eddy current sensor meant for nondestructive testing of electrically conducting materials. Initially, the basic physical principles of the sensors are recalled, and ...
lEEE TRANSACTIONS ON MAG"ICS,
3192
VOL.29, NO. 6, NOVEMBER 1993
A FOCUSED-FIELD EDDY CURRENT SENSOR FOR NONDESTRUCTIVE TESTING Dominique Placko, Isabelle Dufour Laboratoire d'Electricit6, Signaux et Robotique UA CNRS D1375 61, avenue du prdsident Wilson 94235 CACHAN CEDEX
FRANCE Tel: 47-40-21-18, Fax: 47-40-21-99 Absircrct- In this paper, we present an original structure of eddy current sensor meant for nondestructive testing of electrically conducting materials. Initially, the basic physical principles of the sensors are recalled, and afterwards we discuss the fact that it is generally impossible to design a sensor with a good spatial resolution and having at the same time a good range detection. Then, we propose an original idea, which Consists of exploiting the good directivity of large cup sensors associated to a particular set of measurements, in order to extract relevant information only about the small part of the eddy currents induced in the target, below the centre of the sensor. The interest of this method is illustrated by scanning graphite composite plates containing small defects with this novel sensor. The comparison of the results obtained with actual sensors and our focused-field sensor demonstrates the efficiency of the structure.
This results in a sizeable modification of the magnetic field path (and thereby the reluctance) due to the real part of the current i, whereby the magnetic losses are due to the imaginary part of the current.
I. INTRODUCTION: PRINCIPLE OF EDDY CURRENT SENSORS
Fig. 2. Physical principle of cup eddy current sensor
An eddy current sensor is made in an open magnetic core on which an excitation coil (M turns) is driven by a sine wave current (iex>.A voltage measurement coil (N turns) is usually placed to have an exact image of the magnetic flux emitted by the sensor (Fig. 1).
Based on the hypothesis that there is no magnetic leakage, the following equations are derived for the flux amp entwined by the measurement coil, and established along the reluctance R,, path: R,@, = Mi, - i and umeas = jNw@,,. In this way, the impedance of the sensor can be defined as below:
Two interesting cases can be presented now: firstly, when the conductivity tends to be infinite, the induced currents create a flux exactly opposed to the flux emitted by the sensor, that is clearly illustrated by the use of the electrical images methods [l]. In this particular case, when the target is close to the sensor, ii and i, tend respectively to zero and Mim and consequently the impedance tends to zero. secondly, when the conductivity of the target is close to zero or when the target is far from the sensor, i=O, and this impedance becomes,,Z , :
-
Fig. 1.Cupeddycurrentsenm
The sensitive area of the sensor is defined by a volume into which the approach of a conducting object can bring a s i m c a n t variation of the signal, which is the consequence of the induced eddy currents in the target (i=ir+jii) (Fig. 2).
-
Manuscriptreceived February 15,1993
0018-W64/93$03.00 Q 1993 EEE
3193
The usual way ([2]-[4]) to overcome the increment of the impedance with frequency is to define the normalised impedance, noted Zm, :
,z
In addition, this particular structure is designed for a good focusing of the field emitted by the femte rod placed at the centre of the cup, compared to the cup structure (see numerical simulations in axisymmetrical mode on Fig. 5 ) .
zc, == xocup
The major advantage of this structure of magnetic circuit, compared with a U shape core, is that eddy currents are induced only below the sensor, in an area which is not larger than the diameter of the cup. However, the sensitive depth range, which directly depends on the decreasing strength of the field along the vertical axis, is a couple of times lesser than for the cup which is deduced from a U by a rotation around its axis. But the major drawback of these sensors is their lack of lateral resolution, which is close to the diameter of the cup. 11. ORIGINAL STRUCTURE PROPOSED In turn,we propose an original structure which maintains the distance range of the cup, for a gven diameter, but offers a better lateral resolution. A cross-section of the sensor is presented in Fig. 3 [ 5 ] .
Fig. 5. Simulationsof (a) a cup sensor @) a focused-field sensor
Now we shall show how the improved lateral resolution is obtained. Just as in the case of the cup, for the rod measurement, we can write: Rrd(D,& = Mi, - i - i' and umea= jNo(Drd. where i' are the currents induced below the rod. So, the normalised impedance expression is:
The image of the currents induced right below the rod is clearly gwen by the following difference (called the normalised impedance of the focused-field sensor): z,, =,Z - z~~= -(jilt1 -ili) Mlex
is defined as in section I, but the flux (Dcup is deduced from the difference between internal and external voltage measurements, -Z ,
Fig. 3. focused-field eddy current sensor
The main idea consists in a particular set of measurements, keeping only the information about the eddy currents induced under a small area below the centre of the sensor (i' on Fig. 4).
