Materials Transactions, Vol. 56, No. 5 (2015) pp. 743 to 748
© 2015 The Japan Institute of Metals and Materials
EXPRESS REGULAR ARTICLE
Numerical Simulation of a U-Shaped ACFM Inducer
Wenpei Zheng1,+, Laibin Zhang1, Yinao Su2 and Taian Fang2
1
China University of Petroleum-Beijing, 18 Fuxue Road, Changping, Beijing, 102249, China
CNPC Drilling Research Institute, Block A34 CNPC Innovation Centre,
W of Xishatun Bridge Shahe Town, Changping District, Beijing, 102206, China
2
A static numerical simulation model of a U-shaped ACFM inducer is built to observe the distribution of current density and magnetic field
near the crack, and a dynamic model is developed from it to model a real ACFM probe passing above a real specimen with a crack. The dynamic
model is verified by comparison with experimental data and shows good agreement. The influence of various parameters, such as material and
dimensions of core and inducer lift-off on the perturbed magnetic field above the crack is modeled and discussed. The suggested parameters are
given for the design of the inducer according to the influence analysis results. The numerical simulation results will provide guidance to the
design of the U-shaped ACFM inducer. [doi:10.2320/matertrans.M2015005]
(Received January 6, 2015; Accepted February 13, 2015; Published March 27, 2015)
Keywords: alternating current field measurement (ACFM), U-shaped inducer, numerical simulation
1.
Introduction
Alternating Current Field Measurement (ACFM) is an
electromagnetic technique for detecting and sizing surface
breaking defects in metals.1) It was developed at University
College London from Alternating Current Potential Drop
(ACPD).2) It can inspect defects under nonconductive
coatings, which is quite applicable to offshore structures
coated with protective coating or anticorrosion compound.3)
ACFM inducer induces currents on the surface of the
specimen, which will be perturbed in the presence of a defect.
Associated with the perturbation of currents is a magnetic
field above the surface that will also be perturbed in the
presence of a defect.4) The perturbation of the magnetic field
is measured to detect and size defects. So the inducer
determines the perturbation of the magnetic field and thus
the inspection capability of ACFM. Inducer must be well
designed to get the best inspection capability.
Inducer design involves influence analysis of some key
parameters on the perturbation of the magnetic field.
Experimental analysis methods are time-consuming, high
cost and have experimental errors. In order to overcome the
shortcomings of experimental methods, finite element method
(FEM) is employed to simulate this process. In this paper,
a static numerical simulation model of a U-shaped ACFM
inducer is built to observe the distribution of current density
and magnetic field near the crack, and a dynamic model is
developed from it to model a real ACFM probe passing above
a real specimen with a crack. The dynamic model is then
verified by comparison with experimental data. Using the
dynamic model, the influence of various parameters, such as
material and dimensions of core and inducer lift-off on the
perturbed magnetic field above the crack is discussed, which
provides guidance to design of the U-shaped ACFM inducer.
2.
Static Numerical Simulation Model
2.1 Geometry model
In order to observe the distribution of current density and
+
Corresponding author, E-mail: zhengwenpei@cup.edu.cn
Fig. 1 Structure of the U-shaped core.
magnetic field near the crack, a static numerical simulation
model is built. In this model, the U-shaped inducer comprises
a U-shaped core and a current-carrying coil. The dimensions
of the core are 49.8 mm © 21.7 mm © 14.6 mm © 7.3 mm
(length © height © width © thickness), and the thickness of
the leg and waist is the same, as shown in Fig. 1. The coil is
one layer of wire winding around the waist of the core with a
rectangular cross-section. The coil is set as 60 turns and the
diameter of the wire is 0.5 mm. The specimen is modeled by
a plate, and the surface breaking crack in the specimen is
modeled by a semi-ellipse.5) The dimensions of the crack
are 4 mm © 0.2 mm © 0.8 mm (length © width © depth). The
inducer is positioned 3.2 mm above the specimen, and the
center of the region between the two legs is just above the
center of the crack. The inducer and the specimen are
enclosed in a cylinder volume, shown in Fig. 2.
