EVALUATION OF STANDARD CONFIGURATIONS FOR
NONDESTRUCTIVE EDDY-CURRENT TESTING
R. Sikora1'2, H. May3, and R. Palka1'3
technical University of Szczecin, Al. Piastow 17, 70-310 Szczecin, Poland
Institute of Electrical Engineering, Pozaryskiego 28, 04-Warsaw, Poland
3
Institute of Electrical Machines, Traction and Drives, Technical University Braunschweig,
Hans Sommer-Str. 66, 38106 Braunschweig, Germany
ABSTRACT. This paper discusses some practical configurations for finding flaws in well-conducting
materials using the eddy-current non-destructive method (NDT). In order to increase the sensitivity of
impedance changes the optimisation of all properties of these systems e.g. design and dimensions of
the coils, their positions, frequency and measuring system has been carried out. Based on these results
some requests are formulated for the developer of NDT-sensors. This project has been carried out as
the World Federation Second Eddy Current Benchmark Problem.
PROBLEM FORMULATION
Figure 1 shows the basic configuration, where the flaw position/size has to be determined. This measurement set-up consists of one single coil which can be moved along the
infinitely long tube. The coil is energised by an impressed high frequency AC current. The
changes of the impedance of the coil depend on the actual position of the flaw in the tube.
Sensitiveness to the changes of the crack position is the major benchmark for all configurations to be examined.
The main data for the calculation set up:
Tube (INCONEL 600): A? = 22.23 mm, A = 19.69 mm, a = 106 S/m, ji = jio
Flaw:
h - 20%, 40%, 60% of (ZVA)/2, t - 1.0 mm, w = 3 mm,
clearance /o = 0.8
Pancake coil:
do - 3 mm, d\ - 1 mm, hc - 0.8 mm,
winding: n - 400 turns, wire diameter 0,04 mm, current =100 mA,
FIGURE la. Basic measurement arrangement. Single measuring coil within a long
tube with a flaw.
FIGURE Ib. Basic measurement arrangement
(cross sectional view),
CP657, Review of Quantitative Nondestructive Evaluation Vol. 22, ed. by D. O. Thompson and D. E. Chimenti
© 2003 American Institute of Physics 0-7354-0117-9/03/S20.00
1808
The magnetic field distribution (2-D case) within all areas is described by the Poisson
equation with appropriate boundary conditions:
2
A = u(-J + jcocrA),
(1)
where:
A:
complex vector potential,
J:
complex current density vector,
a:
conductivity,
|i:
permeability,
co:
angular velocity.
Additional to the above equation the sum of the induced currents has to be equal to zero
in each conducting region individually.
For field calculations the appropriate finite element algorithm developed by the Institute
of Electrical Machines, TU Braunschweig and described in [1,2,5] has been applied. Material parameter values and required frequencies up to 200 kHz lead to skin-depths of
v = J21 (Djia which are relatively small (i>min - 1.125mm). In order to evaluate the field
penetration properly the reduced value of the skin-depth require a very fine problem
adopted discretisation of all conducting regions. This leads finally to large systems of algebraic equations and can result in instability and inaccuracy of the numerical algorithm.
The voltage induced in any coil can be calculated as [5]:
(2)
U = cjAJ*dS,
s
where S denotes the surface of the coil.
From Equation (2) the calculation of the impedance of each current-carrying coil (I) follows as:
Z = U/I.
(3)
The whole impedance of any magnetically connected coil system can be obtained as an
appropriate superposition of the individual impedances of all current-carrying regions together with the impedance of the coil itself.
EXAMINATION OF THE BASIC MEASUREMENT SET UP
The schematic circuit of this measurement set up is shown in Fig. 2.
High frequency source
Sensor coil
FIGURE 2. Electromagnetic circuit of the basic measurement arrangement.
1809
Figure 3a shows exemplary the field distribution for the above structure for an arbitrary
position "x" of the flaw for a measuring frequency of f=200 kHz and the Fig. 3b represents
the changes of the coil impedance versus the flaw position for h - 60% (Do-D^/2. The applied Finite Element model for this configuration contained about 75000 nodes and the calculation time on a standard PC (Pentium III, 850 MHz, 512 MB) for one position took
about 150 sec.
As can be seen from Fig. 3b the changes of the impedances are almost linear in the vicinity of central position (x=0) of the flaw and the impedances achieves the maximum
value in a displacement of about x=2mm. For increased offsets the sensitivity of this
method is very poor. As can be seen, for the basic measurement set up of Fig. 1 the relative
changes of the impedance are relatively small: ARmax/Ro~0.027%, ALmax/L0~0.848%.
The next figures show the current density distribution within the wall of the tube for two
different positions of the flaw. These displacement dependent current density distributions
conciliate that the changes of the coil impedance are not very high, as the current density
distribution is disturbed by the presence of the flaw only within a small part of the whole
wall [3,4].
——-•-'—
/
**•
••/•
£L
0,03415
^~
— •— 200 kHz
h=60% (Do D)/2
yj.......
