ˇHome ˇTable of Contents ˇMethods and Instrumentation  Probe characterisation and simulation of conductivity
M. ZERGOUG, A. HAMMOUDA, F. SELLIDJ, N. BOUCHEROU, H. HADDAD, S. MEBREK, A. BENCHAALA, G. Oussaid
Laboratoire d'Électronique et d'Électrotechnique,
Centre de Recherche Scientifique et Technique en Soudage et Contrôle,
Roue de Dely Ibrahim, B.P. 64, Chéraga, Alger, Algérie
Tél. & Fax : (213) 2 36 18 50
Contact

ABSTRACT
The sensitivity to defects and other parameters of control can be improved by the optimal choice of the probe.
It appears, after study of the different types of probes (ferritic, sweet steel, insulator) with different geometry (dish, conical,.. ), necessary to underline that the success of a research of feasibility depends largely on the good definition of measure collectors, such sort that they are adapted to the considered problem.
The Eddy Current NDT simulation can be resolve the material characterization problems. The principal rules of simulation is to explain the physical phenomena between the power source and the material testing.
The second approach is to determinate material conductivity simulation by using the diagram impedance and a different variables parameters (Frequency, factor K,....).
The testing probe realization by eddy currents was satisfactory at the sight of control and testing results of coating samples. The fundamental parameters to keep in mind for a probe construction are To diminish the reluctance of the measure circuit.
To allow an exchange between the probe and the material to be tested optimal energy.
A magnetic probe shell be realized in a material of a high magnetic permeability and a low electric conductivity
The results obtained by the probe whose nucleus and coil are conic allows to conclude that Sensibility increases with this geometry.
The resulting field at the contact point with the material to be tested can be assimiled to a material point.
The influence of the lateral field is considerably minimized.
The results obtained by simulation on the material are conform with practice measure.
The simulation application is valuable only for non magnetic material.
1. Introduction
The system of control by eddy current is developing very rapidly these last years by the advancement of the technology brought to devices of measures. The microcomputer contributed enormously the development of the physics of eddy currents that offers the possibility to solve problems of material characterization, of shortcoming localization and to deepen researches to the microscopic ladder. The important development of the data processing and the progress in their capacity, influenced the research to the control by eddy current.
Work that we present in this paper consists in conceiving an electronic card, permitting the measure of the active and reactive part of a control sensor by eddy currents.
The interest of this card is double, it permits to measure the electric conductivity of a material and to automate the chain non destructive testing by eddy current developed to the laboratory.
To this effect we work a software that permits through acquirements of all parameters measured by the electronic card, to join these electric measure results, (variation of the coil impedance excited by a sinusoidal current) with the measure of the electric conductivity of a material.
2. Definition of eddy currents.
Eddy Currents are interference's currents induced in conductor pieces generated by a variation of the magnetic field.
usually these currents represent an inconvenience in the electric machines (transforming, motors,...) dragging a metallic mass overheating by effect joule. An electric and mechanical energy loss characterizes himself by a weakening of output. However their applications are very important in the heating by magnetic induction and in certain brake devices of big contraption.
In other way these induced currents in the metallic carcasses are in direct report with the metallurgic features of materials (dimension, electric conductivity, magnetic permeability, rate of carbon, thickness of the coating,...). Then they are very used in Non Destructive Testing, research and localization of shortcomings (crack, cavity, corrosion,...).
3. Principle of eddy current testing
As it is represented in the figure, the process of eddy currents testing consists To determine the physical and metallurgic features (electric conductivity, magnetic permeability, dimension, coating, cémentation,...), detects some anomalies in the metallic structure by the variation of impedance of the probe.
The determination of these parameters depends on the distribution of eddy currents in the material, the electric conductivity, the magnetic permeability and the structure of the material. All variation or modification of these current's lines appears as a variation of the magnetic flux and a variation of the impedance of the probe.
4. Electric conductivity of metals
Under the influence of an electric field, the electric conductivity of a material is the speed variation of the free electron of bigger energy situated in the last zone of Brillouin no completely full. The potential magazine corresponding to the crystalline structure is disorganized by imperfections of the network. In the same way, the propagation of electrons is disrupted as by different types of shortcoming.
The conductivity is given by:
Where n represents volumique density of electrons,
e the charge of the electron,
m mass of the electron.
5. Construction of eddy currents sensors [9 to 13]
The sensitivity to shortcomings and other parameters of the sample control can be modified by the conception of the probe according to the direction of circulation of eddy currents, the intensity of the magnetic field, the choice of the suitable size coil and the geometry of the piece to control.
Probes do oneoff measures, they are maintained perpendicular to the surface, their profiles must marry as possible the sample.
