Resonant frequency tracking mode on eddy current pulsed thermography non-destructive testing

Abstract

Eddy current pulsed thermography (ECPT) has been widely used in the field of non-destructive testing due to its safety, non-contact detection, high spatial resolution and intuitive results. Inductive excitation source is an important component of ECPT and provides high-frequency alternating current to drive the excitation coil. However, a resonant frequency distortion phenomenon exists in the excitation source during the detection process, which seriously affects the output power of the excitation source and the sample detection effect. This paper presents a fast resonant frequency tracking loop for full bridge series resonant inverter which is used to search the resonance frequency in real time through direct digital synthesizer (DDS) and all-digital phase-locked loop. Theoretical analysis and simulation are presented to explain the working principle of the loop. Then, an experimental prototype is manufactured which serves as an excitation source for the ECPT experimental system. Compared with traditional excitation sources, the prototype does not need a water-cooled device and the tracking speed can be adjusted by modifying the parameters of DDS. Finally, experiments have been conducted on both artificial slot of 45# steel and natural cracks of rail and stainless steel to investigate the influence of resonant frequency tracking speed on the crack detection. The results revealed that reducing the resonant frequency tracking time can efficiently improve defect detectability and the manufactured prototype showed more application potential.

This article is part of the theme issue ‘Advanced electromagnetic non-destructive evaluation and smart monitoring’.

1. Introduction

Any object produces electromagnetic radiation when its temperature is above absolute zero. Infrared thermography (IRT) is a nondestructive, non-intrusive, non-contact technology [1] which is based on the measurement of radiant thermal energy distribution on the surface of objects through infrared sensor. Nowadays, IRT has received extensive attention and has been used in a broad range of applications, such as material characterization [2], diagnostics [3], cultural heritage analysis [4] and fatigue crack detection [5]. Infrared thermography is generally classified into two major types [6]: passive infrared thermography (PIT) and active infrared thermography (AIT). PIT uses the temperature differences of the test object under natural conditions. Conversely, AIT requires an external heat source which is applied to generate a thermal contrast between defective and non-defective areas during the detection process [7]. AIT is superior to PIT because a great variety of excitation sources such as optical excitation, electromagnetic excitation, mechanical excitation and a combination of modes can be used [8].

As a branch of active infrared thermography, eddy current pulsed thermography (ECPT) is a burgeoning multiple modality technique for conductive material which combines the benefits of conventional pulsed eddy current testing with infrared thermography [9]. A large alternating current (AC) signal which circulates in the coil is generated by the electromagnetic excitation source in a short duration, and then eddy currents are induced in the conductor. If the conductive sample under test contains surface or subsurface defects, the distribution of eddy current is disturbed [10], resulting in an increased current density around the crack area. The infrared camera captures the surface heating distribution on the test object, and defect characterization can be achieved by analysing the thermal patterns with the help of various image processing methods e.g. principal component thermography (PCT) [11], pulsed phase thermography (PPT) [12], thermographic signal reconstruction (TSR) [13] and partial least square thermography (PLST) [14]. From the above working principle of ECPT, it can be seen that excitation source holds the balance status in inspection work.

In the past decade, researchers have studied the effects of excitation source parameters on detection. Siakavellas investigated the relationship between the crack detection capability of ECPT and several factors. These include crack orientation, heating rate and the excitation period [15]. Biju et al. analysed the optimum frequency of the excitation source which would generate a maximum temperature rise for a given thickness [16]. Kostson et al. used a series of different excitation currents to study the SNR threshold which made the induced background heat and heat increase at the crack tip distinguishable [17]. Wilson et al. introduced the design, development and optimization of the ECPT inspection system and paid attention to the coil design and selection of excitation parameters including excitation power in order to obtain quantitative information for defect characterization [18]. Several literatures introduced the model and index of excitation source used in ECPT experiment. Liu et al. studied the welded structures via ECPT and an induction heater which provided 40 A current for the excitation coil with a frequency of 150 kHz was used in the experiment [19]. As can be seen from the photo of the experimental platform, an enormous water-cooled machine whose volume was approximately ten times that of the induction heater was needed to reduce the heating of the equipment. Zhao et al. proposed a novel system of circle-ferrite pulsed inductive thermography and the Easyheat 224 induction heater from Cheltenham Induction Heating, Ltd [20] was used. However, the production of excitation source was rarely introduced and few researchers were concerned with the resonance frequency matching of the excitation coil.

