1. Introduction
ECT is based on the electromagnetic effect, and the primary magnetic field of the excitation coil and the secondary magnetic field generated by the induced eddy currents (ECs) inside the conductive object under test are coupled with each other, which will change the inductance of the coil. Due to its non-contact, high sensitivity, low cost, and insensitivity to non-conductive materials such as oil and dust, this technology can easily adapt to harsh industrial environments. The commonly used eddy current detection techniques are the pulsed eddy current technique (PECT) and the multi-frequency eddy current technique (MECT). At present, these techniques have been widely used for the detection of cracks and the determination of thickness or other characteristics of metals [
1,
2,
3].
For the PECT, Amir et al. combine the direct interfacing technique (DIP) and PECT to measure the thickness of aluminum plates [
4]. The curve fitting method is used to process the signal of a single coil probe in samples of different thicknesses, with a maximum relative error of about 2%. Chen et al. propose a signal slice-based method for pulsed eddy current sequence imaging. The method analyzes the differences between a non-defect-subtracted signal (NDSS) and air-subtracted signal (ASS), and obtained image frames that have a better effect than a single feature value [
5]. In order to detect circumferential cracks in a steel pipe, transverse probes that were perpendicular to the cracks were designed [
6]. For MEC testing, Yin and Lu et al. [
7,
8] utilized features extracted from multi-frequency inductance to measure the thickness of metallic plates. For example, they used the peak frequency feature of the multi-frequency inductance imaginary part to measure the thickness of non-magnetic materials and the zero-crossing frequency feature of the multi-frequency inductance real part to measure the permeability of the metallic board. White et al. measured the electrical conductivity and thickness of metallic foils using a forked inductive coil [
9].
CFRP, as an emerging material, has the advantages of high strength, low density, corrosion resistance, and good fatigue characteristics. Therefore, it is widely utilized in aerospace, automotive, and other industries. The electrical conductivity of CFRP differs significantly from that of common metal materials. Firstly, as the main components of CFRP are carbon fiber and epoxy resin, this results in an overall conductivity of only 10
4 S/m, which is much lower than that of metals [
10]. Therefore, to generate sufficient eddy currents in CFRPs, the operating frequency of the sensor needs to be increased [
11]. Secondly, the interior of a CFRP is not a homogeneous single material. The conductivity in the direction of the carbon fiber extension is significantly higher than that in the direction perpendicular to the carbon fiber. This leads to various anisotropies in the conductivity characteristics of CFRPs. Various probe configurations have been designed to meet specific inspection needs [
12,
13]. Koichi et al. detected delamination in CFRPs using a rectangular tangential driver coil under an 18.5 MHz excitation current [
14]. It was found that optimizing the distance between the tangential driver and pickup coils can significantly improve the sensitivity to delamination. Wataru et al. added electrodes perpendicular to the fibers of unidirectional carbon fiber-reinforced plastic (UD-CFRP) and discovered that the eddy current density at depth can be regulated by adjusting the distance between the electrodes [
15]. Kosukegawa et al. characterized the laminated structure of a CFRP using a probe of the differential type [
16].
Increasing the excitation frequency enhances the SNR, but it is also influenced by the lift-off spacing, probe tilt, and the surface roughness of the object being tested in the detection system. These factors tend to introduce significant crosstalk and background noise, thereby reducing the stability of the detection process. Cheng et al. detected the orientation of different fiber layers using a small-sized probe combined with a lock-in amplifier at a low-frequency excitation of 250 kHz [
17]. Dario et al. detected a crack in a CFRP by increasing the eddy current density below the receiving coil using double excitation coils and resonant excitation techniques [
18]. After that, they used guided Lamb wave tomography to locate the crack in the CFRP and evaluated it using an ECT probe with double excitation coils [
19].
The various methods mentioned above typically utilize expensive impedance analyzers for measurements, making it challenging to design portable equipment to accommodate specific scenarios. Since the 1960s, with the rapid development of Micro-Electro-Mechanical Systems (MEMSs), passive wireless sensing has been widely used for measuring parameters such as pressure, temperature, and other variables [
20,
21]. The main structure of this technology is the LC resonant circuit formed by the parallel inductance and capacitance, along with an additional readout coil [
22,
23,
24]. The main working principle is to detect the resonance frequency and quality factor of the LC resonant circuit by using a readout coil. The coupling distance between the reading coil and the LC resonator determines the size of the input impedance, posing a challenge for the design of the readout circuit.