111. DATAPROCESSING The real may be 'lightly merent from the One presented previously, particularly because the sensor is generally lifted from the target and a magnetic flux leakage is tobe accounted for. Under these new conditions, and-if we call the leakage reluctance R,, Zmq becomes:
It is easy to demonstrate that this equation reflects the operating principle of a transformer in whch the primary and the secondary symbolise respectively the sensor and the target, coupled through a coefficient k whch depends directly on the &stance of observation (Fig. 6). The load impedance (Re+jIm) accounts for the induced currents. Fig. 4. Physical principle of the focused-field eddy current sensor
3194
coupling k vnn
--
Fig. 6. External parametricalmodelling
The results of identification between experimental data and theoretical model of transformer are presented on Fig. 7, respectively for the cup and rod measurements for three distances and eighteen fkequencies. Nonnalised Impedance Plane f2MHz
-0.1
1
0
0
20
MMHZ
-0.2 40
60
80
0
20
40
60
80
4”)
d”)
Fig. 8. N o d s e d impedance: improved lateral resolution
0
These curves clearly demonstrate the efficiency of both the sensor structure and the associated pre-processing model: this illustrates the validity of our theoretical analysis.
xcn 0
v. CONCLUSION -0.2
0
0.2
0.4
0.6
0.8
Rcn Fig. 7. N o d i impedance plane of cup and rod
This first identification gives, through the value of k, the average distance of observation [6] and we can easily verify that it is always possible to come back to the ideal case without leakage e l ) , using- the following - relations:
1-x,
=%
and X-., =1-k2 k2 ‘ Consequently, the normalised impedance of the focusedfield sensor can be simply obtained, in the real case, by computing the difference:
R,I
zm,
= zon*l
-z-l.
Iv. EXPERIMENTAL RESULTS Experimental tests have been performed by scanning,with this original sensor, a graphite composite plate having a simulated crack. The results are presented on Fig. 8: full, dashed and dotted lines show respectively the evolutions of Z& ,, , , ,Z and 2as a function of x-axis displacement, which is perpendicular to the axis of the crack (offset have been suppressed).
The feasibility of an origmal sensor, called “field-focused sensor”, for nondestructive testing has been demonstrated in this paper. Moreover, as we discussed in previous publications in the case of usual cup sensors, it is possible, from the new set of raw data given by the novel sensor, to estimate more accurately some physical properties of the sample tested (such as the electrical conductivity, the liftoff). This approach shows how to highly improve the relevance of information given by eddy currents sensors by the use of simple methods. REFE~NCES [l] D. Placko, Contribuhon d la conception de capteurs induchfi pour la robotique industrielle, Rapport de eynthese pour l’habilitation B diriger des recherches en sciences,22Mai 1990. [2] T. Kinsella, G. Mordwinkin ”Elect”agnetic sorting techniques” in Nondestructive testing hanbo& 2nd ed, Vol 4, Eleztmmgnetic testing, ed. Paul McIntire and Michael L. M e , 1986, American Society for Nondestructive Testing,Inc., Colombus, OH. [3] R.C. McMa~ter,S. Udpa “Basic concepts and theory of eddy current testing” in NonakstmcRve testing hanbook, 2nd ed., Vol 4, Eledmnagnetk testing, ed. Paul McIntire and Michael L. Mester, 1986, American Society for NondeshudiveTesting,Inc., Colombus, OH. [SI S. N. Vernon, “A single sided eddy current method to measure electrical resistivity”, Materials W&I&II, V0146, N O V ~ I1988, U ~ pp 1581-1587. [5] H. Chailleux, J. P.C h e , L Dufour, JY. Placko, E. Santander, “Capteur B c~urantede Fouc~u~”, hnch pater4 -92-04167s. [6] D. Placko, I. Dufour, “EddyCUrtDnt sensors for n o ” c t i v e inspeCtion of graphite composite mataials”, 1992 IEEE Industrial Applicdons Society annual meeting,part 11, pp 1676-1682.