Supports of coiling are chosen for a field focusing as the numétal and ferrite. This last is frequently used (presenting the detail to cover a large range of frequency) and exist only as a standard shapes because of the difficulty to machine, and then the impossibility to use them with different shape of piece.
The use of matter neuter PVC, Nylon comes back to make a coiling in air but present an inconvenient : scattering of the field.
The utilization of ferrite as cores of probes permit of :
 to increase the magnetic induction (important permeability) ;
 to increase the magnetic flux (very weak reluctance) ;
 to decrease the surface of contact (to assimilate it to a point) by the focusing of the magnetic field.
We are going to describe only one type of sensor, it has a section circular ferritique and coneshaped with an optimal sensitivity.
51. Influential parameters on the sensibility to anomalies
Eddy currents and the magnetic flux that is associated to them are proportional to the radial distance of the coil center. The magnetic flux is proportional to the probe induction and consequently to the passing current. The theoretic calculation of this induction is given by the following equation :
We improve the penetration of eddy currents by increasing the probe diameter. The useful diameter is generally equal to the coil diameter to which we add four times the standard thickness d
By increasing the probe diameter, we bring down the impedance point along the impedance curve with the same way as the electrical frequency or conductivity. We will describe only one type of probes, namely, the probe with ferritic circular section that we could qualify as punctual with an optimal sensibility. In order to satisfy these conditions, tests will be made to confirm these results by :
 The impedance diagram response of a conductive material.
 The variation response of the real and imaginary parts of the impedance in function of the frequency, with or without the sample presence.
 A cartography of the standard piece containing four defects of known dimensions.
52. Technical characteristics of circular ferrite probe
It is a probe whose the coil support is a small circular sticks with a straight section. The aim of our study is to assimilate the resulting magnetic field to a material point. In order to minimize the lateral field, we have chosen the construction of conical coil where the lateral field at a contact point in respect to a straight configuration is decreased with an exponential factor. The results obtained are as follow :
 The empty imaginary part stands constant.
 The real part increases slightly with the frequency (Joule effect ).
With the presence of material, the inductance variation follows an exponential law. The increase of the coil resistance is more significant in function of the frequency, due to the generation of eddy currents in the material.
As a conclusion to this experiment and in order to optimize the sensibility of the probe it is necessary that the coil shall be on the edge of the ferrite. The results obtained confirm the probe stability.
53. Impedance diagram of the coil
The diagram of impedance is a representation in a complex plan of the coil impedance. The real and imaginary parts of this impedance are function of the different parameter variation governing the construction of a sensor. The curves representing parameters influencing in the plan of impedance can be normalized in a standard curve called normalized impedance diagram.
The different parameters influencing the coil impedance are : the electric conductivity, the frequency, the permeability, the thickness and the presence of shortcoming.
6. survey and conception of the measure and acquisition system
The measure of the electric conductivity of a material will be calculated from the variation of the impedance of the probe to emptiness (as the absence of the material) and in charge (to contacts of a material). Our device is essentially constituted of :
 The measure system
Our system of measure must essentially be able to acquire three parameters :
 The efficient tension to the probe terminal.
 The efficient current crossing the probe.
 The déphasing between tension and the current of the probe.
 The system of analysis and control
It has for objective to manage the essential parameters, as :
 the good working of our measurer,
 the communication with the computer,
 the control and the acquirement of data of the measure system and the excitation circuit,
 the display,
 the measure of parameters wanted.
It is constituted of :
 A microcontroller and its environment (program and data memory, buffer, decoder, multiplexer, interfacing,...).
 A floor of display.
 A floor of conversion of different parameters measure by the analysis system (digital analogic converter).
 A floor of control of the measure system and the excitation circuit (decoder, analogic digital converter,...).
61. Survey of the measure system
The measure of the probe impedance (real and imaginary parts) by our measure system is based on three principles.
 The current (I) crossing the solenoid in serial with reference resistance (Rref) is in phase with tension (VR) to limits of this last..
 The impedance of a coil is equal to the report of the efficient tension to these limits and the efficient current that crosses it :
 The real and imaginary part of an impedance is given by the following formulas :
The measure of the real and imaginary part of an unknown impedance comes back to measure the efficient tension to these limits, the efficient tension to limits of a resistance in serial set of reference, and the measure of the déphasing between these two tensions.
 Synoptic diagram of the measure system
 Measure of the impedance of the probe
The measure of the efficient tension is possible with the R.M.S converter ŤAD 536Ať. Tension to limits of the reference resistance and limits of the probe is collected to the exit of an the amplifiers. The system of control will permit through the analogic multiplexer to select tensions, to measure their efficient values and to transmit their values converted to the system of analysis and, by the last relations the impedance of the probe is determined.
