MFL BENCHMARK PROBLEM 2: LABORATORY
MEASUREMENTS
J. Etcheverry, A. Pignotti, G. Sanchez, and P. Stickar
Centre de Investigation Industrial
L. Alem 1067, 1001 Buenos Aires, Argentina
ABSTRACT. This experiment involves the measurement of the magnetic flux leaked from a
rotating seamless steel tube with two machined notches. The signal measured is the radial
component of the leaked field at a fixed point in space, as a function of the notch position, for four
values of the liftoff and two notches. As the pipe tangential velocity was varied between 0.23 and
0.62 m/s, the sole observed effect was that of increasing the signal by a value that grows linearly
with the velocity and is independent of the notch angular position.
INTRODUCTION
The World Federation of Nondestructive Evaluation Centers, which includes NDE
Centers from all around the world, has for the second consecutive year proposed
"benchmark problems", open to the participating centers, as well as to any other interested
party. The idea is to profit from the comparison of experimental results versus individual
model solutions, and model solutions among themselves. In QNDE 2001 results were
presented by 2 Centers for MFL problem 1, which is 3D, magnetostatic and nonlinear [1].
Subsequently, a second MFL benchmark problem was proposed. Here we report on
experimental results on this MFL Benchmark Problem 2, carried out at our Center for
Industrial Research in Argentina.
PROBLEM STATEMENT AND MOTIVATION
While MFL Benchmark Problem 1 was nonlinear and magnetostatic [1], the
current problem is also nonlinear, but time-dependent, because it involves a rotating tube
and a moving notch. The motivation behind this problem is twofold. In the first place, it
reproduces some features of standard industrial MFL inspection equipment, and thus
provides the opportunity of testing models that may be applicable to industrial processes.
Secondly, because it involves induced currents and a moving geometry, it implies a higher
level of model and computational complexity.
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
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FIGURE 1. Experimental set-up used for the
measurement of the leaked field
FIGURE 2. Sketch illustrating the geometry of the
experiment
The problem involves the determination of the radial component of the magnetic
flux leaked in the vicinity of notches machined on a rotating steel pipe. A photo of the
experimental setup is shown in Fig. 1. A sketch of the yoke and pipe is shown in Figure 2
(not to scale). The coordinate origin in this figure lies on the tube surface. The problem is
approximately 2-dimensional in the x-z plane, but involves a moving notch. The average
gap between the yoke and the tube is equal to 10 mm. The remaining set-up parameters
are:
Yoke vertical span (in the z axis direction): 153 mm
Yoke horizontal span (in the x axis direction): 405 mm
External pipe radius: 88.7 mm
Internal pipe radius: 81.1 mm
The tangential velocity of the external pipe surface was varied between 0.23 and 0.62 m/s.
The magnetizing current was adjusted so that with a stationary pipe the tangential
component of the magnetic field at a symmetrically located point at a 2.5 mm liftoff above
the pipe was equal to 20.0 kA/m.
The following longitudinal notches were machined on this pipe:
Notch 1:
location: external
width (in the x direction): 0.965 mm
depth (in the z direction): 0.96 mm
length (in the y direction): 25.0 mm
Notch 2:
location: internal
width (in the x direction): 0.96 mm
depth (in the z direction): 0.96 mm
length (in the jy direction): 25.0 mm
For the purpose of model calculations, the approximate correspondence between the field
H and the induction flux density B for the steel pipe used, obtained by smooth
interpolation of the measured hysteresis loop, is shown in Fig. 3. The suggested value for
the electrical conductivity is 4.0x106/(Ohm.m).
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( 1 + D! H + D2 H2 )
with
NI = 5.90xl0^esla/(A/m)
N2 = 5.04xlO-10Tesla/(A/m)2
D1=2.70xlO"4/(A/m)
D2 = 2.81xlO-10/(A/m)2
0
5
10
15
20
25
30
35
40
45
50
FIGURE 3. B-H curve provided as part of the benchmark problem specification, and suggested
parametrization
The vertical component of the magnetic induction flux density Bz was measured
using a HGT-2100 Hall probe [2]. The sensor surface normal to the z axis is 1.6 mm wide
by 1.8 long. A simple analog circuit supplied the current and amplified the output, which
was digitized at a constant rate of 4khz. The sensor and the circuit were calibrated together
using a yoke and a commercial Gaussmeter [3].
