PAPERS
FEM Analysis for Constructing Rail Head Transverse Crack Detection System Using Guided Waves
2025 Volume 66 Issue 2 Pages 90-95
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2025 Volume 66 Issue 2 Pages 90-95
We performed simulations of ultrasonic wave propagation in cracked rails to investigate a method for detecting transverse cracks in the rail head using guided waves. The results show that 100-150 kHz input frequencies are suitable for detecting rail head cracks and that the peak intensity of the first few waves in the received signal waves decreases with the degree of cracking. Further investigation shows that transverse cracks greater than 20 mm that have grown below horizontal cracks can be detected by checking the intensity of the first three waves in the received waves at 100 kHz.
Many railway operators regularly inspect rails for crack generation and size using rail inspection vehicles that transmit (or emit) ultrasonic waves from the top surface of the rail and detect the ultrasonic waves reflected from the cracks. However, as shown in Fig. 1, detecting transverse cracks, which account for approximately 40% of rail breakages, is difficult with a rail inspection vehicle. This is because transverse cracks develop below horizontal cracks that occur under the top surface of the rail, and ultrasonic waves cannot reach transverse cracks. Therefore, many railway operators generally detect transverse cracks by transmitting and receiving ultrasonic waves from the side of the rail head. However, this inspection method is manual work because continuous inspection is not possible, and it cannot be used to inspect rails with worn sides of the head and at level crossings. On the other hand, rail inspection methods using contactless air-coupled ultrasonic waves (guided waves) have been investigated in the past both in Japan and overseas [1, 2], and a contactless broken rail detection method using guided waves has also been proposed [3]. In this study, we created an FEM analytical model for contactless ultrasonic transmission and reception on the rail. Basic ultrasonic propagating simulations using this FEM analytical model with a slit in the rail have verified the conditions for ultrasonic waves to be sensitive to defects inside the rail. In addition, we performed ultrasonic propagating simulations using the FEM analytical model with an artificial horizontal crack and transverse crack in the rail to verify the possibility of detecting transverse cracks that exist below horizontal cracks by the received response.
Figure 2 shows an overview of the FEM analysis model. We used ultrasonic analysis software “ComWAVE.” The ultrasonic transmitter and receiver are placed away from the top surface of the JIS 50 kg N rail with a finite total length of 1500 mm. The mediums, which were the spaces between the transmitter (or the receiver) and the rail, were provided. Previous research has reported that the propagation depth in the rail varies depending on the frequency of the guided waves [4]. Therefore, we have to understand the input frequency that is sensitive to rail head defects such as transverse cracks. We then inserted a slit of varying depth into the cross-sectional direction from the top surface of the FEM rail models.
Table 1 shows the analysis conditions of the transverse crack model. In this analysis, we considered that the difference in the type of medium outside the rail does not significantly affect the ultrasonic propagation mechanism inside the rail and set water as the medium to reduce the computational load. This is because ultrasonic propagation wavelength in water is several times longer than that in air, significantly reducing the number of elements and analysis time. The element size of the FEM analysis model was set to approximately 1/20 of the ultrasonic wavelength propagating in the water medium (0.35 to 0.75 mm, depending on the input frequency) to ensure the accuracy of the analysis. Three types (100, 150, and 200 kHz) of the ultrasonic input frequency were used based on a study on rail breakage detection [3]. They were then propagated in the longitudinal direction of the rail as high-power continuous waves (wave bursts, wavenumber 12). The angle of both the transmitter and receiver relative to the horizontal plane was set at 20 degrees, and the critical angle of the transverse wave from the water to the rail was set to maximize the received intensity. This is because a previous study [5] showed that in a mode close to the transverse wave (approximately 3 mm/µs), the guided wave propagates through the rail head as a high-speed and high-intensity mode. Therefore, we can generally transmit the transverse wave with high intensity when the angle of the transmitter relative to the object is close to the critical angle. It has been confirmed that ultrasonic waves can be transmitted and received at a distance of more than 70 mm from the transmitter and receiver to the top surface of the rail when mounted on a railway vehicle [3]. However, since the purpose of this study is to understand the ultrasonic propagation characteristics inside the rail, the distance was set at 10 mm, taking into account the number of elements in the entire FEM analysis model, which affects computational load. The transverse slits inserted as cracks were 1 mm wide and inserted at a depth of 10 to 60 mm from the top surface. We also conducted guided wave propagation tests on a rail simulating this analysis model and have confirmed that these responses are almost identical to the analyses.
