A Study on Depth Sizing for Surface Cracks in KTX Brake Disc Using Rayleigh Wave

School of Mechanical Engineering, Sungkyunkwan University, 2066, Seobu-ro, Jangan-gu, Suwon-si, Gyeonggi-do 16419, Republic of Korea Metropolitan Transportation Research Center, Korea Railroad Research Institute, 176, Cheoldobangmulgwan-ro, Uiwang-si, Gyeonggi-do 16105, Republic of Korea Department of Physics, Andong National University, 1375, Gyeongdong-ro, Andong-si, Gyeongsangbuk-do 36729, Republic of Korea Korea Institute of Nuclear Safety, 62, Gwahak-ro, Yuseong-gu, Daejeon-si 34142, Republic of Korea Department of Civil & Railroad Engineering, Daewon University College, 316, Daehak-ro, Jecheon-si, Chungcheongbuk-do, Republic of Korea


Introduction
High-speed railway, which is an environment-friendly transportation system, was introduced in the 21st century [1].It began in 1964 with the introduction of the Japanese Shinkansen [2], followed by France [3], Germany [4,5], and Spain [5].In Korea, the first high-speed railway system was introduced in 2004, which was fifth in the world [1,6].Korea Train eXpress (KTX), the high-speed railway system in Korea, introduced TGV-R, the third generation model of Train à Grande Vitesse (TGV), the high-speed railway system of France [3,6,7].KTX includes high-speed trains, which have low carbon emissions and relatively low noise levels and are widely regarded as the next-generation transportation.
ey have maximized urban transport speeds and accessibility to the civic center and are used by many commuters.
ey are also more economical and environment-friendly than other modes of transport, such as cars and airplanes, and have the advantage of being free from climatic influences such as fog, heavy snow, and heavy rain [8,9].However, accidents that could occur while transporting passengers and cargo at high speed can cause enormous human and economic losses.Among the key components directly related to the safety of high-speed railways are wheels, rail tracks, frames, and brake discs [9].Particularly, damage to the rail tracks and brake discs can lead to the derailment of vehicles and cause accidents.One of main causes of brake disc failure is the growth of surface cracks, which can be attributed to thermal stress concentration and the temperature rising by heat generated from the friction during braking [9][10][11][12][13][14].
Figure 1 shows the typical location of cracks in the brake disc.
As shown in Figure 1, there are two types of cracks in the brake discs that may occur from the inside of the disc and propagate to the outside of the disc, i.e., from the inner end to the outer end of the disc or vice versa [15,16].
In recent years, various research institutes have conducted studies regarding surface cracks of materials and discs using nondestructive evaluation.In Korea, Song et al. [17] showed the possibility that eddy current testing (ECT) could detect cracks even in extreme environments under high pressure and high temperature such as deep sea.In that study, an interpolation-type coil and a di erential-type coil were designed, which can measure the surface cracks in AISI 1045 standard specimen having 25 mm outer diameter.Lim et al. [18] examined micro fatigue cracks in the material using nonlinear ultrasonic modulation.
ey showed the possibility of monitoring the fatigue crack by applying the ultrasonic inspection system to the Yeongjong Bridge in Korea.Kwon et al. [19] evaluated the surface cracks using the characteristics of surface waves propagating along the surface without penetrating the interior of the material.ey employed velocity dependence of the surface acoustic wave to control the de ection condition more precisely and used the frequency dependence of the scattering to evaluate the depth direction residual stress distribution.
Kwak et al. [20] performed the health evaluation of the brake discs of the aircraft through noncontact air-coupled ultrasonic C-scan.However, it was di cult to quantitatively evaluate cracks and construct an inspection system.Jhang et al. [21] proposed and veri ed a method to evaluate crack depth in compact tension fatigue specimen having notch fatigue cracks, grown from surface to inside, using ultrasonic di raction.In this study, the crack depth was measured at a resolution of 1.6%.Further, Yeom et al. [22,23] quantitatively detected the surface microcracks in the plate and shaft through contact and immersion experiments using the Rayleigh wave.Kim et al. [24] evaluated cracks in the brake disc using the Rayleigh wave.In that study, the inspection system for measuring the surface crack of the brake discs was designed using Rayleigh waves with the local immersion method.
Gao et al. [25] performed thermal imaging nondestructive testing by using temperature recording derived from eddy currents and thermal images fusion techniques.In that study, it was showed that using a combination of high-performance thermal imaging cameras, it is possible to distinguish the surface cracks up to a depth of 1 mm.However, this technique has limitations in measuring the exact depth of the crack even for a crack of 1 mm or more.Yun et al. [26] morphologically analyzed the surface cracks and developed a technique that can be applied for automatic process inspection after building an image.is technology is based on the principle of inspecting surface cracks using a simple digital camera.Fan et al. [27] proposed the possibility of detecting surface cracks on railway tracks using the electronic magnetic acoustic probe technique, and Blanloeuil et al. [28] analyzed and established the e ect of nonlinear scattering in the ultrasonic far eld by using the nite element method (FEM).Panier et al. [29] performed crack analysis on the disc surface during braking mechanism using the thermal imaging camera.
e abovementioned techniques may have good performance but are thermal imaging based that can only measure the length and not the depth of the cracks.
In addition, Li analyzed the growth of cracks through fracture tests [30].Korea Railroad Corporation (KORAIL) suggested a method of regenerating the disc crack using the tungsten inert gas (TIG) welding technique [15].Hong et al. [31] found the cause of heat and cracks through thermodynamic friction analysis using the FEM simulation.
Although various studies have been performed to evaluate the safety of brake discs in various elds, it is still a challenge to quantitatively evaluate cracks in the brake discs.
erefore, in this study, a special system was developed to inspect the surface cracks of the brake discs using the Rayleigh waves, considering the necessity of the crack evaluation index in accordance with the operating conditions in Korea.e software for collecting and analyzing the signals was also developed, and A-scans, cross section amplitude (B-scans), and C-scans were analyzed.e crack characterization algorithms were also developed to quantitatively evaluate cracks in KTX brake discs.

