Innovative Eddy Current Probes Characterization Of Micro Defects
ABER Chifaa / Physics Department Applied power electronics laboratory
University of Science and technology USTO-MB Oran 31000, Algeria
E-mail: [email protected]
HAMID Azzedine / Faculty of Electrical Engineering, Applied power electronics laboratory
University of Science and technology USTO-MB Oran 31000, Algeria
E-mail: [email protected]
Abstract—IN this paper, we designed Eddy Current probes based on two different technologies, depending on the application. The first one is based on traditional probes based on classical winding coils, the second one takes advantage of the small size and high sensitivity of micro-coils etched on a flexible kapton film. Those probes are very efficient in the detection of defects located in complex geometries or in small curvature radius components. The simulation also provides the ability to compare upstream performance of a new probe relative to a conventional sensor and thus guide the choice of investment in innovative technology.
Keywords— Eddy current; Defect characterization; Finite element method; micro coil; arrayed eddy current sensor.
I. INTRODUCTION
The use of arrayed eddy current (EC) sensors in Non Destructive Testing (NDT) provides high speed inspection and better space resolution by miniaturization of their coils [1].
The arrayed sensors can make a measurement of large surfaces without a scan, which results in a gain in time and measurement noise reduction. In this Paper we interest to compare the performance of the new pattern on Kapton to that of a conventional coil without ferrite core. In the next section, we start by modeling a single sensor operating in mode dual functions, and then we present the model of the array sensor.
Model validation is achieved by comparing the results of a calculation of the 3D finite element also sensors for detecting notches of few hundred micrometers in length.
II. DESCRIPTIONOFTHEPROBLEM
The geometry of the problems considered is illustrated schematically in Fig.1 and Fig.2. In the first time a conventional coil is placed above the evaluated plate. The results of the conventional configuration compared to the innovative one are developed in this article.
Fig.1. Geometry of the 2D model (conventional probe).
The modeling approach of an arrayed sensor is then the same as for a single coil sensor. Figure 2 describes the modeled system. It is constituted of a (3 × 3) matrix of identical coils situated above a conductive plate characterized by a conductivity σ and the free space permeability μ0. The plate contains an open crack of a surface S. The arrayed sensor coils are fed in series by a current source with a time harmonic variation I (t)s 2I es jwt
Fig.2. Arrayed eddy current sensor above a plate with a crack.
III. FORMULATIONOFTHEPROBLEM
The eddy current problem can be described mathematically by the following partial differential equation in terms of the magnetic vector potential.
1( ) s A
A J
t
(1)
Where, A represents the magnetic vector potential, μ is the magnetic permeability of the media involved (H/m), σ is the electrical conductivity (S/m), and Js current density (A/m2).
The finite element formulation for the 2D axisymmetric eddy current phenomena was developed in many works. For axisymmetric geometries equation (1) reduces to the 2D form.
2 2
2 2 2
1 1
( A A A A) s
J j A
r r
r z r
(2)
This equation describes the problem shown in Fig. 1. The finite element approaches provides a solution to (2) by minimizing the variation of a functional, which is derived from (2) applying boundary condition. The simulation of this problem is using the ANSYS Parametric Design Language (APDL) software, where it’s based on the finite element analyses (FEA) method. The APDL is used to develop the simulation program so that the impedance of the scanning coil at different positions can be calculated automatically. The real and imaginary parts of the probe impedance are determined by using the magnetic energy and the power losses, respectively [2]. Where
2
1 2
Z R jL ( P j W )
I (3)
In the arrayed sensor the problem is based on the generalization of the crack model to an arrayed eddy current sensor, which we recall briefly in this section.
The electromagnetic problem formulation is given by (2), involving the magnetic vector potential A and the current source density Js. The total electric field induced by all the coils constituting the array sensor is then obtained by (4), making a spatial translation and a superposition of the results obtained for the single coil.
