Eddy Current Simulation Research Articles

Eddy Current Modeling and Simulations for the Characterization of Low Thickness Multilayer Materials

Measuring and determining the parameters and characteristics of multilayer structures have become an important subject for several recent studies. This importance is due to industry needs and structural health requirements. The eddy current inspection is considered an important practical tool that ensures the safety and efficiency of multilayer structures and responds to the above necessities. The diversity of multilayer structure characteristics is one of the principal problems that must be solved. These physical and electromagnetic parameters are not always available or provided by the suppliers. Another problem that arises in the development of different models related to these structures is the difficulty of obtaining a satisfactory diagnosis. This difficulty returns to the complexity of geometry, the presence of small dimensions and sizes, and the existence of various parameters. In this context, it is necessary to achieve a strategy for the development of software and hardware tools concerning the characterization of multilayer structures. These tools must be applied to surmount the above problems and improve the technical advantages of the eddy current inspection. The principal objective of this work is to investigate the efficacy of the eddy current method applied to aeronautical materials, particularly low thickness multilayer structures. The modeling was performed using the finite element method. A software program was developed to investigate changes in the coil impedance. Results are initially validated and compared against the analytical and computational results given for simple cases. They are very similar, and they present a good agreement for both situations. The error is 5% for the calculus of the induction magnetic B. It also varies from 0.17% to 5.32% for impedance responses that enable the application of the developed code to carry out simulations for complex geometries. For various values of parameters and a wide range of applications, the parameters and properties of the problem can easily be introduced into the code. This permits the analysis and calculation of changes in impedance versus the effect of any variation in parameters. The developed approach is sufficiently general. It can simulate various potential cases of defects in low thickness multilayer structures due to its adequate design. It can generate interpretable results for different.

Research on Interstitial Eddy Currents Detection Methods between Two - layer Conductors based on Apparent Conductivity Curve

In aviation, energy and other fields, the Two-layer Conductors Slabbed Construction has a very wide range of applications, so its reliability is crucial to the operation of the system. However, the traditional testing methods are often limited by complex environment and structural characteristics, but as a nondestructive testing technology, eddy current testing has the advantages of non-contact and high resolution, so it has attracted much attention. As for Two-layer Conductors Slabbed Construction, it is of great theoretical and practical value to accurately detect the internal defects and gaps by analyzing the electromagnetic characteristic changes caused by eddy currents. This study takes the eddy current detection method based on apparent conductivity as the research topic, and explores the theory and method of eddy current detection of two-layer conductors slabbed spacing. First, it describes the physical mechanism of eddy current testing. Then, it analyzes the impedance characteristics of eddy current detection, proposes a two-layer conductors slabbed spacing eddy current detection method, and carries out sweep frequency test of eddy current detection impedance characteristics. On this basis, the analysis of two-layer conductors slabbed spacing eddy current inspection simulation is carried out. Finally, an inversion algorithm of eddy current detection based on orthogonal polynomial is proposed, and its validity is verified by simulation analysis.

Yoke-Type Elasto-Magnetic Sensor-Based Tension Force Monitoring Method for Enhancement of Field Applicability.

Tension members are key members that maintain stability and improve the strength of structures such as cable-stayed bridges, PSC structures, and slopes. Their application has recently been expanded to new fields such as mooring lines in subsea structures and aerospace fields. However, the tensile strength of the tension members can be abnormal owing to various risk factors that may lead to the collapse of the entire structure. Therefore, continuous tension monitoring is necessary to ensure structural safety. In this study, an improved elasto-magnetic (E/M) sensor was used to monitor tension force using a nondestructive method. General E/M sensors have limitations that make it difficult to apply them to operating tension members owing to their solenoid structure, which requires field winding. To overcome this problem, the magnetization part of the E/M sensor was improved to a yoke-type sensor, which was used in this study. For the development of the sensors, the numerical design and magnetization performance verification of the sensor were performed through eddy current solution-type simulations using ANSYS Maxwell. Using the manufactured yoke-type E/M sensor, the induced voltage signals according to the tension force of the specimen increasing from 0 to 10 tons at 1-ton intervals were repeatedly measured using DAQ with wireless communication. The measured signals were indexed using peak-to-peak value of induced voltages and used to analyze the signal change patterns as the tension increased. Finally, the analyzed results were compared with those of a solenoid-type E/M sensor to confirm the same pattern. Therefore, it was confirmed that the tension force of a tension member can be estimated using the proposed yoke-type E/M sensor. This is expected to become an effective tension monitoring technology through performance optimization and usability verification studies for each target tension member in the future.

