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Eddy current Testing Simulation on a Personal Computer Theodoros P. Theodoulidis Technology & Quality Control Center Emm. Fili 13, 543 52 Thessaloniki, Greece, Email : theodoul@hellasnet.gr Michael K. Kotouzas Technology & Quality Control Center Zoodohou Pigis, 382 22, Volos, Greece, Email : ketepe@otenet.gr Contact

ABSTRACT

We report on progress made so far in the development of a software package for the simulation of a number of eddy current inspections. The simulation is performed using a variety of existing analytical models. The software has a graphical user interface and runs on a personal computer. It can be used either as an education supplement or as a practical tool for both the researcher and the eddy current technician, since it is designed for the fast computation and plotting of impedance plane diagrams.

INTRODUCTION

The eddy current method of NDT is well suited to simulation through the development of appropriate physics-based models. Such models involve the mathematical solution of Maxwell's electromagnetic field equations to calculate the fields and currents that occur for the specified probe and material. There are two ways of achieving this with the help of software packages.
The first is the use of expensive high-end packages that utilize numerical techniques such as the Finite Element Method (FEM) or the Boundary Element Method (BEM) and solve general electromagnetic problems. Not being NDE specific, these packages require some skill in setting the problem up if accurate answers are to be obtained. Nevertheless, they can model both coils and specimens of arbitrary geometry and arbitrary orientation, which means that there is a huge range of eddy current inspections, which can be simulated.
The second way is the use of cheaper low-profile packages that utilize analytical techniques to solve for the electromagnetic NDE related phenomena. Since the class of geometries that can be treated is usually restricted to problems with canonical boundaries, these packages allow only for an approximation of problems with non-canonical boundaries. However, they are NDE specific and they can be very useful and reliable. In addition, they are extremely fast and require minimal effort by the user.
Development of such eddy current simulators has already been reported. They are either running on older operating systems [1] or require the use of high-end workstations [2]. Unfortunately, no simulator is available for the PC and the Windows^TM environment.
In this paper we are reporting on the development of such a software package, which is called TEDDY and as it will be shown can be used for education, test design and research.
To date, the models that have been incorporated in the package are:

• Dodd models for the inspection of layered plates and layered cylinders
• Self-developed model for the inspection of layered sphere
• Models for the inspection of plates for surface cracks
More analytic models are being added as they become available to the scientific community.
In eddy current testing the most widely recognized model for axisymmetric problems is that of Dodd [3,4]. The eddy current probe is a circular air-cored coil wound with a rectangular cross-section. The conductor can have any number of layers and the geometries studied fall into two major categories: planar and coaxial cylindrical layers. These two categories include many of the more practical and useful testing geometries. We have added a third category, which includes concentric spherical layers. As regards defects, we have used the thin skin model to simulate the inspection of surface cracks in planar surfaces [5,6].
These models result in expressions that can be numerically evaluated for various coil and conductor parameters and predict quantitatively the effect of such parameters as lift-off, conductivity, magnetic permeability, layer thickness and frequency.

SOFTWARE DESCRIPTION

The following cases have been modeled up to this point:
• An air-cored coil in free space.
• A probe coil over a layered half-space.
• A probe coil over a half-space with a crack, in the thin skin limit.
• An ID coil inside a layered bore.
• An OD coil encircling a layered rod.
• A probe coil around a layered sphere.
The software consists of a front-end equipped with a graphical user interface that is responsible for data input and a hidden kernel, which is responsible for all the mathematical calculations.
In Figure 1, the window used for data input in the case of planar geometry with a probe coil over a half-space with one layer is shown. Here, the user enters the coil parameters and is allowed to range over the material parameters and TEDDY produces the impedance loci.
The software presents results in the form of impedance plane diagrams, which is the accepted method of presenting eddy current NDT data because they simulate the display of eddy current instruments. The impedance plane diagrams plot the normalized probe inductive reactance vs normalized probe resistance. The normalizing factor is the probe inductive reactance in free-space. In Figure 2, a typical example of the results plotting is shown. Referring back to the input data of Figure 1, the impedance curves, generated by ranging over the lift-off and conductivity of the half-space, are depicted.

