnet and a Hall element. When the conductor moves beneath the magnet, eddy currents are generated, which further generate a secondary magnetic field that is dependent on the moving speed of the conductor. The Hall element picks up this field to determine the relative speed between the conductor and the sensor. First of all, a 2D analytical model for the induced eddy currents and corresponding magnetic fields has been proposed by solving the Maxwell’s equations using spatial Fourier transforms. Then, the change in current density and magnetic field with conductor speed is analyzed using both the analytical model and the finite element method. Speed sensing experiments were conducted on a rotating conductive disk, the results showed good agreement with the proposed analytical model. Finally, specifications such as accuracy, repeatability, linearity, and resolution of the prototype sensor have been tested.

Finite-Element Study of Motion-Induced Eddy Current Array Method for High-Speed Rail Defects Detection

Nondestructive testing (NDT) methods are widely used in the rail industry to detect and characterize rolling contact fatigue (RCF) defects in railroads, which is very important for railway inspection and maintenance to prevent catastrophic accidents. Existing NDT methods, e.g., ultrasonic testing (UT), magnetic flux leakage (MFL), and eddy current testing (ECT) have been successfully applied in the rail industry, and the state-of-the-art UT method reported recently achieved a high speed of 40 mi/h with a probability of detection (POD) over 80% under 30% false alarms. However, NDT methods still suffer from a bottleneck in that a higher inspection speed causes lower detection sensitivity due to their physical limits, such as negative velocity effect and long sensing time. One of the leading challenges to the rail NDT community is to develop a high-speed high-sensitivity (HSHS) capability that can provide an improved POD of rail defects in high-speed inspection scenarios over 60 mi/h. This article proposes a horizontal U-shaped magnets-based motion-induced eddy current array (MIECA) method to detect rail surface defects with the HSHS capability. The MIECA method deploys a three-axis magnetic sensor array along the rail transverse direction at the middle of the magnets to measure the MIECA signals, which utilizes the wake effect of the diffused motion-induced eddy current (MIEC) caused by the relative high-speed motion between the magnets and the rail track. Finite-element method (FEM) simulations with a wide speed range from 0 to 62.5 mi/h are carried out to investigate the relationships between the MIEC generation, diffusion and magnitude, and the three-axis MIECA signals. The simulation results show that the higher the speed, the greater the magnitude of diffused MIEC, and the greater the peak-to-peak values of three-axis MIECA signals caused by rail surface defects, which shows a great promise for detecting rail surface defects in high-speed scenarios and is superior inspection relative to existing NDT methods in terms of inspection speed, detection sensitivity, and defect characterization capability.

The Effect of Motion-Induced Eddy Currents on Three-Axis MFL Signals for High-Speed Rail Inspection

Nondestructive testing (NDT) methods are widely used in the rail industry to detect rolling contact damage (RCD) defects to ensure railway safety. With the need of monitoring millions of miles of rail tracks more effectively and efficiently that leads to improved rail safety, reliability, and optimized assets management, the research on high-speed and high-accuracy NDT methods that can obtain high signal-to-noise ratio (SNR) and high sensitivity defect signals at higher speeds is of vital importance. Magnetic flux leakage (MFL) is one of the NDT methods used for high-speed rail inspection, which is suitable for detecting surface and subsurface RCD defects on railhead, but the measured MFL signals are distorted severely by the effect of motion-induced eddy currents (MIEC). However, the fundamental understanding of the mechanism of MIEC generation, distribution, and magnitude is lacking, and the physical interaction between MIEC and MFL measurement during high-speed rail inspection has not been well studied. This article investigates the effect of MIEC on three-axis MFL signals through 3-D finite-element method (FEM) simulations. The 3-D distributions of MIEC and 2-D image signals of MFL measurements for high-speed rail MFL inspection are presented and analyzed. The simulations are conducted with an inspection speed range of 0-62.5 mi/h, and a surface hemisphere-type defect and subsurface hole-type defect are both considered. The results show that the motion between the magnetizer and the rail will generate two types of MIEC, which in turn decreases the peak values of three-axis MFL signals from the subsurface defect and affects the MFL signals spatially, especially the base values along rail transverse and vertical directions. The effect of MIEC on the three-axis MFL signals in terms of SNR, sensitivity, and asymmetry is discussed.

