Characterization of Multi-Layer Rolling Contact Fatigue Defects in Railway Rails Using Sweeping Eddy Current Pulse Thermal-Tomography

Abstract

Railways play a pivotal role in national economic development, freight transportation, national defense, and regional connectivity. The detection of rolling contact fatigue (RCF) defects in rail tracks is essential for railway safety and maintenance. Due to its efficiency and non-contact capability in detecting surface and near-surface defects, Eddy Current Pulsed Thermography (ECPT) has garnered significant attention from researchers. However, detecting multi-layer RCF defects remains a challenge. This paper introduces a sweeping Eddy Current Pulsed Thermal-Tomography system (ECPTT) to detect multi-layer RCF defects effectively. This system utilizes varying excitation frequencies to heat defects, altering skin depth and facilitating feature extraction to distinguish multi-layer RCF defects. Skewness and thermographic signal reconstruction (TSR) values are employed as features in the experiments. These features are qualitatively analyzed to differentiate the layers and depths of multi-layer RCF defects. Additionally, five different coils were compared and analyzed quantitatively. The results indicate that the ECPTT system can effectively detect and distinguish multi-layer RCF defects, thereby providing more detailed defect information and enhancing railway safety and maintenance efficiency.

1. Introduction

Railway networks are critical infrastructure to national economies. However, the integrity of train rails faces continual challenges due to mechanical stress and environmental factors, leading to various defects. Foremost among these is rolling contact fatigue (RCF), worsened by acceleration, heavy loads, and extensive railway usage. RCF defects appear as distinct ’fish-scale’ patterns, visible on the rail surface or within its internal structure, leading to layered and overlapping defects. Over time, these defects propagate at inclined angles into the subsurface, posing significant risks to railway integrity. Track breaks caused by RCF require regular monitoring due to chronic environmental hazards inherent in railway operations [1,2]. Hence, continuous monitoring of RCF is essential for ensuring public safety and the uninterrupted functioning of railway systems.

Various non-destructive testing (NDT) methods have been developed to detect RCF defects. Ultrasonic testing (UT) [3] has proven effective in identifying internal rail defects. However, UT requires couplers and cannot detect surface or sub-surface defects [4]. Machine vision (MV) systems [5] excel at detecting surface defects but are less capable of identifying subsurface flaws. Electromagnetic detection methods [6,7] provide a comprehensive solution for detecting both surface and sub-surface defects in railway infrastructure. Eddy Current Pulsed Thermography (ECPT), combining eddy current and infrared thermography, innovatively detects both surface and sub-surface defects in rails, offering visual indications through infrared thermography. ECPT is currently gaining significant interest and adoption for detecting RCF in railway infrastructure.

The sensor structure of ECPT significantly influences the distribution of the electromagnetic field on the surface of the test specimen, thereby influencing the inspection results. Excitation coils play an important role in the ECPT system. In recent years, a lot of studies have focused on optimizing detection effects through adjustments to excitation coil parameters, positioning, and structural modifications within the ECPT detection framework. A variety of excitation coils have been applied in ECPT inspection systems. However, it is noteworthy that these coils are not specifically designed to simultaneously address both the ‘field of view’ and the ‘heating effect’ requirements.

In addition to excitation coils, the excitation frequency plays an important role in the inspection result. Due to the skinfold effect, higher excitation frequencies are used for detecting surface cracks, whereas lower frequencies are utilized for detecting sub-surface cracks. As the depth increases, the eddy current skin depth becomes much smaller compared to the depth of the defect, resulting in the concentration of heat primarily on the surface of the specimen [8]. Consequently, single-frequency experiments may not yield optimal results. In order to obtain information at multiple depths, higher skin depth is required, enabling the acquisition of crack information across different layers of the specimen.

Section 2 introduces the previous studies, analyzes their shortcomings, and presents the improvements and innovations of this paper. Section 3 provides a detailed elucidation of the methodology of sweeping ECPTT and the process of feature preparation. Section 4 describes the experimental platform setup and the specific design of the five types of coils. Section 5 presents the thermal images and includes a quantitative analysis of the results. Finally, Section 6 concludes with a summary of the key findings, their significance, and future work.

2. Literature Review

The Eddy Current Pulsed Thermography (ECPT) system can effectively detect RCF defects in rails. There has been some research regarding the application and development of this system.

