Automated Eddy Current System for Aircraft Structure Inspection

In order to develop a signal processing algorithm for a testing system that integrates harmonic and impulse excitation modes of the probe and to understand the processes of the specified excitation modes, it is necessary to analyse the formation of the signal in different types of ECP. The equivalent circuits of typical single-coil are presented in Figure 1A (where u_G – generator signal, R – the generator output resistance, C₁ – the total capacitance formed by the turn-to-turn capacitance of the coil and other probe parasitic capacitances, R₁ – the coil active resistance, L₁ – the coil inductance, i₁, i₂ and i₃ – the currents in the corresponding branches of the circuit) and differential probes in Figure 1B (R₁ and L₁ – the excitation coil active resistance and inductance, R₂ and L₂ – the receive coil active resistance and inductance, M – the magnetic coupling coefficient, i₁ and i₂ – the currents in the branches) [16].

Figure 1.

It is known that the process of solving these schemes is reduced to the analysis of the input complex resistance and for the single-coil ECP equivalent circuit (Figure 1A) [11, 17], it takes the form: 1Z˙eq(ω)=R+R1+iωL11+R1iωC1+(iω)2L1C1,$${{\dot Z}_{{\rm{eq}}}}(\omega ) = R + {{{R_1} + i\omega {L_1}} \over {1 + {R_1}i\omega {C_1} + {{(i\omega )}^2}{L_1}{C_1}}},$$ where ω – cyclic frequency, and for the differential ECP equivalent circuit (Figure 1B): 2Z˙eq (ω)=1ω2M+R2+iω(L2+M).$${{\dot Z}_{{\rm{eq\;}}}}(\omega ) = {1 \over {{\omega ^2}M}} + {R_2} + i\omega \left( {{L_2} + M} \right).$$

Further analysis of equivalent circuits and Eqs (1) and (2) in the case of harmonic excitation of the probe leads to the formation of a signal containing real and imaginary parts: u_ecp = ReU + j ImU or Z_ecp = ReZ + j ImZ, where Z is the resistance of the circuit. That signal is conventional for most devices in which scanning results are presented using hodographs. ECP with harmonic excitation allows using the informative parameters like amplitude and phase of the signal.

In the case of a pulsed excitation, the analysis of equivalent schemes and Eqs (1) and (2) requires the calculation of transient response with the total current of the circuit which is considered to be equal to the sum of the forced and free currents. The forced current does not contain information about the properties of TO, so it is not of interest to the ECP signals analysis. The free current has a damping character in time and is described by such components^: Ae^αt, where α is the attenuation coefficient, which depends on the circuit parameters, and it can be determined through the roots of the characteristic equation. According to this, there is a ratio of the components of the circuit, at which the circuit begins aperiodic discharge, and which is described by the critical resistance of the circuit. The critical resistance of the circuit is determined by the characteristic equation of the circuit. As a result of analysis, an output signal in the form of damped harmonic oscillations with a certain natural frequency, attenuation coefficient and the initial phase is obtained. The specified parameters can be used as information in the signal-processing algorithm.

It is known from previous research that the complexity of the circuit and the number of its components affect the degree of the characteristic equation and the critical resistance. Therefore, when designing and setting up the device it should be considered to obtain correct testing results [11, 15].

The developed algorithm of the eddy current NDT system is shown in Figure 2. The algorithm provides automated setting and control of the operation modes of the probes and algorithm for processing experimental data. This makes it possible to take into account the specifics of testing and diagnostic problems involving the integration of harmonic and impulse excitation modes of probes.

Figure 2.

The signal processing algorithm involves the selection of the probe excitation mode and implements the traditional method of processing the harmonic (continuous) signals or the proposed method—signals as attenuating oscillations or continuous.

The basis of the proposed technique is the use of the Hilbert transformation for obtaining the amplitude and phase characteristics of the signal (ASC and PSC) for analysis. The analysis of the ECP signal transformation with pulsed excitation is discussed in detail in [11, 18].