Segmented RF shield design to minimize eddy currents for low-field Halbach MRI systems

MRI systems have a thin conducting layer placed between the gradient and RF coils, this acts as a shield at the RF-frequency, minimizing noise coupled into the experiment, and decreasing the coupling between the RF and gradient coils. Ideally, this layer should be transparent to the gradient fields to reduce eddy currents. In this work the design of such a shield, specifically for low-field point-of-care Halbach based MRI devices, is discussed. A segmented double layer shield is designed and constructed based on eddy current simulations. Subsequently, the performance of the improved shield is compared to a reference shield by measuring the eddy current decay times as well as using noise measurements. A maximum reduction factor of 2.9 in the eddy current decay time is observed. The segmented shield couples in an equivalent amount of noise when compared to the unsegmented reference shield. Turbo spin echo images of a phantom and the brain of a healthy volunteer show improvements in terms of blurring using the segmented shield.

Flow-Induced Vibration of Cantilever Type Elastic Material in Straight Tricylinder

The hydrodynamic performance and wake evaluation results of a cantilever flexible cylindrical triangular array at Re = 9000 and with L/D spacing ratios ranging from 3 to 7 are presented in this paper. The improved delayed separation eddy current simulation (IDDES) SST k-ω turbulence model and tetrahedral mesh are employed to solve the three-dimensional instantaneous flow field. The objective is to find the L/D ratio that the upstream cylinder has the most pronounced effect on the downstream cylinders, to quantify whether a flexible upstream cylinder is more favorable than the rigid upstream cylinder, and to know the flexible cylinder wake distribution. The findings indicate that, at Re = 9000, when the spacing ratio is 3~7 and the spacing ratio L/D is 6, the amplitude of the downstream cylinder is most affected by the wake of the upstream cylinder; the amplitude of downstream cylinders of the rigid upstream cylinder exerted a 1% or 2% greater effect than the flexible cylinder, with vortices predominantly concentrated in the middle and upper parts of the flexible cylinder rather than at its top.

Degaussing procedure and performance enhancement by low-frequency shaking of a 3-layer magnetically shielded room.

We report on the performance of a Magnetically Shielded Room (MSR) intended for next level 3He/129Xe co-magnetometer experiments that require improved magnetic conditions. The MSR consists of three layers of Mu-metal with a thickness of 3mm each and one additional highly conductive copper-coated aluminum layer with a thickness of 8mm. It has a cubical shape with a walk-in interior volume with an edge length of 2560mm. An optimized degaussing (magnetic equilibration) procedure using a frequency sweep with a constant amplitude followed by an exponential decay of the amplitude will be presented. The procedure for the whole MSR takes 21min, and measurements of the residual magnetic field at the center of the MSR show that |B| < 1 nT can be reached reliably. The chosen degaussing procedure will be motivated by online hysteresis measurements of the assembled MSR and by eddy-current simulations, showing that saturation at the center of the Mu-metal layer is reached. Shielding factors can be improved by a factor ≈4 in all directions by low frequency (0.2Hz), low current (1A) shaking of the outermost Mu-metal layer.

Simulation Study of Transient Eddy Current Effect in 3T Animal Gradient Coil

In the process of high-field magnetic resonance imaging (MRI), the eddy current modeling and simulation of the cold screen and metal parts are not highly accurate. To solve this problem, this paper uses the target field method to design a 3T animal gradient coil model. To get more realistic simulation results, a complex model including a gradient system, cryogenic vessel, cold screen, epoxy resin, and temperature holes was constructed. The model was refined using the finite element method, and the effects of eddy currents induced by the gradient coil on the cylindrical cryogenic container and cold screen in the superconducting magnetic resonance instrument under the state of multi-physical field coupling were simulated. The model effectively reflects the transient eddy current distributions on the cold screen and cryogenic vessel in the MRI system and their time-dependent temperature rise effects.