Ax=0.20 mrn
Dmmj----
--\^
0,03420
-
0,03425
-^^
0,03 430
^
S
^/
0,03435
0,03440
0,03445
0,03450
R
LFallp.OPJ
FIGURE 3a. Field distribution (partial view of the cross FIGURE 3b. Changes of the coil impedance
section) for one position x of the flaw
versus the flaw position
(h=60% (D0-Di)/2, f=200 kHz).
(h=60% (D0-Di)/2, £200 kHz).
J [mA/mm2]
FIGURE 4a. Cut-out of the current density distribuFIGURE 4b. Cut-out of the current density distrition (real part) within the wall of the tube for a position bution (real part) within the wall of the tube for
x=-2 mm of the flaw (f=200 kHz).
another position x=-l mm of the flaw (f=200 kHz).
1810
The dependencies of the coil impedance as a function of the flaw position for further
feeding frequencies (150Hz and lOOHz) are illustrated for the basic measurement set up in
Figs. 5a and 5b respectively.
Similar dependencies of the impedance have been obtained for another reduced flaw
size (Fig. 6a and 6b).
In order to optimize the measurement system the calculations for different coil highs
have been also performed. Exemplary for a reduced coil height the position sensitivity of
the impedance is shown in Figs. 7a and 7b respectively.
;
^> ^-*
/
u
[
;
!
•
;B
!
•
;
!
•
*~- ^-.
-*— 150kHz
h=60% (D0-D)I2
Ax=0.25 mn
\
0.55945-
=0i
Wrr
^
0.01696
0,02610 0,02612 0,02614 0,02616 0,02618 0,02620 0,02622 0,02624 0,02626
0,01697
0.01699
LF10bp.OPJ
FIGURE 5a. Changes of the coil impedance versus the
flaw position (f=150 kHz).
0.01700
0.01701
0.01702
R[Q] —————•-
0.01703
LF10cp.OPJ
FIGURE 5b. Changes of the coil impedance
versus the flaw position (f=100 kHz).
'
j—^^
/
/*
/
*^>
V
•
~~m— 2C10 kHz
h=40% (Co-Di)/2
Ax=0.25 nim
'/}
0,73835-
1
X4__.
•nx=0mm|-
'
'
LFIOty.ORJ
FIGURE 6a. Field distribution for one position of the
flaw (h=40% (D0-Di)/2, f=200 kHz).
FIGURE 6b. Changes of the coil impedance
versus the flaw position
(h=40% (D0-Di)/2, ^200 kHz).
0,86750,8674 •
0,86730.8672'
0.8671 -
-m— 200kHz
h=60% (D0-D)I2
'" 0.8670'
0.8669-
tl
Ax=0.25 mm
Flat coil
0,8668'
0.8667'
0,86660.04570 0,04575 0,04580 0,04585 0,04590 0,04595 0,04600 0,04605 0,04610
FIGURE 7a. Field distribution for one position of the
flaw (reduced coil height)
(h=60% (D0-Di)/2, f=200 kHz).
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FIGURE 7b. Changes of the coil impedance
versus the flaw position with a reduced coil
height (h=60% (D0-Di)/2, f^200 kHz).
I
L ,
X
X
X
—•— 100 kKz
h=60%(D0-Di)/2
Ax=0.25 mm
x
N
I
x
^
X
=1a
=0
Xr
1,3677-
V,
\ I^H
0,06745
0,06750
0,06755
0,06760
0,06765
RED) ———-
FIGURE 8a. Field distribution for one position of
the flaw (coil with ferrite core)
(h=60% (D0-Di)/2, f^lOO kHz).
0,06770
0,06775
.11M.C
FIGURE 8b. Changes of the coil impedance versus
the flaw position (coil with ferrite core)
(h=60% (D0-Di)/2, f=100 kHz).
If the coil is embedded within a high frequency ferrite core the flux will be concentrated
near the tube wall. This design increases the impedance and improves simultaneously the
sensitivity by a factor of 6 of the measurement system. Some exemplary results are shown
in Figs. 8a and 8b respectively.
MEASUREMENT SET-UPS WITH TWO COILS
The second measurement set-up Fig. 9 (described and partially analysed in [5]) consists
of two differentially connected coils which will be axially and tubular moved along the
tube. The schematic electromagnetic circuit of this measurement set up is shown in Fig. 10.
FIGURE 9a. Second measurement
arrangement.
FIGURE 9b. Second measurement arrangement
Cross sectional view with two differentially connected coils.
High frequency source
Tube with flaw
FIGURE 10. Electromagnetic circuit of the second measurement arrangement
with differentially connected coils.
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The results of the numerical calculations for this configuration are shown in
Figs. 1 la and 1 Ib respectively. As already proposed for the basic measurement set up
(Fig. 8) the application of a ferrite core improves the sensitivity of the system (Fig. 12a
and 12b) by a factor of 3.6 if compared with Fig. 1 Ib. A further possibility to approve
the sensitivity of the measurement system is to use the second coil as an idle running
transformer. The results of the numerical calculations are shown in Figs. 13a,b (coils
without a ferrite core) and 14a,b (coils with a ferrite core) respectively. The electromagnetic circuit of this configuration is shown in Fig. 15.