Thomas et al. [9] utilized Pulsed Eddy Current (PEC) technology to effectively detect RCF defects on rails, encompassing both surface and sub-surface anomalies. Additionally, Eddy Current Thermography (ECT), integrating multi-physical field models, exhibits notable advantages including high spatial resolution and sensitivity in detecting subsurface defects. However, challenges remain, particularly in mitigating lift-off [10] arising from variations in cladding thickness or probe motion. Furthermore, it can influence the accuracy of eddy current detection. The presence of lift-off attenuates the strength of the detected signal, leading to a decay in the performance of the sensor [11], thereby necessitating strategies to suppress this effect.

Excitation coils play an important role in the ECPT system. Gao et al. [12] utilized linear coils for excitation detection of wind turbine gears, encountering issues related to uneven heating. Bai et al. [13] employed square plane coils to detect artificial and natural cracks on steel blades. Although it facilitated relatively uniform heating, presented challenges related to line of sight occlusion. In Song’s [14] experiment, it has been demonstrated that in order to obtain a uniform magnetic field in a given area of a Helmholtz coil, the geometry of the coil increases accordingly. However, when using the ECPT method for rail defect detection, the coils can obstruct the detection process, thereby preventing the infrared cameras from obtaining comprehensive images directly above the rail. To address this issue, Geng and Li [15] devised a novel generation of B-H sensing coils comprising two groups of B-H coils. These coils enable the measurement of magnetic field intensity in different directions, allowing for the analysis of head deflection by comparing measurement results from the two groups. Furthermore, the coils aligned in the same direction are measured in series, thereby effectively enlarging the window area of the coil and enhancing measurement accuracy. Core loop winding is one or more magnetic cores placed in the center of the coil [16], and this configuration offers notable enhancements in both the induction capacity of the coil and the uniformity of heating effects. In a study by Tsopela and Siakavellas [17], experiments were conducted on spiral coils, revealing that optimal sensitivity for defect detection is achieved when the diameter of the coil is twice the lift-off.

The reconstruction of defects has also received attention from researchers. Chen et al. [18] used single-frequency excitation to construct a three-dimensional Pulsed Eddy Current Thermography inspection system. The 3D Pulsed Eddy Current Thermography inspection system has achieved results in detecting multilayer defects. Lugin and Netzelmann [19] developed an algorithm from pulsed thermography data to reconstruct 2D as well as 3D defect shapes. Abidin et al. [20] extracted the slope inclination feature of the transient temperature distribution to estimate the angle and utilized the maximum temperature amplitude feature to quantify the length and depth of the defects. These investigations are based on testing human-made specimens and lack verification of real cracks. Liu et al. [21] uses skewness to quantify the depth of defects in the real cracks under the ECPT system, effectively reconstructing the depth of defects. Zhu et al. [22] evaluated eight spatial and temporal ECPT features on idealized and real RCF cracks. Their results showed that the area-based and kurtosis-based features are suitable for characterizing inclination angles. However, these studies are based on a single excitation frequency and focus only on information such as the depth and angle of the defects, missing the consideration of the number of defect layers. Utilizing a sweeping mode with varying excitation frequencies can acquire the temperature responses at different heating depths. This method can extract crack information from different layers of varying depths, thereby providing a more comprehensive understanding of the specimen’s structural integrity compared to using a single-frequency excitation method.

The aforementioned experiments focused primarily on evaluating the influence of different excitation coils without systematically comparing the effects of various coil structures. In order to address this gap and investigate the influence of both coil structure and excitation frequencies on heating effects, experiments are conducted based on the sweeping Eddy Current Pulse Thermal-Tomography system. This study examines the heating effects of RCF defects with various coil structures, including disc-shaped coils, square plane coils, linear coils, helical coils, and central trench plane coils under different excitation frequencies. Moreover, the experiment distinguishes the number of layers and depths of RCF multi-layer defects by analyzing the thermal response extracted from infrared images obtained at various frequencies.

3. Methodology of Sweeping Eddy Current Pulse Thermal-Tomography

3.1. Ecptt System

The diagram of Eddy Current Pulse Thermal-Tomography (ECPTT) is shown in Figure 1. Initially, the induction heater generates a high-frequency alternating current (HFAC) within the excitation coil, which generates an alternating magnetic field within the space around the test object. According to Maxwell’s equations, eddy currents are induced within the conductive specimen near the excitation coil, generating the Joule heating. Defects in the test specimen disturb the distribution of eddy currents, leading to temperature changes in the surface. An infrared camera captures and records these temperature variations from appropriate angles and positions. Finally, the recorded thermal sequence images is processed and analyzed.

