Structure failure analysis on metro axle-box hanger due to modal resonance with rail corrugation

During the long-term service of a metro vehicle, different kinds of fracture failure occur on the bogie, with the axle-box hanger being a representative one. To investigate the cause of the hanger structure failure, a study was conducted that combined field investigation with finite element analysis, focusing on the modal resonance behavior between the hanger and the rail corrugation. Based on the findings, a structural optimization of the hanger was proposed and an experimental verification was conducted. The results show that the main reason for the hanger fracture failure is that the resonance phenomenon that occurred in the hanger structural modal frequency when exposed to the rail corrugation, leading to the poor lateral vibration environment of the hanger and the fracture failure in the long-term service operation. The first-order structural modal frequency of the hanger is 432 Hz, which is very close to the wheel/rail excitation frequency of 435 Hz caused by the rail corrugation. The modal frequency of three newly designed hangers can prevent the frequency caused by the rail corrugation. Experimental verification of the new hangers showed a 55.49% lower maximum average acceleration of hanger lateral vibration compared to the original structure, confirming the effectiveness of the redesigned hangers.


Introduction
In the long-term service condition of metro vehicles, the dynamic performance of vehicles and tracks deteriorates continuously, which in turn worsens the wheel/ rail contact performance.Additionally, the structure failure of the components installed on the bogie frame, including the frame, 1 gearbox, 2 motor hanger, 3 primary suspension of the coil spring, 4 and motor bogie cowcatchers, 5 may experience structural failures to varying degrees.[8][9][10][11][12][13] Qu et al. 1 conducted a field test on the bogie frame for fatigue cracks in the connection area of the cross beam and the side beam.The results showed that the high equivalent conicity of the wheel/rail contact characteristic and the gap of the primary suspension lead to the vehicle bogie hunting instability for a long time, resulting in structure fatigue cracks in the bogie frame.
To analysis the cause of the gear failure in the railway system.Jiang et al. 2 proposed a spatial dynamics model of a heavy-duty electric locomotive that considers the dynamic coupling effect of the gear transmission system.The time frequency analysis and angle synchronous averaging method were used to study the gear failure characteristics of tooth root cracks and the distribution and variation of the failure characteristics of tooth root cracks was revealed.As the wheel flat often affects the gear system's fault diagnosis and fatigue life and further endangers vehicle operation safety, Mao et al. 3 studied the local cracks on the motor hanger in service to determine the cause of the structure failure.The results showed that welding defects reduced the fatigue strength of the weld and high-amplitude and high-frequency vibrations caused by the pulsating torque of the motor eventually led to the failure of the motor hanger.Sun et al. 4 analyzed that the fracture failure of the coil spring applied on the primary suspension occurred after long-term operation, which caused the bogie abnormal vibration and jeopardized the vehicle operational safety.The field tests and simulation analysis were conducted and the result showed that the wheel out-of-roundness was the main cause of the coil spring failure.The axle-box vibration frequency caused by the wheel out-of-roundness resonated with the natural frequency of the coil spring, resulting in the structure failure of the coil spring.The wheel re-profiling and structural optimization of the coil spring can effectively solve the failure problem of the coil spring.Additionally, Wang et al. 14 analyzed carbody abnormal vibration caused by the suspension failure and proposed a suitable solution to suppress carbody vibration which was verified by a field test.Sharma et al. 15 and Kumbhalkar et al. 16 conducted a systematic study of the coil spring fracture failure problem from the viewpoint of experimental and theoretical studies and proposed improvement suggestions.Wei et al. 5 described the high-frequency vibration fatigue failure of the metro bogie cowcatcher due to short-pitch track irregularities through a field test and numerical simulation.It was found that the modal stress at hot spot locations around the weld lines of the cowcatcher can be easily excited in operations and even coincides with the frequency of the rail corrugation.The measurement of the rail grinding and structural optimization were proposed.Mazzola et al. 17 proposed a damage-tolerant approach for ensuring the safe operation of railway axles with an old, non-EN-compliant design until completion of their life cycle.The results showed that the suitable non-destructive testing (NDT) inspection intervals were highly dependent on the specific axle design and service scenarios, particularly with regard to the effects of braking.Wu et al. 18 investigated on the high frequency vibration-induced fatigue failure of antenna beam through both field tests and numerical simulation, which proved to be caused by the short pitch irregularities of rail.Besides, as wheel flats may excite various vibration modes of wheelsets employed in highspeed trains, the axle-box vibration and wheelset axle stress caused by a wheel flat on flexibility wheelset of high-speed railway trains was studied. 19s shown in Figure 1, the axle-box hanger installed on the metro bogie axle-box has fractured and failed during the operation.Its main function is to work with the stop gear when the bogie is in the lifting state, limiting excessive displacement of the wheelset and preventing the wheelset from separating from the frame when the bogie is in the lifting state.After the hanger structure fails, it may fall to the main line, turnouts, and other key positions, causing serious safety accidents.In addition, after the hanger fails, the movement of the axle box can no longer be restricted, resulting in excessive movement of the wheelset and even abnormal conditions such as extreme intrusion.
In this paper, a systematic study on the problem of axle-box hanger fracture failure is conducted.To analyze the vibration characteristics of the hanger and identify the cause of the failure, a combination of a field test and finite element analysis is utilized.Firstly, a field test of the axle-box hanger fracture failure problem is used as the research background.The time domain and frequency domain analysis of the bogie vibration performance are conducted.Additionally, the potential cause of the hanger fracture failure is pointed out by combining with a test on the rail corrugation.Then, based on the finite element analysis method, a structural modal of the axle-box hanger is performed and the comparison between the test result and the simulation result is carried out to further elucidate the causes of hanger fracture failure.Also, structural optimization is conducted.Finally, a field vibration test is conducted on the improved hanger structure to verify the feasibility of the new structure.