Rayleigh Waves
In this study, Rayleigh waves (a type of ultrasonic waves) were used to measure the surface cracks of the KTX brake disc.When the ultrasound waves incident at the Rayleigh angle on the liquid-solid interface, the transmitted waves in solid start propagating along its surface.In this process, the maximum amount of ultrasonic energy travels on surface but there is no energy deep inside the solid.us, this technique has an excellent resolution for surface cracks.Figure 2 shows the wave structure of a Rayleigh wave propagating on the surface.
e Rayleigh waves propagating on the solid surface, when hit the crack, are usually divided into (1) re ected Rayleigh waves and (2) transmitted Rayleigh waves.e re ected Rayleigh waves are usually received by a single probe.So, as the size of the surface crack increases, the ultrasonic energy of the re ected Rayleigh wave also  Advances in Materials Science and Engineering increases.Contrary to re ected Rayleigh waves, the transmitted Rayleigh waves are received by using the two probes.So, as the size of the surface crack increases, the ultrasonic energy of the transmitted wave tends to decrease [32][33][34][35][36][37][38][39].In the current study, we used the transmitted Rayleigh wave because they showed excellent linearity for sizing the surface crack [24].Figure 3 shows the simulation results of the sound pressure behavior of the Rayleigh waves in the time domain.It can be observed from the gure that the ultrasonic waves were excited by the transducer, and the Rayleigh waves were generated by mode conversation at the boundary between the liquid and the solid.ese Rayleigh waves were then propagating along the solid surface.

