Rectangular wave eddy current testing using for imaging of backside defects of steel plates

Abstract

Accurate, easy, and fast inspection of defects on the backside of thick steel plates is essential for the maintenance of infrastructures. Low frequency eddy current testing (LF-ECT) is a promising method to detect defects of the backside of steel plates, with a thickness of approximately 10 mm. However, it is possible that the signal from the backside defect is smaller than that from the surface magnetic noise, causing difficulty identifying the backside defect. In this study, we propose a method to reduce the surface noise by employing a square wave inverter to generate a harmonic signal (rectangular wave ECT, or RECT), and the result demonstrates that the surface noise is successfully reduced using the harmonic signal.

Keywords

Eddy current testing ferromagnetic material low frequency square wave inverter rectangular wave ECT

1. Introduction

Since over half a century has passed for rapid economic growth, maintaining industrial infrastructures has become a problem. Moreover, developed countries will become a full-fledged aging society. Therefore, the shortage of maintenance personnel is a significant concern. As a result, accurate, easy, and fast inspection methods are required for maintaining infrastructures.

Most of these infrastructures are made of steel. Therefore, eddy current testing (ECT) is useful to detect surface defects in steel structures because it does not need to conduct the sensor to the specimen, and it utilizes a compact instrument [1,2]. Although ECT is widely used for non-destructive testing (NDT) of conductive specimens, conventional ECT is limited to the detection of surface or subsurface defects owing to the skin effect especially when ECT is applied to ferromagnetic materials such as steel. Moreover, steel plates with a thickness greater than 10 mm are often used for large infrastructures. Therefore, low-frequency ECT (LF-ECT) is essential for examining the deeper, or backside defects of a thick ferromagnetic specimen [3–9].

Even though LF-ECT can detect the backside defect, it is possible that the signal from the backside defect is smaller than that from the surface magnetic noise. Therefore, it is difficult to detect backside defects. In previous studies, we recently proposed a simple method to emphasize the deeper defects using excitation current, which consists of two sinusoidal waves [9].

On the other hand, a rectangular wave (or square wave) contains harmonic as well as fundamental sinusoids. We previously demonstrated that an ECT system using a square wave inverter (ECT using rectangular wave current or voltage will be referred to rectangular wave ECT or RECT) can estimate the thickness of a steel plate; in other words, it can detect thinning in steel plates using harmonic as well as fundamental sinusoids [10]. Note that the harmonic and fundamental signals can be simultaneously obtained. In other words, we can obtain much information by using a rectangular wave excitation than using a sinusoidal wave excitation. Moreover, an inverter is more efficient, smaller, and lighter than a linear amplifier, which is often used for generating sinusoidal waves. Therefore, using a square wave inverter contributes to the development of a handheld ECT system as well as cost reduction.

In this paper, we evaluate employing a rectangular wave excitation for LF-ECT systems, or LF-RECT systems, to reduce surface magnetic noise and focus on detecting deeper defects using harmonic sinusoids.

2. Methods

Figure 1 shows the overview of the experimental setup of the developed LF-RECT system, which is based on the system we have reported in [9].

Fig. 1.

Experimental setup of the LF-RECT system.

2.1. Probe

Table 1 shows the detail specifications of the excitation and pickup coils shown in Fig. 1. Two excitation coils with 50 turns were arranged 5 mm above the steel plate, and the distance between the two excitation coils was 50 mm. One pickup coil with 300 turns was placed between these excitation coils to obtain the magnetic flux density of the z component, B.