Field test on metro vibration
The maximum operating speed of the metro vehicle is 80 km/h.After operation for a certain mileage, the phenomenon of axle-box hanger fracture failure occurs.And no obvious bumps and scratches are found on the appearance.To explore the cause of the hanger fracture failure problem and propose solutions to such engineering failure problems, a field test is carried out on the metro vehicle as shown in Figure 2. The vehicle load is AW0 and the test is conducted without passengers.The B & K acceleration sensor is used to collect the vibration acceleration with a range of 6 700g.The Intelligent Measuring and Control Collector (IMC) system is used for data acquisition.
From the fatigue crack position of the axle-box hanger, it is related to the lateral vibration modal of the hanger.Therefore, the lateral vibration acceleration of the metro bogie is analyzed, and the tested results are analyzed by selecting six consecutive station sections among them, as shown in Figure 3.In Figure 3(a), the left Y coordinate is the time domain analysis of the hanger lateral vibration acceleration, and the right Y coordinate is the statistical average value of the vibration acceleration within every 5 s to get the average maximum value.The results indicate that the average maximum value of the hanger's lateral vibration reaches 182g in certain local intervals, while the overall level is around 60g.These values suggest that the lateral vibration environment of the hanger is extremely poor.The time frequency of the hanger vibration is analyzed in Figure 3(b).It is evident that the lateral vibration of the hanger exhibits a prominent main vibration frequency throughout the test section, which is approximately 450 Hz.The frequency domain analysis, shown in Figure 3(c), can further determine that the obvious main frequency of the hanger lateral vibration is 435 Hz, which is the main source of cracks on the axle-box hanger.
To further investigate the source of the hanger vibration at the frequency 435 Hz, the lateral vibration of the axle-box at the position of the hanger with cracks is analyzed as shown in Figure 4. From the time domain analysis, the lateral vibration amplitude of the axle-box is mainly within 10g and the maximum amplitude obtained in the local interval is about 13g.The maximum average value of the axle-box vibration acceleration within every 5 s is 8g.Compared with the lateral vibration of the hanger, the axle-box vibration is obviously smaller.In Figure 4(b), the time-frequency analysis revealed several prominent vibration frequencies in the axle-box lateral vibration, notably around 80, 450, and 880 Hz.Among them, 450 Hz is the frequency related to the main vibration frequency of the hanger.Besides, it can be seen through the time domain analysis in Figure 3(c) that the frequency is 435 Hz, which is the same as the main vibration frequency of the hanger.
From the perspective of vibration transmission relationships, the excitations originating from wheel/rail contact are propagated from the axle-box to the axlebox hanger.It's notable that the amplitude of hanger lateral vibration greatly surpasses that of the axle-box.The amplitude of the hanger lateral vibration is obviously amplified, indicating that the hanger is more likely to have a resonance phenomenon related to its own modal frequency.In addition, the vibration main frequency of the hanger is 435 Hz, and the corresponding frequency also exists in the axle-box.In general, the presence of such a high-frequency vibration in the    Advances in Mechanical Engineering lateral axle-box vibration indicates a close association with rail corrugation.Therefore, a typical section with high vibration amplitude of the hanger is selected and a field test on rail corrugation is carried out.

