Dual Induction Eddy Current Probe for Vibration Noise Reduction

In eddy current testing (ECT), signals originating from product vibration and cracks are detected. Frequency filtering methods are widely used, such as vibration signal suppression. However, this method is not effective when the difference between the frequencies of the vibration and crack signals is small. We have proposed a dual induction method with passive vibration signal suppression that does not require active signal processing, such as the frequency filtering method. This article quantitatively describes the performance of a dual induction eddy current probe that selectively suppresses only the vibration signal from detection signals, comparing this with the frequency filtering method and the multi-frequency method. Simulation and measurement results show that the proposed probe suppresses vibration signals and does not suppress crack signals; however, the current methods suppress both signals. The obtained results suggest that the proposed method provides a higher signal-to-noise ratio than the current method.


I. INTRODUCTION
I N EDDY current testing (ECT), the amplitude of vibration signals is often larger than that of the crack signals [1].In this case, active methods, such as signal processing, and/or passive methods, such as probes with self-differentiating and self-nulling characteristics for the vibration, are widely used to remove signals caused by vibration from the detected signal.Frequency filtering method, multi-frequency method, and other methods are known as active methods [2], [3], [4].However, these active methods are not expected to effectively suppress vibration signals when the difference between the frequencies or phases of the vibration and crack signals is small.Uniform eddy current probe, theta probe, cross point probe, ionic probe, and other probes are known as a passive method that can suppress vibration signals [5], [6], [7].However, these probes require complex equipment, such as multi-channel detection, to inspect large areas.
We have proposed a new ECT probe with passive vibration signal suppression that eliminates the need for the active signal processing and the multi-channel detection equipment [8].As is well known, noise-canceling headphones reduce noise by generating a sound that has the same amplitude as the noise and the opposite phase of the noise.Our probe generates a magnetic flux in the opposite phase of the vibration.This reduces the detection signal caused by vibration.The difference with noise-canceling headphones is that the proposed method is a completely passive one.
In this article, the principle and effect of our proposed method that can suppress vibration signals in detection signals  are discussed in comparison with the frequency filtering method and the multi-frequency method.

II. THEORY OF VIBRATION NOISE REDUCTION
This section describes the principles and features of methods for suppressing vibration signals shown in Fig. 1, using a 3-D FEM simulation.In the simulation, the A-φ method of the "JMAG Designer1 ," which was developed by JSOL Corporation, was used as the simulation software.The vibration of the specimen is limited to static displacements to simplify the simulation discussion.The simulations of the detection signals under the conditions shown in Table I and Fig. 2 were performed.

A. Dual Induction Method
The dual induction method is a fully passive vibration signal suppression technique that requires no signal processing, as shown in Fig. 1(a).This method is realized by probes with self, mutual, and dual induction modes.The probe shown in Fig. 3 is an encircling coaxial type dual induction differential probe.This probe has four coils, L 1 , L 2 , L 3 , and L 4 .L 2 and L 3 are defined as the inner coils.L 1 and L 4 are defined as the outer coils.The self-induction mode uses the inner coils as the excitation and differential detection coils.The mutual induction mode uses the outer coils as the excitation coils and the inner coils as the detection coils.The dual induction mode simultaneously uses the self-and mutual modes.This means that all coils in L 1 , L 2 , L 3 and L 4 are used as excitation coils and L 2 and L 3 are used as detection coils.
Fig. 4(a) shows the simulated displacement signals, which are detected by using the self-, mutual, and dual modes when a brass bar specimen is subjected to displacement represented by the radius offset and rotation.The relationship between the displacement signal, ḋself and ḋmutual , in the self-and mutual induction modes empirically obtained from the simulation is shown in the following equations: where k self and k mutual are the amplitude coefficients, Offset radius is the radius direction offset of the bar, Rotation is the rotation of the bar, and θ is the phase of the detection signals of the self-mode.The amplitudes of ḋself and ḋmutual were proportional to the offset and rotation of the specimen.The phases of ḋself and ḋmutual are inverted when the coil distance is equal to 9 mm.The relationship between the phase and the coil distance was discussed in [8].The displacement signal of the dual induction mode, ḋdual , is shown in the following equation: where g ex is the gain of the excitation in the mutual mode.As shown in Fig. 4(a), ḋdual is suppressed when g ex is determined by the following equation: Therefore, the inner and outer coils should be driven by different power amplifiers, as shown in Fig. 1(a), to maximize the suppression of vibration signals.
Fig. 4(b) shows the simulated displacement signals when the specimen is subjected to displacement represented by the axis offset, radius offset, and rotation.The phases of ḋself and ḋmutual are not completely opposite when the displacement signal that contains the axis is offset.This means that this method requires adjustments of the coil distance, g ex and the phase of the outer excitation for each displacement.The crack signal in the detection signal of the mutual mode is smaller than the crack signal of the self-induction mode because the distance between the crack and excitation coils of the mode is longer than the distance of the self-induction mode.Fig. 4(c) shows the crack signals of the self-and dual induction modes.The crack signal of the dual induction mode is larger than that of the self-induction mode.This means that the phase of the vibration signal in the mutual induction mode is opposite to that of the self-induction mode, and the phase of the crack signals of the self-and mutual induction modes is close.
As described above, the dual induction method requires an optimized probe for each vibration and suppresses only the vibration signal.The amplitude of the crack signal in the dual induction mode is slightly larger than that in the self-induction mode.

