Coil Impedance Research Articles

Edge Detection for Molten Metal Level in Pyrometalurgical Furnaces

This report has found a prospective analytical model for an edge response of a transmit-receive eddy current coil. A probe of this design could be used to determine in real time the molten metal height and remaining wall thickness within a pyrometallurgical furnace. This work heavily uses previously published methods to find a possible expression for the change in mutual coil impedance resulting from a right-angled edge. An advancement in the method includes using the Lorentz Reciprocity relations for a transmit-receive system to calculate impedance change. Awaiting the completion of the model, an expected response has also been modelled in a finite element method software, which will be used to verify the analytical model. Also, an experiment has been designed to be able to validate both models. What remains to be completed is a successful code implementation of the mathematics, to produce results. While analytical solutions to the equations have been obtained, implementation of coded solutions remains incomplete. Some methods for improving the code will be to better condition the matrices described in the linear algebra interface between the three regions, as well as making further improvements on the root-finding code.

High-Frequency Magnetic Pulse Generator for Low-Intensity Transcranial Magnetic Stimulation

This paper presents a high-frequency (HF) magnetic pulse generator designed for low-intensity transcranial magnetic stimulation (LI-TMS) applications. HF pulse stimulation can induce a strong electric field with minimal current and enhance the penetration depth of the electric field in human tissue. The HF magnetic pulse generator was designed and fabricated using a microcontroller unit, gate driver, full-bridge coil driver, and stimulation coil. Measurements with a full-bridge circuit supply voltage of 10 V demonstrated an electric field intensity of 6.8 Vpp/m at a frequency of 1 MHz with a power dissipation of 2.45 W. Achieving a similar electric field intensity at a frequency of 100 kHz required approximately ten times the coil current. Additionally, a quasi-resonant LC load was introduced by connecting a capacitor in series with the stimulation coil, which set the resonant frequency to approximately 10% higher than the frequency of 1 MHz. This approach reduced the coil impedance, achieving higher current with the same bias supply voltage. Experimental results showed an enhanced electric field intensity of 19.1 Vpp/m with a supply voltage of only 1.8 V and reduced power dissipation of 1.11 W. The proposed HF pulse train with quasi-resonant coil system is expected to enable a low-power LI-TMS system.

MAPOD analysis in eddy current testing of flaws considering multiple response signals and multiple flaw parameters

The reliability of the eddy current testing (ECT) in flaw detection is quantitatively evaluated by the probability of detection (POD). Precise and efficient modelling of POD gives direction for the implement of ECT on sites to avoid false or missing flaw detection. Traditional POD analysis focuses on single uncertain factor or single response signal with limited credibility in engineering. This paper considers multiple response signals and multiple flaw parameters to perform POD. The flaw length, the flaw depth, the coil impedance and the magnetic flux density are comprehensively studied under various lift-off distances. A finite element model (FEM) of ECT is established and verified with experiments to obtain sufficient simulation data for discrete POD modelling. The continuous POD function is then fitted based on the discrete values to show the superiority of integrating multiple factors. A comparison with conventional POD analysis further demonstrates the higher reliability of ECT flaw detection considering multiple flaw parameters and multiple response signals, especially for small flaws. Conflict of Interest Statement The authors declare no conflicts of interest.

The transient discharge circuit analysis of single-turn coil

Single-turn coil (STC) is a destructive pulse magnet aiming at a 100–300 T ultra-high magnetic field. A transient discharge circuit model considering the coupling of electromagnetic diffusion and conductor deformation is proposed, and the transient coil impedance characteristics are investigated. The results show that the coil resistance first decreases and then increases due to electromagnetic diffusion and temperature rise, respectively, while the coil inductance always increases because of the conductor’s outward motion. By comparison, the simulation results are consistent with the experimental data, and the correctness of the model is validated.