The excitation coil and the detected sample can be regarded as a load and the equivalent parameters change when the excitation source operates. It results in a variation of the natural resonant frequency of the circuit. The excitation source should operate in the quasi-resonant or resonant state, which requires the control loop to track the resonant frequency. Several control circuits are implemented with phase-locked loop integrated circuit, which was made up of special IC and analogue components. However, the analogue circuits have the disadvantages of poor flexibility, low precision and sensitivity to electromagnetic noise and temperature [21]. FPGA runs at high speed due to its parallel operation structure and it is rich in hardware and logic resources. Therefore, it is suitable for designing fast resonant frequency tracking loops. You et al. presented an FPGA implementation of an all-digital phase-locked loop (ADPLL) with alterable modulus control which is completed by the FPGA IP core 74HC297 and a small amount of independent modules [22]. Roy et al. realized dynamic tracking of resonant frequency by ADPLL in a CSI fed induction heating prototype which works at around 10 kHz in the laboratory test [23]. Nagarajan et al. designed an FPGA-based embedded controller which used the PI controller-based VCO scheme to keep the inverter operating frequency tracking the series load resonant frequency [24].

Although the above control loops introduce some different realization methods of ADPLL and study the performance and locking time of ADPLL, the loop used for induction heating power supply cannot achieve a wide range of frequency sweep and the operating frequency is less than 150 kHz. The frequently used excitation frequency of ECPT [25–30] is higher than 150 kHz. This paper presents a resonant frequency tracking loop for full bridge series resonant inverter by switching between DDS and ADPLL. Theoretical analysis and simulation of the proposed loop is introduced in detail. In addition, an experimental prototype is manufactured in the laboratory, which can achieve sweep frequency from 300.59 kHz to 151.06 kHz and the fastest resonant frequency tracking time is less than 2 ms. By setting the parameters of DDS, the resonance frequency tracking time can be adjusted. Five groups of comparative experiments have been conducted on both artificial slot of 45# steel and natural cracks of rail and stainless steel by the experimental prototype. The influence of resonant frequency tracking speed on the crack detection is reported.

The remainder of this paper is organized as follows. The theory of heat conduction and the resonant frequency tracking loop are presented in §2. The simulation and FPGA implementation are shown in §3. The experimental prototype using the proposed loop is shown and the comparative experiments have been conducted in §4. Finally, conclusions and future work are given the end of this paper.

2. Methodology

(a). Introduction of eddy current pulsed thermography system

The principle schematic diagram of the ECPT is shown in figure 1. The system mainly includes IR camera, signal generator, induction heater, excitation coil, the test sample and PC. The IR camera is fixed above the coil. The signal generator controls the induction heater to work simultaneously with the IR camera. Since crack exists, the distribution of eddy current induced by the induction heater changes, resulting in different temperature distribution on the sample surface. In addition, the IR camera records temperature information and PC performs data processing. The heat conduction is a 3-D process [27] as the heat flow is always transferred from the high-temperature area to the low-temperature region until the thermal equilibrium is finally reached. Lateral thermal diffusion causes a blurring effect while the induction heater is required to operate in a short time to obtain the best thermal contrast between the defective area and the non-defective area.

Figure 1.

ECPT schematic diagram. (Online version in colour.)

(b). Theory of induction heating

When the excitation source supplies the excitation coil with high frequency and large amplitude AC, the generated electromagnetic field induces eddy currents in the conductive material which are converted to heat through ohmic heating, in accordance with Joule’s Law. The general formulation is given as follows:

$$Q=\frac{1}{\sigma }|J_s{|}^2=\frac{1}{\sigma }|\sigma E{|}^2,$$ 2.1

where Q is the sum of the generated heat, J_s is the induced current density, σ is the electrical conductivity and E is the electric field intensity.

By taking account of Fourier’s Law of heat conduction, the inductive heat conduction equation of a specimen can be expressed as [31]

$$\frac{\mathrm{\partial }T}{\mathrm{\partial }t}=\frac{\lambda }{\rho C_p}(\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{y}^2}+\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{z}^2})+\frac{1}{\rho C_p}q(x,y,z,t),$$ 2.2

where T = T(x, y, z, t) is the surface temperature distribution, λ is the thermal conductivity of the material (${\text{W m}}^{-1}\hspace{0.17em}\text{K}$), ρ is the density (kg m⁻³), C_p is specific heat capacity (${\text{J kg}}^{-1}\hspace{0.17em}\text{K}$) and q (x, y, z, t) is the heat generated function per unit volume and unit time. By solving the equation, the value of temperature T and the temperature profile in the sample can be obtained.

