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Magnetic flux leakage by adjacent parallel surface slots
PII: S0963-8695(97)00002-9
ELSEVIER
NDT&E International, Vol. 30, No. 6, pp. 371-376, 1997 © 1997 ElsevierScience Ltd. All rights reserved Printed in Great Britain 0963-8695/97 $17.00+0.00
Magnetic flux leakage by adjacent parallel surface slots Ichizo Uetake*, Tetsuya Saito National Research Institute for Metals 1-2-1, Sengen, Tsukuba-shi, Ibaraki 305, Japan
Received 13 December 1995; revised 5 August 1996; accepted 13 December 1996
This paper clarifies the relation between the magnetic flux leakage signals caused by two adjacent parallel slots on a metal surface and the distance between the two. The depth of smaller slot can be evaluated by considering an effect that the amplitude of leakage flux decreases as the depth ratio of two slots and the slot-to-slot distance increase. A new method is proposed as an alternative to analysing the waveform: it is based on the analysis of locus of the vector consisting of tangential and normal components of the magnetic flux leakage signals. © 1997 Elsevier Science Ltd. All rights reserved.
Keywords:nondestructive testing, magnetic flux leakage testing, adjacent slots
Introduction
distance, slot dimension and lift-off, as well as to investigate the evaluation method of the depth of adjacent slots.
Excess grinding or low cycle fatigue can initiate fine cracks often in close proximity to each other on the surface of structural materials. So far it has been difficult to discriminate and evaluate the depths of two cracks which lie in close proximity, because the leakage flux by one of the two cracks in close proximity is affected by the other and becomes different from that of an isolated crack. However, it is important to detel~aaine the crack size accurately, as it influences the material strength. Hereafter, two such parallel surface cracks in clo:se proximity with each other are simulated by two adjacent parallel slots machined at the material's surface.
Magnetic dipole model for adjacent slots Assuming that the magnetic charge density [31 on the crack flank is equivalent at every point on the flank and the magnetic charge distribution is not varied by the interaction of two parallel slots, we can consider the magnetic dipole model as follows. Figure 1 shows the magnetic dipole model for two parallel adjacent slots. When magnetic fields caused by the magnetic charge on the flank of each slot are defined as HI, H E, H 3, and H4, the sum of the megnetic field H at point P(x,z) is described by Eq. (1)
Regarding the research on adjacent slots, Steinberg et al. [1] estimated the depth of parallel surface cracks in a piston cylinder using various calibration factors. We have measured [z] the resolution of magnetic sensor to the adjacent slots. However, the fundamental relation in the magnetic flux leakage has not been clarified especially regarding the effect of slot-to-slot distance. At present, it is difficult to determine accurately the size of adjacent slots from the waveform or the intensity of magnetic flux leakage.
H = H 1 + / / 2 + / / 3 --FH4
(1)
Considering a rectangular coordinate system with the point 0 in the middle of the distance between the two parallel slots, we define x- and z-axis as shown in Figure 1, with the y-axis parallel to the slot. The tangential and normal components of the magnetic flux leakage, Bx and Bz, can be given by Eqs (2) and (3), respectively, by defining --- Am as the elementary magnetic charge on the flank of slot, dl and dE as the slot depths, 2al and 2a2 as the slot widths, 2s as the distance between the flank of slots, i.e. slot-to-slot distance,
The object of this study is to clarify the fundamental relations between the magnetic flux leakage and slot-to-slot
* Correspondingauthor.
371
I. Uetake and T. Saito
This analytical model holds only in cases where the magnetic charge on the flank of each slot is not affected by the distance of two slots.
P(x, z)
Test material and experimental method r4
The test material used was a low alloy structural steel SM50A, 220 (L)x50 (W)xl0 (H) mm. Artificial slots are perpared by electrical discharge machining. The length direction of the artificial slots are all parallel to the width direction of the material. The dimension of slots is varied from d = 1 to 4 mm in depth and from 2a = 0.3 - 2.4 mm in width, but the length is always constant at 50 mm, which is equal to the specimem width. The slot-to-slot distance is in the range 2s -- 0.7-23.7 mm.
VT///'
x direction
L
.L
J.
I"
T
q"
2ax
Figure I
2s
"] 2am
The experimental setup for the present study is shown in Figure 2. Magnetization of the test specimen is carried out with direct current (DC). Magnetic field intensity is 1910 A/ m at the center between the magnetic poles. The normal component of magnetic flux leakage is measured with a Hall element (size: 0.18 × 0.18 mm2). The scanning direction of the sensor along the test surface is perpendicular to the length direction of slot.