3.2. Physical Modeling of Sweeping Eddy Current Pulse Thermal-Tomography

The physical modeling of ECPTT is based on the thermal diffusion equation in 3D Cartesian coordinates, and the thermal diffusion equation is expressed as

$$\rho C_p{\displaystyle \frac{\partial T}{\partial t}}=\lambda \left({\displaystyle \frac{{\partial }^{2}T}{\partial x^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial y^2}}+{\displaystyle \frac{{\partial }^{2}T}{\partial z^2}}\right)+q$$

(1)

$$\mathrm{q}(\mathrm{x},\mathrm{y},\mathrm{z},\mathrm{t})={\displaystyle \frac{1}{\sigma (\mathrm{x},\mathrm{y},\mathrm{z})}}{\left|J(x,y,z)\right|}^2$$

(2)

where $\rho$, $C_p$, and $\lambda$ are the bulk mass density, specific heat capacity, and thermal conductivity, respectively, q is the Joule heat power density, $\sigma$ is the conductivity of the medium, and J is the current density.

ECPTT workflows consist of a heating phase and cooling phase, and these phases are related to multi-physical interactions, including electromagnetic excitation, eddy current pulse heating, and thermal diffusion. Equation (1) shows that q is influenced by $\sigma$ and J at a particular location, and the presence of defects changes $\sigma$ and J, resulting in different q values around them. In addition, the defect region also has different $\rho$, $C_p$, and $\lambda$, and these changes will have an effect on heating conduction, as mentioned in Equation (1), and hence defects can be detected by anomalous thermal distributions or anomalous transient thermal responses utilizing both induction heating and thermal diffusion. In addition, the induction coil, excitation parameters (duration, frequency, and intensity of the heating pulse) and defect parameters (length, width, orientation, etc.) lead to different thermal responses and distributions.

During the heating phase, eddy current pulse heating dominates. The ECPTT system generates eddy currents within the material under inspection by applying electromagnetic excitation, and currents primarily concentrate in the surface layer of the conductor, enhancing the Joule heating effect in this area. The conductor’s surface generates more heat as the current passes through, which can be effectively detected by thermal imaging equipment.

During the cooling phase, thermal diffusion dominates. The high initial temperature and the narrow shape of the defect result in a fast rate of thermal diffusion, leading to a large temperature gradient. On the other hand, the rail has a large thermal conductivity, and the spatial dimensions of the rail are much larger than the defect, resulting in a uniform cooling phase and a relatively small temperature gradient. Information about the defect can be obtained from the results of thermal diffusion in the thermal image.

The distribution of these eddy currents is influenced by the skinfold effect. The skinfold effect refers to the phenomenon where, under the influence of an alternating current or varying electromagnetic fields, the current density inside a conductor decreases rapidly with increasing distance from the surface, causing the current to tend to concentrate near the conductor’s surface. The degree of this phenomenon is determined by the skin depth, where the current density decreases to approximately 37% of its surface density.

The skin depth can be mathematically expressed as

$$\delta ={\displaystyle \frac{1}{\sqrt{\pi \mu \sigma f}}}$$

(3)

where $\delta$ is the penetration depth; f is the excitation frequency; $\mu$ is the magnetic permeability; $\sigma$ is the electrical conductivity.

The relationship between skin depth and excitation frequency is shown in Figure 2. The skin depth is inversely proportional to the excitation frequency. When a high excitation frequency is used, the skin depth is minimized, allowing for the detection of surface defects. As the excitation frequency decreases, the skin depth increases, enabling the detection of deeper defects. Based on this relationship between frequency and skin depth, effective detection and analysis of defects at different depths can be achieved.

Equation (3) shows that the penetration depth is influenced by the excitation frequency. Consequently, defects with various layers and depth can be detected through different excitation frequency. This method is suitable for detecting multi-layer defects within materials and provides detailed information on defect structures.

3.3. Thermal Signal Feature Extraction

The multi-frequency thermal images provide detailed information on defect structures. However, it is difficult to analyze defects through the thermal images directly; some features are needed to quantitatively analyze and distinguish the defects. To facilitate a comprehensive assessment of the heating efficacy resulting from different frequency excitations on the rail, the thermographic signal reconstruction (TSR) value and skewness are used.