Field investigation on rail corrugation
The rail surface roughness of the selected curve track is tested with a radius of 400 m, shown in Figure 5.The testing instrument can continuously test the wavelength and wave depth of the rail corrugation.The wavelength is associated with the excitation frequency of wheel/rail interaction, while the wave depth provides insights into the extent of wear and unevenness on the rail surface.
Referring to ISO3095 standard, 20 the one-third octave spectrum is applied to quantitatively evaluate the rail roughness level.As shown in Figure 5(a), the right rail along the forward direction exhibits an obvious wave state, with a peak-peak amplitude of 0.18 mm and a wavelength of 50.9 mm.In contrast, the left rail exhibits relatively minor corrugation, with a peak-to-peak amplitude of 0.06 mm.The measured rail corrugation is analyzed in Figure 5(c) and compared with the recommended values of ISO3095.The rail roughness level of the right rail in the section exceeds the recommended limit.The wavelength beyond the limit is mainly around 50 mm.Given a vehicle speed of approximately 80 km/h (more accurately, 79.2 km/h), the wavelength of the rail corrugation is 50.9 mm, then the frequency caused by the rail corrugation is calculated to be 433 Hz.According to Section ''Field test on metro vibration,'' the main vibration frequency of the axle-box and the axle-box hanger is 435 Hz, which is the same as the frequency caused by rail corrugation.Therefore, it can be judged that rail corrugation is the main cause of the vibration with 435 Hz.And the vibration amplitude is transferred from the axle-box to the axle-box hanger is most likely related to the elastic vibration modal of the hanger with 435 Hz.

Structure optimization
To study whether the 435 Hz vibration caused by rail corrugation resonates with the elastic vibration mode of the hanger, a three-dimensional model of the hanger is firstly established by SolidWorks.Then, the structural model is imported into finite element software ANSYS for meshing and calculation.The first three structural vibration modes of the hanger are analyzed.
The modal analysis result of the hanger with the original structure is analyzed in Table 1.The first modal of the hanger is 432 Hz, coinciding with the main vibration frequency of the axle-box hanger.From the modal vibration shape, the stress concentration is most likely to appear at the location of the variable section, which is the same as the location of failure fracture cracks.Therefore, combined with the field test and the results of the hanger modal analysis, the main reason for the fracture failure of the axle-box hanger of the metro vehicle is the resonance between the wheelrail contact excitations caused by the rail corrugation with 435 Hz and the hanger elastic vibration modal with 432 Hz.
From the cause of the hanger structure failure, the problem can be solved mainly from two aspects.One is through the structure optimization of the hanger to avoid the rail corrugation frequency range and avoid resonance caused by the rail corrugation.The other way is to eliminate the rail corrugation by rail grinding, removing the wheel/rail contact excitation within the resonance frequency range.2][23] Therefore, to solve the structure failure problem of the axle-box hanger resonance phenomenon, the structure optimization of the hanger is conducted and the modal analysis result is listed in Table 1.For the elastic vibration mode of the hanger, the modal frequencies of the newly designed hanger structures have been improved to varying degrees.The first modal frequency of Structure A is 537 Hz, Structure B is 819 Hz, and Structure C is 517 Hz, which avoids the resonant frequency with rail corrugation of 435 Hz.In terms of modal frequency, the newly designed structures can avoid the resonance frequency range and the fatigue reliability of the axle-box hanger can be improved.Nevertheless, the effectiveness of these improvements requires validation through experimentation.

Structure modal test
Based on finite element analysis results of the newly designed structure, Structure A is manufactured and installed on the metro vehicle.The structure model test is conducted on the hanger with the impact hammer and the schematic diagram is shown in Figure 6(a).The corresponding hanger vibration data is shown in Figure 6(b).
The impact hammer is applied as the input of the hanger vibration system.Meanwhile, the vibration performance of the impact hammer is fed back to the data acquisition system.When the hammer impacts the hanger, the resulting vibration characteristics of the hanger are recorded as the system's output.This output data is then transmitted to the data acquisition system.Based on the feedback of the impact hammer and the system output, the frequency response function of the hanger is analyzed in the computer, thus obtaining the natural modal frequency of the hanger.From the vibration response of the hanger, the vibration peak occurs under the frequency of 532 Hz.It is indicated that the frequency is the modal frequency of the hanger, belonging to the natural frequency.Compared with the calculated results of the finite element method, the difference between the two is very small, indicating that the design parameter of Structure A meet the requirements, which will be applied to the actual line test later.