Magenticdipole model for two parallel adjacent slots.
and r as the distance from point P(x,z) to each elementary magnetic charge. Here the normal and tangential directions are defined in relation to the specimen surface.
Bx= A m [ t a n - 1
d](x+s)
2a" L
(x -~- S) 2 "q- Z(Z 71-dl )
-
+ tan -
1
tan -
1
tan -1
Am (
1 n
+1,,
Experimental results and discussion Comparison of waveform obtained by calculation and measurement
dz(x - 2a2 - s)
(x - 2a2 - s) 2 + z(z + d2)
Bz = -~r t In --
dl(x+2al +s) (x + 2al + s) 2 + z(z + dl )
d 2 ( x - s)
(x - sT
Figure 3 shows calculated magnetic flux leakage waveforms using Eq. (3) for a pair of adjacent slots at d = 1 mm in depth and 2a = 0.3 mm in width. It is indicated that the normal component of the leakage flux depends on the slotto-slot distance.
(2)
z(z + d2) j
(x + s) 2 + (Z + dl)2 (x + S) 2 "~ Z2
Figure 4 shows the normal component of magnetic flux leakage measured with a set of artificial slots. Vertical and horizontal axes in the figure show, respectively, the intensity of magnetic flux leakage signals and the displacement of the sensor. The figure shows that the flux leakage changes with the distance between two slots of the same depth. It is found that the tendency of waveform change agrees with simulated results for the simplified model, down to about 2s =
(x + 2al + s) 2 + (z + d l )2 (x + 2al + s) 2 + z2
(X -- S)2 + (Z + d2)2 / (x--2a 2 -- s) 2 + (Z + d2)2 1. ( ~ _ ~ j (x - 2a 2 - s) 2 + Z2
(3) Electromagnet
-•
Hall
element
]
~
Test material
Computer
Plotter
Printer
Disk Amplifier[
[converter]
Figure 2 Experimental setup.
372
memory
M a g n e t i c f l u x leakage b y adjacent parallel surface slots
d,=d==1.0m111, 2a1=2a==O.3mmm,
h=O.3mm
P414
L 2s(mm)
0.7
J
Normal component
I
B=
1.0
2.0 Figure 5 Symbols used for amplitudes and peak-to-peak distances of normal component of magnetic flux leakage signal.
Figure 3 Calculated magnetic flux leakage caused by two adjacent slots.
sensor that scans perpendicularly across the slots. It in fact represents a perpendicular section of the intensity profile of the leakage flux distribution around a pair of adjacent slots.
0.7 mm. This fact indicates that the equations derived for the dipole model are useful for estimating the waveform change reflecting the flux field around two adjacent slots of the same depth. Howe, ver, it is difficult to estimate the waveform, when the magnetic charge is varied.
Relation between slot-to-slot distance and intensity of magnetic flux leakage In general, the normal component waveform of leakage flux shows for each of the adjacent slots a pair of maximum and
Here the term waveform is denoted as the signal record of a
200 Crack s i z e
dl =
= 1 .
0
m m
2 a I = 2 a 2 = O.
3
m m
Lift-off
d2 h
= O.
3
dn=d==3 mmm e
o
mm
• 0
0
I o
150 2s(mmm)
X v
Normal component
/ I
O.
7
2 a,=
/
mm
i 100
111111 •
u
7
0.3
h=O.3mm
l
l B= X
2.
2 a,=
I
z~ ,&
__~ b,0 ¢~
/
•
s
i#
it
mmi--
50 3.
7 s
0 B=, •
4. 7
~
!
n=4
i
&
• B,, i
i
20
I0
Slot-to-slot
distance
2s (mmm)
Figure 4 Measured magnetic flux leakage caused by two
Figure 6 Relation between slot-to-slot distance and peak value
adjacent slots.
of magnetic flux leakage for two adjacentslots of a same size.
373
I. Uetake and T. Saito minimum peaks at variable amplitudes according to the slotto-slot distance, as shown in Figure 5. It shows symbols denoting peak-to-peak values and distances used in this paper. The signal from the smaller slot is defined at the left side of the figure with a peak-to-peak value of Bj2.
td,/d,
Pdla
0
•
P,=4 Pd=a Pdt,
o u
5
I' 0
7 5
i
t~
~
I
I
1 Lift-off
~
O
I
I
2 h (mm)
Figure 7 Relation between lift-off and peak-to-peak distance. and
Pd24 = 2s + 2a 2.
Relation between slot-to-slot distance and peak-to-peak distance
(6)
Therefore the values of Pdl3 and Pd24 are confirmed to be dependent on the slot width, but not on the lift-off in the case of two adjacent slots of the same depth.
