Magnetic Dipole Model Research Articles

Solenoid Model for the Magnetic Flux Leakage Testing Based on the Molecular Current

Magnetic flux leakage (MFL) testing is a widely applied method for the ferromagnetic specimen defect detection. In this paper, we present a solenoid analytical model to MFL field based on the molecular current model of a magnetic medium. This model applies $B$ – $H$ characteristics of the material to confirm the homogeneous magnetization of the specimen and to obtain the magnetic moment of solenoids, and then it uses a semi-infinite solenoid as the source to simulate the leakage field. Furthermore, this model proves that the edge effect and defect geometry can be represented properly by setting ellipsoid defects at different positions in the specimen. The results of the proposed model are influenced not only by defect shape as that of the magnetic dipole model but also by the relationship between the magnetization and the normal direction of the defect surface, which leads to the more accurate reconstruction of defects. Based on these findings, the error from the assumption of homogeneous magnetic dipole distribution or magnetization can be explained by the solenoid interaction. This explanation provides a new way to eliminate the computation error, and the solenoid model shows higher computational efficiency compared with the numerical model.

Weld cracks nondestructive testing based on magneto-optical imaging under alternating magnetic field excitation

This paper researches the magneto-optical (MO) imaging law of weld cracks under alternating magnetic field excitation. Weld surface and subsurface cracks are detected by a MO sensor, and the relationship between the MO images’ characteristics and the magnetic field strength is analyzed based on the Faraday MO effect. A magnetic dipole model is proposed to study the magnetic field distribution over the weld crack. A finite element analysis (FEA) model of the weld crack is established, and the relationship between the magnetic flux leakage signal and the crack width is analyzed, which is useful for identifying cracks either on the surface or on the subsurface of the weld. A MO imaging nondestructive testing (NDT) experiment is carried out to detect weld cracks under alternating magnetic field excitation, and the difference among weld cracks is obtained by analyzing the gray values of the weld cracks’ MO images. Research results show that the magnetic flux leakage signals of weld surface and subsurface cracks can be clearly distinguished, the magnetic field intensity of the surface cracks is larger than that of the subsurface cracks at the same width, and the MO image of the weld cracks can reflect the intensity of the magnetic field through varied brightness, that is, the gray value of the MO image can match the corresponding magnetic field intensity.

Solenoid model for visualizing magnetic flux leakage testing of complex defects

Magnetic flux leakage (MFL) techniques are widely used for nondestructive testing of ferromagnetic materials. An analytical model of the MFL field is essential for precise determination and reconstruction of defects. In this paper, we proposed a solenoid model based on magnetization mechanisms of the magnetic medium to explain the MFL principle and simulate the MFL field. By introducing the interaction of solenoids and the Jiles–Atherton model, this model can accurately calculate the MFL field of complex defects, particularly the field distortion caused by the coupling of the defect's components. The solenoid model was experimentally demonstrated with a Z-shaped defect in the specimen and proved to be valid for precise calculation of the magneto-optical image. This work reveals the MFL testing principle from the viewpoint of the magnetic medium and thus helps elucidate and eradicate the simulation errors. The more accurate simulation than the common magnetic dipole model facilitates the inverse calculation of defects, even if field distortion is involved.

Experimental Study on Residual Bending Strength of Corroded Reinforced Concrete Beam Based on Micromagnetic Sensor.

This paper presents a nondestructive test method to evaluate the residual bending strength of corroded reinforced concrete beam by analyzing the self-magnetic flux leakage (SMFL) signals. The automatic scanning device was equipped with a micromagnetic sensor and sensor-based experimental details were introduced. Next, the theoretical formula of the normal component HS(z) of the SMFL signal that originated from the corroded region was derived based on the magnetic dipole model and the experimental results were discussed. The results indicate that the experimental data of HS(z) are consistent with the theoretical calculations, both location and extent of the steel bars corrosion can be qualitatively determined by using HS(z). The gradient K of HS(z) is approximately linearly related to the loss rate, S, of the bending strength, which can be used to evaluate the residual bending strength of the corroded reinforced concrete beam. This work lays the foundation for evaluating the residual bending strength of corroded reinforced concrete beams using the SMFL signal; the micromagnetic sensor is further applied to the civil engineering.