2.2 Material definition
The material of the specimen is 35 steel, common used in
offshore structures. The material of core and coil is Mn-Zn
ferrites and copper. The cylinder volume is set as air. A small
non-zero value of the air conductivity will not substantially
affect the results, but helps the solver converge. So the
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W. Zheng, L. Zhang, Y. Su and T. Fang
Fig. 2
Numerical simulation model of the U-shaped inducer.
Table 1
Material definition.
Model
Material
Relative
permeability
Electrical conductivity
(S/m)
Specimen
35 steel
850
5 © 106
Core
Mn-Zn ferrites
2300
0.15
Coil
Copper
1
6 © 107
Cylinder volume
Air
1
50
electrical conductivity of air is set to be 50 S/m.6) The
definition of the materials are listed in Table 1.
2.3 Impedance boundary condition
Eddy currents induced by alternating current field in the
specimen exhibit the classical skin effect. The current path is
mainly confined to a thin layer close to the surface of the
specimen. The depth of the current layer, the skin depth ¤ is
given by
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
¤¼
®0 ®r ·³f
where · and ®r are electrical conductivity and relative
permeability of the specimen respectively, ®0 is the
permeability of vacuum, and f is the frequency of current.
In this model, the specimen has an electrical conductivity, ·,
of 5 © 106 S/m, relative permeability, ®r , of 850, and the
frequency of exciting current is 6 kHz. Thus skin depth ¤ is
0.1 mm. This skin depth is small compared with the thickness
of the specimen (8 mm), and it can be practically impossible
to solve the skin depth. To simulate this, an impedance
boundary condition is used. This condition essentially sets
the skin depth to zero, making all induced currents flow on
the surface of the specimen and do not penetrate into the
body.7) The interior of the specimen are excluded from the
model, which increases computational efficiency by removing the requirement to mesh the body of the specimen.
2.4 Simulation results
The numerical simulation model is solved and simulation
Fig. 3
Current density distribution on the surface of the specimen.
Fig. 4
Current lines on the surface of the specimen.
results are obtained. The current density distribution on the
surface of the specimen is shown in Fig. 3.
It is clear that the current density is roughly constant in
the region beyond the crack and between the two legs of the
core, which indicates that the current is uniform in this
region. In the region near the crack, the current density
reaches maximum at the ends of the crack, and minimum in
the middle. In order to explain this phenomenon, the current
lines are drawn as shown in Fig. 4.
The current flows on the surface of the specimen. In the
region beyond the crack, the current is uniform and not
perturbed. In the region near the crack, the uniform current is
perturbed and flows around the ends and down the faces of
the crack. Near the crack ends the current lines become closer
together as they pass the crack, and at the bottom of the crack
the current lines become far apart.8) This gives reasonable
explanation of the current density distribution on the surface
of the specimen. A rotation of the current around the crack
ends also occurs, which will be discussed later.
The magnetic flux density of the horizontal component of
magnetic field (By) on the surface of the specimen is shown in
Fig. 5.
It is also clear that By is roughly constant in the region
beyond the crack and between the two legs of the core, which
indicates that the horizontal component of magnetic field is
uniform in this region. In the region near the crack, By is
maximum at the ends of the crack, and minimum in the
Numerical Simulation of a U-Shaped ACFM Inducer
Fig. 5 Distribution of By on the surface of the specimen.
Fig. 6
745
Fig. 7 Distribution of Bz on the surface of the specimen.
By curve above the crack.
Fig. 8
middle. 3D and 2D plot of By (By curve) 2.35 mm above the
crack is drawn to show this phenomenon more clearly, as
shown in Fig. 6. The characteristic of the curve is two peaks
and a trough.
This phenomenon can be explained from Fig. 4. Associated with the current flowing on the surface is a magnetic
field above the surface that will also be perturbed in the
presence of a crack. The changes of the current will introduce
non-uniformity to the magnetic field. Near the crack ends the
current lines become closer and give rise to changes in By
around the crack ends, which produce two peaks in By curve.
As the current goes down the face of the crack, the current
becomes far apart, and produces a trough in By.9) The dip in
By curve relates to the depth of the crack.
