Coil Impedance Variation Research Articles

Conductivity Measurement of Solid Metal Rods Using High-Frequency Eddy Current Method

Conductivity is an essential parameter for solid metal rods, which can be applied to assess quality. In this paper, an eddy current testing(ECT) method is investigate to measure the conductivity of solid metal rods. Above all, the simplified theoretical model is derived for a coil encircling a cylindrical sample. According to the proposed model, the real part of the coil impedance variation at high frequency (~ MHz) is closely related with the reciprocal of root of the rod conductivity. Therefore, a simple and effective conductivity measurement method for solid rod conductivity measurement is investigated based on the relationship between the impedance variation and the solid rod conductivity. Moreover, the effect of metal rods and coils parameters on the proposed method are also analyzed. Finally, the proposed method is verified with measurements of conductive materials. The results demonstrate the investigated simplified theoretical model is accurate and reasonable, and the relative error of the solid rod conductivity measurement is 2.2%.

Eddy current testing for estimation of anisotropic electrical conductivity of multidirectional carbon fiber reinforced plastic laminates

Eddy current testing methods to estimate the anisotropic electrical conductivity of multidirectional carbon fiber reinforced plastics are proposed in this work. Finite element analysis was performed to investigate the contributions of the three-directional conductivities to the coil impedance. The coil impedance variation was expressed as an approximate function with respect to the anisotropic conductivity using the response surface methodology. Three proposed methods were applied to estimate the conductivity from the measured coil impedance and the estimated conductivities were then compared with the conductivities measured using a four-probe method. Use of the response surface enabled prediction of the lower and upper limits of the conductivity while taking the scatter of the electrical properties in the tested material into consideration. The conductivity range was predicted correctly using the proposed methods. There was a trade-off relationship between the accuracy and the simplicity of these estimation methods.

Implementing an Impedance Compression Network to Compensate for Misalignments in a Wireless Power Transfer System

This paper presents an impedance compression network (ICN) design in a wireless power transfer (WPT) system to compensate for distance or alignment variations between coils. In midrange WPT applications, magnetic resonant coupling coils are mainly implemented to achieve high efficiency for charging batteries. However, a distance or horizontal alignment variation between coils changes their coupling coefficient, and it decreases the overall performance of WPT systems because the zero voltage switching in a resonant inverter is lost. In order to reduce coil impedance variation, we propose an ICN that compresses variations in coil impedance. The ICN consists of a resistance compression network and a phase compression network to suppress magnitude and phase variations, respectively, in the coil impedance. Only passive components, such as inductors and capacitors, are used to implement an ICN.

Reduction of lift-off effect in high-frequency apparent eddy current conductivity spectroscopy

Eddy current spectroscopy is capable of mapping conductivities and thicknesses of layered structures due to its frequency-dependent penetration depth. High-frequency apparent eddy current conductivity (AECC) spectroscopy applications typically mandate covering a frequency range beyond 10 MHz to capture depth-dependent conductivity profiles. Following the standard four-point linear system calibration method beyond 10 MHz makes it difficult to achieve accurate AECC measurements due to spurious self- and stray-capacitive effects where complex eddy current coil impedance variation with lift-off becomes more nonlinear. In this study, two different approaches are presented to reduce AECC measurement sensitivity to lift-off. First, a nonlinear lift-off correction is developed as a function of measured apparent eddy current lift-off. Second, a semi-quadratic system calibration is developed to capture the lift-off curvature as a function of frequency and hence minimizes the measurement sensitivity to lift-off variations. Presented calibration techniques allow more robust AECC measurements up to 80–100 MHz with one-order of magnitude improvement in accuracy in comparison to the use of standard four-point linear system calibration in a lift-off range of ±25.4 µm.

Construction and Verification of Analytical Model for Eddy Current Testing Based on Multi-Layered Conductive Structures

Based on the Maxwell equations in time-harmonic conditions, analytical model for cylindrical coil above multi-layered conductive structures of infinite large is built, the general solution for integral expression of coil’s impedance is derived. As the complex computation and inconvenient adjustment for calculating precision of integral form, the truncated region eigenfunction expansion is adopted to derive the series expansion expression of coil’s impedance. Calculating precision is ensured by selecting the truncating radius and the number of summation terms properly. Use Mathematica and CIVA separately compute the impedance variation of coil above the single conductive layer of different thickness. The results are highly identical and verify the validity of series expansion expression. The expression can provide help for optimizing the parameters of eddy current sensor.

Solution to the problem of E-cored coil above a layered half-space using the method of truncated region eigenfunction expansion

In eddy current non-destructive testing, using ferrite cores with different shapes produce interesting and very important predictions on locating underneath cracks, corrosions and flaws in conductive layers. This paper describes a method of calculating magnetic vector potential for an E-cored eddy current probe above a layered half space. The coil impedance variation with frequency and eddy currents are determined. The results of the calculations are in very good agreement with results from COMSOL.