^ <^*^.j*-~
*— 200 kHz
h=60% (Do-D )/2
AX-0.2C mm
^
y
^/
^'
/>
'^
*^
^
yy
yi s
/ ^
s
S*
jx=0
j^
-»--
-00002-
FIGURE lla. Field distribution for the central
FIGURE lib. Changes of the coil impedance versus
position of the flaw (h=60% (D0-Di)/2, f=200 kHz), the flaw position (h=60% (D0-Di)/2, £=200 kHz).
......
^ ^^ ^
^^->
^
^X
^x
x
-•— 100 kHz
h=60% (D0-D,)y 2
x=0.25 mm
^
x/
"7 r=0tr 4
0,00005
0,00010
0,00015
0,00020
0,00025
0,00030
R [fl] —————»•
FIGURE 12a. Field distribution for the central
position of the flaw (coils with ferrite core)
(h=60% (D0-Di)/2, f=100 kHz).
0,00035
Luft1-Fem.OPJ
FIGURE 12b. Changes of the coil impedance versus
the flaw position (coils with ferrite core)
(D0-Di)/2, f=100 kHz).
^^^,
^S
I
\,
N^
N
•h \,s.
—•— Mutual inductaru
0,0
0,5
1,0
1,5
>
"v
N
2,0
x[mm] ———Transf1a.OPJ
FIGURE 13a. Field distribution for the central
position of the flaw (unloaded transformer arrangement) (h=60% (D0-Di)/2, f^lOO kHz).
FIGURE 13b. Changes of the coils mutual inductance
versus the flaw position x (unloaded transformer
arrangement) (h=60% (D0-Di)/2, iMOO kHz).
1813
1
—-.
-~^ ——I
v
>^
"x^
\
^i "s
^
—•— Mutual inductance
N,
N
N,
0.0
0,1
0,2
03
0,4
0,5
0,6
0,7
08
x [mm] ———»•
Transf Ib.OPJ
FIGURE 14a. Field distribution for one position
of the flaw (coils with ferrite core, unloaded transformer arrangement)
(h=60% (D0-Di)/2, f=100 kHz).
FIGURE 14b. Changes of the coils mutual inductance
versus the flaw position x (coils with ferrite core, unloaded transformer arrangement)
(h=60% (D0-Di)/2, f=100 kHz).
High frequency source
Sensor coil
Tube with flaw
FIGURE 15. Electromagnetic circuit of the second measurement set-up. Unloaded transformer arrangement.
COMBINED SET-UP WITH INDIVIDUAL DETECTION AND MEASUREMENT
COILS
It seems to be advantageous to combine both previous examined configurations as
shown in Fig. 16. In order to use their individual attributes as simply the detection of any
flaw by one coil system which covers the hole bore of the tube. After the correct identification of the position of the flaw the coil system will be displaced by A (Fig. 16b). The precise determination of the properties of the flaw will than be carried out by a tubular rotation
of the more sensitive second coil.
The schematic electromagnetic circuits of the combined measurement are shown in
Fig. 10 for the detection coils and in Fig. 2 for the measurement coil.
FIGURE 16a. Combined measurement
arrangement with two coil systems with
individual properties
(detection and quality determination).
FIGURE 16b. Combined measurement arrangement
(cross sectional view).
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CONCLUSIONS
The main purpose of this paper was to examine generally many different measurement
configurations for the nondestructive determination of flaws within walls of conducting
tubes with help of eddy-current identification. According to the individual requirements of
any considered structure it is always necessary to define as many system features (magneto-electrical properties, possible flaw sizes and positions) as possible in order to optimize
the system sensitivity.
The numerical calculations carried out for all considered configurations show that the
absolute changes of the sensor-coil impedance are in the range of 0.5% (depending on the
configuration, frequency and material data) and the determination of the properties of the
flaw seems to be very ambitious.
The sensitivity of the basic configuration is not very high, especially for low frequencies, because of the position of the assumed flaw at the exterior of the tube and the shielding effects associated with the high-conductivity of the tube. Finite element method enables
the proper field calculation in each of the above mentioned structures, but very small skindepth values require a fine grid which leads to extended equation systems and result in a
long computation time.
To raise the sensitivity even for flaws at the exterior of a tube several changes on the
measurement system (coil design and electronic analysis) have been proposed. One layout
focuses the magnetic field into the vicinity of bore surface of the tube by the help of a ferrite core in which the coil is embedded. Furthermore a two coil system is proposed. One
acts for the detection while the other serves for the precise determination of the properties
of the flaw.
REFERENCES
1. May, H., ELMAG - Software Manual, Braunschweig 2001.
2. May, H., Schmid, W. and Weh, H., Archivfur Elektrotechnik 69 (1986), pp. 307320.
3. Sikora, R., Chady,T., Gratkowski, S. and Komorowski, M., COMPEL 17, 4
(1998), pp. 516-527.
4. Sikora, R., Gratkowski, S. and Komorowski, M., COMPEL 19, 2 (2000), pp. 352356.
5. Sikora, R. and Palka, R., Comparison of different measurement configurations for
non-destructive testing of well-conducting materials, Review of Progress in QNDE
2001, Brunswick 2001, pp. 1909-1916.
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