corresponding to each scanning point. The magnetic induction
strength variation along the entire discontinuity is obtained by
connecting the B values of each scan point. The same princi-
ple applies to subsequent trapezoidal discontinuity and inner/
outer discontinuity detection.
Figures 8a and 8b show that the signal peak gradually
increases with the edge angle. Additionally, relative to the
center position of the discontinuity, increasing the edge angle
leads to a greater distance between the peak point and the
center position. The experimental results are largely consistent
with the simulation analysis.
Experimental Analysis of Different Trapezoidal
Discontinuities
Under the premise that the thickness of the steel plate remains
unchanged at 5 mm, right-angled trapezoidal discontinu-
ities with a depth of 2 mm, a width of 4 mm, and a unilateral
edge angle of 39°, 45°, 53°, 63°, 76°, and 90°, respectively, are
processed. The detection signals obtained from their Hall
sensors are shown in Figures 9a and 9b.
From Figures 9a and 9b, it can be seen that under the same
width and depth, as the edge angle increases, the peak of the
radial signal increases, and the distance from the peak point to
the center of the discontinuity widens more rapidly. Although
the axial signal results are slightly different from the simulation,
they all exhibit a single wave peak, and the peak shifts with
changes in the edge angle. Therefore, the experimental results
are generally consistent with the simulation analysis.
Experimental Analysis of Inner and Outer
Discontinuities
A rectangular discontinuity is machined on the inner surface
of the plate, and a V-shaped discontinuity with different edge
angles is machined on the outer surface. The centers of the two
discontinuities are exactly aligned. The thickness of the steel
plate is maintained at 5 mm, and the width of the discontinuity
ME
|
MAGNETICLEAKAGE
0 10
0
20
40
60
80
100
120
20 30
Scanning point
20
40
60
80
0
–20
–40
–60
–80
40 50 60 70 0 10 20 30
Scanning point
40 50 60 70
90°
76°
63°
53°
45°
39°
90°
76°
63°
53°
45°
39°
Figure 9. Magnetic leakage signal detection of trapezoidal discontinuities with different edge angles: (a) radial signal component (b) axial signal
component.
0 10
0
20
40
60
80
100
120
140
160
20 30
Scanning point
20
40
60
80
0
–20
–40
–60
–80
40 50 60 70 0 10 20 30
Scanning point
40 50 60 70
63°
45°
34°
63°
45°
34°
Figure 10. Magnetic leakage signal detection of inner and outer discontinuities with different edge angles: (a) radial signal component (b) axial
signal component.
38
M AT E R I A L S E V A L U AT I O N • M AY 2 0 2 5
B
(mT)
B
(mT)
B
(mT)
B
(mT)

is set to 4 mm. Magnetic leakage signals at 34°, 45°, and 63°
edge angles were detected using Hall sensors. The results are
shown in Figures 10a and 10b.
Figures 10a and 10b show that the radial signal fluctuates
on both the left and right sides of the peak. Additionally, the
signal peak increases and gradually moves away from the
center of the discontinuity as the edge angle increases. The
peak position of the axial signal shifts toward the side with the
larger edge angle, and the peak amplitude increases as the
edge angle of the discontinuity increases. These experimental
findings confirm the accuracy of the simulation results.
Conclusion
In this paper, the relationship between the edge angle of
V-shaped, trapezoidal, and other shaped discontinuities
and the variation of magnetic leakage signals is theoretically
analyzed, simulated, and experimentally verified. Based on the
in-depth analysis of the research results, the following conclu-
sions are drawn:
1. Whether the discontinuity is V-shaped, trapezoidal, or
inside-outside, both the axial and radial signal components
are influenced by the discontinuity’s edge angle. The specific
finding is as follows: as the edge angle increases, the peaks
of both axial and radial signals rise, and the gap between
the peaks of the radial signals widens. At the same time, the
peak position of the axial signal shifts in the direction of the
increasing edge angle.
2. A linear regression equation between the edge angle and
the position of the peak point of the radial signal is obtained
using the control variable method. This provides a basis for
studying the relationship between magnetic leakage signals
and discontinuity characteristics.
3. Combined with the relationship between the discontinuity
edge angle and magnetic leakage signal, in the future more
advanced algorithms, such as machine learning algorithms,
could be employed to analyze large datasets of magnetic
leakage signals from different discontinuities. This would
help construct a more accurate discontinuity reconstruc-
tion model, improve discontinuity detection accuracy, and
provide strong support for precise discontinuity assessment.
ACKNOWLEDGMENTS
This study was supported by the Science and Technology Program of
Anhui Province Market Supervision Administration in 2023 (2023MK041),
the Talent Introduction Program of Shanghai Institute of Electrical Engi-
neering (B1-0288-20-007-01-32), the project of Shanghai Multi-directional
Die-Forging Engineering and Technology Research Center (20DZ2253200),
and the Shanghai Highland Discipline Preliminary Research and Open
Program.
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