1
1
( , , ) ( ) ( , ),
( , , ) ( ) ( , ),
( , , ) 0.
c
c n
k
x sk k
k k
n
k
y sk k
k k
z
oy y
E x y z sign I A r z
r
E x y z sign I x ox A r z r
E x y z
(4)
In (4), A is the magnetic vector potential solution of (2) for one coil, nc is the number of coils constituting the arrayed sensor, “oxk , oyk” are the center coordinates of the coil k,
“x,y,z” are the Cartesian coordinates of the computing point, rk
is the distance between the computing point and the axis of the
coil k, and sign(Isk) indicates the direction of the current in the coil k.
IV. RESULTSANDDISCUSSION
It is interesting to compare the performance of the new pattern on Kapton to that of a conventional coil without ferrite core. In the next section, we start by modeling a single sensor operating in mode dual functions, and then we present the model of the array sensor. Model validation is achieved by comparing the results of a calculation of the 3D finite element also sensors for detecting notches of few hundred micrometers in length.
CALCULATION MODEL FOR SINGLE COIL SENSOR A. Calculation of current in 3D configurations with defect This model provides a fast analytical computation for 3D configurations in homogeneous materials (conductivity and permeability are constant through the plate). The geometry of the problems discussed is illustrated schematically in Figure 1.
An axisymmetric air coil is placed above the plate assessed. In absolute mode, we must perform two simulations: a first configuration with defect and a second flawless. However, it retains exactly the same geometry and the same mesh, only the
"defect" zone of the material differs between the two simulations
Fig.3. Design of the sensor’s coil and the plate used in 3D.
B. Modeling a flat coil etched on a flexible substrate
An etched coil is a geometric area where the height is typically very small [3] compared to the lateral dimensions (form factor can reach the hundred, from 100 microns to 10 mm for example).
The physical model of measurement consists of the target object and the main component of the sensor that is an induction coil when an alternating voltage or current is applied into a square coil etched on a flexible substrate of Kapton. The
parameters of this coil are: inner side: 120 microns; outer side:
1 mm; number of turns: 40. This coil can deform a curved manner. The eddy currents are induced homogeneously along the axis [Oy] at the frequency of 4 MHz.
Fig.4. Design of the sensor 3D model (micro-coil with plate).
Figure 5 represents the current density obtained. The response estimates the form and the position of the crack which is 2mm length located in the middle of the plate. This results are compared than the conventional identical one without loss of accuracy, even in the case of ferromagnetic materials.
Fig.5. Variation of eddy current density in the plate.
CALCULATION MODEL FOR ARRAYED SENSOR COIL There are several configurations of arrayed eddy current sensors [4]; when their coils are fed separately, the effect of the adjacent coils is negligible; the modeling approach is then the same as for a single coil sensors. In this work, we consider an arrayed sensor in which the coils are connected in series and fed simultaneously by a current source as shown in Figure 6.
Fig.6. Design of the Arrayed sensor and the plate used in 3D.
The investigation is done by the measurement of the eddy current density variation in the plate. The purpose is to determine the crack shape and size using the measurements provided by such a sensor in a real time investigation by searching the maximum value of the matrix.
Fig.7. Variation of eddy current density in the plate evaluated by the arrayed sensor.
V. CONCLUSION
This paper presents the application of EC probes for the evaluation of the form and the position of cracks. The simulation results obtained using the finite element method are presented in the first part using a traditional probe based on classical winding coils, in the second part we compare upstream performance of a new probe relative to the conventional one.
The use of the Finite Element Method for different technologies permits to estimate with good results the maps of crack, on the other hand, compared to conventional EC
sensors, innovative arrayed EC sensors provide more information about the defect characteristics.
References
[1] Gilles-Pascaud C., Vacher F., Decitre JM., Cattiaux G., « Eddy Current Array Probe Development For Complex Geometries », 5th ICNDE, San Diego, July 2006.
[2] ANSYS Theory Reference 001099 9th Editions.SAS IP,Inc.
[3] ] Marchand B., Vacher F., Decitre JM., Gilles-Pascaud C., Fermon C. « High Resolution Eddy Current Probes For Non Destructive Testing», QNDE 2007, Golden, July 2007.
[4] ] Grimberg, R.; Udpa, L.; Savin, A.; Stengmann, R.; Palihovici, V.;
Udpa, SS. 2D Eddy current sensor array. NDT&E Int. 2006, 39, 264- 271.
