The lift-off effect caused by the unevenness of the weld seam surface has always been a drawback due to the high sensitivity of eddy current testing to lift-off, which the eddy current testing needs to overcome. The eddy current field generated by the conventional eddy current probe is perpendicular to the surface of the measured object. When the probe is shaken or scanned in the weld seam area, the coil impedance changes due to the up and down fluctuations of the probe, so that the detection signal obtained by the probe responds at the nondefective position as well. The signal-to-noise ratio of the detected signal also becomes worse [
17]. Based on the principle of eddy current detection, this study found through theoretical analysis that when the relative motion direction of the eddy current field and the defect of the tested part changed, the eddy current field was more uniform than that generated by the conventional probe. The detection coil was only sensitive to the eddy current component parallel to the surface of the measured object, which reduced the impedance change of the eddy current probe caused by the fluctuation during the probe scanning process. It also had a decent suppression effect on the lift-off effect caused by the uneven surface of the weld seam.
According to this principle, the author designed a kind of orthogonal axial probe that could form a tangential uniform eddy current in this study. The probe was composed of two oblong rectangular coils placed orthogonal to each other, as seen in
Figure 1. The excitation coil was placed perpendicular to the surface, and the detection coil was placed axially at the center of the excitation coil, and L is Length, H is Width, and D is Height. Compared with the conventional probe, the magnetic field generated by the eddy current of this probe was parallel to the surface of the test specimen. When passing through the uneven weld seam surface, the direction of the eddy current changed little, and the output signal change value caused by the lift-off was small [
18]. Moreover, the eddy current field generated by the tangential excitation coil was more uniform, making the impedance change sensitivity caused by the lift-off effect less than that of the conventional eddy current probe. When passing through the weld seam area, except for the eddy current disturbance to the defect location, the lift-off effect produced by the remaining weld area had no such disturbance. The detection signal had a high signal-to-noise ratio, obvious defect characteristic signal, and high sensitivity, which, to a certain extent, suppressed the eddy current lift-off effect caused by the unevenness of the weld seam.
Figure 2 shows the UEC distribution when using the orthogonal axial prob. When the probe is detected without defects, the detector coil does not generate the electromotive force (EMF). Furthermore, if the probe is scanning the surface similar to the weld, the lift-off value changes, and the EMF will still be zero value since there is no change of direction of the eddy current flow [
10]. As shown in
Figure 2b. When the flaw is located at the edge of the detection coil, it causes the current of the detection coil to change and produces an output, as shown in
Figure 2c. When the flaw is in the middle of the probe, since the electromotive force of the same amplitude is generated on both sides, but the polarities are opposite, this is the output of the detection coil is zero, and this phenomenon is called self-nulling.
2.1. Simulation Model Establishment
In this study, COMSOL Multiphysics was used to establish a carbon steel weld seam defect detection model so as to study the suppression effect of the orthogonal axial probe on the unevenness of the weld seam area and the directionality of the eddy current field generated by the probe on the carbon steel plate surface. The simulation model consists of a circular air domain, excitation coil and detection coil, and carbon steel plate, and the parameters and materials are shown in
Table 1 and
Table 2. The simulation uses the infinite element domain in the setting of the physical field boundary conditions to realize the approximate simulation of the electromagnetic field and uses the impedance boundary conditions for the carbon steel plate specimens, which reduces the calculation difficulty and realizes the analysis of the characteristics of the eddy current. Physics is used to control meshing, and the mesh size is refined. The physical field is selected as the magnetic field under the AC/DC module, and researched and solved in the frequency domain. The above simulation analysis is based on the magnetic vector potential method. In this method, the magnetic scalar potential
Ω and current vector potential
T are used to represent the electromagnetic field [
16]. The equation involving the method are expressed by Ampere’s law, Faraday’s law, and constitutive relation:
where the various quantities are defined as
: Electric field intensity (V/m)
: Magnetic field intensity (A/m)
: Magnetic flux density (T)
: Current density (A/m2)
: Time (s)
: Permittivity (F/m)
: Magnetic permeability (H/m)
: Conductivity (S/m)
Substituting Equation (4) into Equation (1) results in the following equation:
Substituting Equation (2) into Equation (5) After eliminating
:
Finally, by substituting Equations (3) into Equation (6), the governing equations are obtained:
It can be seen from Formula (4)
The software is used together with Equations (7) and (8).