The magnetic flux density of the vertical component of
magnetic field (Bz) on the surface of the specimen is shown in
Fig. 7.
It is also roughly constant in the region beyond the crack
and between the two legs of the core. In the region near the
crack, it is equal in magnitude and opposite in direction at the
ends of the crack, and reaches zero in the middle. 3D and 2D
plots of Bz (Bz curve) above the crack are drawn to show this
phenomenon more clearly, as shown in Fig. 8. There are a
peak and trough in the curve.
This phenomenon can also be explained from Fig. 4. The
vertical component of magnetic field is produced by rotation
of the current around the crack ends. Anti clockwise flow
Bz curve above the crack.
gives Bz trough and clockwise flow gives Bz peak. The peak
and trough mark the beginning and end of the crack.10) So the
distance between peak and trough in Bz curve relates to the
length of the crack.
3.
Dynamic Model and Experimental Verification
In order to model a real ACFM probe passing above a real
specimen with a semi-ellipse crack, a dynamic model is
developed from the static model. The dimensions of the crack
are 16 mm © 0.8 mm © 3.2 mm (length © width © depth).
The probe comprises a U-shaped inducer and a magnetic
sensor, as shown in Fig. 9. The magnetic sensor is mounted
in the center of the region between the two legs of the
inducer, 2.35 mm above the specimen, and measures the
change in By when the ACFM probe scans above the
specimen in the long direction of the crack.
The scanning process is modeled in the numerical
simulation model by parametric sweep. The distance from
center of crack to the magnetic sensor is selected as sweeping
parameter. The distance is swept from ¹50 to 50 mm, with a
step of 1 mm. For each scanning process, the model was run
101 times, and each time By at the position of magnetic
sensor is calculated. Plotting By against distance produces the
By curve.
746
W. Zheng, L. Zhang, Y. Su and T. Fang
Table 2
Properties of different materials.
Material
Relative
permeability
Electrical conductivity
(S/m)
20 Steel
1280
5.7 © 106
Mn-Zn ferrites
2300
0.15
Fig. 9 Illustration of the arrangement of the U-shaped inducer and the
magnetic sensor.
Fig. 11 By curves with different core material.
but the latter is little affected. So the simulation results for
only Bh curve are shown and their behaviors are discussed.
Fig. 10 Experimental verification.
Figure 10 shows the result of the comparison between the
experimental result and the result from the dynamic model.
There is good agreement between the two. However, the
curves in some region do not compare favorably. In the
region ahead of the crack, ¹50 to ¹10 mm from center of
crack, By of experiment is lower than simulation; In the
region after the crack, the two curves intersect at 29 mm,
with By of experiment higher than simulation at 10 to 29 mm
and lower at 29 to 50 mm. The experimental curve is not
as symmetry to center of crack as simulation curve. The
difference probably dues to the experimental error and the
inhomogeneous of relative permeability of the real specimen.
As the peak to peak value of the two are 2.36 and 2.26 Gs
respectively, with relative error of 4.5%, not influenced
favorably by the difference, it is not considered to be a major
drawback of the simulation.
4.
Influencing Parameters to The U-Shaped Inducer
Influencing of several parameters to the U-shaped inducer
is discussed in this section based on the simulation results.
Due to ACFM principle, the peak to peak value of By gives
an indication of crack depth, and the distance from peak to
trough of Bz curve gives an indication of crack length. The
former is affected by the influencing parameters obviously,
4.1 Core material
Mild steel and Mn-Zn ferrites are common used material
for magnetic core. In order to study the influence of core
material to the perturbed magnetic field above the crack, 20
steel and Mn-Zn ferrites are chosen as core material in the
numerical simulation model, the properties of which are
shown in Table 2. The impedance boundary condition was
used to 20 steel. The By curves with different materials are
compared in Fig. 11.
The result shows that By of Mn-Zn ferrites is higher and
perturbed more obviously above the crack than 20 steel. This
is due to the low relative permeability of 20 steel, and large
eddy current loss in it. So Mn-Zn ferrites has better detection
effect than 20 steel.