Figure 7 shows the relation betweeen lift-off h and peak-topeak distance Pd, as a function of depth ratio dz/dl, for cases Ofdl = 1 mm, d2 = 1, 2, 3, 4 mm, 2al = 2a2 = 0.3 mm and 2s = 3.7 mm. It is difficult to determine the amplitude of flux waveform corresponding to dl, which is required for the estimation of Pd, in the case of large lift-off h and large ratio d2/dl, because the amplitude for dl decreases with increasing d2. Pd14 tends to be large with increase of liftoff and Pd23 becomes conversely small for any value of dJ dl. In the case of two adjacent slots of the same dimension, the values of Pal3 and Pd24 are independent of the change in the lift-off. However, in the case of two adjacent slots of different depths, there is a tendency that the value of Pd24 increases and the value of Pal3 decreases with increase of lift-off. In the case of two adjacent slots of different depths and the same width, the relation between the peak-to-peak distance, the slot-to-slot distance and the slot width can be expressed by the equation:
Evaluation methods of adjacent slots Two evaluation methods are investigated for the depth of adjacent slots: evaluation by means of the peak value of leakage flux and by means of the vector locus pattern recognition.
Evaluation method by means of the peak value of normal component From the experimental results it is clear that the slot depth can be evaluated by the peak signals from outside flanks in the case of adjacent slots of the same dimension. In the case of slots with different dimensions, the depth of the larger slot can be evaluated by the peak value Bz4 from its outside flank, as Bz4 is independent of the slot-to-slot distance. However, the evaluation of the depth of the smaller slot is difficult, as the leakage flux from the smaller is generally hidden by the signal from the larger. The influence of slot width is, in any event, neglected in these cases.
(4)
For two adjacent slots of different widths, the relation is shown by the equations: Pd13 = 2s + 2al
2a~=2a==0.3 ~m 2s=3.7 m m - d~=l mm
Figure 6 shows, as a function of slot depth, the relation between the slot-to-slot distance 2s and the peak value B z of the normal component of leakage flux from two adjacent slots of the same depth. The solid lines show the change of the peak values Bzl and Bz4 from the outside flanks of two slots. The broken lines show the changes of the peak values Bz2 and Bzs for the inside flanks of the two slots. The values of Bzl and Bz4 are almost constant and independent of the slot-to-slot distance in the case of d l = d2 = 1 mm. However, they show a decreasing tendency at smaller slotto-slot distances in the case o f d = 2 and 3 mm. This tendency can be understood as follows: it has been found that the leakage flux decreases with increase of slot width [41.As shown with broken lines in Figure 6, Bz2 and Bzs from the inside flanks decrease because the leakage flux signals from the flanks cancel each other out owing to the shorter distance between them. If the slot-to-slot distance is so small, the two adjacent slots can be assumed to act as one slot composed of the two outside flanks and the two inside flanks can be neglected. When adjacent slots are located with much smaller slot-to-slot distances, the imaginary slot becomes narrower and the leakage flux from the ensemble increases again. On the other hand, the magnetic flux leakage Bzl and Bz4 for shallow slots (d~ = d2 ----- 1 mm) does not decrease with decrease of their slot-to-slot distance, because the magnetic flux leakage due to the inside flanks cannot be neglected as the absolute value of leakage flux itself becomes small in this case.
(Pdl3 q- Pd24)]2 = (Pd23 -q-Pdl4)]2 = (2s + 2al ).
=4
As magnetization areas of smaller and larger slots are superimposed when the slot-to-slot distance is very close, it
(5)
374
Magnetic flux leakage by adjacent parallel surface slots
Depth(mm)
d2= 2
t~ ~
Measured wavefor=
Crack s i z e
After processed
to
,,.-I
Lift-off
dl=l
S
=
O.
3
.
0
mm
dl=
O.
1
mm
d2=2. 2al=O. 2a2=0. h = O.
0
mm
3
mm
3
mm
2
mm
inm
O.
5
mm
d2=3 B=
Amplitude
: (x 10-'
T )
2s=O.7mm
dl=l d2=4
1
c~
2.
0
mm
Figure 8 Effect of waveform processing on magnetic flux leakage caused by t w o adjacent slots. Figure 9 Vector locus pattern calculated for two adjacent slots of different sizes.
is difficult to read the anaplitude of signals from the smaller slot. For obtaining exam signals from the smaller slot, it is effective to conduct a waveform processing by subtracting the signal of the larger slot from the ensemble signal of the two adjacent ones, as shown below.
output signals from two elements are sent, respectively, to the vertical and horizontal axes of an XY-recorder or of a oscilloscope to trace a locus figure during the scan of the sensor perpendicularly across the slots. The size of the locus pattern is proportional to the intensity of magnetic flux leakage signals. Consequently, the slot depth can be evaluated from the size of the locus pattern.
