As shown in
Figure 4, the primary factors affecting the output signal of the proposed eddy current sensor and the capability of detection system are considered. These include the excitation frequency
f, the coil parameters (especially the outer diameter of coil
dos), lift-off distance
h (distance between the bottom surface of the coil and the specimen), and the dimension of weld (the thickness of core panel
wc, the gap distance
g, thickness of cover panel
d). As shown in Equation (1):
where
Z is the coil impedance of eddy current sensor,
f is excitation frequency,
dos is coil outer diameter,
d is thickness of cover panel,
wc is thickness of core panel;
g is the gap distance; and
h is the lift off distance.
In this paper, a series of experiments about the influence of the above factors on the output signal of proposed sensor were carried out on the T-joint of a titanium alloy specimen. The experimental results were analyzed together with simulation results.
3.1. Excitation Frequency f
The key to detect the T-joint position based on eddy current technology lies in locating the core panel under the face panel. The excitation field by the eddy current sensor must be capable of penetrating through the face panel and exciting eddy current in the core panel whose current intensity is sufficient to be detected by the sensor. Considering the skin effect, the excitation frequency had a predominated effect on the depth of penetration of eddy current sensor and detection sensitivity.
In order to determine the optimal excitation frequency for the sensor to obtain the highest sensitivity, a series of experiments were carried out with different exciting frequencies from 20 to 40 kHz for the lift off distance of 0 mm. The specimen consisted of a 3 mm-thick TC4 cover panel and a 5 mm-thick TC4 core panel, and the gap distance was 0 mm. The outer diameter of the sensor coils was 20 mm.
As shown in
Figure 5, when the exciting frequency increased from 20 to 32.5 kHz, the output signal became more sensitive to the distance from the seam center. When the frequency was increased to 32.5 kHz, the change in output became the most significant. On the contrary, for the frequency higher than 32.5 kHz, the output signal decreased. Therefore, a frequency of 32.5 kHz was decided to be the optimal exciting frequency of a given specimen.
This paper simulated the distribution of eddy current density in the specimen with different excitation frequencies varying from 20 to 40 kHz based on COMSOL multiphysics. The parameters of the excitation signal and materials are listed as
Table 1 and
Table 2. The other simulation parameters were consistent with above experimental parameters.
Figure 6 shows the distribution of eddy current density along the cross section of specimen while the center of sensor was aligned to the center of core panel. A point
P was located at the center of core panel at a distance of 1 mm from the upper face of core, and the eddy current density at this point was capable of representing the eddy current distribution in the upper area of the core panel.
Figure 7 shows the eddy current density at point
P under variable excitation frequencies. Since the proposed sensor is a self-comparative sensor, the output signal of the sensor was determined by the eddy current density in the upper area of the core panel. The higher excitation would not produce a larger output signal of sensor. While the excitation frequency increases, the eddy current density near the sensor would increase and the eddy current density also decays faster along the depth. When it reaches the core panel, the eddy current density will be smaller than that of the lower excitation frequency. As shown in
Figure 7, with the increase of the excitation frequency, the eddy current density would firstly increase and then decrease. The density was the largest at the excitation frequency of 32.5 kHz. The impedances of the coil L and coil R were separately 112.5 Ω and 113.6 Ω. The difference between impedances of two coils also reached the peak simultaneously.
There is an inverse relationship between the penetration depth of the eddy current sensor and the square root of excitation frequency [
24]. As shown in Equation (2), for a specimen made of given material, the higher excitation frequency leads to the smaller penetration depth of sensor. On the other hand, the induced current density is proportional to the frequency within the range of penetration depth of sensor (see the
Figure 6). The sensitivity of the proposed detection method of the T-joint is determined by the cumulative intensity of the eddy current density in the core panel in the depth and radial directions. Therefore, the appropriate excitation frequency should be determined by the tradeoff between the sufficient penetration depth in the cover panel and the enough induced current density of in the core panel along the depth (the upper area of the core panel). When the cumulative intensity of eddy current density in the upper area of the core panel (sensitive volume of sensor) reaches the maximum and the sensitivity of proposed detection method at this time would be best.
where
hp is the standard penetration depth of sensor,
f is excitation frequency,
σ is electrical conductivity of specimen, and
u0 is the permeability of vacuum, taken as
× 10
−7 h/m.
ur is the relative permeability.