The ideal expression of current in the excitation coil can be written as I(t) = I₀sin (2πft), t ≤ t_h, where I₀ is the current peak value, f is the operation frequency of coil which depends on the values of equivalent capacitance and inductance in the excitation source resonant circuit and t_h is the heating time. When time is greater than t_h, the current disappears. Joule heat and thermal diffusion work together during the heating stage. This temperature rise of the sample is determined by the excitation frequency, the heating time, the high-frequency magnetic field at the sample surface and characteristics of the material such as electrical conductivity, magnetic permeability, thermal diffusivity and thermal conductivity. In fact, the control loop looks for the resonant frequency of the excitation source and the coil current is not an ideal sinusoidal expression in the initial stage. This time has an impact on the temperature rise.

(c). Resonant frequency tracking loop

The excitation source for ECPT is actually an induction heating power supply system and the schematic diagram of this system is illustrated in figure 2. Since electricity is rectified and filtered, a DC voltage U_d is generated and this drives the full bridge converter. The MOSFET switch tubes of the full bridge converter are $Q1\text{–}Q4$, and C_s is the resonant capacitor. In order to increase the coil current and improve the detection effect, a step-down transformer T1 is used. The coil, sample and capacitor constitute the series resonant circuit. Due to the electromagnetic interaction between the excitation coil and the sample, an equivalent circuit model [32] can be used to characterize the relationship between them. The circuit diagram of the full bridge series resonant inverter is shown in figure 3.

Figure 2.

Schematic diagram of the induction heating power supply system. (Online version in colour.)

Figure 3.

Circuit diagram of the full bridge series resonant inverter. (Online version in colour.)

The excitation coil is presented as a series RL circuits. In fact, due to the large excitation current during detection, the inductance and resistance values on the connecting wires of the circuit cannot be ignored. Here, resistance R_s and inductance L_s take into account the electrical parameters of the excitation coil and the connecting wire. The sample is modelled as an inductor L_e and an impedance Z_e = R_e + jX_e, which is related to the material properties of the sample. According to Kirchhoff’s Voltage Law, the following Equations can be obtained:

$$V_2=(R_s+jw{L}_s+\frac{1}{jw{C}_s})I_2-jwM{I}_e$$ 2.3

and

$$(R_e+jw{L}_e+j{X}_e)I_e-jwM{I}_2=0,$$ 2.4

where V₂ and I₂ are the secondary output voltage and current of transformer T₁, respectively. M is mutual induction between the coil and sample and w is the angular frequency. Substituting equation (2.4) into equation (2.3), the impedance of series resonant circuit can be calculated as

$$Z=\frac{V_2}{I_2}=R_s+R_e\alpha +j[w{L}_s-\frac{1}{w{C}_s}-(w{L}_e+X_e)\alpha ]$$ 2.5

and

$$\alpha =\frac{w^2{M}^2}{{R_e}^2+{(w{L}_e+X_e)}^2}.$$ 2.6

The actual resonant frequency can be determined by setting the imaginary component of impedance Z to 0. When there is no sample under test, the value of α is zero and the resonant frequency f_o can be derived as

$$f_o=\frac{1}{2\pi \sqrt{L_s{C}_s}}.$$ 2.7

However, in the ECPT detection process, the parameters in the equivalent circuit of excitation coil and sample system are related to many factors. These include the geometry of coil, test sample, the parasitic parameters on the wire, the material parameters of conductivity and permeability, the appearance of defects in the sample, and the lift-off. In addition, the temperature rise during testing affects the material properties which further increases the complexity of the problem [33]. These impact factors results in distortion of resonant frequency. The resonant frequency cannot be determined by simply measuring the inductance of the excitation coil and the capacitance of the resonant capacitor. The resonance shifting phenomenon prevents the full bridge series resonant inverter from working in the resonance state. A phase difference between output voltage V₁ and current I₁ of the inverter exists, which seriously affects the equipment output power and utilization efficiency. Therefore, the resonant frequency tracking circuit is indispensable for the inverter, especially for short time excitation detection of ECPT.

The proposed resonant frequency tracking loop is shown in the red dotted box in figure 2 and it has two modes, where DDS searches for resonant frequency over a large frequency range and the ADPLL fine-tunes the frequency. The working process of the proposed resonant frequency tracking loop is expressed as follows: the current on the primary side of transformer is measured in real time by using two current transformers. One of the current signals is directly sampled by AD1 to calculate the effective value of the current. If the calculated current value I_rms exceeds the preset current threshold I_set, the operating mode is switched to ADPLL mode, otherwise it works in DDS mode. The other signal passes through the zero-crossing comparator and after sampling by AD2, it is used as the input f_in of the ADPLL which characterizes the full bridge converter output current. Both modes generate two complementary pulse-width modulation (PWM) drive signals with dead zones. One generated PWM signal passes through the delay unit and acts as the input f_out of the ADPLL which characterizes the full bridge converter output voltage. The function of the delay unit is to ensure that the load voltage always exceeds the load current after the phase-locked loop is locked, and the inverter operates in an inductive state.

