Keywords

1 Introduction

Alternating current field measurement (ACFM) is originally developed for sizing cracks on structures as an alternative to MPI [1, 2], based on the alternating current potential drop (ACPD) technology [3, 4]. ACFM probe induces a uniform alternating current on the surface of conductive specimen. The uniform current will be disturbed when crack presents. The distortion of magnetic field caused by electric field can be measured to deduce both the crack depth and length. As shown in Fig. 1, BX (X direction) shows a deep trough, which contains depth information, while Bz (Z direction) shows a negative and positive peak at both end of the crack, which gives an indication of length [5, 6]. However, the theory of ACFM is based on the assumption that the induced current is perpendicular to the crack. As shown in Fig. 2a, when the u-shaped ACFM probe scans the specimen along the crack, the induced current will be perpendicular to crack. Thus, the perturbation of induced current is obvious and the characteristic signals are in accord with the theory of ACFM [7]. While the u-shaped ACFM probe is perpendicular to the crack, as shown in Fig. 2b, the induced current will be parallel to the crack. In this case, the perturbation of induced current is unconspicuous. Due to leakage flux effect, some magnetic field leaks into the air. However, the leakage flux effect does not match the theory of ACFM, which can not make some quantitative detection of the crack (depth and length).

Fig. 1
A 3-D diagram of an A C F M model. It depicts a magnetic core with a crack. The electric field is present perpendicular to the magnetic field. X and Y component peaks of the current are marked.

Theory of ACFM

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Fig. 2
2 3-D diagrams A and B of A C F M crack detection. A depicts an induced current field below a magnetic coil. B depicts a leakage flux effect of current below the magnetic coil.

U-shaped ACFM probe for cracks detection. a The probe is parallel to the crack. b The probe is perpendicular to the crack

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As mentioned above, the traditional ACFM probe needs to scan the specimen along the crack. In practice, it is not clear that the crack is present or not on the specimen, let alone the direction of the crack before the inspection. Hence, to detect the cracks at arbitrary scanning direction effectively, a double u-shaped orthogonal ACFM probe is present in this paper. The double u-shaped orthogonal ACFM probe can produce a rotating alternating current field on the specimen. The induced rotating current field will be perpendicular to the crack at any scanning direction. Thus the cracks can be detected at arbitrary scanning direction using the double u-shaped orthogonal ACFM probe.

2 FEM Model of Double U-Shaped Orthogonal ACFM Probe

As Ferraris effect, a rotating magnetic field can be constructed using two orthogonal coils with 90° phase difference in their AC currents [8]. In this way, two same excitation coils winding on the U-shaped MnZn ferrite material magnetic yokes are placed orthogonally along X direction (excitation X) and Y direction (excitation Y). Excitation X and excitation Y are driven by one pair alternating currents, ix(t) and iy(t) respectively, which are defined as follows:

$$i_{x} \left( t \right) = I_{0} \sin \left( {\omega t + \alpha_{0} } \right)$$
(1)
$$i_{y} \left( t \right) = I_{0} \sin \left( {\omega t + \alpha_{0} + 90^\circ } \right)$$
(2)

where, I0 is the amplitude of the alternating current, ω is the frequency of the alternating current, and \(\alpha_{0}\) is the initial phase of the ix (t).

Because the excitation array is very close to the conductor surface, the conductor will be assumed a half-infinite plate [9, 10]. According to the principle of electromagnetic field propagation, the alternating eddy currents will be induced in the conductor by the alternating primary magnetic fields [11].

The FEM model of the orthogonal excitation array is set up and analyzed by the transient analysis method in ANSYS [12]. The simulation model consists of a double orthogonal U-shaped yoke wound with coils where placed on a mild steel sheet sample, as shown in Fig. 3. The excitation coils X and Y carry the alternating currents with 1 V amplitude, 6000 Hz frequency, and the initial phases of 0° and 90° respectively.

Fig. 3
A 3-D illustration of an orthogonal A C F M probe in Ansys. It depicts a magnetic substance wrapped with coils. It is placed on a mild steel sheet sample.

The FEM model of the double u-shaped orthogonal ACFM probe

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A complete period is divided into 4 transient steps equally. And the transient induced current densities on the surface are simulated and analyzed. The simulation results show that the direction of induced current field at the uniform area revolves periodically with the driving alternating current, which the direction is negative Y at t = 0, and negative X at t = 0.25 T, and positive Y at t = 0.5 T, and positive X at t = 0.75 T, as shown in Fig. 4. The rotating induced current field can be perpendicular to cracks vertically at arbitrary scanning direction producing a larger distortion in magnetic field. The simulation results provide a strong evidence for the detection of cracks at arbitrary scanning direction using a double u-shaped orthogonal ACFM probe.

Fig. 4
4 graphical representations of F E M simulation analysis for induced A C current field around a crack with arrows facing different directions. An index strip with different magnetic field intensities is given below.