Table 1
Specifications of the excitation and pickup coils

Excitation coil Pickup coil

Outer diameter 45 mm 10 mm

Inner diameter 30 mm 6.0 mm

Height 3.0 mm 3.0 mm

Diameter of wire 0.56 mm 0.10 mm

Number of turns 50 300

Resistance 0.44 Ω 16.4 mΩ

Inductance 0.23 mH 0.64 mH

	Excitation coil	Pickup coil
Outer diameter	45 mm	10 mm
Inner diameter	30 mm	6.0 mm
Height	3.0 mm	3.0 mm
Diameter of wire	0.56 mm	0.10 mm
Number of turns	50	300
Resistance	0.44 Ω	16.4 mΩ
Inductance	0.23 mH	0.64 mH

In accordance with our previous study [8,9], the direction of the excitation currents of both excitations coils was identical, as shown in Fig. 2. Note that a magnetic core is not required in the proposed system, i.e., the excitation and detection coils are not required to contact the specimen.

The excitation and detection coils were moved simultaneously by 5 mm for 1 s using two-axis motorized stages (OSMS26-300(XY), Sigma-koki Co., Ltd.) in the range 𝛺 ∈{x, y|− 75 mm ≤ x ≤ 75 mm, −75 mm ≤ y ≤ 75 mm} and the magnetic flux density B (x, y) was measured.

Fig. 2.

Direction of the excitation current.

Fig. 3.

Photo of the coils, specimen, and motorized stage.

2.2. Control and measurement system

A rectangular wave was generated using a D/A converter (National Instruments Corporation NI 9260, 24 bit, 51.2 kS/s). The signal was amplified with a bipolar power supply (NF Corporation HSA4014). The output amplitude of the voltage, E, was set to 20 V. A resistance of 10 Ω is connected to the excitation coil in series, which is greater than the impedance of the excitation coil. Therefore, the output current amplitude was approximately 2 A. The frequency f₀ was set to 4 Hz or 8 Hz taking into account the result in the previous study [9]. The excitation current i (t) was measured using a shunt resistor (1 mΩ). The voltage was amplified with an isolation amplifier (NF Corporation 5325) and was measured using an A/D converter (National Instruments Corporation NI 9239, 24 bit, 50 kS/s). The output voltage of the pickup coil was amplified with a low-noise preamplifier (NF Corporation SA-400F3) and subsequently fed to the A/D converter. The D/A and A/D converters were set in the CompactDAQ chassis (National Instruments Corporation cDAQ-9171), and the modules were controlled using the LabVIEW software. The k-th harmonics of v (t) and i (t), or $\dot{V}_{k}$ and ${\dot{I}}_{k}$ were calculated by using fast Fourier transform (FFT). Subsequently, the harmonics of B, ${\dot{B}}_{k}$ was calculated using $\dot{V}_{k}$ using the Faraday’s electromagnetic induction law as follows: $\begin{eqnarray}\displaystyle {\dot{B}}_{k}=-\frac{\dot{V}_{k}}{j2{\pi}kf_{0}NS} & & \displaystyle\end{eqnarray}$ (1) where j is the imaginary unit ( $j=\sqrt{-1}$ ), N is the number of the turns of the pickup coil (N = 300), and S is the effective sectional area (S = π((6 +10)∕4)² ≈50.3 mm²).

Note that the excitation voltage e (t) can be expressed by using a Fourier series as follows: $\begin{eqnarray}\displaystyle e(t)={\displaystyle \frac{4E}{{\pi}}}\left(\sin {\omega}_{0}t+{\displaystyle \frac{1}{3}}\sin 3{\omega}_{0}t+{\displaystyle \frac{1}{5}}\sin 5{\omega}_{0}t\cdots ∼\right), & & \displaystyle\end{eqnarray}$ (2) where ω₀ =2πf₀. Equation (2) indicates that the fundamental component is 4E∕π ≈1.27E.

To emphasize the deeper or backside defects, we obtained the differential signal as follows [9]: $\begin{eqnarray}\displaystyle {\Delta}{\dot{B}}_{k1,k2}={\dot{B}}_{k1}-w{\dot{B}}_{k2}, & & \displaystyle\end{eqnarray}$ (3) where w is the weight parameter. In this study, w is empirically chosen as 1.4 taking into account our previous study [9]. Furthermore, the in-phase (real part) and out-of-phase (imaginary part) components of the magnetic flux density, $\text{Re}[{\dot{B}}_{k}]$ and $\text{Im}[{\dot{B}}_{k}]$ , were obtained.