Fabrication of Brake Disc Specimens
KTX brake discs are divided into solid-type disc and ventilated-type disc [24].e solid type is a rigid circular disc; however, the ventilated type has ve sectors with spacing between each sector.ese brake discs are di erent in their shapes but have the same crack types.us, in this study, a solid-type disc specimen was fabricated and analyzed.e chosen material of the specimen was AISI 1045, which has similar physical properties as that of the actual KTX brake discs [24].In addition, the cracks were fabricated in the specimen like the actual ones.ere were four types of fabricated cracks, i.e., standard, horizontal double (Hdouble), vertical double (V-double), and triple cracks.
Figure 4 shows the type of crack in the brake disc specimen.
e outer and inner diameters of the fabricated specimen are Φ640 mm and Φ380 mm, respectively, and the disc width is 80 mm. e brake disc specimen has 30 cracks, and the position of each crack is shown in Figure 5.
Table 1 shows the speci cation of the surface cracks in the specimen.In order to develop the characterizing and sizing method for three types of cracks, each type of crack was fabricated with two di erent lengths having various depths.

Development of KTX Brake Disc Inspection System
To analyze the surface cracks of the KTX brake disc using the Rayleigh wave, an inspection system was developed.e system consists of an ultrasonic sensor module, a dynamometa module, acquisition software, and a control system.Here, the fabricated test specimens of the KTX brake disc were mounted on the dynamo-meta system and rotated to inspect the full surface area.
Figure 6 shows the schematic diagram and photo for the KTX brake disc inspection system.

Ultrasonic Sensor Module.
e ultrasonic sensor module in the inspection system consisted of a scanner module and a sensor module.
e scanner module contains a stepper motor, a linear motion guide, and a ball screw to move the sensor module along the radial direction.
e scanning range of the scanner module was 500 mm with an accuracy of 0.1 mm, and it was designed to cover more than half of the whole specimens.
e sensor module was designed to generate ultrasonic Rayleigh waves according to the guidelines given in [24].Moreover, the wedge was specially designed and manufactured to inspect the rough and non at surface of rotating specimen by the local immersion pitch-catch method.is immersion pitch-catch technique can analyze the growth behavior of the cracks and show a linear pattern according to crack size.Additionally, a focused transducer with a frequency of 2.25 MHz was also applied to ensure the separability of each surface braking cracks.
Figure 7 shows a conceptual diagram for the ultrasonic sensor module and the photo of the fabricated ultrasonic sensor module.

Dynamo-Meta Module.
e dynamo-meta module simulates the actual running mode of the KTX and is used to control brake mechanism for brake discs.
Figure 8 shows the dynamo-meta module.Label (a) shows a solid-type specimen, label (b) is an axis used for rotating the test piece, and label (c) is a brushless direct current electric (BLDC) motor, which is a power source for rotating the test piece.Label (d) has a frame structure supporting the entire module, and the frame is made of an aluminum pro le 60 × 60.Moreover, the BLDC motor rotates from a minimum of 30 rpm to a maximum of 500 rpm due to the weight of the test piece.In this study, a BLDC motor was used at 200 rpm, considering the inspection and data analysis time.

Control System and Acquisition/Analysis
Software.
e control system consisted of a computer-controlled ultrasonic pulser/receiver, a high-speed and high-frequency (100 MHz) A/D board to acquire ultrasonic signals, a data acquisition board to acquire the encoder signal, a motion controller, and a motion driver.e control system controls Advances in Materials Science and Engineering the rotation speed of the dynamo-meta module and position of the ultrasonic sensor module and acquires the ultrasonic and encoder signals.
Furthermore, the acquisition software was developed to acquire and save full waveforms together with the location of the sensor during the rotation and scanning of the KTX brake disc specimen.
e position of the ultrasonic sensor on the brake disc surface was displayed by r and θ coordinates.
ese coordinates were controlled by the encoder in the scanner module and the rotation motor mounted in the dynamometa module.ese radial coordinates were then converted into Cartesian X and Y coordinates and combined with A-scan to save the inspection data.
Figure 9 shows a conceptual diagram for calculating the position on the brake disc.e center of the brake disc was set to (0, 0), and each X and Y position was stored every time the brake disc rotated; therefore, the crack signal amplitude at that position was calculated and visualized at the same time.
e A-scan, B-scan signal, and C-scan images were generated on the acquisition program.e ultrasonic signals and position information were stored as binary les.ese binary les were afterwards processed by the analysis software to inspect the position of a crack in the test  4 Advances in Materials Science and Engineering specimen.Figure 10 shows the ultrasonic signal acquisition software.
Figure 11 shows the KTX brake disc inspection data analysis program.As shown in gure, the signal analysis software consists of C-scan image display windows (left and right side of the KTX brake disc), sectional amplitude plot corresponding the cursor position on the C-scan image, and the A-scan signal at the cross-sectional position of the cursor.Using the analysis program, the size (length and depth) and location of the detected aws can be evaluated.
e sizing algorithm implemented in the developed analysis program has been discussed in the following sections.