DDS has a phase accumulator and a waveform memory. By adjusting the frequency control word and the word length of phase register, the frequency and its frequency resolution of the output square wave signal can be changed. DDS can provide an initial driving frequency and achieve frequency sweeping. The sweep range is from f_max to f_min. The maximum frequency f_max and minimum frequency f_min can be expressed as

$$f_{\text{max}}=\frac{f_c\times {\text{FW}}_{\text{max}}}{2^N}$$ 2.8

and

$$f_{\text{min}}=\frac{f_c\times {\text{FW}}_{\text{min}}}{2^N},$$ 2.9

where N is the word length of phase register [bits], f_c is the FPGA system operating clock frequency [MHz], FW_max and FW_min are the maximum frequency control word and minimum frequency control word, respectively. The frequency control word is changed from FW_max to FW_min, and it is decremented by ΔFW every ΔT time interval. The above parameters can be set in advance, thus the total sweep time T_DDS within a single period can be adjusted, namely

$$T_{\text{DDS}}=(\frac{{\text{FW}}_{\text{max}}-{\text{FW}}_{\text{min}}}{\mathrm{\Delta }\text{FW}}+1)\mathrm{\Delta }T.$$ 2.10

ADPLL continuously adjusts the phase difference between the output voltage and current of the full bridge converter. When the voltage and current are close to the same phase, the inverter circuit reaches the quasi-resonant state. The schematic of ADPLL is depicted in figure 4. ADPLL is made up of frequency detector module, adaptive module, digital phase detector, first-order filter, digital controlled oscillator and initial control word module.

Figure 4.

Schematic of ADPLL.

A digital phase detector based on a dual D-trigger phase detector compares the phases of both input signal f_in and feedback signal f_out, and then obtains a phase difference signal. If f_in is ahead of f_out, the advanced phase difference signal up is high level, otherwise, the lag phase difference signal down is high level. The input signal f_in is detected in real time by the frequency detector module and by comparing with the clock signal f_c, control word N₀ characterizing the input signal can be obtained. The first-order filter, which is basically a proportional compensator, filters the phase difference signal. Proportional coefficient K_p can be adjusted adaptively. N_P, which is generated by the first-order filter, and N₀ are added together to obtain the total division value N. This value reflects both the change of input signal and the phase difference. The digital controlled oscillator acts as a variable mode frequency divider and divides the system clock f_c to obtain a feedback signal f_out. The function of the initial control word module is to assign the frequency control word of DDS to digital controlled oscillator as the initial division value N_i when the tracking loop switches from DDS mode to ADPLL mode.

By ignoring the influence of the frequency detector module, the adaptive module and the initial control word module, ADPLL is actually a closed-loop system and its simplified mathematical model is shown in figure 5. θ_in(s) is the phase of the input signal f_in, θ_out(s) is the phase of the output signal f_out. H_dpd(s), H_fof(s) and H_dco(s) are transfer function of digital phase detector, first-order filter and digital controlled oscillator, respectively.

Figure 5.

Simplified mathematical model of ADPLL.

According to the working principle of the digital phase detector, H_dpd(s) can be expressed as [34]

$$H_{\text{dpd}}(s)=-\frac{f_c}{2\pi f_{\text{in}}}.$$ 2.11

The first-order filter is a proportional controller and H_fof(s) can be obtained as

$$H_{\text{fof}}(s)=K_p.$$ 2.12

Based on the relationship between the phase θ_out(s) and the frequency division value of the digital controlled oscillator, the transfer function H_dco(s) can be approximated as

$$H_{\text{dco}}(s)=\frac{\mathrm{\partial }{\theta }_{\text{out}}}{\mathrm{\partial }N}=-\frac{2\pi f_c}{N^{2}s}.$$ 2.13