The simulation uses the infinite element domain to realize the approximate simulation of the electromagnetic field. The impedance boundary condition is adopted in the physical field boundary condition setting, which reduces the calculation difficulty and realizes the approximate distribution characteristic analysis of the eddy current.
Through simulation, it was found that when the lift-off value is 0.5 mm, the sensitivity of the detection coil increased with the number of turns in a certain range. However, when the number of turns continued to increase, it instead affected the probe sensitivity because the probe impedance and heat generation increased [
17]. Therefore, the probe turns were set as 200 turns through the previous relevant tests. At this time, the probe sensitivity is better.
The excitation coil parameters are L1 = 7 mm, H1 = 5 mm, and D1 = 2 mm. The detection coil parameters are L2 = 5 mm, H2 = 3 mm, and D2 = 2 mm. Models were made by COMSOL Multiphysics to study the effect of the orthogonal axial probe on the welding seam area scan so as to suppress the lift-off effect. Moreover, an orthogonal axial probe was constructed on the defect-free carbon steel plate specimen (l = 40 mm, w = 40 mm), to carry out the physics simulation analysis and comparison of a conventional circular eddy current probe of a similar size. First, place the conventional circular probe and orthogonal axial probe above the carbon steel plate with a lift-off value of 0.5 mm. Use 5 V AC voltage and 100 kHz frequency sine wave to excite the excitation coil. After solving, set up and extract the modulus of current density generated by the two probes on the surface of the carbon steel plate.
Figure 3a shows the distribution diagram of the surface current density modulus produced by the conventional circular probe, and
Figure 3b shows the distribution diagram of the current density modulus produced by the orthogonal axial probe. The numerical value of the intensity distribution of the eddy current field generated by the probe was obtained by dividing the contour of the simulation. Compared with the current density mode generated by the conventional circular eddy current probe, the orthogonal axial probe was placed on the side, so that the generated eddy current field passed tangentially parallel through the surface of the carbon steel plate. The intensity distribution of the eddy current field was uniform, while the amplitude of the eddy current field produced by the conventional circular eddy current probe differed much. The difference in the magnitude of the eddy current field generated by the probe was extracted, calculated by Formula (9).
where
is induced eddy current fluctuation difference.
is maximum induced eddy current density (A/m
2).
is minimum induced eddy current density (A/m
2).
The difference in the magnitude of the eddy current field generated by the probe was extracted, and the center amplitude difference of the eddy current field of the conventional circular probe was about 56% larger than that of the orthogonal axial probe. The orthogonal eddy current field distribution of the orthogonal axial probe passing through the defect-free flat plate was found to be more uniform than that of the conventional circular probe, and the eddy current field intensity uniformity was better.
Based on the data in
Table 1, the author establishes a simulation model to compare the uniformity of the eddy current field distribution on the uneven weld seam defects between the conventional circular probe and the orthogonal axial probe. As shown in
Figure 4, the model uses a surface with a bump to simulate a real, uneven weld surface, the crack defect is below the probe, so as to simulate the scene when the probe is scanning the uneven surface of the weld
In order to compare with the simulation results in
Figure 3, we placed the probe in
Figure 3 on the carbon steel plate with welding crack defects under the same excitation conditions and model conditions, and extracted the modulus of current density on welding crack defects. In
Figure 5. When scanning the uneven weld seam defects, the eddy current field generated by the orthogonal axial probe was far more uniform than that generated by the conventional circular probe. The difference in amplitude intensity of the eddy current field was obtained by dividing the contour. The amplitude difference in the eddy current field intensity of the conventional circular probe was calculated to be about 43% larger than that of the orthogonal axial probe, indicating that the eddy current uniformity of the orthogonal axial probe was also better than that of the conventional circular eddy current probe in the process of scanning the uneven weld seam defects.