To compare the square and sinusoidal waves, a sinusoidal wave with an amplitude of 2 A is also generated by using the D/A converter, and ${\dot{B}}_{1}$ was obtained in the same manner.

2.3. Control and measurement system

We used an SM490A steel plate as a test specimen. The relative permeability μ_r was approximately 200, and the conductivity σ was 4.1 ×10⁶ S/m. The size of the steel plate was 300 mm × 300 mm × 12 mm.

A defect of length D_l, width D_W, and height D_h was made on the center of the backside of the steel plate using electrical discharge machining. The defect size was set to D_l = 50 mm, D_W = 1 mm, and D_h = 2–12 mm.

3. Results and discussion

3.1. Comparison between square and sinusoidal waves

Figures 4(a)–(c) show the result of $\text{Im}[{\dot{B}}_{1}]$ , $\text{Im}[{\dot{B}}_{3}]$ , and $\text{Im}[{\dot{B}}_{5}]$ , respectively, when D_h = 4 mm and the rectangular wave current (f₀ = 4 Hz) is used. Figures 4(d)–(f) show the result of $\text{Im}[{\dot{B}}_{1}]$ when the sinusoidal wave current is used and f₀ = 4, 12, and 20 Hz, respectively, and these frequencies correspond to the fundamental, third, and fifth harmonic signals of the rectangular wave when f₀ = 4 Hz.

As shown in Figs. 4(a) and (d), the distributions are almost identical, which indicate the that rectangular wave current is applicable instead of the sinusoidal wave current. The signals from the backside defect appear at the center. However, the other signals also appear in the vicinity at (x, y) = (40 mm, 60 mm), which is assumed to be surface noise. The peak of $\text{Im}[{\dot{B}}_{1}]$ in Fig. 4(d) is 1.92, whereas that in Fig. 4(d) is 1.56. The overall ratio is 1.92∕1.56 = 1.23, which corresponds to the ratio of the fundamental component (4∕π ≈1.27) shown in Eq. (2).

Furthermore, comparing Figs. 6(b) and (e) and Figs. 6(c) and (f), the third and fifth harmonic signals of the results of the rectangular waves are almost identical to the results of the sinusoidal waves that correspond to the same frequency. As shown in Figs. 6(b), (c), (e), and (f), the signals from the surface defect dominantly appear in the vicinity at (x, y) = (40 mm, 60 mm).

Fig. 4.

Results of the imaginary part of the magnetic flux density distribution when D_h = 6 mm. (a)–(c) correspond to $\text{Im}[{\dot{B}}_{1}]$ , $\text{Im}[{\dot{B}}_{3}]$ , and $\text{Im}[{\dot{B}}_{5}]$ , respectively, when the square wave current is used and f₀ = 4 Hz. (d)–(f) correspond to $\text{Im}[{\dot{B}}_{1}]$ when the sinusoidal wave current is used and f₀ = 4, 12, and 20 Hz, respectively.

3.2. Comparison between square and sinusoidal waves

Figure 5 shows the result of the imaginary part of the differential magnetic flux density distribution of the third and fifth harmonics when D_h = 6 mm and f₀ = 4 Hz to emphasize the backside defect using Eq. (3). As shown, the surface noise can be successfully reduced using both the third and fifth harmonic signal. Especially, the noise that appears when y >0 mm and y <0 mm is more successfully reduced using the third harmonics. Therefore, we use the third harmonic signal to reduce the surface noise for subsequent analysis.

Fig. 5.

Results of the imaginary part of the differential magnetic flux density distribution when D_h = 6 mm and f₀ = 4 Hz. (a) $\text{Im}[{\Delta}{\dot{B}}_{1,3}]$ and (b) $\text{Im}[{\Delta}{\dot{B}}_{1,5}]$ .