When the input signal changes near the lock frequency point, the following expression is satisfied: f_in ≈ f_out ≈ f_c/N. Therefore, the transfer function of ADPLL is

$$H_{\text{ADPLL}}(s)=\frac{H_{\text{dpd}}(s)\times H_{\text{fof}}(s)\times H_{\text{dco}}(s)}{1+H_{\text{dpd}}(s)\times H_{\text{fof}}(s)\times H_{\text{dco}}(s)}=\frac{K_p{f}_{\text{in}}}{s+K_p{f}_{\text{in}}}.$$ 2.14

3. Simulation and FPGA implementation

Assuming that the input signal frequency is 200 kHz, the dynamic response of ADPLL is obtained by using Matlab/Simulink. Figure 6 shows the step response curve of the system under different K_p parameters. It can be seen that the speed of system response is related to K_p and the higher the K_p value, the faster the response curve. Table 1 shows the value of K_p and the response time when the output phase difference of digital phase detector is in a different range. The phase-locked loop is quickly adjusted when the phase difference is large, and fine-tuning is performed when the phase difference is small. Thus, the purpose of fast phase locking can be achieved.

Figure 6.

Step response curve under different K_p parameters. (Online version in colour.)

Table 1.

K_p and response time under different phase difference.

phase difference Pe	Kp	response time (ms)
0 < Pe < π/8	1/8	0.185
π/8 ≤ Pe ≤ π/4	1/4	0.095
Pe > π/4	1/2	0.046

ISE Design Suite 14.7 simulation software of XILINX and SPARTAN-6 AX309 FPGA are used as the design platform. The chip clock frequency is 50 MHz. Figure 7 shows the phase locking simulation waveform of ADPLL when the frequency of input signal f_in is 200 kHz and the initial phase difference is 90^°. It can be seen that ADPLL reaches the phase locking after 13 input cycles, and the steady-state error is two master clock cycles. Simulation results show that the locking speed of ADPLL is fast and the steady-state error is small, and it can meet the requirement of fast resonant frequency tracking.

Figure 7.

Dynamic locking simulation waveform of ADPLL (f_in = 200 kHz). (Online version in colour.)

This paper adopts the hardware description language (Verilog HDL) and the top-down system design method to complete the module. The RTL top-level map of ADPLL and the proposed resonant frequency tracking loop realized by FPGA schematic are depicted in figures 8 and 9, respectively. Each module in figure 8 corresponds to the schematic diagram of ADPLL. Figure 9 adds the serial port module, heating time module and interface module. These modules realize the selection of DDS frequency sweep time interval and precisely control the heating time of excitation source.

Figure 8.

RTL top-level map of ADPLL.

Figure 9.

RTL top-level map of the proposed resonant frequency tracking loop.

The traditional PWM module generates the four-channel complementary drive signals with dead zone by delaying the output signal which comes from DDS or ADPLL. At a fixed FPGA clock frequency, the delay period occupies a large proportion in a cycle for high-frequency application, leading to phase-locking failure. For example, if the operating frequency is 250 kHz and the dead zone is set to 400 ns, the delay difference is approximately π/5 of the output signal which cannot be ignored. This paper makes an improvement by using the frequency control word of DDS and the frequency division value of digital controlled oscillator. It is not necessary to shift the output signal, which makes the excitation source more suitable for high-frequency operation.

4. Experiments set-up and discussion

(a). Prototype and eddy current pulsed thermography experimental system

The experimental prototype using the proposed resonant frequency tracking loop is described in figure 10a. A programmable DC power supply Chroma 62024p-80-60 is used to produce DC power for the full bridge series resonant inverter. An auxiliary DC power supply is used to provide positive and negative voltages for the chips. The current on the primary side of the transformer is collected by two current transformers with a ratio of 1000:1. One signal, which is directly sampled by the AD acquisition module AD9226 of the FPGA, is used to monitor the effective value of the full bridge converter output current, and an enabling signal is generated when the threshold value is reached. The other signal passes through the zero-crossing comparator LM311 and is converted into a square wave signal, then it is also sampled by the AD9226 and is used as an input signal of ADPLL. The main parameters of the full bridge series resonant inverter are shown in table 2. The excitation coil adopts the double-turn coil structure with L-shaped yoke [35] as shown in figure 10b. It is made of copper tube with 12.7 mm radius and 4 mm wire diameter and the inductance of this coil structure measured by the LCR measuring instrument is 1 μH.

Figure 10.

(a) Photograph of the experimental prototype, (b) double-turn coil structure with L-shaped yoke. (Online version in colour.)

Table 2.