Figure 8 shows an example of the waveform processing. Arrows in the figure indicate an irregularity caused by the smaller slot at 2s ---- 0.7 mm. The irregularity tends to be unclear with increase in the depth of the larger slot. The net waveform caused by the smaller slot can only be obtained after waveform processing, as demonstrated here. For the slot depth ratios of d J d l = 2, 3 and 4, amplitudes of the magnetic flux leakage fi'om the smaller slot are found to be 7.6, 3.8 and 3.5 ( × 10 -4 T), respectively, after the waveform processing. The depth of the smaller slot of different depths can be estimated by usage of the relation between slot-toslot distance and amplitude of the magnetic flux leakage by applying the waveform processing.
Figure 9 shows the effect of slot-to-slot distance on vector locus patterns calculated with Eqs (2) and (3) for the magnetic dipole model. The pattern changes dependening on the slot-to-slot distance 2s and the dimension of the slots d J d v This figure depicts the case of adjacent slots with different depths. A smaller circle is observed in the larger one for 2s = 2 mm, and this state shows that the signals from two slots of different depths can be easily separated from each other. In the case of 2s = 0.5 mm, the smaller circle becomes much smaller than that for 2s = 1 mm influenced by the larger slot and the location is closer to the maximum B z by the larger slot. In the case of 2s = 0.3 mm, the diameter of the smaller circle is much smaller and the maximum B z decreases because of the influence of the smaller slot. In summary, the vector locus pattern exhibits an inscribed small circle within a larger one in the case of adjacent slots of different depths. The location of the smaller circle caused by the smaller slot is dependent on the slot-to-slot distance.
Evaluation method by means of vector locus pattern recognition In fact, the waveform we are looking at represents only a section profile of the normal component of leakage flux distribution around a p~dr of two adjacent slots. Therefore, we propose a new method for discriminating the signals from two adjacent slots In the proposed method, the magnetic flux leakage is measured with a sensor composed of two elements to detect both normal and tangential components of signals. The
375
I. Uetake and T. Saito It is thought that the discrimination and evaluation of adjacent slots can be carried out easily by means of characeristic pattern of vector locus. For actual flaw testing of materials, it is recommended to use both the vector pattern method and the waveform analysis simultaneously, as the latter is a more direct means of determining the slotto-slot distance or the location of the slot on the test surface. When a small slot signal is buried in the waveform of a large slot by means of decrease in the slot-to-slot distance, the signal of the small slot must be detected by using the waveform process. In this case, the data is obtained with the help of the waveform process and the vector locus pattern method is used. The detectability of the peak value and the vector locus pattern methods are found to be equal to each other because they are used with the same waveform processed data.
decreases markedly with decrease of slot-to-slot distance. The leakage flux caused by the inside flank of the larger slot decreases slightly. (2) A new evaluation method for the depth of two adjacent slots by means of the amplitude of waveform and the vector locus pattern. (a) The peak value of the normal component of leakage flux can be used to evaluate the depth of two adjacent slots. Waveform processing is useful to extract essential waveform by the smaller slot from measured raw data. (b) Vector locus pattern recognition is also used to evaluate the depth of two adjacent slots. The vector locus shows the characteristic pattern of two adjacent slots.
Acknowledgements Conclusions
The authors are indebted to Dr S. Nishijima at NRIM for his kind reading and suggestions during the preparation of the manuscript.
The magnetic flux leakage around a pair of adjacent slots is investigated. Main results obtained are summarized as follows:
References
(1) The magnetic flux leakage by adjacent slots depends on slot-to-slot distance as well as the depth ratio of two slots.
1 Steinberg, A.P., Hagemaier, D.J., Barton, J.R. and Williams, R.D.,
Determining crack depth in a high-strength steel cylinderusing magnetic perturbation. Materials Evaluation, 1982,40, 288-293. 2 Uetake, I., Ito, H. and Saito, T., Resolution by sensor size on magnetic flux leakage testing (in Japanese). J. Japan. Soe. Nondestruct. Inspec., 1990, 39(2A), 165. 3 Zatsepin, N.N. and Shcherbinin, V.E. Calculation of the magnetic field of surface defects. 1. Field topographyof defect models. Soy. J. NDT, 1966, 2, 50-59. 4 Bruder, B., Magentic leakage field calculated by method of finite differences. NDTInt. , 1985, 18, 353-357.