Fig 1: Data input for the "Planar geometry - Probe coil - 1 layer" case.

Fig 2: Impedance plane diagram for the input in Figure 3


The well-known straight lines of lift-off and arc curves of conductivity appear. Another diagram, also shown in Figure 2, can depict a part of the impedance diagram after magnification. This is a very useful feature, especially when the change of parameters is very small and the resulting curves cannot be clearly visualized in the impedance plane diagram.
Some comments concerning performance of the code should be made at this point. In all numerical calculations, the relative accuracy attained is the highest possible and extends over 6 decimal digits. The CPU-time needed for the computation of an impedance value on a Pentium class computer is actually a few milliseconds, thus making the presentation of impedance plane results a real time event.

APPLICATIONS

One of the possible applications of TEDDY is for education. It provides a teaching and training tool by using a standard PC to evaluate coil impedance in a number of eddy current tests.
Some of the key parameters of the eddy current test method, which must be duly understood and recognized by an inspector in order to perform effective and reliable NDT are:
• The characteristics of the probe.
• Lift-off between the probe and the testpiece or fill-factor for cylindrical testpieces.
• The electrical conductivity and the magnetic permeability of the testpiece.
• The geometry of the testpiece including its thickness.
• The test frequency selected and used during inspection.
• The existence of defects and their characteristics in the testpiece.
TEDDY conveys a fundamental understanding of the concepts of the method by allowing the user to concentrate on the effect that a particular parameter has on the eddy current signal and to visualize it on the impedance plane.
But the most exciting thing about TEDDY is that it facilitates the reproduction of all these impedance plane diagrams that so frequently appear in eddy current textbooks [7,8]. We'll try to show this with the help of two examples.
The first example involves the study of wall thinning when inspecting a conductive tube from the bore side with a bobbin coil. The cylindrical geometry with ID coil and two layers conductor is chosen. The window for input data in this case is shown in Figure 3.

Fig 3: Data input for the "Cylindrical geometry - ID coil - 2 layers" case

Fig 4: Phase separation of ID and OD thinning at f90/2, f90, and 2f90.


By setting the conductivity of the second layer to zero, we can simulate a bobbin coil inside a tube. We have chosen three frequencies: f₉₀/2, f₉₀ and 2f₉₀. The f₉₀ frequency is supposed to give equal sensitivity between ID and OD thinning and a 90 degrees phase separation between shallow defects. We decrease the wall thickness from the ID and from the OD by 10% and we get the corresponding curves. Since the resulting impedance curves are very small, by using the magnifier on the impedance plane we get the results of Figure 4.
We can easily observe the well-known 90 degrees phase angle between shallow ID and OD defects when inspecting tubes at the characteristic frequency of f₉₀. Decreasing and increasing the frequency has two observable effects:
• The separation angle between ID and OD thinning decreases and increases respectively.
• The amplitude of OD thinning increases and decreases respectively due to the skin effect.

Fig 5: Encircling coil around a conductive rod. Separation of conductivity and diameter effects is shown at two different frequencies.