Sizing Algorithm and Results
In order to develop a crack sizing algorithm for the surface breaking cracks in the KTX brake discs, the signal waveform   Advances in Materials Science and Engineering analysis and pattern analysis were performed according to the types of cracks present in Table 1.

Sizing of Standard-Type Crack.
Figure 12 shows the schematic of the experimental setup and C-scan image of the standard-type cracks.It can be seen that the emitted ultrasonic beam propagates across the crack and received by a receiving transducer.
e standard-type surface braking cracks are denoted as No. 1 and No. 5 in Table 1.
e crack signals were collected using the KTX brake disc inspection system and software.e typical inspection includes A-scan, cross section signal (B-scan), and C-scan result for the standard-type crack.
e A-scan is an amplitude scan that shows the amplitude of the ultrasonic signal and can be used to check the signal at one point.
e cross-sectional signal is the brightness scan, B-scan, which can be obtained from the A-scan signal and shows the cross section of the specimen.
e C-scan is a contrast scan.It is possible to create a C-scan image using the A-scan signal to examine the position data and to calculate the size of the crack using the image cross section and examination location information.
e A-scan along with cross section amplitude and C-scan are present in Figure 13 where Figure 13(a) shows the A-scan signal propagating through the standard-type crack, Figure 13(b) shows the C-scan image for the analysis region, and Figure 13(c) shows the cross section of the C-scan image, which shows the amplitude variation along the standard-type crack.
As shown in Figure 13(c), the depth and length of the crack can be estimated using a cross section amplitude plot.Principally, with the increasing depth of the crack, the transmitted amplitude of the ultrasonic wave decreases while the re ected amplitude of the ultrasonic wave increases, which means that the cross section amplitude and depth of crack have an inversely propositional relationship.Furthermore, the length of the crack can be estimated by measuring the distance between the start and end points of the amplitude drop.Figure 14 shows the obtained  6 Advances in Materials Science and Engineering relationship between the amplitude of the transmitted ultrasonic signal and depth of the standard-type crack after performing the standardization with the amplitude of the signal when there is no crack.e relationship demonstrates that the amplitude of the signal decreased with the increment in crack size.e correlation between the crack depth and crack signal was analyzed, and equation (1) was derived using the tted trend line of the graph in Figure 14.
where α represents the amplitude of the signal and d represents the depth of the crack.e inspection system with derived correlation expression provides a good mean to predict the magnitude of the crack using the amplitude of the signal for the KTX brake disc.e developed depth sizing equation was then applied for all other types of cracks for depth estimation.Table 2 shows the estimated sizes result   Advances in Materials Science and Engineering for the standard-type crack with the developed sizing algorithm.
As shown in Table 2, the error of estimated depth compared to the actual depth is approximately 7.2%, and the lengths of the cracks were estimated to be 2.8% for the 7 mm cracks and 4.0% for the 10 mm cracks.ese errors are less than the required size estimation of 10%.