(a) In the case of two adjacent slots of the same depth, peak values of leakage flux caused by the inside flanks of two adjacent slots decrease along with the slot-to-slot distance, while the peak values caused by their outside flanks are independent of the slot-to-slot distance. (b) In the case of two adjacent slots of the same width but different depths, leakage flux caused by the smaller slot
376
ELSEVIER
NDT&E International, Vol. 30, No. 6, pp. 371-376, 1997 © 1997 ElsevierScience Ltd. All rights reserved Printed in Great Britain 0963-8695/97 $17.00+0.00
Magnetic flux leakage by adjacent parallel surface slots Ichizo Uetake*, Tetsuya Saito National Research Institute for Metals 1-2-1, Sengen, Tsukuba-shi, Ibaraki 305, Japan
Received 13 December 1995; revised 5 August 1996; accepted 13 December 1996
This paper clarifies the relation between the magnetic flux leakage signals caused by two adjacent parallel slots on a metal surface and the distance between the two. The depth of smaller slot can be evaluated by considering an effect that the amplitude of leakage flux decreases as the depth ratio of two slots and the slot-to-slot distance increase. A new method is proposed as an alternative to analysing the waveform: it is based on the analysis of locus of the vector consisting of tangential and normal components of the magnetic flux leakage signals. © 1997 Elsevier Science Ltd. All rights reserved.
Keywords:nondestructive testing, magnetic flux leakage testing, adjacent slots
Introduction
distance, slot dimension and lift-off, as well as to investigate the evaluation method of the depth of adjacent slots.
Excess grinding or low cycle fatigue can initiate fine cracks often in close proximity to each other on the surface of structural materials. So far it has been difficult to discriminate and evaluate the depths of two cracks which lie in close proximity, because the leakage flux by one of the two cracks in close proximity is affected by the other and becomes different from that of an isolated crack. However, it is important to detel~aaine the crack size accurately, as it influences the material strength. Hereafter, two such parallel surface cracks in clo:se proximity with each other are simulated by two adjacent parallel slots machined at the material's surface.
Magnetic dipole model for adjacent slots Assuming that the magnetic charge density [31 on the crack flank is equivalent at every point on the flank and the magnetic charge distribution is not varied by the interaction of two parallel slots, we can consider the magnetic dipole model as follows. Figure 1 shows the magnetic dipole model for two parallel adjacent slots. When magnetic fields caused by the magnetic charge on the flank of each slot are defined as HI, H E, H 3, and H4, the sum of the megnetic field H at point P(x,z) is described by Eq. (1)
Regarding the research on adjacent slots, Steinberg et al. [1] estimated the depth of parallel surface cracks in a piston cylinder using various calibration factors. We have measured [z] the resolution of magnetic sensor to the adjacent slots. However, the fundamental relation in the magnetic flux leakage has not been clarified especially regarding the effect of slot-to-slot distance. At present, it is difficult to determine accurately the size of adjacent slots from the waveform or the intensity of magnetic flux leakage.
H = H 1 + / / 2 + / / 3 --FH4
(1)
Considering a rectangular coordinate system with the point 0 in the middle of the distance between the two parallel slots, we define x- and z-axis as shown in Figure 1, with the y-axis parallel to the slot. The tangential and normal components of the magnetic flux leakage, Bx and Bz, can be given by Eqs (2) and (3), respectively, by defining --- Am as the elementary magnetic charge on the flank of slot, dl and dE as the slot depths, 2al and 2a2 as the slot widths, 2s as the distance between the flank of slots, i.e. slot-to-slot distance,
The object of this study is to clarify the fundamental relations between the magnetic flux leakage and slot-to-slot
* Correspondingauthor.
371
I. Uetake and T. Saito
This analytical model holds only in cases where the magnetic charge on the flank of each slot is not affected by the distance of two slots.
P(x, z)
Test material and experimental method r4
The test material used was a low alloy structural steel SM50A, 220 (L)x50 (W)xl0 (H) mm. Artificial slots are perpared by electrical discharge machining. The length direction of the artificial slots are all parallel to the width direction of the material. The dimension of slots is varied from d = 1 to 4 mm in depth and from 2a = 0.3 - 2.4 mm in width, but the length is always constant at 50 mm, which is equal to the specimem width. The slot-to-slot distance is in the range 2s -- 0.7-23.7 mm.
VT///'
x direction
L
.L
J.
I"
T
q"
2ax
Figure I
2s
"] 2am
The experimental setup for the present study is shown in Figure 2. Magnetization of the test specimen is carried out with direct current (DC). Magnetic field intensity is 1910 A/ m at the center between the magnetic poles. The normal component of magnetic flux leakage is measured with a Hall element (size: 0.18 × 0.18 mm2). The scanning direction of the sensor along the test surface is perpendicular to the length direction of slot.
Magenticdipole model for two parallel adjacent slots.
and r as the distance from point P(x,z) to each elementary magnetic charge. Here the normal and tangential directions are defined in relation to the specimen surface.