The case of continuous excitation of the differential probe is considered below. In this case, the output signal can be represented by the equation: 3uecp(t)=U(1+a(t))⋅cos(2πft+φ(t)),t∈(0,Tc),$${u_{{\rm{ecp}}}}(t) = U(1 + a(t)) \cdot \cos (2\pi ft + \varphi (t)),t \in \left( {0,{T_c}} \right),$$ where f – frequency of the exciting signal, a(t), φ(t) – functions that depend on the variety of TO parameters, U – signal amplitude, T_c – observation time. As mentioned, signal processing is carried out by determining the Hilbert image of the signal u_H(t) = H[u_ecp(t)], based on which the ASC and PSC are determined: 4Uˇ(t)=uect 2(t)+uH2(t),$$\mathop U\limits^ (t) = \sqrt {u_{{\rm{ect\;}}}^2(t) + u_H^2(t)} ,$$ 5Φˇ(t)=arctguH(t)uect (t),$$\mathop {\rm{\Phi }}\limits^ (t) = arctg{{{u_H}(t)} \over {{u_{{\rm{ect\;}}}}(t)}},$$

Considering (4) and (5), the modulating functions associated with the TO parameters are determined by the equations: 6a(t)=Uˇ(t)−UU=u2(t)+uH2(t)U−1,$$a(t) = {{\mathop U\limits^ (t) - U} \over U} = {{\sqrt {{u^2}(t) + u_H^2(t)} } \over U} - 1,$$ 7φ(t)=(arctguH(t)uect(t)+L(uH(t),uect(t))−2πft)mod2π,(−π2,π2),$$\varphi (t) = \left( {arctg{{{u_{\rm{H}}}(t)} \over {{u_{{\rm{ect}}}}(t)}} + L\left( {{u_{\rm{H}}}(t),{u_{{\rm{ect}}}}(t)} \right) - 2\pi ft} \right)\bmod 2\pi ,\left( { - {\pi \over 2},{\pi \over 2}} \right),$$ where L – the PSC expansion operator outside the interval.

Also, in order to confirm the possibility of determining the ASC and PSC of the ECP and evaluating their changes in real-time with high accuracy, a simulation was carried out. The absolute errors of the estimation of the parameters (a(t) and φ(t)) in the conducted model experiments did not exceed 0.04 at B and 0.02 rad, respectively.

The traditional ECP signal processing is based on informative signal parameters such as amplitude and phase, and also it presents the testing results in the form of a hodograph [19].

The structure of the developed ECNT system is shown in Figure 3. The system consists of a measuring probe unit (transducing unit) and a results processing unit.

Figure 3.

The ECP receives a signal from a signal generator (current source) and generates a signal which is amplified and digitised by an analogue-to-digital converter (AD converter). Received data are saved in storage (buffer) for the next transfer to the processing unit. This transfer is realised with the help of a microcontroller (MC) and wireless communications unit. The Bluetooth module is used for wireless communications and it provides the connection between the processing and transducing units within some distance. The operation of the unit’s main components is synchronised by a control block. The processing unit consists of a receiving box and a personal computer with software that realised the signal processing algorithm.

The experiments were carried out on a sample made from steel St.20 (μ > 1) with 5 mm thick, 100 mm long, and 30 mm wide. Artificial defects imitating surface cracks 0.2 mm wide and δ = {0.2, 0.5, 1.0} mm deep, were located on one of the surfaces of the sample. The roughness of the sample surface did not exceed 1.6 μm.

Experimental signal amplitude values of the single-coil ECP with continuous excitation are presented in Figure 4 (curve 1), and the peak values of the signal amplitude of the same ECP with pulsed excitation are presented in Figure 4 (curve 2). Analysis of these figures shows that the signal amplitude of the ECP with pulsed excitation has a weak dependence on the crack depth h. Instead, an increase in the depth of the crack in the TO leads to an increase in the values of the signal amplitude of the ECP with harmonic excitation. A slight change in the peak values of the signal amplitude of the ECP with pulsed excitation is observed in the h = 0÷0.5 mm, and the sensitivity, in this case, is lower than for the ECP signal with harmonic excitation (S_{A_pulsed} = 1.3 mV/mm < S_{A_harm} = 0.3 mV/mm).

Figure 4.

The results of the analysis of the signal attenuation of the single-coil ECP during its pulsed excitation are shown in Figure 5A. The graph shows that the nature of the dependence of the ECP signal attenuation on the TO crack depth is close to linear form, therefore, the attenuation is an informative parameter suitable to use for testing and assessing the crack depth in the TO. In the performed experiments, the relative error in determining the crack depth did not exceed ±0.5%, and the average sensitivity to the crack depth was estimated as Sα = 0.2 μs^–1/mm.

Figure 5.

The results of determining the variation of the natural frequency oscillations of the ECP signal with pulsed excitation as a function of the crack depths in the sample are shown in Figure 5B. The graph of dependence f(δ) has a linear character in the section, and the value of the natural frequency oscillations of the ECP signal decreases with an increase in the crack depths in the sample.