Sizing of H-Double Type
Crack.H-Double is a type of crack which represents two standard cracks successively formed in the horizontal direction.Figure 15 demonstrates the schematic for acquiring signals to analyze depth and width of these cracks while their speci cations are present in Table 1 as No. 2 and No. 6.
For the H-double type cracks, the crack gap between two cracks also needs to be estimated along with depth sizing.erefore, in this study, the cross section amplitude along the circumferential direction (θ direction) is used to calculate the crack gap between two cracks.Figure 16 shows the 7 mm length of the H-double type crack's C-scan images  8 Advances in Materials Science and Engineering and cross section amplitude along θ direction by changing crack gaps from 1 mm to 4 mm with step size of 1 mm.It can be seen from Figure 16 that with C-scan images, it is di cult to classify two cracks because they have similar widths as those of the standard-type cracks.However, the shape of the cross section amplitude along θ direction is di erent for the standard-type crack.erefore, the H-double type cracks can be identi ed using the cross section amplitude plot.It can also be inferred from Figure 16 that when the crack gap between the cracks is 1 mm, the signal is analyzed in a manner similar to that of the standard-type crack; however, as the crack gap between the two cracks exceeds 1 mm, the width of the cross section amplitude also increases although the minimum amplitude for the cross section amplitude plot is similar to that of the standard-type cracks.
Figure 17 shows that the cross section amplitude of the 10 mm H-double type cracks have the same result as that of the 7 mm H-double type cracks.us, the H-double type cracks were also analyzed through the crack sizing algorithm shown in equation (1).Table 3 shows the analysis result for the H-double type cracks using the developed crack sizing algorithm.
As shown in Table 3, the estimated depth and crack gap were relatively accurate, and the error is less than 0% and 11.5%, respectively.

Sizing of V-Double Type
Crack.V-Double type of crack represents a series of two standard-type cracks in the radial direction.Figure 18 shows the inspection setup for the V-double type cracks.
e speci cation of the V-double type cracks is present in Table 1 as No. 3 and No. 7. Figure 19 shows the C-scan image and cross section amplitude of the V-double type crack of 7 mm length.
Again, it is easy to distinguish between the V-double type crack and standard-type crack using the cross section amplitude plot.e shape of the cross section amplitude shows the connected double-grooves.Each groove represents a Advances in Materials Science and Engineering crack in the V-double type crack, and the distance of each groove increases with an increasing gap between the two cracks.
Figure 20 shows the C-scan image and cross section amplitude of the V-double type crack of 10 mm length.Compared to the 7 mm V-double type crack, the width of    10 Advances in Materials Science and Engineering each groove for the 10 mm V-double type crack is larger.us, to estimate the gap between the two cracks, either the 7 mm or 10 mm V-double type crack was used along with the center-to-center crack gap of each groove.
Table 4 shows the sizing results of the 7 mm and 10 mm V-double type cracks with varying depths.
is demonstrates that the estimated depth and gap of each crack in V-double type were similar to those of the actual one.

Sizing of Triple-Type Crack.
e triple-type cracks represent both single-and double-type cracks present at the same time.e acquired C-scan image for this type of crack is shown in Figure 21 while the speci cation of the tripletype cracks is denoted as No. 4 and No. 8 in Table 1.
Figure 22 shows the C-scan image and cross section amplitude plots of the triple-type cracks with 7 mm length.For triple-type cracks, the ultrasonic beam was passed over the single-crack area and three-crack area, to obtain crossamplitude plots from the upper part, middle part, and the lower part of specimen for amplitude variation investigation.It can be seen from Figure 22 that the cross section amplitudes have di erent starting positions along θ direction for the second line (middle part).When the length of one part in the triple-type crack was 1 mm, the di erence between each part was 1 °; therefore, it was not easy to classify the cracks.However, in the case of 2 mm and 3 mm cracks, it can be expected that the cracks can be classi ed through a change of approximately 3 °-4 °.In addition, the patterns of the estimated signals were similar to each other, and it was investigated that the lower part of the signal was distorted due to the intersignal interference in the case of the 3 mm cracks.
Figure 23 shows the result of the C-scan image and cross section amplitude for the depth of the 10 mm crack.
Figure 23 shows similar tendency to the result of the 7 mm crack; however, the longer the crack, the more di cult it is to classify the crack.In the case of the 7 mm crack, the di erence between lines 1 and 3 and line 2 of the B-scan signal was changed by approximately 3 °-4 °; however, it was investigated that the change was approximately 1 °-2 °with the 10 mm cracks.is is because the longer the length, the more interference occurs between the cracks; therefore, the ultrasonic signals tend to occur at similar positions.
As shown in Table 5, the estimated depth and crack gap are similar to the actual one, and the estimated error is around 8.19%.