The Hall effect transducer was positioned over the topmost pipe generatrix, half
way along the yoke horizontal span, and also half way along the notch length. A plastic
film provided the only separation between the tube and the sensor (the liftoff was just the
thickness of the film). The values used for the liftoff were 0.5, 1.0, 1.5, and 2.0 mm with
an estimated error of 0.05 mm. The pipe was mounted on a lathe, and rotated at almost
constant speed (within 0.5%). Every 360 degrees a pulse was generated by a proximity
sensor, which was also digitized.
The plastic film was lubricated in order to avoid wear. Because a small amount of
wear in the separator would imply a change in the liftoff that could give rise to significant
changes in the signal, all measurements were carried out twice without replacing the
plastic separator. Both sets of measurements were found to coincide.
RESULTS
Several consecutive measurements of the signal were recorded and averaged for
each one of the liftoffs and rotating velocities. Because of small fluctuations in the tube
rotating speed, the time delay between two consecutive signals is not exactly constant, as
evidenced in Fig. 4, in which the apparent position of the notch signal is seen to fluctuate.
Therefore, before averaging those signals, the following procedure was used to reduce
each one of the signals to its own local coordinate system (see Fig. 5):
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150
100
50
f
0
5 -50
J-100
-150
-200
-250,
55
Angle
FIGURE 4. Consecutive recorded signals,
exhibiting some relative angular shift due to
fluctuations in the rotation velocity.
FIGURE 5. Illustration of the procedure used to
define the local coordinates.
o
Angle
FIGURE 6. Radial component of the leaked
field for an external notch, for a 0.5 mm liftoff.
FIGURE 7. Radial component of the leaked field
for an internal notch, for a 0.5 mm liftoff
•
a straight line tangent to the recorded signal at half way between the signal maximum
and minimum was drawn
• the straight line that simultaneously describes the asymptotic behavior of the signal in
both directions was also drawn
• the local coordinate system for each signal was chosen to have its origin at the
intersection of these two lines.
Using these local coordinates, an average signal was computed for each location
(external/internal), velocity, and liftoff combination. On Fig. 6 the curves for external
notches, 0.5 mm liftoff and all velocities are drawn, and only one line is observed, which
shows that in local coordinates the signals were found to be independent of pipe rotational
speed within the range examined (tangential velocity between 0.23 and 0.62 m/s). A
similar result was found for internal notches (see Fig. 7), and for the other values of the
liftoff. Some selected numerical values for these curves are quoted in Table 2. The
systematic error on these results is estimated at 1%.
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O
External defect
D
Internal defect
O
External defect
D
Internal defect
-e-..
—&-.
0.5
1
1.5
2
6.5
1
1.5
2
Liftoff (mm)
Liftoff <mm)
FIGURE 8. Signal amplitude as a function of
the liftoff (dotted line only meant to guide the
eye).
FIGURE 9. Peak-to-peak angular distance as a
function of the liftoff (dotted line only meant to
guide the eye).
TABLE 1. Slope of the signal additive constant as a function of the pipe tangential velocity, in gauss/(m/s),
for internal and external notches, and 0.5, 1, 1.5 and 2 mm liftoffs.
Internal notch
External notch
0.5 mm liftoff
29.0 ± 0.9
26.4 ± 0.4
1.0 mm liftoff
28.3 ±0.3
29.3 ± 0.8
1.5 mm liftoff
29.6 ± 0.5
29.0 ± 0.6
2.0 mm liftoff
28.3 ±0.6
30.1 ±0.4
Figures 8 and 9 show the dependence of the signal amplitude and angular distance
between peaks on the liftoff. As the liftoff is increased, the expected decrease in the
amplitude and increase in the width are observed.
