NUMERICAL PREDICTION OF SIGNAL FOR MAGNETIC FLUX
LEAKAGE BENCHMARK TASK
V. Lunin, D. Alexeevsky
Moscow Power Engineering Institute (TU), Russia
Electrical Engineering & Introscopy Department
Krasnokazarmennaja 14,111250 Moscow, Russia
ABSTRACT. Numerical results predicted by the finite element method based code are presented. The
nonlinear magnetic time-dependent benchmark problem proposed by the World Federation of
Nondestructive Evaluation Centers, involves numerical prediction of normal (radial) component of the
leaked field in the vicinity of two practically rectangular notches machined on a rotating steel pipe
(with known nonlinear magnetic characteristic). One notch is located on external surface of pipe and
other is on internal one, and both are oriented axially.
INTRODUCTION
Magnetic testing is one of the most popular nondestructive testing techniques for
detecting defects in ferromagnetic materials. One of hte typical application of the magnetic
testing is pre-service inspection of the steel tubes, where the testing is based on the
measurement of the magnetic flux leakage (MFL) field around the tube. Energy source
consists of electromagnet or permanent magnet used to magnetize the tube to near
saturation, and some kind of magnetic flux sensitive sensor (such as Hall-effect sensor)
responds to anomalies and defects in the tube. By this inspection, it is necessary to detect
and characterize defects in the tubes reliably so that proper remedial measures can be taken
in time and the safe operation of tubes can be guaranteed.
To compare experimental results with numerical model predictions, the World
Federation of Nondestructive Evaluation Centers, which includes NDE Centers from many
countries around the world, proposed the next MFL benchmark problem for 2002.
Experimental results on this MFL problem were carried out at Center for Industrial
Research in Argentina.
This benchmark problem involves the prediction of the magnetic flux leaked from a
rotating seamless steel tube with two rectangular notches. The signal calculated is the
normal (radial) component of the leaked field at a fixed point in the vicinity of outer tube
surface, as a function of the notch position, for four values of the liftoff and two notches,
external and internal.
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
1830
PROBLEM
PROBLEMDEFINITION
DEFINITION
The
Theconsidered
consideredMFL
MFLbenchmark
benchmarkproblem
problemhas
hassome
somefeatures
featuresofofstandard
standardindustrial
industrial
magnetic
magneticinspection
inspectionequipment
equipment(see
(seeFigure
Figure1 1inin[1]),
[1]),and
andthus
thusprovides
providesthe
theopportunity
opportunityofof
testingnumerical
numericalmodels
modelsthat
thatmay
maybe
beapplicable
applicable to industrial processes.
testing
processes. Besides
Besidesof
ofthis,
this,ititis
a rotating
tube
andand
a moving
notch
and,
is nonlinear
nonlinearand
andtime-dependent,
time-dependent,because
becauseit itinvolves
involves
a rotating
tube
a moving
notch
fromfrom
a mathematical
pointpoint
of view,
it involves
inducedinduced
currentscurrents
and a moving
and,
a mathematical
of view,
it involves
and a geometry,
moving
therefore, therefore,
it is computationally
more complex
andcomplex
it needs in
level numerical
model
geometry,
it is computationally
more
andhigh
it needs
in high level
for predictions.
numerical
model for predictions.
Numericalresults
results were
by the
elementelement
code MagNum3D
developed
Numerical
werecalculated
calculated
by finite
the finite
code MagNum3D
at MoscowatPower
Engineering
(Technical
University).
The preprocessor
developed
Moscow
Power Institute
Engineering
Institute
(Technical
University).view
Theon
the experimental
of the problem
as it was
by new
modeller,byis
preprocessor
view equipment
on the experimental
equipment
of prepared
the problem
as itversion
was prepared
shown
on Figure
1. is shown on Figure 1.
new
version
modeller,
Nonlinearmagnetic
magneticcharacteristic
characteristicofofsteel
steelmaterial
materialisisknown
known(see
(seeFigure
Figure2).
2).ItItisis
Nonlinear
necessary
to
numerically
predict
a
normal
(radial)
component
of
the
leaked
field
the
necessary to numerically predict a normal (radial) component of the leaked field ininthe
vicinity
of
two
practically
rectangular
notches
machined
on
a
rotating
steel
pipe.
One
notch
vicinity of two
rectangular notches machined on a rotating steel pipe. One
is located
on external
surface
of pipe
on internal
one, and
both
oriented
notch
is located
on external
surface
of and
pipeother
and is
other
is on internal
one,
andareboth
are
axially axially
(Figure(Figure
3, not in3,scale).
oriented
not in scale).
FIGURE 1. Illustration of the geometry of the experimental equipment as it was presented in modeler.
FIGURE 1. Illustration of the geometry of the experimental equipment as it was presented in modeler.
1831
5
10
15
20
25
30
35
40
45
50
FIGURE
FIGURE2.2. Magnetizing
Magnetizingcharacteristic
characteristic of
of steel
steel material
material used
used in
in calculations.
calculations.