 The déphasing Measure
The measure of the déphasing introduces by the probe is based on a digital measure, that consists in measuring a number of impulses generated by a clock, during the time of delay between tension of the probe and tension of the reference resistance.
62. Survey of the analysis and control system
The system of analysis is constituted of the family's microcontroller ŤMCS 51ť, of a memory of 2k octet (EPROM 2716 and RAM 6261), The memory of programs contains a permanent program that manages the good working of the card and the tandards subprogram. (loading of registers, loading of display, command of the oscillator, loading of the DAC, the control of the converter, management of the memory and the communication with the computer).
The memory of data is charged mainly by a complementary program transmitted by the computer as extension of the main program.
7. Simulation of the electric conductivity
For the determination of the material conductivity, we opted for a physical approach based on the simulation. We noticed, in return for certain hypotheses, that the variation of the conductivity or the frequency in the diagram of impedance presents the same curve.


Normalized impedance diagram of some sample of materiel not ferromagnetic of different conductivity

It is to note that this simulation is valid for materials not ferromagnetic, and that it is necessary to saturate samples ferromagnétiques in order to give back their near relative permeability of the unit.
Besides, a defect in a conductor is a variation of conductivity. Our card can be used in the control no destructive by eddy currents, it is sufficient to conceive a probe adapted to the control.
Results of this survey can be exploited in the control of materials by eddy currents.
For the simulation of the conductivity, it would be interesting to generalize the measure of this parameter to material ferromagnetic without saturating this last, while working in the domain of Weiss. For it, a physical approach of the relative magnetic permeability and by following the simulation of the phase between parts activates and reactive impedance is necessary.
Normalized impedance Diagram of ferromagnetic sample having a thermal treatment

For the simulation of the electric conductivity of materials ferromagnetic we have proceeded a control for a sample (20NC6) having a thermal treatment at a temperature of 1100° at different maintain time 1h 30mn, 3h, 4h 30mn and 6h.
A metallurgic transformation was observed, and then a variation of conductivity and permeability. After a control testing by eddy current we observed two displacement of point of measure on the diagram of impedance at different frequency of control (500hz, 800hz or 1500hz) for each samples that explain a variation of conductivity (displacement according to the curve) and a variation of permeability (a displacement out the curve).
The simulation of this displacement would permit to measure the conductivity for materials ferromagnetic very interesting for the control.
8. CONCLUSION
The eddy currents testing probe realization was satisfactory at the sight of the control and the testing results of coating samples. The fundamental parameters to keep in mind for a probe construction are :
 Diminishing the reluctance of the measure circuit.
 Allowing an optimal energy exchange between the probe and the material to be tested.
 A magnetic probe should be realized in a material of a high magnetic permeability and a low electric conductivity.
The results obtained by the probe whose nucleus and coil are conic allows to conclude that :
 Sensibility increases with this geometry.
The resulting field at the contact point with the material to be tested can be assimilated to a material point. The influence of the lateral field is considerably minimized and the conductivity measure give a good results.
The relative survey to the conception and the realization of a conductivity measurer by eddy currents, permits to obtain the following conclusion.
 The card gave satisfying results as :
 The measure of tension and the current with a precision to the hundredth precision.
 A frequency generator sinusoidal is controlled with a hundredth precision.
 The measure of the déphasing, the real and imaginary parts of impedance give good satisfaction.
The choice of a microcontroller is interesting in the sense or the clutter of the card is reduced. It integrates several modules to know the delay time program, parallel and serial interfacing and a very flexible instruction game.
 For the determination of the material conductivity, we opted for a physical approach based on the simulation. We noticed, in return for certain hypotheses, that the variation of the conductivity or the frequency in the diagram of impedance presents the same curve.
It is to note that this simulation is valid for materials no ferromagnetic.
Besides, a defect in a conductor is a variation of conductivity. Our card can be used in the control no destructive by eddy currents, it is sufficient to conceive a probe adapted to the control.
Results of this survey can be exploited in the control of materials by eddy currents.
For the simulation of the conductivity, it would be interesting to generalize the measure of this parameter to material ferromagnetic without saturating this last, while working in the domain of Weiss. it is not necessary to saturate samples ferromagnetic. A physical approach of the relative magnetic permeability and by following the simulation of the phase between parts activates and reactive impedance is necessary. Certain materials like iron, nickel and cobalt are ferromagnetic. Under the influence of a magnetic field, these materials produce an inner magnetic induction clearly higher to that produced by the same empty field. This result is important, because it allows to characterize metallurgical states of materials (conductivity).
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