An LDC provides a solution with low cost, low power consumption, and reliable performance for frequency signal measurement [
25]. Its typical applications include metal testing in the automotive industry, buttons on household electronic products, and inductive equipment, such as noninvasive cerebral blood flow monitoring [
26], heart activity monitoring, cardiac activity detection [
27], and other inductor equipment. Brittany Rapp et al. used an LDC to detect the nanofluids (NFs) system containing golden nanoparticles (NPs). The error of the experimental results and the finite element simulation is less than 1.0%, which proves the high sensitivity of the LDC [
28]. Kong et al. designed a magnetic eddy current sensing system based on a field programmable gate array, combining an LDC and over-sampling technology to enhance the resolution and SNR of detection signals. This system achieved the synchronous real-time monitoring of cardiopulmonary signals [
29].
In this paper, a resonant eddy current testing method based on the LDC is proposed. Different from the existing resonant eddy current testing method, where the excitation frequency of the probe is typically fixed near the self-resonant frequency (SRF) of the coil, a capacitor is introduced to create an LC resonator. This design ensures that the coil’s operating frequency is significantly lower than its SRF, effectively minimizing potential background noise interference. Through proper coil design, the induction distance of the LC resonator is increased, while the SRF of the coil is also increased. This allows the operating frequency of the LC resonator to be maximized, enhancing the detection capability of surface defects. The method has a higher SNR and sensitivity than conventional T-R probes. It can operate at higher lift-off heights, partially overcoming the lift-off effect.
The rest of the article is organized as follows:
Section 2 describes the working principle of the resonant eddy current sensor.
Section 3 describes the specific setup of the experimental platform.
Section 4 presents the experimental results and discussion.
Section 5 concludes the article.
2. Principles of Operation
The method proposed in this paper utilizes the LC resonator as the fundamental detection structure. When the detection probe is near a conductive material, such as metal or CFRP, the presence of eddy currents alters the resonance state of the LC resonator, leading to a shift in the resonance frequency. The operating schematic is shown in
Figure 1, where U represents the excitation source voltage. The portion within the dashed line illustrates the parasitic component resulting from the circuit connection, which should be taken into account in the circuit design to minimize its impact on the circuit. The main operating part of the resonator is a parallel capacitive and inductive structure, although the following analysis ignores its effect on the circuit operation, where the capacitance is denoted by
, and the inductance under AC excitation can be equated to the series connection of the inductance,
, and the equivalent resistance,
. The resonant frequency of the LC resonator,
, can be expressed as
Since the experimental setup of this paper satisfies
, Equation (1) can be simplified as follows:
The eddy current in the measured object can be equated to a secondary coil, which consists of a secondary inductive component,
, and a secondary resistive component,
. The energy of the eddy current magnetic field is coupled to
through
, which induces a change in the inductance of the primary coil, resulting in a shift in the resonant frequency of the LC resonator, which can be characterized by Equation (3):
where
represents the inductance of the coupled resonator.
2.1. Lift-Off
Figure 2 shows a schematic of LC resonator detection. Parameters such as coil radius,
, number of turns, wire diameter, and the distance (lift-off spacing),
, between the coil and the object to be measured, as well as the properties of the object to be measured, such as conductivity, permeability, thickness, surface roughness, etc., are all important factors affecting the change in inductance of a resonator. According to Mohammad’s research [
30], the effect of lift-off height and coil radius on inductance can be expressed by Equation (4):
where
,
; inductance does not change. The values of
and
are related to the geometry of the coil and target, and the conductivity. When the coil is a flat coil with a radius of 7 mm and the target is an aluminum plate with a thickness of 2 mm,
= 0.51,
= 7.22; the normalized graph of the inductance variation is shown in
Figure 3, which shows that the inductance variation is almost zero when
. This may be due to the fact that the magnetic field energy of the coil is mainly concentrated within the radius of the coil.
