Eddy-current signal analysis and inversion for semielliptical surface cracks

Auld, B. A.; Jefferies, Steven R.; Moulder, John C.

doi:10.1016/0308-9126(90)90913-9

Cited by 9 publications

(23 citation statements)

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“…Namely, the change in the inductance can be approximated by (1) where is a constant that depends only on the coil and is independent of the conductivity and permeability. Furthermore, the zero-crossing frequency is given by (2) where denotes the permeability of free space, denotes the relative permeability, denotes the conductivity, and denotes a characteristic spatial frequency of the coil (typically one over its smallest dimension). Finally, the scaling function can be approximated by…”

Section: Introductionmentioning

confidence: 99%

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Inductance of a coil on a thick ferromagnetic metal plate

et al. 1998

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We study the frequency-dependent inductance of a small air-cored coil of wire placed flat upon various ferromagnetic metal plates. The change in the complex inductance of the coil, measured with an HP 4194A impedance analyzer, is reported for frequencies between 1 kHz and 1 MHz. The metal plates consisted of commercially pure (99.7% and 99.9%) Ni, commercially pure (99.9%) Fe, and a suite of medium carbon steels. For the steel plates, inductance changes were consistent with a simple halfspace model that treats the metal as a continuum defined by a conductivity and a relative initial-permeability where these material parameters are isotropic, local, and uniform throughout the plate. The inductance changes for Ni and Fe could not be fit to the half-space model for any values of and , but were consistent with a model that assumes a thin (10 m) surface layer with a significantly reduced permeability-a dead layer. We tested the existence of the hypothetical dead layer in several ways. We found that the inductance increased when the surface was chemically etched (presumably eroding the dead layer) and decreased when the surface was mechanically polished (presumably increasing the dead layer). We also found that the inductance of the Fe and Ni samples decreased substantially over the course of days and months when exposed to air.

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Section: Introductionmentioning

confidence: 99%

“…E DDY-CURRENT probes are used to find defects in metals [1], [2]. At their simplest, such probes consist of a wire coil.…”

Section: Introductionmentioning

confidence: 99%

Inductance of a coil on a thick ferromagnetic metal plate

et al. 1998

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“…Auld proposed an approximate boundary condition for the crack mouth which neglects the perturbed field due to the flaw. This approximation gives predictions that are in reasonable agreement with measurements in some cases [2], but comparisons with experimental results for a probe whose diameter is smaller than the crack depth reveals significant inaccuracies [3]. An alternative to Auld's approximation has been developed which takes into account the perturbed field at the crack mouth [4].…”

Section: Introductionmentioning

confidence: 88%

“…Putting (2) in (1) shows that (3) where is the Laplacian operator defined for a surface transverse to the direction. Thus the TM potential satisfies a two-dimensional (2-D) Laplace equation on the crack face regardless of the frequency of excitation or the skin depth.…”

Section: A Scalar Decompositionmentioning

confidence: 99%

“…1) Edge Boundary Condition: Following other authors who have considered the thin-skin regime [2], [7]- [10], the magnetic field in the plane of the crack normal to the edge is taken to be zero. Applying this condition to the TM field gives (4) where the subscript refers to points at the crack edge and is a unit vector in the plane of the crack, normal to the edge.…”

Section: B Boundary Conditionsmentioning

confidence: 99%

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Thin-skin eddy-current interaction with semielliptical and epicyclic cracks

Bowler

Harfield

2000

IEEE Trans. Magn.

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Eddy-current probe impedance variations due to interactions with planar cracks have been calculated for the thin-skin regime. In this regime, the skin depth of the induced current is small compared to the crack depth and length, allowing approximations to be made. The approximations have been used by others to show that the thin-skin field at the surface of a crack is governed by a potential satisfying the two-dimensional (2-D) Laplace equation. In fact, the transverse magnetic potential at the crack face, defined with respect to the normal to this surface, satisfies a 2-D Laplace equation at an arbitrary skin depth. However, thin-skin boundary conditions applied at the crack perimeter greatly simplify the problem. Solutions of the Laplace problem for semielliptical cracks have been found by conformal mapping to a rectangular region. The surface potential in the rectangular domain is expressed as a Fourier series expansion and the coefficients of the series determined from the boundary conditions. Curved crack profiles of a general class, including semielliptic cracks as a special case, have been approximated by using ordered elliptical epicycles, a representation that retains the ability to map the crack domain to a rectangle. The probe impedance change due to a crack has been expressed in terms of the transverse magnetic potential and calculated from a line integral. Predictions of the probe impedance variations with position and frequency have been compared with an analytical solution for a semicircular crack and with experimental coil impedance measurements on semielliptical and epicyclic slots. Good agreement is observed in all comparisons.

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An eddy current transducer model for image restoration

1991

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We describe in this short paper a new imaging model for the spatial magnitude response of an absolute eddy current transducer to a flaw. This model is appropriate for image restoration purposes in that it captures the transducer response with sufficient accuracy for image restoration, yet is simple enough to be computationally practical.The model described in this paper is based on a simple resistive loop approximation to the transducer impedance changes induced by a flaw, and is efficiently implemented as layers of linear blurring functions and nonlinear point operations. The model is shown to accurately reflect the magnitude response of an absolute transducer to an EDM slot in a non-ferrous alloy. Furthermore, the model is shown to produce good restoration results for synthetic images of flaws. The model may be adapted to a particular combination of absolute transducer and surface flaw type by optimizing the model parameters, either by forming the partial derivatives with respect to the parameters and minimizing by gradient descent, or by a straightforward implementation of a neural net back-propagation algorithm. Other types of eddy current transducers may be modeled by simply modifying the spatial layers to combine the local terms appropriately for the geometry of the transducer.

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Eddy-current signal analysis and inversion for semielliptical surface cracks

Cited by 9 publications

References 0 publications

Inductance of a coil on a thick ferromagnetic metal plate

Inductance of a coil on a thick ferromagnetic metal plate

Thin-skin eddy-current interaction with semielliptical and epicyclic cracks

An eddy current transducer model for image restoration

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