Motion compensation using principal component analysis and projection onto dipole fields for abdominal magnetic resonance thermometry.

High intensity focused ultrasound (HIFU) has the potential to locally and non-invasively treat cancer with fewer side effects than alternative therapies. However, motion and tissue heterogeneity in the abdomen can compromise the HIFU focus and confound current thermometry methods. The proposed thermometry method combines principal component analysis (PCA), as a multi-baseline technique, and projection onto dipole fields (PDF), as a near-referenceless method. PCA forgoes tracking tools by projecting incoming images onto a subspace spanning the motion history. PDF is subsequently used to synthesize the naturally feasible components of the residual phase using a magnetic dipole model. This leaves only the phase shifts that are induced by HIFU. With in vivo measurements, in porcine and human kidneys, the mean pixel-wise temperature SD was 0.86 ± 0.41°C in selected regions of interest (ROIs) across all data sets, without any user-interaction or supplementary tracking tools. This is an improvement over a benchmark hybrid method, which scored 1.36 ± 1.20°C on the same data. Uncorrected subtraction of the data yielded a score of 3.02 ± 2.87°C. The PCA-PDF hybrid method achieves superior artifact correction by exploiting the motion history and intrinsic magnetic susceptibility of the underlying tissue.

Predictive value of unshielded magnetocardiographic mapping to differentiate atrial fibrillation patients from healthy subjects

P-wave duration, its dispersion and signal-averaged ECG, are currently used markers of vulnerability to atrial fibrillation (AF). However, since tangential atrial currents are better detectable at the body surface as magnetic than electric signals, we investigated the accuracy of magnetocardiographic mapping (MCG), recorded in unshielded clinical environments, as predictor of AF occurrence. MCG recordings, in sinus rhythm (SR), of 71 AF patients and 75 controls were retrospectively analyzed. Beside electric and magnetic P-wave and PR interval duration, two MCG P-wave subintervals, defined P-dep and P-rep, were measured, basing on the point of inversion of atrial magnetic field (MF). Eight parameters were calculated from inverse solution with "Effective Magnetic Dipole (EMD) model" and 5 from "MF Extrema" analysis. Discriminant analysis (DA) was used to assess MCG predictive accuracy to differentiate AF patients from controls. All but one (P-rep) intervals were significantly longer in AF patients. At univariate analysis, three EMD parameters differed significantly: in AF patients, the dipole-angle-elevation angular speed was lower during P-dep (p<0.05) and higher during P-rep (p<0.001) intervals. The space-trajectory during P-rep and the angle-dynamics during P-dep were higher (p<0.05), whereas ratio-dynamics P-dep was lower (p<0.01), in AF. At DA, with a combination of MCG and clinical parameters, 81.5% accuracy in differentiating AF patients from controls was achieved. At Cox-regression, the angle-dynamics P-dep was an independent predictor of AF recurrences (p=0.037). Quantitative analysis of atrial MF dynamics in SR and the solution of the inverse problem provide new sensitive markers of vulnerability to AF.

Research on short-range azimuth detection accuracy based on magnetic dipole model

In order to achieve the target azimuth detection, this paper uses magnetic measurement azimuth on the basis of laser ranging. A rotary scanning magnetic dipole model was established and the target-azimuth solution was achieved using a periodic-phase detection algorithm. Combining magnetic dipole model and target azimuth solution method, the influence of the distance between the sensor and the magnetic core, the rotation scanning detection period, the signal detection threshold and the standard deviation of the probability density of noise signal on the statistic distribution of azimuth measurement are analyzed. The accuracy of azimuth detection is studied by numerical simulation and measurement experiment.