2.2. Coil Parameters
SRF is an intrinsic property of the coil, uniquely determined by the physical structure of the coil. It is the frequency at which the reactance of the inductor cancels out the reactance of the parasitic capacitor. As shown in
Figure 4, when the excitation frequency of the coil is in region III above the SRF, the coil’s reactance becomes capacitive, which is not the normal operating condition of the coil. The eddy current probe facing the metal generally operates in region I to meet the need for detection sensitivity. When facing a CFRP, due to the low conductivity characteristics of the material, the same excitation frequency generates eddy currents much smaller than in metal. To improve the SNR of defect detection, it is common to place the eddy current probe’s operating frequency in region II. The enhanced signal is sensitive to all characteristics of the material under test, such as defects and surface roughness. It may be challenging to distinguish between the detection signals generated by different characteristics, leading to a decrease in the stability of the detection signal. For the LC resonator to operate stably, the coil’s operating frequency is set within region I, and the SRF of the coil is increased by enhancing the coil structure. This allows the coil to function at higher frequencies while maintaining better stability.
The main factor that determines the size of the coil SRF is the self-contained parasitic capacitance of the inductor, and the magnitude of this parasitic capacitance is contingent on the construction and geometry of the coil. When using a typical air-core closely wound coil, the LC resonator will not function properly at high frequencies due to the relatively large parasitic capacitance of this coil shorting out. In this paper, a flat coil design is utilized, where the parasitic capacitance of this coil is small enough compared to a closely wound coil, ensuring that the resonator will not short out due to excessive excitation frequency. The flat coil is directly integrated onto the PCB for better mechanical stability and increased volume efficiency. Moreover, this coil reduces the need for cable connections, and its series resistance is small enough (10 mΩ) to significantly enhance the quality factor of the resonator at higher operating frequencies. This improvement can enhance the immunity to stray magnetic fields in challenging operating environments.
In order to verify the validity of the selection of spaced flat coils, the following finite element simulation analyses are carried out for both closely wound and spaced coils. The complete model consists of a spiral copper inductor, a PCB, and an air domain that surrounds them. The copper wires are surrounded by a layer of epoxy varnish insulation that is tightly bonded to the PCB. A boundary layer mesh is utilized to mesh the surface of the copper inductor, taking into account the skin effect of the conductor at high frequencies. The setup of the two inductor models is shown in
Table 1.
Figure 5a illustrates the structure of a tightly wound helical copper coil, while
Figure 5b depicts the structure of a spaced helical copper coil. It can be seen that, when the coil is under high-frequency excitation, the current density is maximal at the surface of the copper wire and decays exponentially toward the center of the copper wire. The current density at the surface of the closely wound coil is higher than that of the spaced coil for the same space occupation. The SRF of the densely wound coil shown in
Figure 5c is approximately 5.05 MHz, while the SRF of the spaced coil depicted in
Figure 5d is around 481.8 MHz. The LDC1612, chosen for this study, can operate at up to 10 MHz. To fully utilize the chip’s performance and ensure stability of the LC resonator, a spaced flat coil is selected.
Commonly used planar coils are in the shapes of a circle, square, octagon, etc. Among them, circular coils produce the best magnetic field symmetry, the smallest equivalent resistance of the inductor, and the highest quality factor.
Figure 6 shows the physical and structural diagrams of a circular planar coil. The main structural parameters of the coil include the outer diameter,
; inner diameter,
; wire diameter, w; and spacing, s. The inductance of a circular single-layer planar coil can be calculated using Equation (5) based on the current sheet approximations (COSAs) proposed by Mohan et al. [
31].
represents the self-inductance of the circular planar coil, stands for the filling ratio, denotes the mean diameter, represents the permeability, and is the number of turns.
When the outer diameter of the coil is fixed, the total inductance can be controlled by adjusting the number of turns and the inner diameter. There are two ways to increase the number of turns: by reducing the wire diameter and spacing, and by reducing the inner diameter. Due to the PCB fabrication process, the minimum PCB alignment width and spacing are both 0.1 mm.