Investigation of DC Electromagnetic-Based Motion Induced Eddy Current on NDT for Crack Detection

Cracks caused by long-term cyclic loading and harsh working environment may seriously lead to the catastrophic industrial safety accidents. Therefore, a quantitative and accurate characterization for the cracks is necessary to ensure safety of the key component (e.g. rolling contact fatigue of high speed rail track in particular). This article investigates the motion induced eddy current (MIEC) of a direct current (DC) electromagnetic nondestructive testing (NDT) and proposes an approach to quantitative characterization the cracks in moving ferromagnetic material. The velocity effect as well as the distribution of MIEC of the ferromagnetic material under the DC electromagnetic probe are investigated firstly. Then, the relationships between the crack depth/width and detection signals are discovered. Finally, a quantitative characterization method of crack depth/width is proposed by experiment. The investigations indicate that for DC electromagnetic NDT, the dragging effect is related to the rate of the MIEC diffusion time, which is inversely proportional to the conductivity and permeability of metal, therefore, the higher speed, the more obvious the dragging effect is. The experiments show that the crack depth/width can be characterized quantitatively by the peak separation and differential value. The investigation in this article show that the DC electromagnetic based on MIEC can be used not only for the crack detection in moving ferromagnetic metals such as bearings, gears, etc., but also for the quantitative characterization of cracks when there is rapid relative motion between the detection devices and the ferromagnetic metals (e.g., rail, pipe, etc.).

A Novel Probe of DC Electromagnetic NDT Based on Drag Effect: Design and Application in Crack Characterization of High-Speed Moving Ferromagnetic Material

Electromagnetic nondestructive testing (NDT) of high-speed moving ferromagnetic material is a challenging topic; due to the relative motion between ferromagnetic material and detection devices, motion-induced eddy current (MIEC) will be generated and the drag effect will show up, which result in a more complex magnetic field distribution in the ferromagnetic material than static or quasi-static testing. Therefore, an electromagnetic NDT probe, which is suitable for multiple crack detection in high-speed moving ferromagnetic materials, is urgently required. In this article, a novel probe of dc electromagnetic NDT based on drag effect is designed considering the strength and sensitivity of the detection signal by experiment, and then it is applied to crack characterization of high-speed moving ferromagnetic material. After that, the measurement uncertainty of the detection signal based on a multiconvolutional approach is investigated and estimated. The investigation indicated that the proposed probe can quantitatively characterize the multiple cracks at 20 m/s within the relative error and standard deviation of 10% when the crack depth is deeper than 1.0 mm; furthermore, the deeper the crack, the higher the experimental repeatability. Accordingly, the proposed probe can be expected to detect the multiple cracks in high-speed moving ferromagnetic materials, such as rotating bearings, pipelines, and high-speed railway.

Motion induced eddy current based testing method for the detection of circumferential defects under circumferential magnetization

Magnetic flux leakage (MFL) testing is widely applied in the online detection of steel pipes. Different magnetizing directions are required for the detection of defects in different directions. As the speed of online MFL testing increases, the motion induced eddy current (MIEC) effect becomes significant, and the direction of the MIEC is perpendicular to defects in the same direction as the magnetization. Therefore, the magnetic field signal generated by the MIEC perturbation is analyzed by simulation and compared with MFL signal. It is found that the amplitude of the magnetic field signal generated by the MIEC perturbation increases with the rise of the rotational speed and magnetization. In high rotational speed and strong magnetization, the amplitude of the magnetic field signal caused by MIEC perturbation is greater relative to the amplitude of the MFL signal, providing a possibility for detecting defects that are parallel to the direction of magnetization.