(1)

TSR

The TSR value is calculated using the formula

$$\mathrm{TSR}={\displaystyle \frac{log\left(T_{\max }-T_{\mathrm{init}}\right)}{log\left(T_{\mathrm{init}}\right)}}$$

(4)

where $T_{max}$ denotes the maximum temperature attained during heating and $T_{init}$ represents the initial temperature prior to heating.

When a uniform thermal excitation is applied to a thicker specimen, the logarithm of the surface temperature is linearly related to the logarithm of the response time [23]. Through Equation (4), each pixel point of the thermal image is quantified as a TSR value, which reinforces the linear relationship between each datum and facilitates the assessment of the heating effect. A higher TSR value represents a greater temperature rise.

(2)

Skewness

The skewness is calculated using the following formula:

$$\mathrm{skewess}={\displaystyle \frac{n}{(n-1)(n-2)}}\sum _{i=1}^n{\left({\displaystyle \frac{x_i-\overline{x}}{s}}\right)}^3$$

(5)

where n is the sample size, $x_i$ is the i-th sample value, $\overline{x}$ is the sample mean, and s is the sample standard deviation.

Skewness provides useful information on the asymmetry of thermal distribution. During the heating and cooling phases, due to the rapid heating and cooling phases of the defects, there is a significant asymmetry in the temperature distribution, leading to a great negative skewness.

4. Experimental Study

4.1. Experimental Setup

(1)

ECPTT Configuration

The ECPTT system includes an induction heating device, an excitation coil, a test specimen, an infrared thermal imaging camera, a water-cooling device, and a PC, as shown in Figure 3. The water-cooling device utilizes the hydrological cycle to lower the temperature of the coil and eliminates the influence of the coil’s thermal resistance on the detection effect. This experiment uses multi-frequency excitation to induce different heating depths. In this study, 9 kHz, 16 kHz, and 25 kHz excitation frequencies are applied to detect multi-layer RCF defects. Different excitation frequencies lead to different heating depths, and thus the defects can be analyzed layer by layer through the thermal response of different excitation frequencies. The excitation current is set at 45 A. To ensure consistent input power of different excitation frequencies, the coil turn ratios corresponding to 9 kHz, 16 kHz, and 25 kHz are set at 46, 37, and 33, and the coil current are 2070 A, 1665 A, and 1485 A, respectively. The heating duration is 600 ms. The Flir 655SC infrared camera made by FLIR System Inc. (Wilsonville, OR, USA) is utilized to record the heating process of the RCF cracks.

(2)

Excitation Coils

The experiment tested five excitation coils, as depicted in Figure 4.

Figure 4a shows the helical coil positioned perpendicular to the specimen, generating an excitation magnetic field distributed in a spiral pattern within the specimen. Helical coils offer advantages such as the ability to produce a uniform magnetic field of consistent strength and simplicity in construction, as well as facilitating closed magnetic circuits. However, similar to Helmholtz coils, they require increased sizes to achieve a broader range of uniform magnetic fields. Empirical investigations by Tsopela and Siakavellas [17] indicate that the heating effect of helical coils is not particularly pronounced. Additionally, optimal heating efficiency and detection sensitivity are observed only when the multi-turn helical coil is elevated to a height equal to half of its radius.

Figure 4b shows the disc-shaped coil and Figure 4c shows the square plane coil. These coils are juxtaposed for comparative analysis owing to their similar geometric profiles. Figure 4d shows the linear coil, renowned for its exceptional linearity and measurement accuracy, making it a staple in various experimental contexts. Furthermore, linear coils find utility in applications such as generating excitation for detecting false soldering in SMD circuit boards [24] and assessing changes in material properties [12], and while linear coils afford a comprehensive field of view during excitation generation, their heating efficacy is often suboptimal and lacks uniformity. Figure 4e shows the center trench plane coil.

Figure 5 illustrates the five types of coils utilized in the experiment.

Coils can shade the defect part of a rail and may have the uniformity of heating. The viewing angle shown in Figure 5 is also the view angle of the infrared camera. Coils a, b, and c shade the defect part of the rail as shown in Figure 5, thus affecting the infrared camera’s recording of the thermal response. The uniformity of coil heating also affects the quality of defect heating. If coil heating is not sufficiently uniform within the defect space, defects of the same depth and number of layers may exhibit different thermal responses at different locations, complicating the analysis of experimental results.