Figure 7 illustrates the inductance value of a circular coil with an outer diameter of 14 mm, where the number of turns increases as the inner diameter decreases. The inductance changes more rapidly when the number of turns is between 5 and 20, and stabilizes when the number of turns exceeds 30.
Double-layer coils can effectively increase the total inductance per unit volume.
Figure 8 shows the structure of a double-layer coil. In order to concentrate the magnetic field of the inductor, the two coils should be aligned at the top and bottom, and the wiring of the two coils should be in opposite directions to ensure that the current and magnetic field directions are the same when they are connected in series. The total inductance of the double-layer coil can be expressed as Equation (6):
represents the inductance of the top coil,
represents the inductance of the bottom coil, and
represents the mutual inductance between the two coils. The coupling coefficient of the two coils, denoted by
, is determined by the distance between the coils and ranges in magnitude from 0 to 1. Mutual inductance increases the total inductance of the coils without increasing the equivalent resistance of the coils and improves the quality factor of the coils.
Figure 7.
Inductance versus number of turns for 14 mm circular flat coil.
Figure 7.
Inductance versus number of turns for 14 mm circular flat coil.
Figure 8.
Operating schematic of double-layer coils.
Figure 8.
Operating schematic of double-layer coils.
3. Experimental Methodology
As shown in
Figure 9a, the experimental platform consists of four parts: the LC resonator working board, the three-axis moving platform, a personal computer (PC), CFRP specimen, and aluminum specimen. The specimens to be tested are placed on the table of the three-axis mobile platform. The LC resonator working board consists of LDC1612, an LC resonator, and MPS430. Among them, LDC1612 and MPS430 are both produced by Texas Instruments in the U.S. LDC1612 drives the LC resonator by adjusting the dynamic current to keep the amplitude of the LC resonator at around 1.7 V. Simultaneously, it detects any frequency changes in the LC resonator. During working hours, the PC controls the movement of the three-axis moving platform to complete the scanning. The configuration and signal acquisition of LDC1612 by the PC are facilitated by MPS430. Communication between MPS430, the PC, and LDC1612 is achieved using USB and I2C. The LC resonator setup ultimately adopted in this paper is as follows. The inductor part consists of a double-layer circular PCB coil with the parameters as shown in
Table 2. The shunt capacitance is 330 pF, and the resonance frequency of the LC resonator in free space is approximately 1.9752 MHz. The experimental specimen is shown in
Table 3.
In order to test the performance of the designed LC resonator, a conventional concentric T-R probe and a side-by-side T-R probe were used for signal comparison. The experimental platforms of these two probes are shown in
Figure 9b. Compared with the LC resonator, the system mainly includes an additional FPGA-based electromagnetic device. The electromagnetic instrument, developed by the University of Manchester, features an advanced FPGA and can generate excitation signals from 1 to 200 kHz and perform digital demodulation at a rate of 100 kps to achieve high-speed processing.
These two probes were used in our previous research. Both probes consist of two closely wound coils with the same coil parameters used in this experiment. The only difference between the two probes is their spatial position, and their structural parameters are illustrated in
Figure 10 [
32].
5. Conclusions
In this paper, a resonant eddy current detection method based on LDC is proposed to realize the miniaturized design of an LC resonator, which can be used to identify defects on the CFRP surface at a high lift-off height. The sensitive element in the LC resonator is an inductor, and the physical structure chosen is a double-layered planar coil with a spacer. This design has a higher SRF than the commonly used hollow densely wound coils, enabling the LC resonator to work stably at a higher resonance frequency and achieve a sufficiently high detection sensitivity. This allows the LC resonator to operate stably at a higher resonance frequency and achieve a high level of detection sensitivity.
Through scanning experiments on aluminum plates with defects, it has been verified that the designed LC resonator has a higher SNR compared to conventional concentric T-R probes and side-by-side T-R probes. Additionally, it is independent of the scanning angle and can accurately estimate the width of defects. Through scanning experiments on CFRPs, the anti-interference capability of the LC resonator has been confirmed. Surface defects of CFRPs can be detected at a lift-off height of 7 mm, even in the presence of highly conductive materials. When the lift-off height is less than 3 mm, the LC resonator becomes highly sensitive to interference from other conductive materials.