Investigation on Velocity Effect in Pulsed Eddy Current Technique for Detection Cracks in Ferromagnetic Material

Nondestructive testing (NDT) for ferromagnetic material under motion condition is a challenging topic, because the distribution of the magnetic fields inside the ferromagnetic material is more complicated due to motion-induced eddy current (MIEC) and ferromagnetic material magnetization. Therefore, a fast, accurate, and automatic NDT technique for quantitative detection of crack in the moving ferromagnetic material is an urgent issue. Currently, the pulsed eddy current (PEC) technique is widely applied in quantitative crack characterization in metals; however, the literature focus on the investigation of the velocity influence on PEC is rare. This article performs a deep investigation on the velocity effect of PEC technique by numerical simulation and experiments, and the relationships of speed and PEC signal are discovered. The results show that the velocity effect can change the baseline value of the detection signal in the PEC detection system. Moreover, the crack location, width, and depth can be characterized by PEC with high speed when crack appears in the high-level stage of the excitation signal, and in contrast to static PEC testing, motion detection has a stronger capability to characterize the crack depths. Based on the results, it is beneficial to propose a new high-speed inspection technique for crack characterization in ferromagnetic material components, such as rotating metal components, pipelines, and rail tracks.

A Novel Eddy Current Speed Sensor With a Ferrite E-Core

This letter presents a novel speed sensor based on motion-induced eddy currents in conductive moving parts. The magnetic yoke is an E-shaped ferrite core. The excitation coil is on the center leg of the E-core, and two antiserially connected pick-up coils are on the side legs. Solid iron and aluminum materials are used for the moving part in the simulations and in the measurements. Two-dimensional and 3-D finite element methods are used for a detailed analysis and for the parametric calculations of the eddy current speed sensor. Despite its simple structure, the proposed eddy current speed sensor shows high linearity. The analysis and the measurements are performed at various speeds and excitation frequencies for an evaluation of the performance of the eddy current speed sensor. The minimum linearity error is less than 0.5%.

Improved Coupling Strategy to Cover Curved FE-Facets in the Non-Conforming Mesh Method

A measure of the quality of coupling nodes in non-conforming meshes along the sliding surface is introduced as the stiffness of the coupling. It is shown that the stiffness can be improved by increasing the number of master nodes. The new approach is verified using a simple example involving motion-induced eddy currents. The steady-state reference solution is obtained by a conforming mesh using the velocity term and compared to a time transient simulation, coupling a stationary mesh to a non-conforming moving one.

The effect of motion-induced eddy current on axial MFL inspection for a steel pipe

The effect of motion-induced eddy current on axial MFL inspection for a steel pipe

Study of Rotating Magnet Array-Based Motion-Induced Eddy Current Thermography

To achieve high-speed scanning of defect detection, this paper proposes a motion-induced eddy current (MIEC) thermography method, which utilizes the relative movement between permanent magnet array and the inspected object to induce the eddy current. Specifically, a set of circumferentially arranged permanent magnets rotating in a steel pipe is used to implement the proposed method. Numerical simulation and experimental studies are conducted to investigate the MIEC and thermal distribution influenced by speed, crack orientation, and lift-off effects. The results show that thermal contrast of the crack rises with its orientation to MIEC flowing path changing from parallel to perpendicular; thermal contrast decreases sharply with the lift-off distance of the magnet array increasing. One merit of the proposed MIEC thermography is that MIEC intensity (thermal contrast) increases with scanning speed and benefits the defect detection.

SCSM for Calculation of Motion-Induced Eddy Currents in Isotropic and Anisotropic Conductive Objects

A new approach to determine the defect response signals from defects located in isotropic/anisotropic conducting objects of any size based on the surface charge simulation method is presented in the framework of Lorentz force eddy current testing. The results are verified by finite element method and validated by measurements. Normalized root mean square deviations are less than 5% with respect to measurements.

Motion-induced eddy current thermography for high-speed inspection

This letter proposes a novel motion-induced eddy current based thermography (MIECT) for high-speed inspection. In contrast to conventional eddy current thermography (ECT) based on a time-varying magnetic field created by an AC coil, the motion-induced eddy current is induced by the relative motion between magnetic field and inspected objects. A rotating magnetic field created by three-phase windings is used to investigate the heating principle and feasibility of the proposed method. Firstly, based on Faraday’s law the distribution of MIEC is investigated, which is then validated by numerical simulation. Further, experimental studies are conducted to validate the proposed method by creating rotating magnetic fields at different speeds from 600 rpm to 6000 rpm, and it is verified that rotating speed will increase MIEC intensity and thereafter improve the heating efficiency. The conclusion can be preliminarily drawn that the proposed MIECT is a platform suitable for high-speed inspection.