FIGURE3.3.Model
Modelofofthe
theinvestigated
investigatedproblem
problem for
for prediction
prediction of
FIGURE
of the
the leaked
leaked field
field (not
(not in
in scale).
scale).
The coordinate
coordinate origin
origin lies
lies on
on the
the top
top tube
tube surface.
surface. The
The average
average gap
The
gap between
between the
the
yokeand
andthe
thetube
tubeisis equal
equal to
to 10
10 mm.
mm. The
yoke
The remaining
remaining set-up
set-upparameters
parametersare:
are:
Externalpipe
pipediameter:
diameter: 177.4
177.4 mm
mm
External
Internal
pipe
diameter:
162.2
mm
Internal pipe diameter: 162.2 mm
Spanofof yoke
yokeininvertical
vertical direction:
direction: 153
153 mm
mm
Span
Span
of
yoke
in
horizontal
direction:
405
mm
Span of yoke in horizontal direction: 405 mm
Pipe
angular
velocity:
20
RPM
and
40
RPM
Pipe angular velocity: 20 RPM and 40 RPM
1832
The geometry parameters of rectangular notches machined on the pipe is the
following:
Notch 1 (external):
width (in the azimutal direction): 0.965 mm
depth (in the radial direction): 0.96 mm
length (in the axial direction): 25.0 mm
Notch 2 (internal):
width (in the azimutal direction): 0.96 mm
depth (in the radial direction): 0.96 mm
length (in the axial direction): 25.0 mm
The magnetizing current was set so that in static state of pipe the tangential
(azimutal) component of the magnetic field at a point on a surface above the pipe was equal
to 20.0 kA/m.
MODEL PREPARATION DETAILS
The problem was considered as two-dimensional (plane) for predicting signal for
central cross-section. Two considered pipe angular velocities correspond to outer point
linear velocities (maximal values) due to the following:
20 RPM corresponds to 0.186 m/s
40 RPM corresponds to 0.372 m/s
Therefore, due to not very large linear velocity, the problem can be considered as
static too. The rotation effect in this case was replaced by movement of a notch-model
circumferentially with small step adjusted to a sampling rate of field measurement.
With known sampling rate (4kHz) and for rotating velocity 20 RPM angle
increment is equal to 0.03 Gradus per second, for rotating velocity 40 RPM this angle
increment is 0.015 Gradus per second. It is convenient to select 3 Gradus as angular step
value for calculations.
The boundary conditions for magnetic vector potential in the numerical models
were selected so that satisfy to the required field level (tangential component) on the pipe
surface in the absence of notch.
For material magnetic saturation condition, the intensity field H = 20 kA/m
corresponds to the induction B = 1.858 T (due to nonlinear magnetizing characteristic
shown in Figure 2). The static permeability for this curve point is JUsteej = 74.
The magnetic flux in pipe wall cross-section (with thickness Tpipe =1.6 mm) is
0 = 0.01412 Wb-m2 (considering 1 m in axial direction). The vertical size for problem
domain was selected as Ttotal = 160 mm (only top half geometry was modelled). Therefore,
full (horizontal) flux is equal to
1833
NUMERICAL RESULTS
NUMERICAL
RESULTS
For calculations
there was used the finite element program MagNum3D with
19836 nodes for triangular mesh elements of first order in two-dimensional solution
For with
calculations
there in
wasdefect
used the
finite elementarea.
program
19836
domain and
27 nodes
cross-section
The MagNum3D
numbers ofwith
nonlinear
nodes for
triangular
mesh
elements
of first order
in two-dimensional
solution
domain (one
and
iterations
were
between
7 and
10 depending
on defect
position in pipe.
Each variant
with 27
nodes in
defect
cross-section
area.
ThePentium
numbersIVof2GHz/1,5GB.
nonlinear iterations were
position
of defect)
needs
about
100 seconds
on PC
between
7 and
10 depending
on and
defect5 position
pipe. Each
(one position
of
Figures
4 (external
defect)
(internal indefect)
show variant
the dependence
of the
defect)
needs
about
100
seconds
on
PC
Pentium
IV
2GHz/l,5GB.
calculated signal on angular distance with different liftoffs for static situation, Figures 6
4 (external
defect)
and 5velocity
(internal
show the
dependence
of the
(external) Figures
and 7 (internal)
– for
rotational
20 defect)
RPM. Figure
8 (external)
shows
the
calculated
signal
on
angular
distance
with
different
liftoffs
for
static
situation,
Figures
6
dependence of the MFL signal on angular distance with different liftoffs for rotational
(external) and 7 (internal) - for rotational velocity 20 RPM. Figure 8 (external) shows the
velocity 40 RPM. As the liftoff is increased, the expected decrease in the signal magnitude
dependence of the MFL signal on angular distance with different liftoffs for rotational
are observed in all cases.
velocity 40 RPM. As the liftoff is increased, the expected decrease in the signal magnitude
are observed in all cases.