Inspection of the Natural KTX Brake Disc
To evaluate the performance of the developed sizing algorithm, inspection and analysis of natural surface brake cracks in the KTX disc were performed.
Figure 24 shows the location of the natural crack in the KTX brake disc (C-2), where C-2-1 crack has 50 mm length and 3 mm width while the C-2-2 crack has 42 mm length and 4 mm width.
Figure 25 shows the inspection result of the C-2-1 crack that includes the C-scans and cross section amplitudes (Bscans) for the radial and circumferential (θ) directions.
B-Scans of the radial direction of the C-2-1 cracks show that the depth of the natural crack gradually increases from the measuring points (1)∼(5).However, the change of cross section amplitude along the circumferential direction is negligible.us, in this study, the depth was estimated at ve points, and the width was estimated at only one point.
Figure 26 shows a C-scan image and cross section amplitude plots for the C-2-2 natural crack.
As shown in Table 6, the estimated length and width agreed well with the actual ones.12 Advances in Materials Science and Engineering e estimated depth could not be compared to the actual depth because the actual depths of C-2-1 and C-2-2 need to be measured using a destructive test.However, the depth of cracks gradually increased from the inside of the disc to the outside.

Conclusions
In this study, a KTX brake disc inspection system along with software was developed to formulate crack sizing algorithm to detect surface cracks in the KTX brake discs and quantitatively evaluate their sizes.e types of cracks occurring on the surface of the KTX brake disc were analyzed, and from the experimental results, it was inferred that the amplitude of the crack signal and the depth of crack are inversely proportional.A crack sizing algorithm was developed using the derived relational expression.e patterns of the cross section amplitudes were analyzed, and the cracks were classi ed.Furthermore, the C-scan images of each crack were obtained.Using the developed sizing algorithm, the estimation of length and depth for standard-, V-double,    Advances in Materials Science and Engineering H-double, and triple-type cracks were performed.Based on the estimation results, the developed algorithm showed good reliability to size cracks.Moreover, the developed algorithm was also evaluated with natural cracks, and it was veri ed that the algorithm could be applied to the natural cracks in the KTX brake disc as well.Based on the natural cracks in the specimens, it was found that the crack grew gradually from the inside to the outside of the brake disc. is study is expected to be eld applicable if a complementary algorithm is developed through experiments on various natural crack test pieces.

Figure 4 :Figure 5 :
Figure 4: Types of cracks in brake disc specimens.

Figure 6 :
Figure 6: (a) Schematic diagram and (b) photo of the KTX brake disc inspection system.

Figure 7 :
Figure 7: (a) Conceptual diagram and (b) photograph of the ultrasonic sensor module.

Figure 11 :
Figure 11: e interface of software for crack analysis.

Figure 17 :
Figure 17: Inspection results for 10 mm H-double type crack: C-scan (left) and cross section amplitude (right).

Figure 19 :
Figure 19: Inspection results for 7 mm V-double type crack: C-scan (left) and cross section amplitude (right).

Figure 20 :Figure 22 :
Figure 20: Inspection results for 10 mm V-double type crack: C-scan (left) and cross section amplitude (right).

Figure 23 :
Figure 23: Inspection results for 7 mm triple-type crack: C-scan (left) and cross section amplitude (right).

Figure 24 :
Figure 24: Natural crack in KTX brake disc: (a) crack location and (b) photograph.

Figure 25 :
Figure 25: Inspection results for the C-2-1 crack: (a) C-scan and cross section amplitude of (b) radial direction and (c) circumferential direction.

Figure 26 :
Figure 26: Inspection results for the C-2-2 natural crack: (a) C-scan and cross section amplitude of (b) radial direction and (c) circumferential direction.

Table 1 :
Speci cation of cracks in the brake disc specimen (mm).

Table 2 :
Inspection results for standard-type cracks (mm).

Table 3 :
Inspection results for H-double type crack (mm).

Table 4 :
Inspection results for V-double type crack (mm).

Table 5 :
Inspection results for triple-type crack.