| (a) Fixed conditions | |||
| Size of transmitter and receiver | 25 mm square | ||
| Angle of transmitter and receiver | 20° | ||
| Distance from transmitter to cracks | 200 mm | ||
| Distance from transmitter and receiver to top surface | 10 mm | ||
| Type of cracks | Transverse slit in rail head | ||
| Horizontal distance between transmitter and receiver | 950 mm | ||
| Type of input wave | Wave burst | ||
| Input wavenumber | 12 | ||
| (b) Relationship between frequency of input wave and number of elements in FEM model | |||
| Input frequency | 100 kHz | 150 kHz | 200 kHz |
| Number of elements, approx. | 50 million | 170 million | 500 million |
Figure 3 shows the ultrasonic propagation on the rail surface (contour map of the displacement). It was confirmed that the slit points inserted from the top surface of the rail show a change in the propagation of ultrasonic waves. In this study, unless otherwise noted, the intensity of the volume strain was used. Volume change in strain was obtained from the volume change calculated from the displacement in each direction of the three dimensions as the intensity of the received signal of the ultrasonic waves. The intensity of the peak values obtained from the analysis results of rails without cracks (slit) was considered to be 1.0, and then with this peak value, each analysis result was normalized.
Figure 4 shows the received waveforms when there is no slit, a slit with a depth of 10 mm and a slit with a depth of 40 mm in the FEM rail model, for 100 and 200 kHz, of the input frequency, respectively. It was confirmed that the intensity decreases with slit depth. Figure 5 shows the change in peak intensity as a function of the difference in slit depth for each input frequency. At the input frequencies 150 and 200 kHz, the peak intensity dropped sharply to about 0.6 when the slit was inserted at a depth of 10 mm from the top surface of the rail. At the input frequency of 100 kHz, the intensity decreased significantly when the slit was inserted at a depth of 20 to 40 mm deep. In addition, at the input frequency of 150 kHz, it was confirmed that the decrease in peak intensity was also large when the slit with a depth of 10 to 30 mm deep was inserted.
The transverse crack depth that should be detected through planned track inspections before rail breakage is 20 to 30 mm. The above results showed that guided waves with a frequency of 100-150 kHz are likely to be suitable for detecting transverse cracks in the rail head.
We further considered the change of depth of propagation in the rail as a function of the difference in ultrasonic frequency. We acquired waveforms at interval of 5mm in the longitudinal direction of the rail at a depth of the top surface and 40 mm from it and produced dispersion curves (color maps) of the volume strain by using two dimensional Fast Fourie Transform [7]. Figure 6 shows the produced dispersion curves. In Fig. 6, the horizontal axis indicates the frequency, and the vertical axis indicates the wavelength. Note that the strong intensity lines (volumetric strain amplitude) with white to red color represent the vibration modes of the waves that propagate prominently at each depth in the rail. The dispersion curves in Fig. 6 show that vibration modes below 200 kHz are stronger at a depth of 40 mm compared to the top surface. Therefore, we assumed that at a depth of 40 mm from the top of the rail, ultrasonic waves in the frequency band of 100 to 150 kHz propagated predominantly. In addition, the slit interrupting this depth partly blocked largely ultrasonic waves in these frequency bands.
We created rail models with inserted artificial horizontal and transverse cracks and conducted FEM analysis to verify the detectability of transverse cracks that developed below the horizontal cracks. Figure 7 shows an overview of the analysis model for the rail model. The calculation process of the analysis was divided into three parts of a series of ultrasonic wave propagation processes from the transmitter to the receiver: propagation from the transmitter in the air to the inside of the rail, propagation in the longitudinal direction inside the rail, and propagation from the inside of the rail to the receiver in the air. We then created an independent model for each part and carried out the calculation in order. As a result, by setting a different mesh size for each model, we can perform calculations using air as the medium and significantly reduce the calculation load while maintaining the calculation accuracy.
