A pot-core eddy current sensor based on DC magnetization

Due to the limitation of the skin effect of traditional eddy current sensors, it is difficult to sense internal defects. This paper proposes a pot-core eddy current sensor based on DC magnetization, which uses DC magnetization to excite the permeability perturbation of internal defects in the surface of samples and uses a pot-core eddy current sensor with higher efficiency to sense the perturbation, thus realizing the detection of defects. The phenomenon of permeability perturbation is analyzed by simulation, and experiments are conducted to verify the performance of the sensor. Also, the effects of magnetizing current and defect size are investigated experimentally. The results show that the sensor can realize the detection of the small internal defect with an unsaturated magnetizing current.


Introduction
A variety of nondestructive testing technologies have been widely applied in the defect detection of tanks, pipelines, wire ropes, etc. to guarantee the safe operation of industrial production, such as ultrasonic testing (UT), magnetic flux leakage (MFL), and eddy current testing (ECT) [1][2][3][4].UT has the advantages of high detection accuracy and large penetration depth; However, it is not sensitive to surface defects and requires the precision surface of samples and coupling medium, which restricts its application [5].Electromagnetic acoustic transducer (EMAT) avoids the problem that traditional UT needs a coupling medium, but has the problem of low energy conversion efficiency [6].MFL uses the change of magnetic field caused by defects to identify defects of saturated magnetized samples and has the advantage of fastly detecting external and internal defects, but it is limited by the magnetic shielding effect and magnetic compression effect [7,8].ECT has the advantages of high resolution and non-contact, but it is difficult to detect deeply buried defects due to the skin effect [9].Although new methods such as remote field eddy current and pulsed eddy current testing have been developed, there is still a problem of low sensitivity in detecting small defects [10,11].Alternating current field measurement (ACFM) can be used for the quantitative evaluation of surface defects [12].However, it is also limited by the skin effect.
Therefore, many detection methods have been developed for detecting deeply buried defects.For example, Gotoh et al. magnetized the steel plate with a DC magnetic field and used a small U-core coil as a probe to conduct AC excitation on the steel plate for detecting defects, and indicated that this method could detect the opposite-side defects with small size [13].Deng et al. found that deeply buried defects would cause permeability perturbation in the surface of ferromagnetic materials with DC magnetization.Thus, air-core and I-core eddy current probes were used to detect internal defects based on sensing the permeability [14].Li et al. studied the quantitative evaluation of buried defects using array eddy current probes based on the permeability perturbation under DC magnetization [15].In conclusion, many internal defect detection methods combined with DC magnetization and air, I-shaped, and U-shaped magnetic core eddy current probes have been proposed.However, there is still a significant need to further improve the detection sensitivity of small internal defects.
It is well known that the pot magnetic core has a higher efficiency because of less magnetic leakage compared with other types of magnetic cores [16].Hence, this paper proposes a pot-core eddy current sensor based on DC magnetization to sense the permeability perturbation caused by internal defects.The basic principle and the experiments of the sensor are presented as follows.

Simulation
The detection principle of the sensor is based on the measurement of the permeability.Therefore, a two-dimensional simulation model was used to study the distribution of electromagnetic characteristics around defects.The simulation model is shown in Figure 1(a), in which the width of the yoke is 20 mm, the thickness of the sample is 8 mm, the number of turns of the DC magnetization coil is 500, and the air gap between the sample and the yoke is 0.1 mm.The relative permeability μ of the sample and yoke followed the magnetization curve shown in Figure 1(b) to simulate the nonlinearity of ferromagnetic material.The cloud charts under different magnetizing currents I were calculated to obtain permeability and magnetic flux line distributions around the defect of the sample.The results are shown in Figure 2, where the internal defect's width and depth are both 2 mm.As shown in Figure 2, when the magnetizing current increases to 1.5 A, a near-saturation magnetization of 1.69 T can be observed, and an obvious leakage magnetic field is formed above the internal defect.However, when the magnetizing current reaches 0.5 A, a relatively obvious permeability perturbation distribution has been formed and transmitted to the surface of the sample.Therefore, it is possible to detect deep defects by detecting the permeability perturbation of the surface of the sample using a small DC magnetizing current.To further study the influence of different size defects on the permeability perturbation, a signal extraction line of 40 mm was set at 0.1 mm from the surface of the sample (y-axis=-0.1 mm), and relative permeabilities of the line were extracted to obtain the permeability perturbation curve.Figure 3(a) shows the permeability perturbation curves of the sample with different internal defect widths w, where the depths of defects are 3 mm and the magnetizing current is 0.3 A. Figure 3(a) indicates that the width of the defect has less impact on the amplitude difference of the permeability curve and has a great impact on the peak width value of that.Figure 3

Experimental equipment
In this section, a pot-core eddy current sensor was proposed to sense the permeability perturbation, and thus the internal defects can be detected.A series of experiments were performed to investigate the pot-core eddy current detection method using DC magnetization.

The testing system
Figure 4 shows the detection system, mainly including a DC magnetization device, an eddy current probe, and detection equipment.The DC magnetizing device is composed of a DC power supply, a pure iron U-shaped yoke, and a DC magnetization coil.The inner distance between the two magnetic poles of the U-shaped yoke is 60 mm, and the outer distance between them is 100 mm.The width of the yoke is 100 mm.The number of turns of the coil is 500.The magnetization of the sample can be changed by adjusting the magnetizing current of the coil.
The eddy current (detection) probe is composed of two coils with the pot-core shown in Figure 4.The excitation and signal pickup are simultaneously realized by the single coil, which has turns of 100.The excitation signal is provided by the eddy current testing device, which also includes amplification, filtering, and signal detection circuits.The output signal of the eddy current testing device, related to the inductances of the coils, is acquired and stored by the acquisition system for further processing.In the next experiments, the excitation frequency of the coil is 15 kHz.The air gap between the yoke and the sample is 0.1 mm.The lift-off value of the detection probe is 0.1 mm.And, the detection device scans the sample along the direction shown in Figure 4.