B. Multi-Frequency Method
The multi-frequency method simultaneously uses multiple excitation frequencies to detect wanted signals, such as crack signals, suitable for each frequency and to selectively suppress unwanted signals, such as vibration signals [2], [3].
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.This method requires multiple oscillators, multiple lock-in amplifiers, and signal processing, as shown in Fig. 1(b).
The following equations show the frequency signal processing of this method: where vmix is the mixed signal, vBase is the signal of the base frequency, vi is the signal of the subfrequency, n is the number of subfrequencies, func is a function of the signal processing, and g xi , g yi , and θ i are the coefficients of func.g x , g y , and θ are decided, so that the following equation holds when vBase and vi contain only unwanted signals, such as vibration signals: As shown in Fig. 5(a), there is a difference between the phases of the crack and displacement, and when the same crack and vibration are detected at different excitation frequencies, the difference varies at each excitation frequency, as shown in Fig. 5(b).The difference between 16 and 64 kHz is 1.8 • .Fig. 5(c) shows the result of applying this method with two frequencies.When the phase difference is smaller than 90 • , the crack signal of this method is smaller than that of the self-induction mode, as shown in Fig. 5(c).This method is often used when the phase difference between the crack signal and the unwanted signal is large, such as when removing signals caused by support plates that occur outside of heat  transfer tubes when detecting cracks on the inner surface of the tubes [3].

C. Frequency Filtering Method
The frequency filtering method suppresses unwanted signals by focusing on frequencies [3].The faster the sample is transported and the shorter the distance between the detection coils, the higher the frequency of the crack signal.This method is used as a high-pass filter or bandpass filter (BPF) in almost all in-line inspections to the best of our knowledge and is set to transmit the frequency of crack signals.However, this method might sufficiently suppress unwanted signals when the difference between the frequencies of the crack and unwanted signals is small.

III. EXPERIMENTAL RESULTS
This section measures the vibration suppression effect of the three methods and compares the amplitudes of the vibration and crack signals.The phase of the measured signal is often rotated, so that the peak of the vibration signal is in the negative direction of the x-axis.In this article, the amplitude of the vibration signal is defined as the peak-to-peak of the x component of the measured signal after the phase rotation.The amplitude of the crack signal is defined as the peak-to-peak of the crack signal with no vibration in the complex plane.A photograph of the experimental setup used and measurement conditions is shown as Fig. 6 and Table II.The probe shape is the same as in Fig. 3.