In addition, the high permeability of the carbon steel plate resulted in the lower penetration depth of the eddy current. Part of the eddy current field generated by the orthogonal axial probe was distributed on the surface of the carbon steel plate [
19], and the rest of the eddy current field passed tangentially through the weld seam surface of the carbon steel plate, making the distribution of the eddy current field in the detection area uniform. Furthermore, the probe had the effect of self-compensating the reverse eddy current field when detecting uneven surfaces because of its symmetrical distribution, so that it could better suppress the lift-off effect caused by the weld seam unevenness when scanning the uneven weld seam area.
2.2. The Influence of Coil Width on Output Signal
Probe sensitivity is important in judging how good the detection effect is. Many factors influence the sensitivity of the probe, including the size of the coil, number of turns, distance between the coils, distance of the probe lift-off, and size of the excitation signal [
20,
21]. This study compared the absolute average value of the amplitude obtained after the probe scans for defects to explore the detection sensitivity of the probe, in Formula (10).
The values of
and
are the maximum amplitude and minimum amplitude during scanning. Here are the maximum and minimum values of the simulated waveform during the parametric sweep in the simulation, as shown in
Figure 6 for the highest point value and the lowest point value of each waveform. In this study, the amplitude of the simulated scanning was determined by parameterized scanning, and the absolute average values were obtained and compared. The detection coil size of the probe was the most important influencing factor for sensitivity. The coil size needs to be designed to ensure the maximum sensitivity of the probe [
22]. This study used COMSOL Multiphysics software to explore the relationship between the size of the excitation coil and the sensitivity of the probe. The excitation and detection coils were initially set as L
1 = 7 mm, H
1 = 3 mm, D
1 = 2 mm, and L
2 = 7 mm, H
2 = 3 mm, D
2 = 2 mm to ensure that the detection coil had enough space to change the size of the excitation coil.
The influence of the detection coil width H
2 on the probe sensitivity was studied without changing other data. Input with an excitation voltage of 5 V and an excitation frequency of 100 kHz. The size of the excitation coil remains unchanged, increase the detection coil width H
2 from 3 mm to 6 mm at step of 0.5 mm. The weld seam crack defects dimensions,
l = 20 mm,
w = 0.3 mm, and
h = 2 mm. Furthermore, scan parametrically from 5mm on the left of the defect to 5 mm on the right of the defect. The analog scan waveform is shown in
Figure 5. Among them, Y/V means that the unit of Y axis is V, which represents the value of the induced voltage of the detection coil to simulate scanning defects. X/mm means that the unit of X axis is mm, which means the distance the probe moves.
From the aforementioned Equation (9), the equivalent amplitude measured by the probe at each width and the relationship change graph between the coil width and the sensitivity could be obtained in
Figure 7.
In the process of coil width change from 3 mm to 6 mm, it was found that when the probe coil width was between 3 mm and 4.5 mm, the sensitivity growth rate was approximately linear, while at 4.5 mm and 6 mm, the sensitivity still increased as the coil width increased, but the growth rate declined. In addition, if the coil width was too large, the size of the missed detection was relatively small, so it was not suitable to make an array probe. Therefore, this study selected 4.5 mm as the detection coil width, and the coil layer thickness was 1 mm, that is, the inner diameter width was 2.5 mm.
2.3. The Influence of Coil Length on Output Signal
While keeping other parameters unchanged, the inner diameter of the detection coil was set to 2.5 mm, and then the simulation analysis of the detection coil length and the detection sensitivity was carried out. With the same input conditions as above, increasing the detection coil length L
2 from 5 mm to 11 mm at step of 1 mm, and scan parametrically from 7 mm on the left of the defect to 7 mm on the right of the defect. The analog scan waveform is shown in
Figure 8.
The amplitude of the probe’s simulated scanning waveform was substituted into Equation (9) to find the equivalent amplitude of the probe in each length change interval and obtain the relationship change diagram between the coil length and the sensitivity in
Figure 9.