An Adaptive Actuator Driver for AC Contactors

The actuator drivers are rarely transplanted among different contactors because the self-tuning of excitation control parameters either takes a long time or is relevant to many contactor structural parameters. An adaptive actuator driver for AC contactors is proposed based on the coil impedance estimation and mathematical equations between the coil impedance and excitation control parameters. The coil impedance estimation and its error correction are established through the voltage balance equation when the contactor is in the open position. The coil inductance estimation is established through the zero-state response equation when the contactor is in the closed position. The mathematical equations are established based on the equivalence of the electromagnetic force under different excitation methods, the power consumption model, and the control system's transfer function. A geometric feature of the flux linkage waveform is established to identify whether a contactor is in the closed position and realize the self-transition of the driver's working state. Then, self-tuning regulators for the excitation control parameters are realized. This driver has a plug-and-play function for AC contactors and can reduce the contactor's power consumption. This driver may be prospectively reduced to a chip.

Study on influencing factors and regularity analysis of eddy current method applied to detection of reinforcement corrosion

Abstract Rebar corrosion is one of the main reasons for the deterioration of concrete structures. In order to ensure the safe operation of reinforced concrete structures, it is necessary to detect the corrosion rate of rebars in time. This article adopts the eddy current method based on electromagnetic induction to detect steel corrosion, studies the mechanism of alternating current (AC) impedance change induced by steel corrosion in coils, and establishes a mathematical model between steel corrosion and coil AC impedance. Meanwhile, the quantitative relationship between excitation signal frequency, concrete thickness, coil parameters, and coil impedance is studied. Through experiments, it was found that in the early stages of steel corrosion, there is a linear relationship between the scanning peak value of the coil impedance and the mass loss rate of the steel bars, and the slope of the fitting curve decays exponentially with the increase of the concrete thickness. The method used in this paper has an absolute error of less than 0.01 and a relative error of less than 8 % in detecting the mass loss rate of rebars at the initial stage of steel corrosion. When the concrete thickness is less than 20 mm, the relative error is lower than 4 %.

A decoupling calculation method of separating temperature component from the nano-scale metal film thickness measurement output by the eddy current sensor

The eddy current method has been widely applied in the field of nano-scale metal film thickness detection. The output signal of an eddy current sensor is generally tiny in practice, and it is easily affected by the ambient temperature variation, which results in a decrease in the measurement accuracy. How to separate the temperature effect on film thickness measurement for achieving a high precision is a major problem. Therefore, a coupling model of an eddy current sensor with an electromagnetic field and a temperature field is established in this study, and the influence of the film thickness and temperature on coil impedance is calculated. It is found that the inductance and resistance of the coil vary monotonically as thickness and temperature with a measure of linearity in a certain range, as well as the real part and imaginary part of the output voltage by using an AC bridge. Then a film thickness-temperature decoupling calculation method is proposed, and a group of linear calibration intervals are further divided considering the linearity and measurement accuracy. According to the calculation results, it is confirmed that the method can decouple the two, and accomplish a higher accuracy. In addition, the method is verified by a series of experiments, and the variation trend of real and imaginary parts of output voltage with thickness and temperature is consistent with simulation results. At the same time, it is feasible to realize a synchronous detection of metal film thickness and ambient temperature in a certain range.

Analytical model of eddy current bobbin coil probe responses at support plates in steam generator and heat exchanger tubes

The steam generators (SGs) of CANadian Deuterium Uranium nuclear reactors require periodic inspections to ensure their safe operation. Eddy current (EC) testing is the primary method by which the SG tubes are inspected. Many conditions in the SG tubes affect the EC response, such as fretting, pitting, cracking, as well as tube expansion, and the presence of tubesheet and support structures. When two or more of these parameters overlap, the EC signals from degradation induced wall losses are frequently difficult to interpret because these wall loss signals are often distorted due to interference with background signal variations. In this paper, a novel analytical model that describes the impedance of a bobbin coil with a plate encircling an arbitrary number of cylindrical conductors is developed. The model is validated against finite element method modelling and experiment. This model can be used to simulate the main probe response, while inspecting SG tubes near the tubesheet and support structures and thereby, provides the potential to separate out smaller flaw responses.