A. Dual Induction Method
Fig. 7(a) shows the measured signals when the brass bar specimen was subjected to static displacements of 0 mm axis offset.As with the simulation results of Fig. 4(a), the phase of the mutual induction mode was the opposite to that of the self-induction mode.The amplitude of the self-and mutual induction modes was proportional to the rotation of the displacement.The gain of the excitation voltage for the mutual induction mode, g ex , required to match the amplitude of the displacement signal in the mutual induction mode to the amplitude of the self-induction mode was 1.11.Fig. 7(b) shows the measured signals when the specimen was subjected to dynamic vibration, which was generated by the pulley in Fig. 6.The optimal gain g ex in Fig. 7(b) was 1.62, unlike that with the 0 mm axis offset.It is assumed that the position of the radius and axis offsets was not constant and was moving.The reason is that the vibration was applied to only one side of the specimen using the other side of the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.specimen as the fulcrum.As shown in Fig. 4(b), this method requires adjustments of the coil distance, g ex and the phase of the outer excitation for each displacement.Using the g ex obtained in Fig. 7(b), the measurement results of crack signals are shown in Figs. 8 and 9.The used brass bar specimen had two circumferential cracks of 0.1 and 0.2 mm depth.Compared to the results when the self-induction mode was employed, the crack signal was larger and the vibration signal was suppressed.the measurement results were different at each excitation frequency as shown in the simulation results.The signal-tonoise ratio of Fig. 10(b) was lower than that of Fig. 10(a).This is because the coils are optimized for an excitation frequency of 16 kHz.Therefore, to obtain a better signal-to-noise ratio at both 16 and 64 kHz, it is desirable to use coils optimized for frequencies around 32 kHz.The g x and g y calculated from these measurement results were 0.519 and 0.306, respectively.The results of applying the multiple frequency method are shown in Figs.10(c) and 11.It can be confirmed that the vibration signal was suppressed.However, the crack signal when using this method was lower than that using the selfinduction mode.

C. Frequency Filtering Method
In this article, a software BPF using the discrete Fourier transform as the frequency filter method was applied.Hamming was used as the window function.The frequency of the crack signal of the self-induction mode was about 10 Hz.Therefore, the high-and low-pass filter cutoff frequencies f HPF and f LPF were set to 5 and 20 Hz, respectively.
The result of applying the BPF to the measured signal of Fig. 9(a) is shown in Fig. 12.The decrease in the vibration signal was slight.This was because the frequency of the vibration signal was about 10 Hz and passed through the BPF.
The suppression effects of the vibration and crack signals are shown in Table III.Under the conditions described in this article, where the frequencies of the crack and vibration signals were close, the dual induction method was found to be the most effective in suppressing the vibration signal.

IV. CONCLUSION
The dual induction method was proposed to selectively suppress only the vibration signal from the detection signal containing both crack and vibration signals.The novelty of the proposed method lies in its simultaneous use of self-and mutual induction.The advantages of the proposed method are that vibration signals can be selectively suppressed, and the system does not require signal processing, unlike multi-frequency or frequency filtering methods.Simulations and experiments confirmed that the vibration signal was suppressed by the probe using the proposed method, which is difficult to suppress by the frequency filter method, even when the frequencies of the crack signal and the vibration signal were close.
The application of the dual induction method to surface probes is currently under consideration.

Fig. 4 .
Fig. 4. Simulated displacement and crack signals of the dual induction method.(a) Displacement signals with radius offset and rotation.(b) Displacement signals with radius and 0.5 mm axis offset.(c) Crack signals.

Fig. 5 .
Fig. 5. Simulated signals of the multi-frequency method.(a) Crack and displacement signals at 16 kHz.(b) Phase difference between the notch and phases for each frequency.(c) Mixed crack signals of the multi-frequency method with 16 and 64 kHz.

Fig. 7 .
Fig. 7. Measurement vibration signals of the self-and mutual induction modes.(a) Static displacement signals with 0.5 mm radius offset and 0 mm axis offset.(b) Dynamic vibration signals with the vibration generating pulley.

Fig. 8 .
Fig. 8. Measured signals of 0.2 mm depth crack with g ex = 1.62 without the vibration.

Fig. 9 .
Fig. 9. Measurement signals of the dual induction mode in the dynamic environment.(a) Self-induction.(b) Dual induction.

Fig. 10 .
Fig. 10.Measured signals of the base and subexcitation frequency and the multi-frequency method.(a) Self-induction with base frequency at 16 kHz.(b) Self-induction with subfrequency at 64 kHz.(c) Multi-frequency method.

Fig. 11 .
Fig. 11.Measured signal after the signal processing using the multi-frequency method at 16 and 64 kHz.

Fig. 10
Fig. 10(a) and (b) shows the measured signals at excitation frequencies of 16 and 64 kHz.The phase differences in

Fig. 12 .
Fig. 12. Measured signal after the signal processing using the frequency filtering method with f HPF = 5 Hz and f LPF = 20 Hz.

TABLE III VIBRATION
AND CRACK SIGNALS SUPPRESSION EFFECTS