Table 2 shows the conditions in this analysis. Since the medium was air, the angle of the transmitter and receiver concerning the horizontal direction was 6 degrees, which is the critical angle of the transverse wave from air to rail. Considering the results of Fig. 5 in Chapter 2, two ultrasonic input frequencies were set at 100 and 120 kHz, which are expected to have higher sensitivity. In addition, the input wavenumber was set to three. This is because, in general, the frequency distribution of the propagating wave becomes broader as the number of waves decreases [8]. Thus, we considered the possibility of capturing the change in the characteristics of the frequency distribution due to the cracks. Figure 8 shows the frequency distribution of the received wave in the case of 3 and 12 of the input wavenumbers obtained by FEM simulation without cracks in the rails. The frequency distribution of the received wave was broader when the input wavenumber was three than when it was 12. Figure 9 shows the schematic shape of the cracks inserted into the rail model. As an artificial horizontal crack, an internal slit with a width of 30 mm and a length of 50 mm was provided at a depth of 7 mm from the top surface of the rail head. On the other hand, as an artificial transverse crack, a semicircular slit was provided at depths of 20 and 30 mm, extending vertically under the center of the horizontal crack. Furthermore, an artificial transverse crack opening to the top of the surface was provided at the same depth. For both cracks, the slit is 1 mm thick. Unless otherwise noted, the simple terms “horizontal crack” or “transverse crack” refers to the artificial cracks shown in Fig. 9. In the case of transverse crack, a semicircular slit that exists below the horizontal crack is described as “inside transverse crack” and a semicircular slit that opens at the top of the rail head is described as the “open transverse crack.”
| (a) Fixed conditions | |||
| Size of transmitter and receiver | 25 mm square | ||
| Angle of transmitter and receiver | 6° | ||
| Distance from transmitter to cracks | 200 mm | ||
| Distance from transmitter and receiver to top surface | 10 mm | ||
| Type of cracks | Horizontal and transverse cracks (depth of 20 mm and 30 mm) | ||
| Horizontal distance between transmitter and receiver | 950 mm | ||
| Type of input wave | Wave burst | ||
| Input wavenumber | 3 | ||
| (b) Relationship between frequency of input wave and number of elements in each FEM model | |||
| Input frequency | 100 kHz | 120 kHz | |
| Number of elements, approx. | Model (1) | 140 million | 250 million |
| Model (2) | 30 million | 30 million | |
| Model (3) | 200 million | 350 million | |
Figures 10 and 11 show the ultrasonic propagation in a model without cracks in the rail and a model with a horizontal crack and an inside transverse crack with a depth of 30 mm in the rail at an input frequency of 100 kHz. Figure 10 shows the state of the ultrasonic waves immediately after it reaches the crack. Figure 11 shows the state of the ultrasonic waves after they almost penetrate the crack. Compared with the model with cracks, the model without cracks shows the state from transmission at the same time. As found in Fig. 10 (a), it is confirmed that several ultrasonic waves stably propagate in the rail model, in which there is no crack. On the other hand, as found in Fig.10 (b), several ultrasonic waves are blocked by cracks in the cracked rail model. Comparing Fig. 10 with Fig. 11, it was confirmed that the number of propagating waves increases in Fig. 11. This seems to be due to an increase in mode changing and reflection during propagation inside the rail. Comparing Fig. 11 (a) with Fig. 11 (b), in the case of the models with cracks, only the first five to six waves of the series of propagating waves decrease in displacement. We assumed that this is because the preceding wave in a series of waves that eventually reached the receiver was greatly affected by cracks.