In this experiment, the center trench plane coil ensures unobstructed visibility of defect in the thermal images as well as the heating uniformity, and this coil couples best with low excitation frequencies such as 9 kHz.

4.2. Specimen

The rail specimen is a square steel block, 800 mm in length, 70 mm in width, and 45 mm in height. To simulate ideal RCF cracks, U75V steel was employed as the material, and six human-made cracks were fabricated. The grooves were processed using electric discharge wire cutting, with a crack width of 0.2 mm. The buried depths are 0 mm, 0.5 mm, and 1 mm, respectively, while the horizontal depths are 2.7 mm, 3.2 mm, and 3.7 mm. Subsequently, by arranging and combining these three types of cracks, RCF cracks with varying burial depths and layers were simulated. Defects 1, 4, and 6 are single-layer defects, with depths of 0 mm, 0.5 mm, and 1 mm, respectively. Defects 2 and 5 are double-layer defects, and the depths of the first layer are 0 mm and 0.5 mm, respectively. Furthermore, defect 3 is a triple-layer defect, and the depth of the first layer is 0 mm. For multi-layer defects, the distance between two layers is 0.5 mm. The schema of the test piece is shown in Figure 6.

5. Results Analysis

The experiment obtained thermal images of six defects heated by five coils at three excitation frequencies. The thermal responses of different defects will be analyzed in terms of the images and quantitative characteristics.

5.1. Thermal Image Comparison

Table 1. Thermal image of different excitation frequency.

Excitation Frequency	Central Trench Plane Coil	Linear Coil	Helical Coil	Square Plane Coil	Disc-Shaped Coil
9 kHz
16 kHz
25 kHz

presents the thermal images of five coils at the peak temperature (using defect 1 as an example). Due to the large total number of frames, only the frame with the highest temperature from each dataset is selected for display. For a specific coil, the heating power remains constant with frequency, but higher frequencies concentrate eddy currents and heat in a shallower area due to the skinfold effect, leading to a higher maximum temperature on the steel rail surface. The thermal response signals from the steel rail surface are primarily influenced by the excitation frequency and structure of the defects. Table 1 demonstrates the thermal response of defect 1, which is the shallowest single-layer defect in the specimen. All frequencies can effectively heat this defect, and the heat is concentrated more on the rail surface as the frequency increases, resulting in a noticeable increase in the surface’s highest temperature above defect 1. Each coil exhibits similar conclusions, differing mainly in field of view and heating uniformity. This analysis is verified in Table 1.

Figure 7 presents the skewness-based location of a defect within the thermal image (using the excitation frequency of 25 kHz as an example), maintaining the same resolution with the infrared camera of 480 × 640. Skewness is a third-order moment statistic that primarily represents the uniformity of the temperature distribution, and thus the highest temperature as well as differences in coils have less effect on it. Throughout the heating process, the defect area will have a rapid warming up and a slower cooling down, resulting in a notably lower negative skewness in the surrounding regions. As a result, the location of the defects can be readily identified in the skewness images.

Although differences among coils do not affect the locating of defects, they do affect the analysis of the type of defect. Therefore, a suitable coil needs to be selected before analyzing the defect type. As for the helical coil, the dimensions limit the range and strength of the uniform magnetic field that can be generated, which is ineffective for the specimen [17]. Square plane and disc-shaped coils produce an uneven magnetic field with high intensity on the inside edge of the coil, resulting in an inability to effectively heat the entire defect. This can be observed from the skewness image Figure 7. Linear coils are capable of generating a uniform magnetic field over a sufficiently large range, but their coupling to low excitation frequencies is not as effective as that of the central trench plane coil. The central trench plane coil also has the best visibility at the defect area, and hence the following analysis will be based on the central trench plane coil.

Table 2. Distribution of magnetic flux density and temperature.

Excitation Frequency	9 kHz	16 kHz	25 kHz
Simulation magnetic flux density of single-layer defect (cutaway view)
Simulation temperature of single-layer defect (cutaway view)
Simulation magnetic flux density of triple-layer defect (cutaway view)
Simulation temperature of triple-layer defect (cutaway view)

shows the simulation distribution of magnetic flux density and temperature in the cutaway view. As the frequency increases, the penetration distance of the magnetic field and the depth of downward heat transfer become shallower, verifying the skinfold effect.