Modeling of Eddy Current NDT Simulations by Kriging Surrogate Model

ABSTRACT In this article, the Kriging surrogate model is proposed to accelerate the model-assisted probability of detection (MAPoD) analysis for eddy current nondestructive testing (NDT). The Kriging surrogate model is the key for enabling the efficient MAPoD analysis, considering huge number of uncertainties propagate in the eddy current NDT system, by replacing the time-consuming physical model. To generate the model responses of NDT system, a precise physical model based on the adaptive cross approximation algorithm accelerated boundary element method (BEM) is applied. In the numerical case, the MAPoD study of eddy current for detecting surface flaws in the conducting plate is analyzed. By comparing the PoD metrics achieved by the pure physical model and by the Kriging surrogate model, the accuracy and efficiency of the proposed surrogate model are demonstrated.

A Novel MSFEM Approach Based on the A-Formulation for Eddy Currents in Iron Sheets

The multiscale finite element method has been shown to be an efficient tool in the simulation of eddy currents in laminated cores. It allows for the accurate simulation of the electric and magnetic field without needing to resolve the individual steel sheets in the finite element mesh. This paper presents a novel multiscale formulation for the low-frequency case which corrects some shortcomings of the approach used up to now. It enforces more physically accurate continuity and divergence conditions on the solution while also increasing its accuracy. The advantages of the new approach are studied both analytically and by means of a numerical example.

A stress detection method for metal components based on eddy current thermography

The metal components are subjected to various complex stresses during processing and use, which may lead to material failure in severe cases. Therefore, the detection of stress in these components has practical and important application value. In this study, a theoretical model of stress detection was constructed based on the principle of eddy current thermography, and the expression between temperature change and stress was deduced. Especially in the cooling stage, the relationship expression between stress and temperature change was obtained. By establishing an eddy current thermography simulation model, the change of the temperature response of the sample surface was analyzed, and a stress detection method based on the relationship between time-temperature change law-stress distribution was developed. An eddy current thermography stress detection system was built, and the stress detection equation was constructed based on the experimental data to verify the effectiveness of the method. Then, to eliminate the interference of factors such as excitation parameters, the stress detection method was optimized by using cooling data, and its measurement error is 5.37%, which further improved the stability and accuracy of stress detection. Finally, according to the idea of deep learning, a convolutional neural network (VGG19 and ResNet101) assisted method was used to evaluate the stress state. By training the temperature thermal aberration map, the stress distribution state of the structure can be quickly and effectively evaluated, the test accuracy can reach 99%, and the accuracy of the cooling data set after excluding the influence of factors such as eddy current excitation is higher. It also verified the accuracy of the stress detection method based on the time-temperature change law-stress distribution proposed in this paper. In addition, it provided technical support and data reference for subsequent quantitative stress detection and damage assessment of more complex structures.

Analytical Methodology for Eddy Current Loss Simulation in Armature Windings of Synchronous Electrical Machines With Permanent Magnets

This article describes a novel analytical methodology for eddy current losses simulation in the windings of permanent magnet synchronous machines. The methodology is based on subdomain modeling technique in conjunction with solving of ordinary differential equations system. The main advantage of the proposed method is high accuracy and significant reduction of simulation time in comparison with finite-element modeling (FEM) technique that is frequently used for eddy current loss modeling. The proposed model allows fast and accurate evaluation of proximity and skin effect in conductors in time domain for an arbitrary current waveform and machine duty cycle. The main difference from previously presented analytical methods is the possibility to evaluate losses for a wider range of conductors geometries, regardless their shape, dimensions, location in the stator slots, and rotor speed. The main contribution and novelty of the proposed analytical approach is simultaneous implementation of subdomain modeling technique and strands segmentation concept followed by the eddy current effect representation through the equivalent circuit. This approach allows reducing the computational time while keeping the accuracy close to the FEM result. The proposed model was compared to FEM, using different types and sizes of conductors and also validated experimentally.

Application of a Fractional Transfer Function for Simulating the Eddy Currents Effect in Electrical Systems

Some electrical devices contain a solid nonlaminated magnetic core as a component. In the case of variable magnetic flux, eddy currents arise in such a core, which should be taken into account for computer simulation if higher precision is needed. The fractional order transfer function (FOTF) based on the simple traditional model of excitation circuit of a DC machine is proposed for eddy current simulation. This model is illustrated by mathematical (based on differential equations and the Laplace operator) and structural approaches to the excitation circuit of a common DC generator with a solid core. The skin effect for more precise simulation of eddy currents is also considered by means of fractional order transfer functions in the computer models. Magnetic saturation and hysteresis were not taken into account in this case. The proposed model is simple and ensures adequate accuracy, confirmed experimentally using the FOTF Toolbox for MATLAB and Simulink. This model is distinct and proposed for the fast and accurate computer simulation of eddy currents in electrical devices with a solid magnetic core.