Modeling and Experimental Studies on 3D-Magnetic Flux Leakage Testing for Enhanced Flaw Detection in Carbon Steel Plates

ABSTRACTFor enhanced detection of flaws in engineering components using magnetic flux leakage (MFL) technique, measurement of the leakage magnetic field components along the three perpendicular directions is beneficial. This article presents the three dimensional-magnetic flux leakage (3D-MFL) modeling and experimental studies carried out on carbon steel plates. Magnetic dipole model has been used for the prediction of MFL signals and images. Sensitivity of the MFL signals peak amplitudes of tangential (HX), circumferential (HY), and normal (HZ) components with respect to flaw length, width, depth and lift-off have been studied. A 3D-GMR sensor has been used for simultaneous measurement of all the three components of leakage magnetic fields from surface flaws in 12 mm thick carbon steel plates. The experimental MFL images have been compared with the model predicted MFL images. The sensor has shown the capability to detect and image 0.9 mm deep surface flaws with a signal to noise ratio of 8 dB. Principal component analysis (PCA)-based image fusion has been performed for fusion of the 3D-MFL images to obtain a geometrical profile of the flaws. Study reveals that 3D-GMR enhances the capability for detection of flaws having irregular geometries.

Quench Propagation in Nb&lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$_\text{3}$&lt;/tex-math&gt; &lt;/inline-formula&gt;Sn Cos-Theta 11 T Dipole Model Magnets in High Stress Areas

A large number of training quenches at various currents, temperatures, and ramp rates, have been performed on six 11 T dipole model magnets. Quenches in the midplane of these magnets were of special interest, since the quench current in the last three models measured in 2016 was limited to between 84% and 92% of the magnets short sample limit. Measurements of quench propagation velocity, based on both voltage taps and quench antennas, yield a high propagation velocity of 50 to 80 m/s. Due to the high magnetic field gradient over the width of the midplane turn such a high propagation speed cannot be explained by propagation in longitudinal direction of the strand following the twist pitch. In these cases, current and heat sharing at the thin cable edge (where the field, stress, and cable compaction are high) are likely to provoke strand-to-strand quench propagation at higher velocities than along the strands. This investigation is focused on analyzing the quench propagation along the strands and strand-to-strand of various measured cases.

Quantitative Study on Corrosion of Steel Strands Based on Self-Magnetic Flux Leakage.

This paper proposed a new computing method to quantitatively and non-destructively determine the corrosion of steel strands by analyzing the self-magnetic flux leakage (SMFL) signals from them. The magnetic dipole model and three growth models (Logistic model, Exponential model, and Linear model) were proposed to theoretically analyze the characteristic value of SMFL. Then, the experimental study on the corrosion detection by the magnetic sensor was carried out. The setup of the magnetic scanning device and signal collection method were also introduced. The results show that the Logistic Growth model is verified as the optimal model for calculating the magnetic field with good fitting effects. Combined with the experimental data analysis, the amplitudes of the calculated values (BxL(x,z) curves) agree with the measured values in general. This method provides significant application prospects for the evaluation of the corrosion and the residual bearing capacity of steel strand.

Detection of vehicle tracks by a three-axis magnetometer

A novel approach for target tracking enabled by a magnetic anomaly detection (MAD) system with a single three-axis magnetic sensor is demonstrated. Twelve types of three-dimensional target MAD signals at a cross road were calculated using a magnetic dipole model. Characteristic features derived from Bxy curves were used to identify the type of tracks. A nonlinear non-diagonal three-axis giant magnetoimpedance sensor (GMI) was used to validate the model, which operated in range of ± 500 mGs with a noise level below RMS 200 pT at the frequency ranging from 0.1 to10 Hz. Experimental results showed that the identification by the model was in good agreement with real tracks.

Dynamic Behavior of Laminated Magnets With Solid Tension Bars

An important criterion for the design of fast-ramping accelerator magnets is their field distribution in the time-transient regime. Eddy current effects in different components of the magnet become more or less significant depending on the field level, the ramp rate, the magnet geometry, and the materials used. In this paper, we focus on eddy currents in solid tension bars of laminated magnets and quantify their effects based on finite-element simulations of a dipole model magnet. Several configurations are studied to derive empirical laws for the dynamic behavior of the magnets. The simulation results are validated with magnetic measurements.