Bx= A m [ t a n - 1
d](x+s)
2a" L
(x -~- S) 2 "q- Z(Z 71-dl )
-
+ tan -
1
tan -
1
tan -1
Am (
1 n
+1,,
Experimental results and discussion Comparison of waveform obtained by calculation and measurement
dz(x - 2a2 - s)
(x - 2a2 - s) 2 + z(z + d2)
Bz = -~r t In --
dl(x+2al +s) (x + 2al + s) 2 + z(z + dl )
d 2 ( x - s)
(x - sT
Figure 3 shows calculated magnetic flux leakage waveforms using Eq. (3) for a pair of adjacent slots at d = 1 mm in depth and 2a = 0.3 mm in width. It is indicated that the normal component of the leakage flux depends on the slotto-slot distance.
(2)
z(z + d2) j
(x + s) 2 + (Z + dl)2 (x + S) 2 "~ Z2
Figure 4 shows the normal component of magnetic flux leakage measured with a set of artificial slots. Vertical and horizontal axes in the figure show, respectively, the intensity of magnetic flux leakage signals and the displacement of the sensor. The figure shows that the flux leakage changes with the distance between two slots of the same depth. It is found that the tendency of waveform change agrees with simulated results for the simplified model, down to about 2s =
(x + 2al + s) 2 + (z + d l )2 (x + 2al + s) 2 + z2
(X -- S)2 + (Z + d2)2 / (x--2a 2 -- s) 2 + (Z + d2)2 1. ( ~ _ ~ j (x - 2a 2 - s) 2 + Z2
(3) Electromagnet
-•
Hall
element
]
~
Test material
Computer
Plotter
Printer
Disk Amplifier[
[converter]
Figure 2 Experimental setup.
372
memory
M a g n e t i c f l u x leakage b y adjacent parallel surface slots
d,=d==1.0m111, 2a1=2a==O.3mmm,
h=O.3mm
P414
L 2s(mm)
0.7
J
Normal component
I
B=
1.0
2.0 Figure 5 Symbols used for amplitudes and peak-to-peak distances of normal component of magnetic flux leakage signal.
Figure 3 Calculated magnetic flux leakage caused by two adjacent slots.
sensor that scans perpendicularly across the slots. It in fact represents a perpendicular section of the intensity profile of the leakage flux distribution around a pair of adjacent slots.
0.7 mm. This fact indicates that the equations derived for the dipole model are useful for estimating the waveform change reflecting the flux field around two adjacent slots of the same depth. Howe, ver, it is difficult to estimate the waveform, when the magnetic charge is varied.
Relation between slot-to-slot distance and intensity of magnetic flux leakage In general, the normal component waveform of leakage flux shows for each of the adjacent slots a pair of maximum and
Here the term waveform is denoted as the signal record of a
200 Crack s i z e
dl =
= 1 .
0
m m
2 a I = 2 a 2 = O.
3
m m
Lift-off
d2 h
= O.
3
dn=d==3 mmm e
o
mm
• 0
0
I o
150 2s(mmm)
X v
Normal component
/ I
O.
7
2 a,=
/
mm
i 100
111111 •
u
7
0.3
h=O.3mm
l
l B= X
2.
2 a,=
I
z~ ,&
__~ b,0 ¢~
/
•
s
i#
it
mmi--
50 3.
7 s
0 B=, •
4. 7
~
!
n=4
i
&
• B,, i
i
20
I0
Slot-to-slot
distance
2s (mmm)
Figure 4 Measured magnetic flux leakage caused by two
Figure 6 Relation between slot-to-slot distance and peak value
adjacent slots.
of magnetic flux leakage for two adjacentslots of a same size.
373
I. Uetake and T. Saito minimum peaks at variable amplitudes according to the slotto-slot distance, as shown in Figure 5. It shows symbols denoting peak-to-peak values and distances used in this paper. The signal from the smaller slot is defined at the left side of the figure with a peak-to-peak value of Bj2.
td,/d,
Pdla
0
•
P,=4 Pd=a Pdt,
o u
5
I' 0
7 5
i
t~
~
I
I
1 Lift-off
~
O
I
I
2 h (mm)
Figure 7 Relation between lift-off and peak-to-peak distance. and
Pd24 = 2s + 2a 2.
Relation between slot-to-slot distance and peak-to-peak distance
(6)
Therefore the values of Pdl3 and Pd24 are confirmed to be dependent on the slot width, but not on the lift-off in the case of two adjacent slots of the same depth.