The main parameters of full bridge series resonant inverter.

item	value
input voltage	60  V
coil inductor	1 μH
capacitor	0.48 μF
transformer turn ratio	5:1
output current (peak value)	130 A
operating frequency	178.6 kHz

The sweep frequency range of DDS is selected from 300.59 kHz to 151.06 kHz and the change of frequency per 20 μs is 1.53 kHz. The total heating time of excitation source is set to be 100 ms. Since it is difficult to directly measure the resonance frequency tracking time, a small multi-turn induction coil is placed next to the excitation coil. The voltage of induction coil is collected by the NI USB 6366 acquisition card and the supporting software DAQ EXPRESS in real time. Through Matlab data processing, the voltage curve of the induction coil under different time is obtained, which is shown in figure 11a. It can be seen from the figure that the voltage of the induction coil is very small and negligible at the initial stage. After a brief time, the voltage value increases significantly.

Figure 11.

(a) Voltage curve of the induction coil, (b) a partial magnification of the voltage curve. (Online version in colour.)

By amplifying the voltage signal in the ellipse box of the red dotted line in figure 11a, an enlarged figure can be obtained in figure 11b. In the initial stage, when the MOSFET drive signal of the full bridge series resonant inverter is scanned from high frequency to low frequency, the actual operating frequency gradually approaches the resonant frequency, and the measured output voltage gradually increases. When the resonant frequency is reached, the output voltage is large and basically stable, which indicates that the output current of the full-bridge series resonant inverter is the maximum at the resonant frequency. It can be seen that the fastest resonant frequency tracking time is 1.5 ms.

An ECPT experimental system was built where an experimental prototype serves as the excitation source as shown in figure 10a. The configuration system is shown in figure 12. The FLIR A655sc infrared camera is used, which has an uncooled micro-bolometer with a high resolution 640 × 480 array. The camera has a sensitivity of 30 mK and its spectral range is $7.5\text{–}14\hspace{0.17em}\mu \text{m}$. The adjustable platform which contains a ruler could precisely control the distance between the excitation coil and sample and the lift-off is 2 mm.

Figure 12.

The configuration of the ECPT experimental system. (Online version in colour.)

(b). Description of the samples

In this study, one sample with artificial defects and two samples with natural defects were tested. The 45# steel is shown in figure 13a. The dimensions of 45# steel are 140 × 60 × 10 mm³ and it is made up of ferromagnetic material. The four artificial slot defects labelled 1–4 have the same length (8 mm) and width (1 mm), but depths are 7 mm, 6.5 mm, 6 mm and 5.5 mm, respectively. In the experiment, only the defect labelled 2 is selected for detection. A cut-off rail sample with rolling contact fatigue cracks is described in figure 13b. There are clusters of microscopic oblique cracks in the surface along the rail tread. The stainless steel sample is shown in figure 13c and the dimensions are 200 × 100 × 20 mm³. The stainless steel has discontinuous natural defects in the interior of the specimen, but they cannot be observed by the naked eye.

Figure 13.

The test samples and the crack area. (a) 45# steel, (b) rail, (c) stainless steel. (Online version in colour.)

(c). Results and discussion

(i). Influence of the resonant frequency tracking speed on the crack detection

DDS parameters and heating time can be adjusted through the FPGA serial port in the proposed resonant frequency tracking loop. Five different groups of experimental parameters are set in this paper, as described in table 3. The heating time, DDS sweep frequency range and frequency variation are the same, however the duration of each frequency is 20 μs, 120 μs, 240 μs, 480 μs and 720 μs, respectively. The total DDS sweep time within a single period becomes larger with the increase of time interval ΔT, which also means that the resonance frequency tracking time is longer.

Table 3.

Five different groups of experimental parameters.

serial number	th (ms)	fmax (kHz)	fmin (kHz)	ΔFW (kHz)	ΔT (μs)	TDDS (ms)
E-1					20	1.98
E-2					120	11.88
E-3	200	300.59	151.06	1.53	240	23.76
E-4					480	47.52
E-5					720	71.28

According to the parameter settings in table 3, five groups of comparative experiments were conducted on each specimen to study the effect of resonance frequency tracking speed on defect detection. In the experiment, except for the differences in the resonance frequency tracking times, other parameters such as the position of specimen and the lift distance remain unchanged. A frame rate of 200 Hz for the FLIR infrared camera with a 640 × 120 array was used to detect the cracks and the thermal images of the sample under test were collected. Figure 14 depicts the relationship between the time DDS requires to complete the single cycle frequency sweep and the number of frames when the defect first appears under different experimental conditions. The result illustrates that the resonance frequency tracking time is positively correlated with the time of defect appearance. This indicates that the proposed resonant frequency tracking loop is beneficial for the rapid detection of defects.