Data-driven modeling of nonlinear materials in normal-conducting magnets

Accurate numerical modeling of normal-conducting accelerator magnets requires a reliable characterization of the iron saturation and hysteresis as well as a precise knowledge of the magnet geometry as built. Computations of the field quality are not easily achieving the accuracy required by the accelerator operation, particularly for eddy-current effects in fast-ramping magnets. This paper proposes a (measurement) data-driven model for the nonlinear magnetization of normal-conducting magnets. The model adopts a volume integral formulation compatible with eddy-current simulations. A two-step updating procedure is applied. The first step is the fitting of material parameters directly in the magnet model. The second step is the updating of the magnetization by measurements of the integral field harmonics. The result is a full-order updated model that can be employed in static or dynamic simulations. Finally, the procedure is validated on an iron-dominated, normal-conducting magnet.

Nested kernel degeneration-based boundary element method solver for rapid computation of eddy current signals

In this article, the nested kernel degeneration (NKD) based integral equation fast solver is proposed to compress the dense system matrix generated by boundary element method (BEM) for calculating eddy current signals in 3D nondestructive evaluation (NDE) problems. The near and diagonal block interactions are computed and stored by full matrices. However, for the far block interactions, not like in the single level kernel degeneration-based method that all the interaction matrices are compressed by the interpolations, the nested approximation framework makes the expression of the higher-level matrices by the ones at leaf levels and the transfer matrices between neighboring levels. Different integral kernels are degenerated and nested to ensure the performance of NKD based method. The robustness and efficiency of the proposed solver are validated and verified by making numerical predictions and comparing them with the ones achieved by analytical method, numerical methods and experiments. Our numerical experiments show that the NKD solver is more efficient than the butterfly solver (multilevel adaptive cross approximation algorithm (MLACA)) for electrically small eddy current NDE problem. With the NKD based method, O ( N ) computational complexity is achieved for multiscale low frequency eddy current simulations without sacrificing accuracy, where N is the number of unknowns. So far, to our best knowledge, the proposed method with linear complexity is the most efficient integral equation-based BEM forward solver to predict the eddy current signals from cracks and flaws.

A Novel Acceleration Method for Crack Computation Using Finite Element Analysis in Eddy Current Testing

Finite element analysis plays an essential role in the field of eddy current computation and analysis for non-destructive testing applications. There are some analytical solutions that can be used to solve eddy current problems, however, in most cases, there is no suitable analytical method, i.e., the test sample with arbitrary geometry or with arbitrary shape of crack. Therefore, finite element method is a fundamental tool in conducting the investigations. A key feature of using finite element method for eddy current simulation is being versatile but slow. In this paper, exploiting the fact that the crack only causes a small perturbance in fields in the surrounding region, a novel crack calculation acceleration method is proposed. The algorithm proves that the calculation can be mainly executed within the perturbance domain. Both numerical and experimental tests have been conducted for verification. The speed of the calculation is enhanced greatly (up to 34 folds in the tested cases) while deviation from the full solution is within 5%. Moreover, the measured results have a good agreement with the simulated ones under different depths of crack.

A Comparative Study for Evaluating Passive Shielding of MRI Longitudinal Gradient Coil.