The FEM simulation analysis results for induced AC field on the surface at different transient time, a t = 0, b t = 0.25T, c t = 0.5T, and d t = 0.75T

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3 Cracks Detection Experiments

The double u-shaped orthogonal ACFM probe is set up, as shown in Fig. 5a. The excitation array is built by two orthogonal U-shaped MnZn ferrite yokes wound with 500 turns current-carry coils of 0.15 mm enameled copper wire each, according to theory model and FEM model. The experiment system is shown in Fig. 5b. The signal generator provides a sine signal with 6 kHz frequency and 1 V voltage as the initial driving signal. The initial driving signal and the orthogonal driving signal provided by the 90° phase shifter are used to drive the current-carrying coils of double u-shaped orthogonal ACFM probe. The detecting sensor picks up the disturbance magnetic signals caused by the disturbed uniform rotating alternating current filed. After the signal amplification, phase sensitive rectification and low pass filtering by the condition module, these analog signals are transformed to digital signals and sent into the PC using the DAQ module. The intelligent identification software in PC will display the signals and identify arbitrary cracks with one pass scanning.

Fig. 5
2 photographs A and B and a diagram C. A depicts a U-shaped orthogonal A C F M probe with a detecting sensor. B depicts a computer connected to a signal processing box to detect a crack. C depicts the scan direction of the crack from 0 to 90 degrees.

The double u-shaped orthogonal ACFM probe. a The double u-shaped orthogonal ACFM probe and detecting sensor. b The experimental system. c Detection of cracks at arbitrary scanning direction

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The specimen is a Q235 mild steel sheet with 45 mm length and 7 mm depth artificial rectangular crack. As shown in Fig. 5c, the double u-shaped orthogonal ACFM probe scans the crack from 0° to 90° with 10° increase simulating the detection of cracks at arbitrary scanning direction. The 0° angle indicates the double u-shaped orthogonal ACFM probe is parallel to the crack, while the 90° angle indicates the probe is perpendicular to the crack.

Figure 6a–d show the 0°, 30°, 60°, 90° angle cracks detection experimental results using the double u-shaped orthogonal ACFM probe. Comparing Fig. 5a with Fig. 1, it is clear that the BX and BZ signals are in accordance with the principle of ACFM, which proves the feasible of the experiment system. As shown in Fig. 6b, the perturbations of ACFM experiments results are still obvious at 30°. At 60°, as shown in Fig. 6c, the BX and BZ are also according with the principle. Finally, when the scanning direction is perpendicular to the crack, as shown in Fig. 6d, the crack still can be recognized by the double u-shaped orthogonal ACFM probe perfectly.

Fig. 6
4 lines graphs from A to D of amplitude versus scanning path X in millimeters. 2 lines of X and Z components are plotted on the graphs, with the X component higher than Z in each case.

BX and BZ signals from experiments using the double u-shaped orthogonal ACFM probe. a Crack detection at 0°. b Crack detection at 30°. c Crack detection at 60°. d Crack detection at 90°

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The parameters for characterizing the inspection sensitivity, SX and SZ, are given as follows to reduce detection error and improve the SNR (Signal to Noise Ratio) [13].

$$\left\{ {\begin{array}{*{20}c} {S_{X} = \frac{{MX_{max} }}{{MX_{0} }} \times 100\% } \\ {S_{Z} = \frac{{MZ_{max} }}{{MX_{0} }} \times 100\% } \\ \end{array} } \right.$$
(14)

where, MX0 is the amplitude of BX signal without crack, and MX max and MZ max are the maximum perturbations of BX and BZ caused by crack respectively.

As shown in Fig. 7, there is a little decrease of sensitivity by the double u-shaped orthogonal ACFM probe at different scanning detection. The maximum sensitivity of SX is 32.6%, while the minimum sensitivity of SX is 27.2%. The maximum decrease of sensitivity in SX is 16.8%, which meets requirements of sensitive detection of cracks at arbitrary scanning direction. Meanwhile, the maximum sensitivity of SZ is 69.1% and the minimum sensitivity of SZ is 59.8%, whose maximum decrease is 13.5%. It suggests that the detection sensitivity of double u-shaped orthogonal ACFM probe changes a little for inspecting cracks at arbitrary scanning direction.

Fig. 7
2 lines graphs from A and B of sensitivity parameters percentage versus crack angle in degrees from 0 to 90. A line of X component is plotted on A and that of Z component is plotted on B.

Detection sensitivity for cracks at different scanning direction. a Bx, b Bz

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4 Conclusion

In this paper, a double u-shaped orthogonal ACFM probe is present for cracks detection at arbitrary scanning direction on structures. The induced rotating current field is analyzed by simulations. The cracks detection experiments at arbitrary scanning direction are carried out by the double u-shaped orthogonal ACFM probe test system. From these results, we conclude that the feasibility of double u-shaped orthogonal ACFM probe is verified by both EFM model and experiments. It is apparent that the double u-shaped orthogonal ACFM probe proposed in this paper can detect cracks effectively at arbitrary scanning direction.