The second example is taken from [8]. In the chapter devoted to the analysis of encircling coil tests of wire, rods and bars it is stated that at very low frequencies the angle between the conductivity locus curves and the diameter effect is very small and thus separation between diameter and conductivity effects is difficult. On the other hand the separation of diameter and conductivity effects is more readily carried out at higher test frequencies because the angle between the loci of diameter and conductivity effects is greater than at lower frequency ratios. Relevant impedance diagrams are depicted in the chapter. We can reproduce such a diagram by selecting the cylindrical geometry with an OD coil and a one-layer rod, giving arbitrary values for the coil dimensions and ranging the parameters of conductivity and rod diameter for a number of frequencies. The resulting curves are shown in Figure 5.
By observing the impedance plane diagram, the user can easily verify the accuracy of the above statement.
Application of TEDDY is not limited to just training. It can provide solutions to both the designer of eddy current tests and the researcher in many ways: optimization of test coils and frequencies, measurement verification and inverse problem solution.
When setting up a new procedure to inspect a new part or use a new method, a simulator, such as TEDDY, provides a quick way to optimize the inspection parameters and measure performance even if the part is unavailable.
The design engineer can achieve quick, accurate answers to eddy current test problems. Suppose that he is designing an inspection with an air-core probe and would like it to be optimum for thickness monitoring of around 1mm aluminum plates. Such an optimization involves probe dimensions and frequency selection to provide lift-off separation and an adequate thickness variation signal. He can then use the software to compute the response to such a series of probes simply by ranging the dimensions of the plate thickness and comparing the results. Displaying the results for all probes together, he can quickly see which probe gives the best signal and therefore best suits the inspection.
The software solves the direct problem, which is described as the computation of the coil impedance when the parameters of the test are known. Another type of problem is the inverse, which can be described as the reconstruction of an unknown distribution of electrical conductivity from a set of eddy current probe impedance measurements, recorded as a function of probe position, excitation frequency or both.
A layered conductor with unknown layer conductivities and thickness is treated as an example of this type of inversion problem [9].
In order to apply optimization techniques to solve the inverse layered conductor problem, one has to solve a series of direct layered-conductor problems and this is where TEDDY proves its value as it solves the direct problem efficiently.
The researcher who studies various inversion algorithms and uses the Windows^TM environment can link the kernel of TEDDY to his own programs. This is possible because the kernel has the form of a dynamically linked library (DLL), a useful feature of the Windows^TM environment.

SUMMARY

The software presented and called TEDDY was designed to simulate a number of eddy current inspections which include axisymmetric layered structures tested by probe, bobbin and encircling coils. The software runs on a PC and has a graphical user interface which makes it an excellent education supplement. The results are presented instantly and have the form of curves plotted on impedance plane diagrams. The fact that the kernel of Teddy can be linked to other programs running in the Windows^TM environment makes it a practical tool for the researcher and in particular for the solution of a class of inversion problems. Future versions will include additional coil systems, electromagnetic field computation - in the event of a field sensor being used instead of a coil - and transient excitation in view of the increasing interest in the pulsed eddy current method.

REFERENCES

1. Jenkins S.A., Lowden D.W., "Eddy Current Simulators: Computer-Aided Learning", Materials Evaluation, Vol.51, November 1993, pp.1226-1236.
2. Nakagawa N., Garton M., Moulder J.C., Rose J.H., Xu J., "Recent Developments of Eddy Current Inspection Simulator", Review of Progress in QNDE, Vol.16, pp.959-966, 1997.
3. Cheng C.C., Dodd C.V., Deeds W.E., "General Analysis of Probe Coils Near Stratified Conductors", International Journal of Nondestructive Testing, Vol.3, pp.109-130, 1971.
4. Dodd C.V., Cheng C.C., Deeds W.E., "Induction coils coaxial with an arbitrary number of cylindrical conductors", Journal of Applied Physics, Vol.45, No.2, pp.638-647, 1974.
5. Harfield N., Bowler J.R., "Theory of thin-skin eddy-current interaction with surface cracks", Journal of Applied Physics, Vol.82, No.9, pp.4590-4603, 1997.
6. Auld B.A, Jefferies S.R., Moulder J.C., Journal of Nondestructive Evaluation, Vol.7, pp.79-, 1988.
7. Hagemaier D.J., Fundamentals of Eddy Current Testing, ASNT, 1990.
8. Nondestructive Testing Handbook: 2^nd ed., Vol. 4, Electromagnetic Testing, ASNT, 1986.
9. Baltzersen O., "Model-Based Inversion of Plate Thickness and Liftoff from Eddy Current Probe Coil Measurements", Materials Evaluation, Vol.51, January 1993, pp.72-76.

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