Dipole modeling of stress-dependent magnetic flux leakage

Existing magnetic dipole models cannot provide the accurate prediction result of the effect of the stress on the magnetic flux leakage (MFL) induced by defects in ferromagnetic materials. To solve this problem, an improved dipole model is proposed to investigate the stress-dependent MFL in tensioned specimens of Q235 steel. The stress concentration around the defect of a cylindrical through-hole leads to heterogeneous distribution of magnetization along the defect surface. Classic Timoshenko's theory is used to solve the localized compressive stress and tensile stress around the defect. The J-A model is employed to determine the stress-dependent magnetization distribution, which is the key parameter in the magnetic dipole model. The stress-dependent MFL signals predicted by the improved model are well consistent with the results of verification experiments and the peak-to-peak amplitude of the normalized MFL signal demonstrates the parabolic dependency on the applied tensile stress. A stress increment of 100 MPa can increase the amplitude of the MFL signal by 24%, which may cause a significant error in defect sizing. The proposed improved magnetic dipole model can reveal the effect of the stress concentration on the induced MFL signals and it is also applicable to solve the inverse problem for estimating the shapes and sizes of the defects even though the stress is involved.

AStudy on Accuracy Improvement of Defect Cross Section Evaluation Using Magnetic Dipole Model

AStudy on Accuracy Improvement of Defect Cross Section Evaluation Using Magnetic Dipole Model

Validation of a Source Identification Method for Prediction of Low-Frequency Magnetic Fields in Space Missions

Specific care is required for recent and upcoming space missions regarding magnetic cleanliness of slowly time-varying magnetic fields. The sources of these very low frequency fields may be approximated with multiple dipole sources, and their parameters can be identified from near magnetic field measurements. In this letter, a practical method is discussed and analyzed for on-ground verification of low-frequency ac magnetic fields at the unit and system level, complementing the well-established dc magnetic cleanliness verification methods. The developed method entails the identification of the parameters of a magnetic dipole model in the frequency domain that can be later used to represent real spacecraft equipment. Furthermore, near magnetic field measurements of a current-fed coil are used to validate the method.

Modeling and analysis of Galfenol cantilever vibration energy harvester with nonlinear magnetic force

Galfenol traditional cantilever energy harvesters (TCEHs) have bigger electrical output only at resonance and exhibit nonlinear mechanical-magnetic-electric coupled (NMMEC) behaviors. To increase low-frequency broadband performances of a TCEH, an improved CEH (ICEH) with magnetic repulsive force is studied. Based on the magnetic dipole model, the nonlinear model of material, the Faraday law and the dynamic principle, a lumped parameter NMMEC model of the devices is established. Comparisons between the calculated and measured results show that the proposed model can provide reasonable data trends of TCEH under acceleration, bias field and different loads. Simulated results show that ICEH exhibits low-frequency resonant, hard spring and bistable behaviors, thus can harvest more low-frequency broadband vibration energy than TCEH, and can elicit snap-through and generate higher voltage even under weak noise. The proposed structure and model are useful for improving performances of the devices.

Passive magnetic-based localization for precise untethered medical instrument tracking

Background and objectiveMotion tracking and navigation systems are paramount for both safety and efficacy in a variety of surgical insertions, interventions and procedures. Among the state-of-art tracking technology, passive magnetic tracking using permanent magnets or passive magnetic sources for localization is an effective technology to provide untethered medical instrument tracking without cumbersome wires needed for signal or power transmission. Motivated by practical needs in two medical insertion procedures: Nasogastric intubation and Ventriculostomy, we propose a unified method based on passive magnetic-field localization, for enhanced efficacy and safety. MethodsTraditional approaches to passive magnetic tracking involve solving the inverse localization problem. Limited by the idealistic magnetic field dipole model and computationally intense nonlinear optimization algorithm, the overall accuracy and computational cost are greatly compromised. The method introduced here features direct localization with artificial neural network (ANN) models that bypasses the need to resolve the inverse problem and is adaptable for a variety of real-time localization and tracking applications. ResultsThe efficiency of the two methods, the inverse optimization method and the direct ANN method are experimentally evaluated by comparing the estimated position of reference trajectories for typical nasogastric and ventriculostomy insertion paths performed by a dexterous robotic arm which provides ground truth measurement. It was found that within the region of interest (ROI), the direct ANN technique could significantly improve the localization accuracy, with an average experimental localization error of less than 2 mm, while that of the traditional inverse optimization method using a dipole-based mathematical model at greater than 5 mm. Ex-vivo experiments were performed to validate the localization methods in clinical settings. ConclusionsWhile the proposed method for passive magnetic tracking requires a procedure-specific pre-procedural calibration, it is able to provide real-time tracking with high accuracy, robustness and diversity. It could be the missing piece to the puzzle to bring passive magnetic tracking technology into practice, therefore leading to untethered medical instrument tracking.