4.2 Core thickness
The influence of core thickness is studied in the model. In
this case, the thickness varies from 3 to 13 mm, with a step of
2 mm, while the length, width and height remain unchanged.
In the model, the rectangular coil is assumed to cover the
whole length of waist of core (shown in Fig. 2). So the turn
of coil varies with core thickness, as shown in Table 3.
The model was run several times for various core
thickness, along with corresponding turn of coil. By curves
with different core thickness are shown in Fig. 12, and the
perturbation of By against core thickness, described by peak
to peak value, is shown in Fig. 13.
The result shows that, By increases with the increase
of core thickness, and the peak to peak value of By first
increases and then decreases with increase of core thickness
Numerical Simulation of a U-Shaped ACFM Inducer
Table 3
747
Turn of coil versus core thickness.
Thickness of core
Turn of coil
3
5
74
67
7
61
9
54
11
47
13
40
Fig. 14 By curves with different core height.
Fig. 12 By curves with different core thickness.
Fig. 15 Peak to peak value of By against core height.
Fig. 13 Peak to peak value of By against core thickness.
and reaches maximum value when thickness is 7 mm. The
reason for this phenomenon is that, as thickness increases, the
area of cross-section of coil increases, and By increases with
increase of area of cross-section of coil; meanwhile, By
decreases with decrease of turn of coil. So there is maximum
value at a certain thickness. The thickness of 7 mm, which
can produce the largest perturbation of By, is deemed to be
best thickness.
4.3 Core height
The influence of core height is studied in the model. The
height varies from 10 to 28 mm, with a step of 3 mm, while
the length, width and thickness remain unchanged. By curves
with different core height are shown in Fig. 14, and peak to
peak value of By against core height is shown in Fig. 15.
The result shows that, By decreases with the increase of
core height, and the curves almost coincide when height is
22 and 25 mm. The peak to peak value of By increases with
increase of core height, but slows down when height reaches
19 mm. The curves begin to fluctuate obviously when height
is over 19 mm, which is to be avoided. So 19 mm is a
reasonable choice as the core height.
4.4 Inducer lift-off
The influence of inducer lift-off is studied in the model.
The lift-off varies from 1 to 6 mm, with a step of 1 mm. By
curves with different inducer lift-off are shown in Fig. 16,
and peak to peak value of By against inducer lift-off is shown
in Fig. 17.
The result shows that, By decreases with the increase of
inducer lift-off, and the peak to peak value of By decreases
with increase of lift-off, but slows down when lift-off is over
4 mm. It is desired to keep lift-off small to ensure a large
perturbation of By. But with a small lift-off, a slight variation
748
W. Zheng, L. Zhang, Y. Su and T. Fang
Fig. 16 By curves with different inducer lift-off.
and magnetic field near the crack, and a dynamic model is
developed from it to model a real ACFM probe passing
above a real specimen with a crack. The dynamic model is
verified by comparison with experimental data and shows
good agreement. The influence of material, thickness and
height of core and inducer lift-off on the perturbed magnetic
field above the crack is modeled and discussed. The results
show that:
(1) Mn-Zn ferrites can induce larger perturbation of By
above the crack than 20 steel, and Mn-Zn ferrites is
suggested as core material.
(2) The perturbation of By first increases and then decreases
with the increase of core thickness, reaching maximum
value when thickness is 7 mm, and core thickness is
suggested to be 7 mm.
(3) The perturbation of By increases with the increase of
core height, with By curves fluctuating when height is
over 19 mm, and core height is suggested to be 19 mm.
(4) The perturbation of By decreases with the increase of
inducer lift-off, but slows down when lift-off is over
4 mm, and inducer lift-off is suggested to be 4 mm.
Acknowledgements
This work was supported by National Natural Science
Foundation of China (51404283), PetroChina Innovation
Foundation (2014D-5006-0602) and Science Foundation of
China University of Petroleum, Beijing (YJRC-2013-47).
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Fig. 17 Peak to peak value of By against inducer lift-off.
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5.
Conclusions
A static numerical simulation model of a U-shaped ACFM
inducer is built to observe the distribution of current density
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