The samples
The samples are Q235 steel plates, which have a length of 500 mm, a width of 100 mm, and a thickness of 8 mm.There are four rectangular defects on each sample, and the distance between defects is 100 mm.As shown in Figure 5, the length, width, and depth of defects are defined as l, w, and d, respectively.In the experiment, the defects are located on the back side of the sample and away from the surface of the probe to simulate internal defects.

Experimental results and discussion
According to the detection principle, the DC magnetizing current and the size of the defect are closely related to the permeability perturbation of the surface layer.Therefore, the detection signal is directly affected by these important factors.

The effects of magnetizing current
The main advantage of the proposed sensor is to detect internal defects under unsaturated magnetization.Therefore, the experiments with different magnetizing currents were performed, and the results are shown in Figure 6, where the smallest size defect (width=1 mm, depth=1 mm) in the sample is selected as the internal defect.From Figure 6, when there is no DC magnetizing current (I=0 A), the internal defect cannot be identified because of the low penetration depth of traditional eddy current testing.However, the internal defect can be detected after magnetizing the sample, and the detection performance (signal-tonoise ratio) increases with the increasing magnetizing current.In fact, the pot-core eddy current probe mainly measures the permeability and conductivity of the surface layer of the sample because of the skin effect.It is obvious that the surface conductivity is difficult to be disturbed by internal defects.However, if the sample is magnetized, the surface permeability may be disturbed by internal defects, and thus the internal defect can be detected by the pot-core probe.Moreover, the internal defect can be identified with a small DC magnetizing current of 0.3 A, although the signal-to-noise ratio is relatively low.In brief, the proposed sensor can detect internal defects with small sizes under unsaturated magnetization according to the experimental and simulation results.

The effects of defect length
Four defects with different lengths were tested to study the effects of defect length on the detection signal, where the width and depth of defects are 4 mm.In the experiment, the magnetizing current is set to 0.5 A. The detection results are shown in Figure 7.
As shown in Figure 7, the amplitude difference of the detection signal increases with the defect length.The main reason is that the increase in defect length leads to the stronger magnetization state perturbation around the internal defect, which makes the permeability perturbation transmitted to the surface of the sample more obvious, thereby resulting in the eddy current detection signal increasing with the defect length.

effects of defect width
To explore the effects of defect width on the detection signal, the experiments under different defect widths were conducted with the same defect depth of 3 mm and length of 30 mm.The magnetizing current is set to 0.5 A. The excitation frequency of the probe is set to 15 kHz.The experimental results are shown in Figure 8.
Figure 8 shows that the signal amplitude remains roughly unchanged with the increasing defect width.This experimental trend is basically consistent with the trend of the simulated permeability perturbation curves in Figure 3(a).Also note that the signal peak width value (Sw, the normalized distance between the two troughs as shown in Figure 8) increases with the defect width, which is also consistent with the trend of the simulated curves in Figure 3(a).The experiments and simulations indicate that the defect width has less impact on the amplitude of the detection signal and more impact on the peak width value of that.

The effects of defect depth
According to the simulation, the defect depth has a greater influence on the permeability perturbation.Therefore, the experiments with different defect depths (length=30 mm, width=7 mm) were performed to obtain the detection signals of Figure 9, where the other experimental parameters are the same as before.As can be seen from Figure 9, the peak-to-peak value of the defect signal significantly increases with the defect depth.The reason is that the surface permeability of the sample is greatly affected by the defect depth, and the permeability perturbation is enhanced with the growing defect depth according to the simulation results in Figure 3(b), thus resulting in the increase of the detection signal of the pot-core eddy current probe.

Conclusions
Internal defects of magnetized samples will cause the permeability perturbation of the surface layer, therefore eddy current testing can be used to measure the permeability, thereby detecting internal defects.This paper proposes a pot-core eddy current sensor using DC magnetization to further improve the efficiency of the sensor.Experiments and simulation results show that the proposed sensor has the following advantages.
(1) The proposed sensor can detect internal defects with small sizes under unsaturated magnetization or small magnetizing current.
(2) The peak-to-peak value and the peak width value of the detection signal are related to the defect size, which means that the proposed sensor has the potential for quantitative evaluation.

Figure 1 .
Figure 1.(a) The two-dimensional simulation model and (b) the magnetization curve.

Figure 2 .
Figure 2. Permeability and flux line distributions with different DC Magnetizing currents I.
(b) depicts the results under different defect depths d, where the widths of defects are 3 mm and the magnetizing current is 1 A. It can be seen that the amplitude difference of the permeability curve increases with the increasing defect depth.In addition, the baseline of the permeability curve in Figure3(b) has changed greatly.The reason is that the magnetization of the sample is affected by the defects.

Figure 4 .
Figure 4.The diagram of the detection system and the picture of the pot-core eddy current probe.

Figure 5 .
Figure 5. Schematic and picture of the experimental samples.

Figure 6 .
Figure 6.Detection signal under different magnetizing currents I.

Figure 7 .
Figure 7. Detection signal under different defect length l.

Figure 8 .
Figure 8.Detection signal under different defect width w.

Figure 9 .
Figure 9. Detection signal under different defect depth d.
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