Model of an E-cored probe over layered conductor containing corrosion for eddy current testing

PurposeIn eddy current nondestructive testing, ferrite-cored probes are usually used to detect and locate defects such as cracks and corrosion in conductive materials. However, the generic analytical model for evaluating corrosion in layered conductor using ferrite-cored probe has not yet been developed. The purpose of this paper is to propose and verify the analytical model of an E-cored probe for evaluating corrosion in layered conductive materials.Design/methodology/approachA cylindrical coordinate system is adopted and the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived first, and then the expansion coefficients of the solution are obtained by matching the boundary and interface conditions between the regions and the subregions. Finally the closed-form expression of the impedance of the multi-turn coil is derived by using the truncated region eigenfunction expansion (TREE) method, and the impedance calculation is carried out in Mathematica. In the frequency range of 100 Hz to 10 kHz, the impedance changes of the E-cored coil and air-cored coil due to the layered conductor containing corrosion are calculated, respectively, and the influences of corrosion on the coil impedance change are investigated.FindingsAn analytical model for the detection and evaluating of corrosion in layered conductive materials using E-cored probe is proposed. The model can quickly and accurately calculate the impedance change of E-cored coil due to corrosion in layered conductor. The correctness of the analytical model is verified by finite element method and experiments.Originality/valueAn accurate theoretical model of E-cored probe for evaluating corrosion of multilayer conductor is presented. The analytical model can be used to detect the inhomogeneity of layered conductor, design ferrite-cored probe or directly evaluate the corrosion defects of layered conductors.

A metal object detection system for electric vehicle wireless charging based on LC oscillating circuit and reverse-winding-incorporated detection coils

In magnetically coupled wireless charging systems for electric vehicles, it is common for metal objects to enter the charging system. In this case, the strong magnetic field of wireless charging causes an eddy current effect in the metal object, which generates a large amount of heat. This heat accumulation poses a risk of fire. In this paper, a novel metal object detection system designed for wireless charging of electric vehicles is proposed. The system utilizes the principle that the coil impedance and coupling coefficient change with the presence of metal objects, and a set of composite coils is designed to improve the sensitivity of detection. The detection coil and feedback coil in the composite coil are decoupled by reverse series connection. An LC oscillating circuit based on transformer feedback is used to detect metal objects, and the circuit can make good use of the parameter changes of the composite coil. Finally, an experimental platform for wireless charging metal detection in electric vehicles has been built to validate the proposed system. Through testing, it has been demonstrated that the system can detect the presence of metal objects in a timely and accurate manner.

Low-frequency incremental permeability for the evaluation of deep carburization treatments: Theoretical understanding

Precise evaluation of deep carburization treatments is essential to prevent degradation of high-performance mechanical components. A nondestructive magnetic method called low-frequency incremental permeability testing appears to be particularly suitable for this purpose. This method consists of slowly magnetizing the specimen to be controlled and then superimposing a relatively low-frequency eddy current testing process on the specimen (<2 kHz). The sensor’s coil impedance is monitored along with the magnetization cycle. When plotted versus the magnetic excitation, the impedance produced butterfly-shaped curves that were dependent on the carburization depth. Operating at low frequency increases the scanned layer thickness up to the untreated inner part of the specimen and induces characteristic variations in the butterfly-shaped curves. A model to solve for the indirect relationship between the magnetic properties and the carburization treatment properties is presented in this manuscript. This model combines the Dodd and Deeds analytical expression for a flat sensor coil above a two-layer conductor with Jiles-Atherton theory for consideration of the hysteresis. The magnetic and electromagnetic responses are well considered, providing accurate reconstructions of experimental data. The model predictions reveal magnetic indicators that are highly correlated with the carburization depth and provide optimal conditions for nondestructive testing observation.