Gradient coils are vital for Magnetic Resonance Imaging (MRI). Their rapid switching generates eddy currents in the surrounding metallic structures of the MRI scanner causing undesirable thermal, acoustic, and field distortion effects. The use of actively shielded gradient coils does not eliminate such undesirable effects totally. Use of passive shielding was proposed lately to particularly help in mitigating eddy currents and loud acoustic noise. Numerical computations are necessary for calculating eddy currents and evaluating the efficacy of passive shielding. Harmonic and temporal eddy current analysis caused by gradient coil(s) using network analysis (NA) can be faster and more flexible than the traditional FDTD and FEM methods. NA was used more than a decade ago but was limited to analyzing eddy currents resulting from z-gradient coils of separated turns. NA with stream function was recently modified resulting in the more general Multilayer Integral Method (MIM) for simulation of eddy currents in thin structures of arbitrary geometries. In this work, we compared the performance of the NA method and an adapted MIM method to analyze eddy current in both the passive shielding and cryostat to the Ansys Maxwell 3D analysis thus evaluating the performance of gradient configurations with and without passive shielding. Both an unconnected and a connected z-gradient coil configuration were used. Our analysis showed high agreement in the profiles of eddy ohmic losses in metallic structures using the three methods. The NA method is the most computationally efficient however, it is limited to specific symmetries unlike the more general MIM and Ansys methods. Our implementation of the adapted MIM method showed computational efficiency relative to Ansys with comparable values. We have developed a computationally efficient eddy current analysis framework that can be used to evaluate more designs for passive shielding using different configurations of MRI gradient coils.

Investigation of Rotating Eddy Current Testing Simulation Using Simplified Model

To reduce the time of simulation for rotating Eddy current testing (RECT) technique, a simplified model without modeling probe was proposed previously. However, the applicability of the simplified simulation model was unknown. In this paper, the applicability of the simplified model for the RECT technique was investigated. The application condition of the simplified model was provided by comparing it with the results of the traditional simulation model. The simplified model was suitable for the study of cracks shorter than 70% size of the uniform Eddy current induced by the probe in a traditional model or experiment. The experiment was conducted to validate the simplified model. Moreover, using the simplified model, the effects of crack depth, orientation, and exciting frequency were studied. The deeper the crack depth was, the greater peak value of [Formula: see text] signal was. The crack angle was linear with the phase of signal. The exciting frequency affected the amplitude and phase of the signal at the same time.

Model Construction for Far Field Eddy Current Examination Simulation on Ferromagnetic Tubes

Ferromagnetic tubes are widely applied in fossil power plants such as waterfall tubes, overheat tubes or reheating tubes. Outer surface corrosion, wearing, depth reduction, cracks are common defects during manufacturing and long term operation. Eddy current detection is a traditional method for the examination of surface and near surface defects. However the efficiency is restricted by lift-off effect and skim effect. Far field eddy current overcomes the above disadvantages with high efficiency and fast examination speed and high sensitivity. In this paper, numerical simulation has been carried out to study the far field eddy current Detection for defects in small diameter ferromagnetic tubes in fossil power plants.

Simulation on the Effect of Frequency and Ferromagnetic Tubes Specifications by Far Field Eddy Current Examination

Tube leakage frequently occurred in on-service fossil power plants. Traditional NDT testing methods, including RT, UT, MT and PT are not applicable for the examination of large amount tubes. Fat eddy current examination is a new technique for testing ferromagnetic tubes defects, such as inner corrosion, thickness reduction and cracks. Far field eddy current simulation and verification for different specification tubes has been carried out. The result shows that the position of far field eddy current moves backwards with the increase of wall thickness and tube ID. To the defects with same size, examination sensitivity is higher in far field eddy current area. When the defect with same size locates in the inner and outer surface of the tube, the change of magnetic intensify differences is approximately the same, which is in accordance with the experimental result and is satisfied with far field eddy current examination theory. It has been concluded that defects in ferromagnetic tubes could be judged and recognized by far field eddy current examination technique, which shows prospective for the on-line examination and safety evaluation for in-service tubes in fossil power plants.

Permeability and resistivity estimations of SMC material particles from eddy current simulations

• Randomized 3-D geometries are used to imitate an SMC material. • Complex permeability and resistivity are estimated. • Regions of feasible permeabilities and resistivities are found. In this article, we estimate numerical values of a complex permeability and an electrical resistivity of soft magnetic composite (SMC) material particles. The estimations are carried out against a measured loss curve and a measured effective dynamical permeability curve. The SMC material is imitated using automatically generated geometries with control over the scalings of the geometries as well as the thicknesses of the electrical insulations between individual particles. The estimation procedure is repeated for a wide range of insulation thicknesses and scalings. Consistency with the measured effective dynamical permeability suggests the estimated relative permeability of the particles to be of the order of hundreds. An estimate of 250–500 is found. If the scalings of the geometries are chosen using a microscope image of the SMC material as a reference, the estimated resistivity of the particles is of the order of 10 - 7 Ωm.