Table 3. Comparison of simulation and experiment.

Excitation Frequency	Experimental Results (Surface View)	Simulation Results (Surface View)
9 kHz
16 kHz
25 kHz

compares the simulation and experiment results of defect 1. In the simulation results, the maximum surface temperature increases with frequency, and heat is more concentrated on the defective side of the gap, consistent with the experimental results. The simulated images in both tables are transient images at the end of heating (T = 0.6 s), in the same state as the experimentally captured thermal images.

Table 4. Thermal image of center trench plane coil.

Excitation Frequency	Defect 1	Defect 2	Defect 3	Defect 4	Defect 5	Defect 6
9 kHz
16 kHz
25 kHz

shows the heating results of various defects at the highest temperature under different excitation frequencies. The surface of the defect area exhibits a noticeable region of high temperature. However, due to the aging of the central trench plane coil, high-temperature regions also appear at the edges of the coil, potentially interfering with observation. The defect areas requiring attention are shown in Figure 8. Table 4 demonstrates that the heating effect varies significantly among defects with different layers and depths.

5.2. Quantitative Analysis

(1)

Feature Extraction to Thermal Response

Prior to extracting the characteristic, it is necessary to establish reference positions and reference maximum heating frames. The reference position is the crevice where the rail surface is defectively grooved, as demonstrated in Figure 9a. As mentioned in Section 5.1, the heating process results in a large negative skewness of the defect location compared to the surrounding area, helping to locate the reference position. Figure 9b illustrates the skewness observed along the lines of the reference positions of six defects (using the excitation frequency of 25 kHz as an example). The reference maximum heating frames can be selected through the temperature curves.

This experiment provides a detailed examination of the relationship between temperature information extracted from sweeping frequency heating infrared images and the depth and layer number of defects. The experiments are controlled for the same heating power at different excitation frequencies, and TSR values are used to characterize and distinguish different types of defects. During the heating and cooling phases of the ECPTT, the temperature changes are close to a logarithmic curve [23]. TSR quantifies the information about the temperature change into a value by taking a logarithm, reinforcing the linear relationship between the different thermal signals. Therefore, the value of TSR is more capable of distinguishing the characteristics of different thermal images.

Table 5. Thevalues of TSR at different frequencies.

Defect Number	Excitation Frequency
	9 kHz	16 kHz	25 kHz
1	1.17	1.18	1.27
2	1.10	1.24	1.30
3	1.04	1.10	1.38
4	1.19	1.20	1.26
5	1.15	1.15	1.20
6	1.15	1.17	1.18

shows the values of TSR in the defect region at different frequencies. The mean, the standard deviation, and the coefficient of variation in TSR are 1.1906, 0.0792, and 0.0665, respectively. The coefficient of variation measures the dispersion of the data; it can be seen that the dispersion of TSR values are pronounced enough to distinguish different types of defects. Consequently, the TSR value is used to analyze the differences among various types of defects.

(2)

Feature Analysis for Distinguishing Multi-layer Defects

(a)

The Depth of Defects

The temperature curves of characteristic points for single-layer and double-layer defects with different depths are shown in Figure 10. From the TSR noticed in Figure 11, it can be seen that when the excitation frequency increases, the temperature curves of shallow defects have a significant increase, while the temperature curve rise of deeper defects is significantly smaller. The result indicates that changing frequency excitation is beneficial for distincting defects with different depths.

(b)

The Layer of Defects

The temperature curves of multi-layer defects in three excitation frequencies at characteristic points are shown in Figure 11. In this experiment, defects 1, 2, and 3 are single-layer, double-layer, and triple-layer defects in the same depth, respectively. As the excitation frequency increases, the temperature curve of single-layer defects varies smoothly, while the temperature curve of multi-layer defects changes abruptly at a certain frequency value (double-layer defect in 16 kHz and triple-layer defect in 25 kHz). It shows that sweeping excitation frequency is beneficial for detecting defects with different layers.

(c)

Discussion

Based on the analysis, defects with different properties exhibit different characteristics under swept-frequency excitation.

In this experiment, the infrared camera records the temperature of the defect surface. The temperature of the defect surface is mainly influenced by the depth of heating and the structure of the defect. The depth of heating depends directly on the excitation frequency due to the skinfold effect. The structural factors of defects are mainly the depth and number of layers that can affect the temperature of the defect surface.