Non-destructive testing method of fiber content in steel fiber reinforced concrete based on magnetization loss

Steel fiber reinforced concrete (SFRC) has been widely used in construction engineering due to its superior crack resistance and flexural capacity. Its mechanical properties mainly depend on the distribution of fibers, and the uneven distribution will reduce the structural performance. Therefore, this paper proposed a fast non-destructive testing method for steel fiber content evaluation based on magnetization loss. This method could solve the problem that the traditional methods were difficult to detect in situ. It is found that the higher the steel fiber content, the greater the magnetic loss and electrical loss of the fiber under sinusoidal excitation, resulting in the changes of the excitation coil impedance. Based on this phenomenon, the impedance difference modulus and quality factor evaluation index of the excitation coil are proposed, which can be used to accurately estimate the internal fiber content of concrete in-situ detection. The feasibility of the method is verified by experiments, which is of great significance to the quality control in the manufacturing process of SFRC.

On the Fabrication of High-Performance Additively Manufactured Copper Winding Using Laser Powder Bed Fusion

Due to its exceptional electrical and thermal conductivity, pure copper is frequently employed in industry as the base metal for thermal management and electromagnetic applications. The growing need for complicated and efficient motor designs has recently accelerated the development of copper additive manufacturing (AM). The present work aims to improve the power density of the copper laser powder bed fusion (Cu-LPBF) coil by increasing the slot-filling factor (SFF) and the electrical conductivity. Firstly, the dimensional limitation of Cu-LPBF fabricated parts was identified. Sample contouring and adjusting beam offset associated with optimum scan track morphology upgraded the minimum feature spacing to 80 μm. Accordingly, the printed winding’s slot-filling factor increased to 79% for square wire and 63% for round wire. A maximum electrical conductivity of 87% (IACS) was achieved by heat treatment (HT). The electrical impedance of full-size Cu-LPBF coils, newly reported in this study, was measured and compared with solid wire. It can reflect the performance of Cu-LPBF coils (power factor) in high-frequency applications. Furthermore, surface quality benefited from either sample contouring and HT, where the side surface roughness was lowered by 45% and an additional reduction of 25% after HT.

Self-Sensing of a Magnetically Actuated Prism

We demonstrate a method for self-sensing of a magnetically actuated prism that can be used, e.g., in a feedback-loop without the need of additional sensors. In order to use the impedance of the actuation coils as a measurement parameter, we first obtained the optimal measurement frequency that is well separated from the actuation frequencies and at the same time provides the best compromise between sensitivity to the position and robustness. We then developed a combined actuation and measurement driver, and correlated its output signal to the mechanical state of the prism using a defined calibration sequence. We demonstrate that we can reliably measure the state of each actuator and determine the tilt angle of the prism with an accuracy of ±0.1∘ in the polar angle over a range of ±4∘ and ±20 mrad in the azimuthal angle.

A Novel Method for Distinguishing Discontinuities In Ferromagnetic Materials Based On Eddy Current Testing Under Magnetization

Detecting inner- and outer-surface discontinuities of drill pipe is of great significance to the evaluation of the quality of the drill pipe. This paper proposes a method based on a magnetized eddy current testing technique to detect inner- and outer-surface discontinuities by analyzing the difference of the imaginary part signal characteristics of the receiving coil. For eddy current testing, the outer-surface discontinuities cause the local conductivity to be zero, while inner-surface discontinuities cause the perturbation of the magnetic permeability on the material surface. In this paper, the effects of conductivity distortion and permeability perturbation on induced eddy currents are analyzed by simulation. The conductivity distortion increases the magnetic field above the discontinuity compared to the magnetic field without the discontinuity, while the permeability perturbation reduces the magnetic field. Next, the difference in coil impedance can be used to distinguish the inner- and outer-surface discontinuities. Finally, the feasibility of the method is verified by experiments, and the results show that the inner- and outer-surface discontinuities can be discriminated.

A Lightweight and Robust Drone MHz WPT System via Novel Coil Design and Impedance Matching

This paper proposes a comprehensive approach to address the challenges posed by the simultaneously varying dc load and coil coupling in drone wireless charging, which inevitably occur during battery charging and landing positioning. The combination of two new coil designs, a quasi-elliptic transmitting (Tx) coil and a “belt” receiving (Rx) coil, enables adequate power transfer at megahertz (e.g., 6.78 MHz) and over a large circular landing area. The on-board “belt” Rx coil (5.8 g) especially helps achieve lightweight and minimize air resistance. A load-pull-based impedance analysis is then performed to clarify the need for an impedance matching network (IMN) on both Rx and Tx sides (i.e., Rx-IMN and Tx-IMN). A new Rx-IMN explicit design is specially developed to significantly limit the range of variation in the coupling coil input impedance, thereby helping to simplify the design of the Tx-IMN to ensure an efficient power amplifier operation. With the proposed coil and IMN designs, actual drone wireless charging experiments demonstrated improved system dc-dc efficiency (max. 83.5%) and dc-dc voltage ratio stability at three representative landing positions (i.e., minimum, medium, and maximum coil coupling).