Figure 7 shows the relation betweeen lift-off h and peak-topeak distance Pd, as a function of depth ratio dz/dl, for cases Ofdl = 1 mm, d2 = 1, 2, 3, 4 mm, 2al = 2a2 = 0.3 mm and 2s = 3.7 mm. It is difficult to determine the amplitude of flux waveform corresponding to dl, which is required for the estimation of Pd, in the case of large lift-off h and large ratio d2/dl, because the amplitude for dl decreases with increasing d2. Pd14 tends to be large with increase of liftoff and Pd23 becomes conversely small for any value of dJ dl. In the case of two adjacent slots of the same dimension, the values of Pal3 and Pd24 are independent of the change in the lift-off. However, in the case of two adjacent slots of different depths, there is a tendency that the value of Pd24 increases and the value of Pal3 decreases with increase of lift-off. In the case of two adjacent slots of different depths and the same width, the relation between the peak-to-peak distance, the slot-to-slot distance and the slot width can be expressed by the equation:
Evaluation methods of adjacent slots Two evaluation methods are investigated for the depth of adjacent slots: evaluation by means of the peak value of leakage flux and by means of the vector locus pattern recognition.
Evaluation method by means of the peak value of normal component From the experimental results it is clear that the slot depth can be evaluated by the peak signals from outside flanks in the case of adjacent slots of the same dimension. In the case of slots with different dimensions, the depth of the larger slot can be evaluated by the peak value Bz4 from its outside flank, as Bz4 is independent of the slot-to-slot distance. However, the evaluation of the depth of the smaller slot is difficult, as the leakage flux from the smaller is generally hidden by the signal from the larger. The influence of slot width is, in any event, neglected in these cases.
(4)
For two adjacent slots of different widths, the relation is shown by the equations: Pd13 = 2s + 2al
2a~=2a==0.3 ~m 2s=3.7 m m - d~=l mm
Figure 6 shows, as a function of slot depth, the relation between the slot-to-slot distance 2s and the peak value B z of the normal component of leakage flux from two adjacent slots of the same depth. The solid lines show the change of the peak values Bzl and Bz4 from the outside flanks of two slots. The broken lines show the changes of the peak values Bz2 and Bzs for the inside flanks of the two slots. The values of Bzl and Bz4 are almost constant and independent of the slot-to-slot distance in the case of d l = d2 = 1 mm. However, they show a decreasing tendency at smaller slotto-slot distances in the case o f d = 2 and 3 mm. This tendency can be understood as follows: it has been found that the leakage flux decreases with increase of slot width [41.As shown with broken lines in Figure 6, Bz2 and Bzs from the inside flanks decrease because the leakage flux signals from the flanks cancel each other out owing to the shorter distance between them. If the slot-to-slot distance is so small, the two adjacent slots can be assumed to act as one slot composed of the two outside flanks and the two inside flanks can be neglected. When adjacent slots are located with much smaller slot-to-slot distances, the imaginary slot becomes narrower and the leakage flux from the ensemble increases again. On the other hand, the magnetic flux leakage Bzl and Bz4 for shallow slots (d~ = d2 ----- 1 mm) does not decrease with decrease of their slot-to-slot distance, because the magnetic flux leakage due to the inside flanks cannot be neglected as the absolute value of leakage flux itself becomes small in this case.
(Pdl3 q- Pd24)]2 = (Pd23 -q-Pdl4)]2 = (2s + 2al ).
=4
As magnetization areas of smaller and larger slots are superimposed when the slot-to-slot distance is very close, it
(5)
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Magnetic flux leakage by adjacent parallel surface slots
Depth(mm)
d2= 2
t~ ~
Measured wavefor=
Crack s i z e
After processed
to
,,.-I
Lift-off
dl=l
S
=
O.
3
.
0
mm
dl=
O.
1
mm
d2=2. 2al=O. 2a2=0. h = O.
0
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3
mm
3
mm
2
mm
inm
O.
5
mm
d2=3 B=
Amplitude
: (x 10-'
T )
2s=O.7mm
dl=l d2=4
1
c~
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0
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Figure 8 Effect of waveform processing on magnetic flux leakage caused by t w o adjacent slots. Figure 9 Vector locus pattern calculated for two adjacent slots of different sizes.
is difficult to read the anaplitude of signals from the smaller slot. For obtaining exam signals from the smaller slot, it is effective to conduct a waveform processing by subtracting the signal of the larger slot from the ensemble signal of the two adjacent ones, as shown below.
output signals from two elements are sent, respectively, to the vertical and horizontal axes of an XY-recorder or of a oscilloscope to trace a locus figure during the scan of the sensor perpendicularly across the slots. The size of the locus pattern is proportional to the intensity of magnetic flux leakage signals. Consequently, the slot depth can be evaluated from the size of the locus pattern.