As was pointed out above, in local coordinates there is no dependence of the signal
on the pipe rotational velocity. This reduction to local coordinates implies a subtraction of
a constant value that is the only observable dependence of the signal on the velocity. Even
though the absolute value of this constant could not be ascertained, its variation with the
velocity could be determined consistently, and was found to be fairly linear and
independent of both the liftoff and the notch location (see Table 1). Indeed, because this
signal increase is independent of the notch position, it is present even when the notch is no
longer there. Therefore, we conclude that it is not caused by the moving notch but, rather,
by the distortion of the magnetic field generated by the currents induced in the rotating
pipe. These currents depend of course on the pipe rotational velocity, and are present even
if there is no notch.
CONCLUSIONS
As expected, the measured signal depends on the liftoff and on the location
(external/internal) of the notch. However, in the range of values examined, it depends on
the pipe rotational velocity only through an additive constant. The absence of a significant
dependence of the shape of the signal on the pipe rotational speed is a noteworthy
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TABLE 2.
Selection of measured values for the external and internal notch signals, for a 0.5
mm liftoff, in local coordinates (see Figs. 6-7).
Angle (°)
-25.0459
-20.0417
-15.0375
-10.0334
-8.7823
-7.5313
-6.2802
-5.0292
-4.5288
-4.0284
-3.5279
-3.0275
-2.5271
-2.2769
-2.0267
-1.7765
-1.5263
-1.2761
-1.0259
-0.7756
-0.5254
-0.2752
External notch
(gauss)
-0.22
0.06
-0.30
1.85
2.29
6.01
8.62
12.65
15.21
18.62
23.95
31.08
42.51
50.71
61.29
75.30
92.97
115.02
139.88
159.54
157.36
108.95
Internal notch
(gauss)
0.22
1.30
1.35
1.94
3.58
6.59
10.76
16.85
20.48
25.21
31.58
39.61
48.59
53.00
56.83
59.92
61.10
59.48
55.44
47.07
35.10
20.02
Angle (°)
-0.025
0.2252
0.4754
0.9758
1.226
1.4762
1.7264
1.9766
2.2269
2.4771
2.9775
3.4779
3.9783
4.4787
4.9791
6.2302
7.4812
8.7323
9.9833
14.9875
19.9917
24.9958
External notch
(gauss)
10.88
-98.11
-167.32
-162.08
-133.32
-106.29
-84.85
-67.91
-55.15
-45.39
-32.13
-24.14
-18.68
-15.07
-12.54
-8.09
-5.76
-5.26
-3.66
-2.27
-1.82
-0.90
Internal notch
(gauss)
2.92
-14.69
-31.43
-55.74
-62.17
-65.00
-64.69
-62.01
-57.95
-52.94
-42.85
-33.82
-26.96
-21.13
-17.26
-10.52
-6.91
-4.81
-3.65
-1.80
-0.69
-0.24
experimental result that deserves further theoretical/numerical analysis. Whether or not a
similar result holds for the tangential component of the leaked field, is a point that will be
checked in future experiments, as a continuation of the MFL Benchmark Problem 2.
ACKNOWLEDGMENTS
This work was done as part of a program sponsored by the tube manufacturers
Tamsa and Siderca.
REFERENCES
1.
2.
3.
A. Pignotti, Y. Li, Z. Zhang, Y. Sun, L. Udpa, S. Udpa, R. Schifmi and A.C. Bruno,
"Numerical simulation results on a magnetic flux leakage benchmark problem", in
Review of Progress in QNDE, Vol. 2 IB, Eds. D. O. Thompson and D. E. Chimenti,
AIP Conference Proceedings 615, Melville, New York, 2002, pp. 1894-1901.
Lakeshore Cryotronics, Inc., http://www.lakeshore.com.
F. W. Bell 9500 Gaussmeter, http://www.fwbell.com.
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