The electrical conductivity σ of titanium was 7.047 × 10
5 s/m and the relative permeability
ur was 1. These parameters were substituted into Equation (2) and the standard penetration depth
hp was 3.24 mm. This depth is approximately equal to the thickness
d of the cover panel.
Several experiments were performed on the aluminum alloy specimen at different excitation frequencies [
23]. The specimen consists of a 3 mm-thick cover panel and 10 mm-thick core panel of the 6061 aluminum alloy. The experiments are carried out from 500 to 2000 Hz with the interval of 500 Hz. The experimental result indicates that the detection sensitivity was highest when the excitation frequency was 1500 Hz. The electrical conductivity σ of 6061 aluminum alloy was 2.265 × 10
7 s/m, these parameters were substituted into Equation (2), the standard penetration depth
hp was 2.52 mm, which was also close to the thickness of the cover panel.
The sensitivity of the proposed detection method of the T-joint was determined by the cumulative intensity of eddy current density of sensitive volume in the core panel. With the increase of the excitation frequency, the eddy current density in the core panel would first increase and then decrease. Thus, the optimal excitation frequency could be acquired to penetrate the cover panel and induce sufficient eddy current density of sensitive volume in the core panel. According to Equations (2) and (3), an approximate optimal frequency could be estimated, and then the optimal frequency can be obtained by testing under multiple frequencies around the estimated approximate frequency.
3.2. Coil Outer Diameter dos
As described in
Section 2, the seam center could be determined by the center of two locations with the maximum amplitude values. With the spacing of two separated maximum value decreased, the shorter scanning distance along the cross section of T-joint in single scanning period would be required to determine the center position of weld. The dynamic performance of the proposed detection method would be improved. This paper studies the influence of variable coil outer diameters on the detection results.
In order to analyze the influence of variable coin outer diameters on the sensor output signal, several experiments were carried out with changing coil outer diameters of sensor as shown in
Table 3.
Figure 6 shows the amplitude curve of sensor output signals for variable outer diameters.
Table 4 lists the distance between separated maximum values of output signal for variable outer diameters. The experimental results indicate that the distance between separated maximum values increased with the increase of the coil outer diameter. The ratio of the max-to-max distance to the coil outer diameter was approximately 1.0. When the coil outer diameter was 10 mm, the distance between separated maximum values was 10.3 mm, the ratio of diameter to max-to-max distance was 0.97; when the coil outer diameter was 15 mm, the distance between separated maximum values was 15.4 mm, the ratio of diameter to max-to-max distance was 0.97. When the coil outer diameter of sensor was 20 mm, the distance between separated maximum values was 19.6 mm, and the ratio of the diameter to the max-to-max distance was 1.02.
As shown in
Figure 8, the center of the core panel was aligned with the center of the coil L of the sensor while the offset distance between the center of sensor and core panel was 0.5 ×
dos. The sensitive volume of the specimen within the detection range of the coil L reached the maximum. Thus, the effect of the specimen on the equivalent impedance of the coil L also reached the maximum, which led to the maximum difference between equivalent impedances and voltage of coil L and coil R.
Figure 9 shows the inductance curves of the separated coils of sensor during single scanning of the weld seam.
As shown in
Figure 10, with the increase of the coil outer diameter, the hump widths on both sides of the sensor output signal increased gradually. The radial detection range of the eddy current sensor is proportional to the outer diameter of the coil, and the radial sensitive range of the sensor is determined by the outer diameter of the coil [
25].
In summary, the distance between the separated maximum values of the output signal in a single scanning period is determined by the coil outer diameter of sensor. The other parameters such as inductance and resistance have little influence on the max-to-max distance. Compared with the electrical parameters, the dimensions of sensor coils are easier to keep consistent in manufacturing process of different coils, which is helpful to ensure the symmetry of maximum values and detection stability of the proposed method. The reduction of coil outer diameters not only increases the sensitivity but also weaken the anti-noise performance of the detection. Therefore, it is necessary to comprehensively consider the outer diameter of the coil according to the noise level and dynamic requirements during the detection process. The sensors with smaller outer diameter coils should be selected in the actual detection process on the premise of the anti-noise performance. The smaller sensors would be helpful to shorten the scanning distance along the cross section of the weld and increase the scanning frequency. The higher scanning frequency would increase the number of feature points obtained in unit time and improve the recognition accuracy of whole weld seam.