The
Figure 9 shows that when the detection coil length was 5–8 mm, the probe sensitivity increased with the increase in the coil length, and when the length was 8–11 mm, the probe sensitivity hardly changed. In addition, in actual inspection work, large-sized coils tended to miss small defects and had a low resolution. After comprehensively considering the resolution, sensitivity, missed detection, and other issues, this study selected 7 mm as the length parameter of the detection coil.
This study found that the detection coil sensitivity of the orthogonal axial probe increased with the increase in the coil width and length within a certain range. However, as the coil length continued to increase, the coil sensitivity tended to decline. Combining the simulation analysis results, the characteristics of the defects in the actual detection work, and the requirements of the coil size itself, it could be determined that when the coil width was 5 mm and the length was 7 mm, the coil sensitivity was strong, the size was suitable, the probe resolution was decent, and the overall performance was the best. Finally, the size of the orthogonal axial probe coil was selected in
Table 3.
2.4. The Influence of Scanning Mode on Output Signal
The distribution of the eddy current field generated was not the same as that of the circular coil and was a nonaxisymmetric eddy current field since the structure of the rectangular coil was different from that of the circular coil. When performing defect detection, the magnetic field excited by the probe had a directional characteristic so that the magnetic field intensity was a value obtained by adding the magnetic field vectors in different directions [
23]. The orthogonal axial probe was studied theoretically and through the magnetic field and eddy current field simulation to explore the position of the maximum magnetic field intensity during the probe scanning process.
First, the coil size determined in
Table 3 was selected to simulate the magnetic field distribution. The X-component cloud image of the probe’s magnetic field on the surface of the test piece was studied. The direction of the magnetic field component had a certain angle with the direction of the defect. Similarly, the Y-component cloud image of the magnetic field had the same angle. The position of the vector sum of the largest magnetic field component between the orthogonal axial probe and the defect during the scanning of the defect was studied by changing the direction coefficient of the magnetic field relative to the defect when the probe detected the defect, that is, changing the detection angle of the probe scanning defects. In
Figure 10, it shows the surface current density mode distribution when the probe and the crack defect formed an angle of 45°. Compared with
Figure 4b, the eddy current intensity of the defect position after the probe had a deflection angle of 45° was found to be higher than the eddy current intensity of the defect position without the deflection. Similarly, after simulating the random angle, the comparison chart of the eddy current intensity at the defect showed that the eddy current intensity of the defect detection when the probe had a deflection angle was greater than the eddy current intensity when the probe had no deflection. However, the intensity of the eddy current changed as the angle changed, indicating a maximum value of the magnetic field intensity.
The excitation probe was placed in parallel with the simulated defect in the simulation test software, the initial angle was set to 0°, and the step was 10° to get the best sensitivity of the probe scan and make the vector sum of the magnetic field components reach the maximum value. The variation range being 0°–90°.
Figure 11 shows the top view of the model when the scanning angle of the orthogonal axial probe scanning defects was 0°, 30°, and 60°. The red line in the figure represents the vector sum of the magnetic field in the X and Y directions when the probe scanned for defects at different rotation angles.
As shown in
Figure 12, the simulated scan waveform is obtained by the scan parametrically from 5 mm on the left of the defect to 5 mm on the right of the defect. Then, the sensitivity of the probe was calculated at each angle from the obtained data, and the relationship between the probe scanning angle and the probe sensitivity was obtained, in
Figure 13. During the rotation of the probe, when the angle was 0°–30°, the sensitivity increased with increasing angle, while when it exceeded 30°, the probe sensitivity decreased with increasing angle.
The simulation proved the existence of the vector sum of the magnetic field of the orthogonal axial probe and the influence of the scanning angle of the orthogonal axial probe on the sensitivity of the probe in the scanning mode. At the same time, it was found that when changing the angle between the probe and the defect, the sensitivity changed with the angle, and the sensitivity of the probe was the strongest when the deflection angle is 30°. Therefore, when we use the orthogonal axial probe, we can rotate the probe 30° for scanning inspection.