Fig. 6.

Results of the imaginary part of the differential magnetic flux density distribution, $\text{Im}[{\Delta}{\dot{B}}_{1,3}]$ , when f₀ = 4 Hz. (a)–(f) D_h = 2, 4, 6, 8, 10, and 12 mm.

3.3. Effect of crack height on the magnetic signal

Figure 6 shows the result of the imaginary part of the differential magnetic flux density distribution, $\text{Im}[{\Delta}{\dot{B}}_{1,3}]$ , when D_h = 2–12 mm and f₀ = 4 Hz. As shown, the backside defect is successfully detected when D_h ≥ 4 mm.

3.4. Effect of fundamental frequency

Figure 7 shows the result of the imaginary part of the differential magnetic flux density distribution, $\text{Im}[{\Delta}{\dot{B}}_{1,3}]$ , when D_h = 2–12 mm and f₀ = 8 Hz. Comparing the results in Figs. 6(e) and 7(b), the magnetic signal becomes greater as f₀ increases, and the backside defect is clearly visible. However, comparing the results in Figs. 6(b) and 7(a), the backside defect is more obvious when f₀ = 4 Hz owing to the skin effect. Therefore, f₀ should be properly chosen taking into account the height of the crack and the thickness of the steel plate.

Fig. 7.

Results of imaginary part of the differential magnetic flux density distribution when D_h = 6 mm and f₀ = 8 Hz. D_h is (a) 4 mm and (b) 10 mm.

Here, we compare RECT with other NDT methods. The magnetic flux leakage (MFL) method [11] and DC-biased magnetization based ECT (ECMECT) [12], which magnetize the specimen to suppress magnetic noises and the skin effect, are applicable for backside defect detection of ferromagnetic plates. Compared with MFL method and ECMECT, the advantage of RECT is that a magnetic core is not required and the probe need not be in contact with the steel plate. The pulsed ECT (PECT) [13] is considered to be similar NDT method to RECT. Compared with PECT, RECT do not require a large magnetic field because the repetitive magnetic pulses are applied, and the signal to noise ratio increases.

4. Conclusion

In this paper, we evaluated employing a rectangular wave excitation to LF-ECT systems, or LF-RECT systems, to reduce the surface magnetic noise and focus on detecting deeper defects using the harmonic signal. The results demonstrate that the surface noise can be successfully reduced using the harmonic signal. The results consider both the increasing information from the specimen and simplification of the ECT system by using a square wave inverter.

Footnotes

Acknowledgements

This work was supported in part by the Cross-Ministerial Strategic Innovation Promotion Program (SIP), Cabinet Office, Government of Japan, and the Iron and Steel Institute of Japan (ISIJ) Research Promotion Grant.

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Rectangular wave eddy current testing using for imaging of backside defects of steel plates

Abstract

Keywords

1. Introduction

2. Methods

Table 1 Specifications of the excitation and pickup coils Excitation coil Pickup coil Outer diameter 45 mm 10 mm Inner diameter 30 mm 6.0 mm Height 3.0 mm 3.0 mm Diameter of wire 0.56 mm 0.10 mm Number of turns 50 300 Resistance 0.44 Ω 16.4 mΩ Inductance 0.23 mH 0.64 mH

3. Results and discussion

3.1. Comparison between square and sinusoidal waves

3.4. Effect of fundamental frequency

Footnotes

Acknowledgements

References

Table 1
Specifications of the excitation and pickup coils

Excitation coil Pickup coil

Outer diameter 45 mm 10 mm

Inner diameter 30 mm 6.0 mm

Height 3.0 mm 3.0 mm

Diameter of wire 0.56 mm 0.10 mm

Number of turns 50 300

Resistance 0.44 Ω 16.4 mΩ

Inductance 0.23 mH 0.64 mH