CONCLUSION
CONCLUSION
Presented numerical results show that, as expected, the calculated MFL signal
significantly
dependsnumerical
on the liftoff
on the
(external/internal)
of MFL
the notch
in
Presented
resultsandshow
that,location
as expected,
the calculated
signal
thesignificantly
pipe wall. Moreover,
there
is
no
significant
dependence
of
the
magnitude
and
the
shape
depends on the liftoff and on the location (external/internal) of the notch in the
of pipe
the radial
componentthere
MFLissignal
on the pipe
rotational
velocity
in theand
range
values
wall. Moreover,
no significant
dependence
of the
magnitude
the of
shape
of
examined.
the radial component MFL signal on the pipe rotational velocity in the range of values
It would be interesting to investigate other components of leaked field at the same
examined.
sensor position.
It would be interesting to investigate other components of leaked field at the same
sensor position.
Static
Static
Z = 0.5 mm
Z = 1 mm
Z = 2 mm
Z = 3 mm
0.06
0.05
0.04
0.03
0.02
B, Tl
0.01
0.00
-0.01
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
-0.02
-0.03
-0.04
-0.05
-0.06
Angle,
Angle,degree
degree
FIGURE
4. Radial
component
of of
thethe
leaked
(0,5; 1,0;
1,0; 1,5
1,5 and
and
FIGURE
4. Radial
component
leakedfield
fieldfor
forananexternal
externalnotch
notch with
with varying
varying liftoff
liftoff (0,5;
2,0 2,0
mm),
for for
a static
state.
mm),
a static
state.
1834
Static
= 0.5mm «"HB—»z = i mm
*" 'Z=2m
Angle, degree
FIGURE 5. Radial component of the leaked field for an internal notch with varying liftoff (0,5; 1,0; 1,5 and
2,0 mm), for a static state.
0.333 Hz Rotation (20 RPM)
= 0.5 mm «-H»—»Z = 1 mm , ;,
Z = 2 mm --••»>&—Z = 3 mm
Angle, degree
FIGURE 6. Radial component of the leaked field for an external notch with varying liftoff (0,5; 1,0; 1,5 and
2,0 mm), for rotational velocity 20 RPM.
1835
Static
Static (20 RPM)
0.333 Hz Rotation
Z = 0.5 mm
Z = 1 mm
Z =2 mm
Z = 3 mm
Z•Z
= 0.5
mm «HHH»Z
Z ==11mm
Z=
Z=
3 mm
= 0.5mm
mm ••^fii«^ Z
=22mm
mm «&^»«s-z
=3
0.015
0.015
0.010
0.010
B,B,
TT
0.005
0.005
0.000
0.000
55
55
60
60
65
65
70
70
75
75
80
80
85
85
90
90
95
95
100
100
105
105
110
110
115
115
120
120
125
125
-0.005
-0.005
-0.010
-0.010
-0.015
-0.015
Angle, degree
Angle,
Angle,degree
degree
FIGURE 5. Radial component of the leaked field for an internal notch with varying liftoff (0,5; 1,0; 1,5 and
FIGURE 5. Radial component of the leaked field for an internal notch with varying liftoff (0,5; 1,0; 1,5 and
Radial
component of the leaked field for an internal notch with varying liftoff (0,5; 1,0; 1,5 and
2,0 FIGURE
mm), for a7.static
state.
2,02,0
mm),
forfor
a static
state.velocity 20 RPM.
mm),
rotational
0.333 Hz Rotation (20 RPM)
0.333
0.667Hz
HzRotation
Rotation(20
(40RPM)
RPM)
Z = 0.5 mm
Z = 0.5 mm
Z = 1 mm
Z = 1 mm
Z = 2 mm
Z = 3 mm
Z = 2 mm
Z = 3 mm
= 2 mm •«««*««z = 3
0.060
0.060
0.040
0.040
B,B,TlTl
0.020
0.020
0.000
0.000
55
55
60
60
65
65
70
70
75
75
80
80
85
85
90
90
95
95
100
100
105
105
110
110
115
115
120
120
125
125
-0.020
-0.020
-0.040
-0.040
-0.060
-0.060
Angle,degree
degree
Angle,
Angle, degree
FIGURE 8. Radial component of the leaked field for an internal notch with varying liftoff (0,5; 1,0; 1,5 and
FIGURE
6.6.Radial
component
of
the
leaked
FIGURE
Radial
component
of40
theRPM.
leakedfield
field for
for an
an external
external notch
notch with
with varying
varying liftoff
liftoff (0,5;
(0,5; 1,0;
1,0; 1,5
1,5 and
and
2,0 mm),
for
rotational
velocity
2,0
2,0mm),
mm),for
forrotational
rotationalvelocity
velocity20
20RPM.
RPM.
1836
REFERENCES
1. J. Etcheverry, A. Pignotti, G. Sanchez, and P. Stickar, "MFL Benchmark Problem 2:
Laboratory Measurements", in Review of Progress in QNDE, Eds. D. O. Thompson and
D. E. Chimenti, this volume.
1837