The Effect of Motion-Induced Eddy Current on Circumferential Magnetization in MFL Testing for a Steel Pipe

Eddy current effect essentially occurs when a relative movement happens between steel pipes and the circumferential magnetizer in high-speed magnetic flux leakage (MFL) testing. To improve the MFL testing for longitudinal defects, the effect of motion-induced eddy current (MIEC) on circumferential magnetization is analyzed. First, in terms of Maxwell equations, the eddy current effect and the MIEC distribution in the steel pipe are analyzed. Then, the finite-element simulations are conducted to investigate the MIEC distribution, the magnetization status change, and the sensitivity difference. With the rotational speed increasing, the MIEC and circumferential magnetic flux density gradually become asymmetrical and non-uniform. The MFL testing signal amplitudes of external and internal defects in the arriving and leaving parts change in different variation trends. Finally, the relevant high-speed MFL testing experiments for steel pipes are performed to confirm the effect of MIEC. The experimental results match well with the theoretical analysis and numerical simulation results.

Evaluation of Subsurface Defects Using Diffusion of Motion-Induced Eddy Currents

The need for inspecting conductive materials using nondestructive methods faster and more efficiently has always been a challenge. This paper presents a method to evaluate the subsurface defects in nonferromagnetic materials using the diffusion of motion-induced eddy currents. A probe, including a permanent magnet and a magnetic field sensor, is moved with a constant speed in the vicinity of an aluminum plate with subsurface defects machined at different depths. The constant magnetic field due to the magnet, which moves relative to the plate, induces eddy currents that diffuse inside the material. At higher speeds, the eddy current diffusion creates a tilted transition zone. The location of the interaction between the frontiers of this transition zone with the defect shall be used to determine the depth of the subsurface defect. This study was carried out using a numerical model to verify the progression of the eddy currents along the depth of the conductive plate as it moves relatively to the probe and obtain the magnetic field perturbation due to the presence of the subsurface defects. The validation of the model is done comparing the results obtained experimentally with those obtained by simulation for identical situations at lower speeds.

Upwind 3-D Vector Potential Formulation for Electromagnetic Braking Simulations

The calculation of motion-induced eddy currents in massive conductors yields a 3-D convection-diffusion problem. Up-winding and SUPG formulations are well established methods to obtain stable discretizations of the scalar convection-diffusion equations in the case of singular perturbation, but there is very little reported experience with the stability of convection in the vector case, i.e., electromagnetism. Numerical experiments with the up-winding method proposed by Xu (Trans. on Mag., 2006; 42:667-670, 2006) has proven it to be insufficient. Building on the work of Heumann (Research report 2008-30, Seminar für Angewandte Mathematik, Eidgenssische Technische Hochschule, Oct. 2008), an alternative approach based on a finite-element discretization of the Lie derivative implied by the convection phenomenon is proposed.

Large systems of equations in a discrete electromagnetism: formulations and numerical algorithms

The description of discrete electromagnetic fields is achieved with the Maxwell grid equations, a set of matrix equations representing a spatial discretisation of Maxwell's equations in integral form on a dual mesh pair. Based on this matrix formalism the calculation of electromagnetic fields requires efficient techniques for the solution of commonly large, sparse systems of linear or nonlinear algebraic, differential–algebraic and ordinary differential equations. Field formulations and modern numerical-solution algorithms especially for the solution of static and quasistatic electric and magnetic fields are presented. Numerical schemes for fast-varying transient and time-harmonic current-driven or resonator electromagnetic fields are added. Details such as regularisation techniques, the modelling of motion-induced eddy currents, possible field excitation sources and the algorithmic treatment of ferromagnetic material properties are addressed. The numerical schemes include error-controlled adaptive time-domain algorithms featuring advanced extrapolation methods, linearisation methods for the nonlinear algebraic systems of equations with the possible inclusion of ferromagnetic hysteresis modelling and iterative solution methods for large sparse linear systems of equations.