Unshielded magnetocardiography: Repeatability and reproducibility of automatically estimated ventricular repolarization parameters in 204 healthy subjects.

Magnetocardiographic mapping (MCG) provides quantitative assessment of the magnetic field (MF) induced by cardiac ionic currents, is more sensitive to tangential currents, and measures vortex currents undetectable by ECG, with higher reported sensitivity of MCG ventricular repolarization (VR) parameters for earlier detection of acute myocardial ischemia. Aims of this study were to validate the feasibility of in-hospital unshielded MCG and to assess repeatability and reproducibility of quantitative VR parameters, considering also possible gender- and age-related variability. MCG of 204 healthy subjects [114 males-mean age 43.4±17.3 and 90 females-mean age 40.2±15.7] was retrospectively analyzed, with a patented proprietary software automatically estimating twelve VR parameters derived from the analysis of the dynamics of the T-wave MF extrema (five parameters) and from the inverse solution with the effective magnetic dipole model giving the effective magnetic vector components (seven parameters). MCG repeatability was calculated as coefficient of variation (CV) ±standard error of the mean (SEM). Reproducibility was assessed as intraclass correlation coefficient (ICC). The repeatability of all MCG parameters was 16±1.2 (%) (average CV±SEM). Optimal (ICC>0.7) reproducibility was found for 11/12 parameters (mean values) and in 8/12 parameters (single values). No significant gender-related difference was observed; six parameters showed a strong/moderate correlation with age. Reliable MCG can be performed into an unshielded hospital ambulatory, with repeatability and reproducibility of quantitative assessment of VR adequate for clinical purposes. Wider clinical use is foreseen with the development of multichannel optical magnetometry.

Comparison of Measurement Models for 3D Magnetic Localization and Tracking.

In this paper, we consider magnetic positioning and tracking of objects and provide a comparison of the characteristics of two major measurement models: the magnetic dipole model and the mutual inductance model. The numerical results obtained by applying these models to a short-range position measurement application, with a maximum operating distance of approximately 50 cm, are compared. Based on the results of this comparison, a prototype 9-sensor array is developed, experimental tests are performed, and extensive measurement results are presented. Outcomes show the feasibility of tracking the position and orientation of a mobile coil in real time with a median positioning error below 1 cm and a worst-case error of about 2 cm and 11 degrees inside a spatial region of 30 × 30 × 30 cm3 operational volume.

An Improved 6-D Pose Detection Method Based on Opposing-Magnet Pair System and Constraint Multiple Magnets Tracking Algorithm

Magnetic tracking method is mainly based on sensing of the magnetic field generated by the magnetic source. Usually a small permanent magnet is used as the magnetic source, and magnetic dipole model is used to estimate the magnetic field. The disadvantage of this approach is that only 5-D pose information can be estimated, but the spin rotation with respect to the direction of magnetic moment cannot be detected. In our previous work, we proposed a novel 6-D (3-D position and 3-D orientation) pose detection method, which was based on an opposing-magnet pair system. The disadvantage is that different rotational parameters may lead to the same pose result due to the symmetric structure of object magnets. In order to solve this problem, we propose an improved 6-D pose detection method in this paper, which is based on a novel constraint multiple magnets tracking algorithm. Two magnets of different sizes with opposite magnetic directions have been combined together to serve as the tracking target. By applying the constraint multi-magnet tracking algorithm, 5-D pose of each magnet can be obtained. Therefore, we can estimate the missing spin rotational information according to the relative movement between these two magnets. Experimental results verified the feasibility of the proposed method. The average position error is 2.3 mm and the orientation error is 4.36°, when the volume ratio between these two magnets is 1:1.5.