3.3. Lift off Distance h
Lift-off effect is one of the most influential factors to be overcome in eddy current testing. In this paper, several experiments with different lift-off distances from 0 to 2 mm are performed.
As the lift off distance increased from 0 to 2 mm, the maximum values of the output signal decreased from 8.9 to 3.1 mV. As shown in
Figure 11, the exponential function and linear function were respectively utilized to fit the relationship between the lift off distance and the maximum value of sensor output signal. The mean squared error of the exponential fit was 0.08 while the mean squared error of the linear fit was 0.04. The linear fit was more accurate than the exponential fit.
Keeping the other influence parameters of the eddy current sensor fixed, the output voltage
Vl and
Vr of coil L and coil R could be regarded as a single-valued function of the lift off distance
h. The relationship between the coil voltage and the lift off distance within a small range is nearly linear. The relationship could be expressed as:
where
Vl is the output voltage of coil L;
K1 is the influence coefficient of the lift off distance on the coil L alone,
h is the lift off distance;
Vr is the output voltage of coil R; and
K2 is the influence coefficient of the lift off distance on the coil R alone.
Therefore, the relationship between the sensor output signal and the lift off distance is nearly linear:
3.4. The Dimensions of Specimen
3.4.1. Thickness of the Core Panel wc
As one of the dimensional parameters of the weld, the thickness of the core panel is also a primary factor affecting the output signal of the sensor. In this paper, several experiments were carried out on joints with different thicknesses of core panel, and the output signals of sensor were tested. The specimen consisted of a 3 mm-thick TC4 titanium alloy cover panel and TC4 titanium alloy core panel with different thickness (5 mm, 7 mm, and 10 mm).
As the thickness of core panel increased from 5 to 10 mm, the maximum value of the output signal gradually increased from 8.9 to 33.7 mV. Due to the increase of the thickness of the core panel, the sensitive volume of the core panel within the detection sensitive area of the eddy current sensor increased significantly. Thus, the thicker thickness of core panel would lead to the increase of detection sensitivity of the sensor while the other influence parameters of the sensor kept fixed.
3.4.2. The Gap Distance g
The gap distance is an important process parameter, which is critical for the quality of the weld. Ideally, the gap distance should be kept constant during the welding process. Nevertheless, considering assembly deformation of specimen and welding deformation during the welding process, the gap distance would change in the process. The fluctuation of the gap distance will adversely affect the quality of the weld.
Several experiments with different gap distances were carried out in this paper. The gap distance varied from 0 to 2 mm at a spacing of 0.5 mm.
Figure 12 shows the amplitude curves of sensor output signal under variable gap distances. As the gap distance increased from 0 to 2 mm, the maximum values of the output signal were reduced from 8.9 to 3.3 mV. In the meanwhile, the distances between the separated maximum values increased from 15.4 to 19.1 mm.
3.4.3. Thickness of the Cover Panel d
Several experiments were carried out on the specimen with different thicknesses of cover panel. The face panel was made of TC4 titanium alloy with a thickness varies from 3 to 5 mm, while the core panel was made of 5 mm-thick TC4 titanium alloy.
Figure 13 shows the amplitude curves of sensor output signals under different thicknesses of the cover panel. The maximum values of the sensor output signals decreased from 8.9 to 2.1 mV with the increase of thickness of cover panel from 3 to 5 mm, the detection sensitivity also decreased. With the same increase, the cover panel thickness had stronger attenuation effects than the gap and liftoff distance on the output signal.
According to the Equations (2) and (3), we concluded that the optimal excitation frequency was not only related to the electrical conductivity and magnetic permeability of the specimen, but also inversely proportional to the square of the thickness of the cover panel. The effect of different material properties on the optimal excitation frequency was verified above on an aluminum/titanium alloy specimen with the same thickness of the cover panel. To verify the influence of the thickness of the cover panel on the optimal excitation frequency, we changed the thickness of cover panel and performed the detection experiments on the specimen with different excitation frequency. The specimen consisted of a 2 mm-thick TC4 titanium alloy cover panel and a 4 mm-thick TC4 titanium alloy core panel. The gap distance was 0 mm. The coil outer diameter was 10 mm. The excitation frequency varied from 50 to 80 kHz. The lift-off distance was kept 0 mm. As shown in
Figure 14, the detection sensitivity reached the peak at the frequency 70 kHz. According to the Equation (2), the penetration depth reached 2.21 mm, which was close to the thickness of the cover panel.