For single-layer defects of different depths, the defect can be heated effectively under three excitation frequencies when it is shallow. Due to the constant power, the heat will concentrate more on the defective surface as the frequency rises, and thus the temperature of the defect surface increases significantly when the frequency is increased. However, only the 9 kHz excitation frequency can effectively heat the deep defect, and even if the higher excitation frequency concentrates more heat on the defective surface, it lacks the heat that the defect gives off when it is effectively heated, and hence the temperature change in the deep defect surface is not much different from the lower excitation frequency. Therefore, the variation in TSR values with frequency is significant for shallow defects and insignificant for deep defects. This analysis can be verified by comparing the images in Figure 10.

For multi-layer defects, the number of layers that can be heated varies with excitation frequencies. If the defect is heated at a low frequency, all layers can be heated efficiently. For single-layer defects, most of the heat is concentrated on a single defect. However, for multi-layer defects, the heat is distributed to defects in different layers, which results in the first-layer defect receiving significantly less energy than the single-layer defect. Therefore, the maximum temperature of a single-layer defect surface will be significantly higher than those of double- and triple-layer defects. Comparatively, a higher excitation frequency led to a shallower penetration depth of the magnetic field, which can only effectively heat up to the first layer of defects. Single-layer defects have the rail material underneath them, while multi-layer defects have other layers of defects underneath the first layer of defects. Since the defects are filled with air, which has a lower thermal conductivity than the rail material, deeper defects in a multi-layer defect prevent the first layer of the defect from dissipating heat downward, resulting in a significant increase in the surface temperature of the multi-layer defect. This leads to a mutation in the maximum surface temperature of the multi-layer defects between two excitation frequencies. In this experiment, the double-layer defect has the mutation in the maximum surface temperature from the excitation frequency of 9 kHz to 16 kHz, while the triple-layer defects have the mutation in the maximum surface temperature from the excitation frequency of 16 kHz to 25 kHz. This analysis can be verified by comparing the images and TSR values in Figure 11.

In this experiment, the lowest excitation frequency selected is 9 kHz, providing sufficient heating depth to reach the deepest defects in the experimental specimens. Three excitation frequencies are selected for effectively identifying the three layers of defects in the specimen. In practice, a wider range of excitation frequencies should be selected to detect potential defects in rails, reducing the impact of detection limits on the detection effects.

This experiment uses manual specimens, and thus the defect locating based on skewness is accurate enough. In practice, the defects in real specimens may be more complex and the accuracy of locating using only the skewness may be reduced; thus, a specific algorithm may be required to detect and locate defects. After detecting the defects, the method described in this paper can be used to distinguish different types of defects, aiding in the subsequent treatment.

6. Conclusions

This paper proposes a sweeping Eddy Current Pulse Thermal-Tomography system (ECPTT) and verifies the feasibility of sweeping frequency heating for detecting multi-layer defects. This study compares the detection effect of five coils and selects the center trench plane coil as performing the best. In this paper, skewness is used to detect and locate defects. Furthermore, TSR values are used to quantify the temperature rise of defects, enhancing the linear relationship between different sets of data and facilitating comparative analyses. The distinctions of types of multi-layer defects are based on the variation in TSR values with frequency.

The differentiation can be summarized as follows: the TSR value of shallow defects increases significantly with increasing excitation frequency, while deeper defects show no significant change. Single-layer defects display no mutation in the TSR value with varying excitation frequency, while double-layer defects and triple-layer defects show a mutation in the TSR value when the excitation frequency increases to a certain value. In this experiment, the double-layer defect has a mutation in maximum temperature at an excitation frequency of 16 kHz, while the triple-layer defect has a mutation in maximum temperature at an excitation frequency of 25 kHz.

Most previous studies have used a single excitation frequency to heat the specimen for detection. However, the heating depth of a single frequency is limited by the skin effect, impacting the detection and reconstruction of defects. This paper uses multiple excitation frequencies to heat the defects, overcoming the heating depth limitation and facilitating the acquisition of defect information at various depths, particularly for identifying multi-layer defects. The number of layers and depths of rolling contact fatigue (RCF) multi-layer defects can be distinguished through the transient thermal response at scanning frequencies.

Future work will focus on the tomographic reconstruction of artificial RCF multi-layer defects and the application of the proposed system to the detection and reconstruction of natural multi-layer RCF defects.