Lift-off effect in high-frequency eddy current conductivity spectroscopy

Precision eddy current measurements have been shown to be capable of characterizing the near-surface residual stress and cold work profiles in surface-treated components. To capture the peak compressive residual stress in moderately shot-peened (Almen 4–8 A) nickel-base superalloys, the eddy current inspection frequency has to be as high as 50–80 MHz. Unfortunately, spurious self- and stray-capacitance effects render the complex eddy current coil impedance variation with lift-off, the so-called lift-off curve, highly nonlinear, which makes it difficult to achieve accurate eddy current conductivity measurements beyond 25 MHz in the presence of even the slightest lift-off uncertainties. As opposed to the well-known inductive lift-off effect that decreases with increasing probe size, the capacitive lift-off effect increases with probe size. Both effects increase with frequency with the inductive effect being initially stronger, but then taken over at high frequencies by the faster growing capacitive effect. Since the two effects produce opposite curvature in the lift-off curve, in the frequency range where they are approximately equal to the lift-off curve becomes essentially linear and fairly accurate, conductivity measurements can be conducted even in the presence of lift-off variations.

Coil impedance variation due to induced current at the edge of a conductive plate

The time-harmonic induced current in a conductive plate has been calculated for an excitation by a normal coil near the plate edge. Using series expansions in elementary functions, the quasi-static solution for the plate is matched to the solution for the region outside the plate to ensure continuity of the tangential magnetic field and the normal magnetic flux density at the air–conductor interface. The continuity of the field is achieved by mode matching in a truncated domain. Predictions of the coil impedance as a function of position derived from this theory have been compared with experiment showing good agreement.

Eddy currents induced in a finite length layered rod by a coaxial coil

We describe the calculation of eddy currents in a two-layer conducting rod of finite length excited by a coaxial circular coil carrying an alternating current. The calculation uses the truncated region eigenfunction expansion (TREE) method. By truncating the solution region to a finite length in the axial direction, we can express the magnetic vector potential as a series expansion of orthogonal eigenfunctions instead of as a Fourier integral. The restricted domain can be arbitrarily large to yield results that are as close to the infinite domain results as desired. Integral form solutions for an infinite rod are well known and relatively simple. For a finite length cylindrical conductor, however, additional boundary conditions must be satisfied at the ends. We do this by comparing series expansions term by term to match the solutions across the end of the cylinder. We derive closed-form expressions for the electromagnetic field in the presence of a finite two-layer rod. A special case of the solution is that for a conductive tube. We illustrate the end effect by calculating the coil impedance variation with respect to the axial location of the coil. The results are in very good agreement with those obtained by using a two-dimensional finite-element code.

Eddy current coil interaction with a right-angled conductive wedge

The time-harmonic electromagnetic field in an electrically conductive right-angled wedge due to an inductive excitation by circular coil in air has been calculated. Using a formulation in Cartesian coordinates, the problem domain is truncated in a dimension whose axis is normal to a wedge face, and an approximate series solution found using elementary functions satisfying Maxwell's equations in the quasi-static limit. The coil impedance variation with position and frequency is calculated and compared with measurements made on a coil near the edge of a large aluminium block which approximates the effect of a conductive quarter-space. The comparison between theory and experiment shows very close agreement.

Eddy currents induced in a conducting rod of finite length by a coaxial encircling coil

This paper describes the calculation of eddy currents in a cylindrical conductive rod of finite length due to a coaxial circular coil carrying an alternating current. The coil impedance variation with frequency is determined from the field for an arbitrary coaxial location of the coil. Expressions for electromagnetic field and impedance of a coil encircling an infinite cylindrical rod are well known, the results being expressed as infinite integrals involving Bessel functions. For a finite length rod, additional boundary conditions must be satisfied at the ends. The extra boundary conditions are accommodated here by recasting the problem in a domain of finite extent in the axial direction. The axial length of the truncated domain is arbitrary and can be large compared with the coil length or the length of the rod. Therefore, the truncated domain solution can yield results that are numerically as close to the infinite domain solution as desired. The results provide a simple means of calculating the impedance of an inductor with a lossy core and can be used to investigate the linear properties of the core material.

Eddy-current interaction of a long coil with a slot in a conductive plate

We describe a truncated-domain method for calculating eddy currents in a plate with a long flaw. The plate is modeled as a conductive half-space and the flaw is a long slot with a rectangular cross section. A long two-dimensional (2-D) coil carrying an alternating current is aligned parallel to the slot. The coil impedance variation with frequency is determined for an arbitrary coil location. The electromagnetic field due to a long coil above a conductive half-space can be expressed as integrals of trigonometric functions. For a half-space with a long slot, however, additional boundary conditions must be satisfied at the slot walls. The truncated-domain method makes this possible by recasting the problem in a finite domain; as a result, the Fourier integral is replaced by a series. The domain can be made arbitrarily large, thereby yielding results that are numerically as close to the infinite domain solution as desired. We have used the truncated domain approach to study both eddy-current flaw interactions and edge effects in the limiting case of a very wide and deep slot. We confirmed the theoretical predictions by comparing them with results of a 2-D finite element calculation and of experiments.

Evaluation of Frequency Behavior of Coils for Reference Magnetic Field Generation

The frequency behavior of coils for the generation of reference time-varying magnetic fields is evaluated starting from the coil construction parameters (geometrical dimensions, number of turns). A coil equivalent circuit with lumped parameters is considered and the related equation system is solved in the frequency domain. The computed frequency behavior of the coil impedance is validated by comparison with experimental data. The operating frequency limit is identified from the analysis of the coil impedance variation with frequency as a function of the construction parameters.