Figure 14.

The relationship between frequency sweep time and the frame when the defect first appears. (Online version in colour.)

The thermal images at different times can be obtained and table 4 lists the thermal images of 45# steel and rail at 15 ms and 25 ms and the thermal images of stainless steel at 25 ms and 50 ms under the five different experimental conditions.

Table 4.

Thermal images at different times under five groups of experimental conditions.

For 45# steel, since the crack direction is perpendicular to the eddy current generated by L-shaped yoke coil, the disturbance of the eddy current at the crack tips is strong and hot spots are generated during the heating process. At 15 ms, clear hot spots on both ends of the slot can be seen under experimental condition E-1. Compared with the thermal images collected at experimental condition E-1, defects under experimental condition E-2 are blurred and almost submerged by the background information. Hot spots cannot be observed under the experimental conditions E-3, E-4 and E-5. With the increase of time, defects information also appears under experimental condition E-3 at 25 ms; however, the clearest hot spots are achieved in the first group of experiments.

In the test of rail, all the oblique cracks can be seen under experimental condition E-1 at 15 ms, while only partial defect information can be seen under experimental condition E-2. At 25 ms, the fatigue cracks of the rail appear in the experimental conditions E-1, E-2 and E-3, and the temperature rise of defects is the highest in the first group of experiments. However, due to the influence of heat increase and thermal diffusion, the edges of defects observed under experimental condition E-1 at 25 ms are not as clear as those observed under the sample experimental condition at 15 ms. For materials with large thermal conductivity, it is of great significance to defect cracks before thermal diffusion occurs. Rapid resonance frequency tracking time is beneficial to the detection of such material in a short time.

Since the electrical conductivity and permeability of the stainless steel specimen are smaller than the 45# steel and rail, the temperature rise of stainless steel during heating is lower than the other two samples and the defects appear later in the thermal image. Therefore, for the stainless steel different time thermal images have been chosen to observe the defects. The cracks of stainless steel specimens which are caused by corrosion are intermittent high-temperature points. Several high-temperature points appear under experimental condition E-1 at 25 ms and all defects information is displayed under the sample experimental condition at 50 ms. The crack defection effect under experimental condition E-1 is better than the other comparative experiments at the same instant. For better comparison of experiment results, signal-to-noise (SNR) is used to evaluate the defection results in table 5. The SNR is calculated by the defect area temperature T_D and the non-defect area temperature T_N and its expression is as follows [35].

$$\text{SNR}=20{\log }_{10}\left(\frac{T_D}{T_N}\right)[dB].$$ 4.1

Table 5.

The SNR at different experimental conditions.

		experimental conditions
sample	time	E-1	E-2	E-3	E-4	E-5
45#steel	15 ms	0.7768	0.7123	×	×	×
	25 ms	0.8205	0.7980	0.7358	×	×
rail	15 ms	1.4508	0.0833	×	×	×
	25 ms	2.0953	1.3291	0.6727	×	×
stainless steel	25 ms	0.1683	0.1569	×	×	×
	50 ms	0.3204	0.2817	0.2533	×	×

The calculated SNR results are presented in table 6, where × refers to the absence of defect information. In the test of 45# steel, the SNR is equal to 0.7768 dB and 0.7123 dB under experimental condition E-1 and E-2 at 15 ms. The value of the first group of experiments is larger than that of the second group of experiments, which indicates that the detection performance under experimental condition E-1 is better. This is consistent with the results shown in the thermal images. The SNR is equivalent to 0.8205 dB, 0.7980 dB and 0.7358 dB, respectively, under the experimental conditions E-1, E-2 and E-3 at 25 ms and they gradually decrease. The two specimens with natural defects show the same phenomenon as 45# steel in the comparative experiments although they have different material properties and defect patterns. Both thermal image analysis and SNR calculation show that the resonance frequency tracking speed is related to the crack detection and fast tracking time will enhance the detectability of cracks.

Table 6.

Thermal images at 50 ms under different experimental configurations.