Equivalent circuit of high frequency inductor to consider eddy currents and resonance

The resistance and inductance of an inductor working at high frequencies depend on frequency because of eddy currents caused by the skin and proximity effects. In addition, the stray capacitance among winding coils would give significant influence. This paper proposes an equivalent circuit model which can consider the displacement and eddy currents simultaneously in frequency and time domain. In the proposed circuit model, the capacitance and complex inductance are determined by solving electrostatic and magnetostatic equations with finite element method (FEM). It is shown that the input impedance of an air-core coil is consistent with that computed by FEM at low frequencies. Moreover, the former is shown to be consistent with the measured result.

Research on Short-Circuit Impedance Analysis Method of Auto-transformer for Side Column Voltage Regulation

In order to realize the accurate analysis of the impedance of transformers with complex connection relations, this paper derives the impedance calculation method of low-voltage excitation side column linear voltage regulating autotransformer by using the power method. The transformer network with different taps is analyzed, and the calculation formulas of transformer HV-MV impedance, HV-LV impedance and MV-LV impedance are derived. The analysis is simplified to the solution of concentric column coil impedance and magnetic potential of each coil. By comparing the calculated data of actual products with the measured data, the calculation deviation of this method is controlled within 2.03%; By using the finite element method, the impedance of the transformer with the measures to control the magnetic shielding is analyzed and calculated. By comparing the impedance of the transformer with different measures, it can be confirmed that the magnetic leakage measures have an impact on the impedance of the transformer.

Investigation of Flux Transfer along Ferrite Core of Probe Coil for Eddy Current Nondestructive Evaluation

Abstract A probe coil with a T-core above a layered conductor with surface hole is investigated for magnetic flux transfer along the ferrite core and enhancement of eddy currents in conductor. The cylindrical coordinate system is adopted and an artificial boundary is added to the solution domain with radius b, and the general formula for calculating the impedance of the T-core coil is derived using the truncated region eigenfunction expansion (TREE) method. For four special cases with different probe configurations, coil impedance changes due to the layered conductor and defect are calculated with Mathematica software over a frequency change ranging from 100 Hz to 20 kHz. The analytical results are in good agreement with those obtained by the finite element method and experimental measurements. The results show that under the same lift-off height and excitation frequency, the impedance change caused by the conductor or defect in the coil of long core column is greater than that of the short core column coil. It indicates that the probe coil with a long core column can transfer magnetic flux to the conductor, thereby enhancing eddy currents in the conductor.

Frequency-Based Estimation of the B-H Curve of Steel Strips in a Continuous Induction Furnace*

A parameter estimation strategy for continuous inductive heating of ferromagnetic steel strips is developed and investigated. During strip processing in an induction furnace, the parameters of the magnetization curve (B-H curve) of the strip material are identified by a moving horizon estimator (MHE). This estimator uses measurements of the resonance frequency of the electric circuit. A tailored 2D harmonic model of the electromagnetic subsystem is used to calculate the complex coil impedance. Other model parameters are identified in a scenario, where the magnetization curve of the strip is known. The approach does not require a thermal model of the induction furnace in favor of the computing time and the achieved accuracy. For model validation, the simulated resonance frequency is compared with measurements. To avoid a high computational effort, the effective magnetization approach is applied to approximate the solution of the nonlinear Maxwell equations. The effective B-H curve is mathematically expressed in terms of a linear and an exponential function and parametrized by two parameters. The MHE is validated in a test scenario using a strip with a known magnetization curve.