Figure 12 shows examples of received waveforms at input frequencies of 100 kHz and 120 kHz. Regardless of the type of crack, the wavenumber of all received waveforms became greater than three, the input wavenumber. In addition, the model with cracks showed that the amplitude of the first three waves (in the range by the red arrows in Fig. 12) was reduced compared to the amplitude of the fourth and subsequent waves. We can say that the characteristics in Fig.12 are generally consistent with the characteristics shown in Figs. 10 and 11, which visualize the state of ultrasonic propagation. Thus, we set a time range of 3 periods from the point at which the absolute extreme value of 0.01 or higher was first reached in the received waveform without cracks. The maximum amplitude of the waveform in this time range was then organized as the peak intensity. Figure 13 shows the relationship between crack conditions and peak intensity, with the peak intensity extracted for the entire received waveform and the peak intensity extracted over a time range. Figure 13 (a) shows no significant change at any input frequency under the condition of only a horizontal crack and the condition of horizontal and transverse cracks. In contrast, Fig. 13 (b) shows a different change in the peak intensity. In the case with an input frequency of 100 kHz, the decrease in peak intensity was about 0.15 at horizontal and inside transverse crack depth of 20 mm and about 0.2 at a depth of 30 mm compared to the condition where there was only a horizontal crack. In addition, we confirmed that the peak intensity was further reduced by about 0.1 under the condition of a horizontal crack and an open transverse crack. Therefore, by setting the threshold value to about 0.6, it is highly likely that we can judge the part below the threshold to be the location where the transverse crack with a depth of 20 mm or greater will exist. In the case with an input frequency of 120 kHz, the decrease of the peak intensity was about 0.045 at an open transverse crack depth of 20 mm and about 0.14 at that of 30 mm compared to the condition where the crack was only a horizontal crack. The change in peak intensity depending on the presence or absence of a transverse crack was small. Therefore, it may be difficult to set an accurate threshold to distinguish between the presence and absence of horizontal cracks and detect transverse cracks with a depth of 20 mm or deeper compared to the case with an input frequency of 100 kHz.
Furthermore, by comparing the frequency distribution of the received waves for each crack condition, we examined the possibility of detecting transverse cracks by focusing on changes in frequency distributions. Figure 14 shows the frequency distribution of the received wave under each crack condition. In both cases, with the input frequency of 100 and 120 kHz, there were two peaks around 100 kHz and 130 to 150 kHz. In addition, we confirmed that the peak at 130-150 kHz decreases according to the size of the horizontal and transverse cracks. By focusing on the reduction characteristics of this peak, it may be possible to determine the kind of crack.
There are still many parameters, such as the width, length, position of the horizontal crack, and the angle of the transverse crack progress. We plan to study further by FEM analysis.
We created FEM analytical models for contactless ultrasonic transmission and reception on the rail with various cracks. We then performed ultrasonic propagation simulations using FEM analysis models we developed, to examine the possibility of detecting the transverse crack of the rail head using guided waves. The results obtained in this study are summarized as follows.
(1) We performed ultrasonic propagation simulations using FEM analysis models in which a slit is inserted from the top surface of the rails. The results showed that ultrasonic waves with an input frequency of 100 to 150 kHz are suitable for detecting transverse cracks with a depth of 20 to 30 mm.
(2) From the results of (1), we performed ultrasonic propagation simulations using FEM analysis models in which artificial horizontal and transverse cracks were inserted in the rails at an input frequency of 100 and 120 kHz. The results showed that the first few propagating waves were significantly affected by cracks. We confirmed that the peak intensity of only the first three waves of the received waveform decreased with the depth of the transverse crack under the horizontal crack. We also confirmed that the peak intensity was reduced in the case with an input frequency of 100 kHz rather than 120 kHz. By setting the threshold value to about 60% for the peak intensity under the condition of no cracks and extracting points below this threshold, it is possible to detect transverse cracks with a depth of 20 mm or more. In addition, by comparing the frequency distribution of the received waves, it was suggested that it may be possible to distinguish between horizontal and transverse cracks.
(3) Based on the results of this study, we plan to conduct further studies in the analysis and proceed with the construction of the system for detecting transverse cracks in rail heads using guided waves.
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Yuki KONAYA
Researcher, Rail Maintenance and Welding Laboratory, Track Technology Division Research Areas: Non-destructive Inspection of Rails, Rail Welding |
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Mitsuru HOSODA, Ph.D. Senior Researcher, Rail Maintenance and Welding Laboratory, Track Technology Division Research Areas: Non-destructive Inspection of Rails |
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Ryuichi YAMAMOTO, Ph.D. Senior Chief Researcher, Head of Rail Maintenance and Welding Laboratory, Track Technology Division (Former) Research Areas: Non-destructive Inspection of Rails, Rail Welding |