(ii). Comparison with excitation source using the traditional frequency tracking loop

A high-power induction heating power supply controlled by the traditional frequency tracking loop is shown in figure 15a. This frequency tracking control circuit is designed based on PLL IC CD4046 [36]. CD4046 consists of two different phase comparators which have a common signal-input amplifier and a common comparator input, a low-pass filter and a linear voltage-controlled oscillator (VCO). Generally, the frequency range and frequency offset of VCO are related to the external resistor and capacitor. This device chooses the edge-controlled phase comparator II and it can be seen from the technical manual that the resonant frequency range is from 80 kHz to 130 kHz. Due to the narrow frequency range, the induction heating power supply cannot work properly when using the double-turn coil structure with L-shaped yoke. Replacing the coil with the double-turn round coil shown in figure 15b, the device operates normally. The output current and the operating frequency are 290A and 90.9 kHz, respectively. By placing the induction coil next to the excitation coil, the voltage curve of the induction coil under different time is illustrated in figure 16a. It can be seen that the resonant frequency tracking time is 404 ms. When the manufactured prototype is matched with the same double-turn round coil, the measured voltage waveform of the induction coil is shown in figure 16b and the resonant frequency tracking time is only 1.1 ms. The operating frequency at this time is 222.2 kHz. This indicates that the proposed resonant frequency tracking loop is more suitable for high-frequency applications, and can achieve frequency tracking in less than 2ms when matching different types of coils.

Figure 15.

(a) The high-power induction heating power supply, (b) double-turn round coil. (Online version in colour.)

Figure 16.

(a) Voltage curve of the induction coil when the induction heating power supply uses a double-turn round coil, (b) voltage curve of the induction coil when the manufactured prototype uses a double-turn round coil. (Online version in colour.)

Tests have been conducted on the artificial slot of 45# steel and natural cracks of rail as well as stainless steel when adopting the above two prototypes as the excitation sources of ECPT. Table 6 lists the thermal images at 50 ms under the different experimental configurations. Here, prototype 1 refers to the high-power induction heating power supply controlled by traditional frequency tracking loop, and prototype 2 refers to the manufactured prototype using the proposed resonant frequency tracking loop. Coil 1 is the double-turn round coil while coil 2 is the double-turn coil structure with L-shaped yoke. The SNR values of these thermal images are given in table 7.

Table 7.

The SNR of thermal images at 50ms under different experimental configurations.

		sample
excitation source	coil	45#steel	rail	stainless steel
prototype 1	coil 1	0.0557	0.2300	0.1495
	coil 2	×	×	×
prototype 2	coil 1	0.3881	0.5895	0.1754
	coil 2	0.8162	1.4671	0.3204

When the double-turn round coil is used for defect detection, the induced eddy currents in the sample are distributed under the coil, which causes non-uniform heating. For prototype 1, the frequency tracking control circuit takes a long time to reach the resonance state and the excitation frequency of the device is low, so the detection effect is poor. As shown in table 7, the defect information of 45# steel and stainless steel is disturbed by the surrounding noise and only a few shallow oblique cracks of the rail can be seen. In addition, it can be proven by the smallest SNR in this configuration when compared to other experimental conditions. For prototype 2, the thermal images results obtained with double-turn round coil are significantly better than those of prototype 1 and the thermal contrast of defects is enhanced, which can be seen from the increased SNR values. For 45# steel, the crack tip near the excitation coil has a high thermal intensity due to the non-uniform heating and a hot spot appears in the thermal image. The detection result of stainless steel is the same as that of 45# steel and the thermal image shows a high-temperature point near the coil. For the rail, the temperature rise of the oblique cracks is more obvious, nevertheless only partial defect information can be seen. Unlike the double-turn round coil, the double-turn coil structure with L-shaped yoke can generate an approximately uniform electromagnetic field in the inspection area. The prototype 2 using this coil has the best detection effect on the test samples, and the appearance of the defects can be fully displayed. The highest SNR values prove the excellent detection performance of this ferrite-yoke coil.

The obtained experimental results demonstrate that the proposed resonant frequency tracking loop has a faster tracking speed and a wider sweep frequency range than the traditional control circuit. It is more suitable for short-term ECPT defect detection and efficiently improves defect detectability.

5. Conclusion

In this paper, a resonant frequency tracking loop for full bridge series resonant inverter is proposed. It can achieve a wide range of frequency sweep through DDS and the fastest resonant frequency tracking time is less than 2 ms. The fast tracking time leads to rapid defects detection and enhances the detectability of cracks. In particular, for materials with large thermal conductivity, the test can be completed before the onset of thermal diffusion. In addition, the manufactured prototype using this tracking loop shows more application potential. It does not require a water-cooled device, which effectively reduces the volume of the excitation source, and the maximum current peak value provided by the prototype is 130 A.

Future work will focus on improving the performance of the experimental prototype and further increasing the working current of excitation source under the condition of fast resonance frequency tracking.

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Authors' contributions

All authors contributed to the writing and revision of the manuscript.

Competing interests

We declare we have no competing interest.

Funding

No funding has been received for this article.