Figure 8 shows an example of the waveform processing. Arrows in the figure indicate an irregularity caused by the smaller slot at 2s ---- 0.7 mm. The irregularity tends to be unclear with increase in the depth of the larger slot. The net waveform caused by the smaller slot can only be obtained after waveform processing, as demonstrated here. For the slot depth ratios of d J d l = 2, 3 and 4, amplitudes of the magnetic flux leakage fi'om the smaller slot are found to be 7.6, 3.8 and 3.5 ( × 10 -4 T), respectively, after the waveform processing. The depth of the smaller slot of different depths can be estimated by usage of the relation between slot-toslot distance and amplitude of the magnetic flux leakage by applying the waveform processing.
Figure 9 shows the effect of slot-to-slot distance on vector locus patterns calculated with Eqs (2) and (3) for the magnetic dipole model. The pattern changes dependening on the slot-to-slot distance 2s and the dimension of the slots d J d v This figure depicts the case of adjacent slots with different depths. A smaller circle is observed in the larger one for 2s = 2 mm, and this state shows that the signals from two slots of different depths can be easily separated from each other. In the case of 2s = 0.5 mm, the smaller circle becomes much smaller than that for 2s = 1 mm influenced by the larger slot and the location is closer to the maximum B z by the larger slot. In the case of 2s = 0.3 mm, the diameter of the smaller circle is much smaller and the maximum B z decreases because of the influence of the smaller slot. In summary, the vector locus pattern exhibits an inscribed small circle within a larger one in the case of adjacent slots of different depths. The location of the smaller circle caused by the smaller slot is dependent on the slot-to-slot distance.
Evaluation method by means of vector locus pattern recognition In fact, the waveform we are looking at represents only a section profile of the normal component of leakage flux distribution around a p~dr of two adjacent slots. Therefore, we propose a new method for discriminating the signals from two adjacent slots In the proposed method, the magnetic flux leakage is measured with a sensor composed of two elements to detect both normal and tangential components of signals. The
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I. Uetake and T. Saito It is thought that the discrimination and evaluation of adjacent slots can be carried out easily by means of characeristic pattern of vector locus. For actual flaw testing of materials, it is recommended to use both the vector pattern method and the waveform analysis simultaneously, as the latter is a more direct means of determining the slotto-slot distance or the location of the slot on the test surface. When a small slot signal is buried in the waveform of a large slot by means of decrease in the slot-to-slot distance, the signal of the small slot must be detected by using the waveform process. In this case, the data is obtained with the help of the waveform process and the vector locus pattern method is used. The detectability of the peak value and the vector locus pattern methods are found to be equal to each other because they are used with the same waveform processed data.
decreases markedly with decrease of slot-to-slot distance. The leakage flux caused by the inside flank of the larger slot decreases slightly. (2) A new evaluation method for the depth of two adjacent slots by means of the amplitude of waveform and the vector locus pattern. (a) The peak value of the normal component of leakage flux can be used to evaluate the depth of two adjacent slots. Waveform processing is useful to extract essential waveform by the smaller slot from measured raw data. (b) Vector locus pattern recognition is also used to evaluate the depth of two adjacent slots. The vector locus shows the characteristic pattern of two adjacent slots.
Acknowledgements Conclusions
The authors are indebted to Dr S. Nishijima at NRIM for his kind reading and suggestions during the preparation of the manuscript.
The magnetic flux leakage around a pair of adjacent slots is investigated. Main results obtained are summarized as follows:
References
(1) The magnetic flux leakage by adjacent slots depends on slot-to-slot distance as well as the depth ratio of two slots.
1 Steinberg, A.P., Hagemaier, D.J., Barton, J.R. and Williams, R.D.,
Determining crack depth in a high-strength steel cylinderusing magnetic perturbation. Materials Evaluation, 1982,40, 288-293. 2 Uetake, I., Ito, H. and Saito, T., Resolution by sensor size on magnetic flux leakage testing (in Japanese). J. Japan. Soe. Nondestruct. Inspec., 1990, 39(2A), 165. 3 Zatsepin, N.N. and Shcherbinin, V.E. Calculation of the magnetic field of surface defects. 1. Field topographyof defect models. Soy. J. NDT, 1966, 2, 50-59. 4 Bruder, B., Magentic leakage field calculated by method of finite differences. NDTInt. , 1985, 18, 353-357.
(a) In the case of two adjacent slots of the same depth, peak values of leakage flux caused by the inside flanks of two adjacent slots decrease along with the slot-to-slot distance, while the peak values caused by their outside flanks are independent of the slot-to-slot distance. (b) In the case of two adjacent slots of the same width but different depths, leakage flux caused by the smaller slot
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