Experimental verification and discussion
To study whether the optimized hanger structure can avoid the resonance with the rail corrugation frequency, Structure A is installed on the metro vehicle.The experimental verification was carried out on the same vehicle in Section ''Research background,'' with the hanger being the only component replaced.The analysis results are obtained as shown in Figure 7.
The time domain results and average maximum values of vibration acceleration for the newly designed hanger clearly illustrate a reduction in lateral vibration.Based on the average vibration acceleration value within a 5-s interval, the maximum average lateral vibration value of Structure A is 81g, while the maximum average value of the original hanger is 182g, which is reduced by 55.49%.The overall lateral vibration level of Structure A remains at approximately 25g.From the time-frequency analysis result in Figure 7(b), the lateral vibration of the hanger is mainly present in two frequency ranges between 400 and 600 Hz.Notably, one frequency resides around 450 Hz, and the other around 550 Hz.As indicated from the frequency domain analysis in Figure 7(c), the main frequencies are 435 and 535 Hz, where 435 Hz is corresponding to the wheel/rail contact excitation frequency from the rail corrugation.And the main vibration frequency of 535 Hz is the elastic vibration frequency of Structure A from the modal analysis result in Table 1.
The experimental verification carried out on the hanger demonstrates a substantial improvement in the vibration characteristics of the newly designed hanger structure, notably with a significant reduction in vibration amplitude.The maximum average acceleration amplitude is reduced by 55.49%.Although there is still the vibration main frequency of 435 Hz, it is a forced vibration caused by rail corrugation.The vibration of the hanger also has the main frequency of 535 Hz, corresponding to the elastic vibration modal frequency of the hanger structure.Furthermore, no resonance phenomena occurred during vehicle operation, confirming the effectiveness of the newly designed hanger structure.
Moreover, in terms of the vibration amplitude of the newly designed hanger, there is still significant amplification of the hanger vibration compared to the axlebox.The installation method of the axle-box hanger on the axle-box is similar to the cantilever structure.For this kind of fixed form, the vibration of the hanger must be amplified.By mounting the hanger on the bogie frame to replace the axle-box, the vibration level of the hanger may be further reduced by the damping effect of the primary suspension system.Also, canceling the split design of bolt connection between the axle-box and the hanger, the integrated design of the axle-box and the hanger can significantly decrease the vibration magnification from the axle-box to the hanger.Besides, the usage of new materials such as carbon fiber to improve the structural stiffness of the hanger may also solve the problem of the hanger structure failure.Further research and development efforts will be directed toward exploring these avenues.

Conclusion
To address the issue of axle-box hanger fracture failure in metro vehicles, an experimental research and structural modal analysis were conducted to identify the failure reasons.Additionally, structural optimization was performed, and the effectiveness of the new design was verified through experimental verification.The following conclusions were drawn: (1) The fracture failure of the metro axle-box hanger occurs during operation.The field test shows that the main frequency of the hanger fracture failure is 435 Hz and lateral vibration acceleration of the hanger is significantly amplified due to vibration transmission from the axle-box.By the rail corrugation test on the railway line, the rail roughness level of the right rail exceeds the recommended limit of ISO 3095, and the wheel/rail contact excitation frequency is 435 Hz.It is preliminarily concluded that rail corrugation is the main reason of the hanger fracture failure.(2) Combined with the results of the structural modal analysis of the hanger, it was found that the first order structural modal frequency of the hanger is 432 Hz, which is very close to the wheel/rail excitation frequency of 435 Hz caused by the rail corrugation.Consequently, the main reason of the hanger fracture failure is the occurrence of resonance between the hanger structural modal frequency and the excitation of the rail corrugation, leading to poor lateral vibration conditions and eventual fracture failure during long-term service operation.(3) Three newly designed structures are proposed through structure optimization, and all of them avoid the frequency caused by the rail corrugation.During the experimental verification test of Structure A, the lateral vibration amplitude of the hanger is effectively reduced by 55.49%.
From the frequency domain analysis, the newly designed structure hanger avoids the frequency caused by the rail corrugation and no resonance phenomenon occurs, which verifies its effectiveness.Further research will focus on new structure design and new materials to improve the hanger vibration condition.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figure 1 .
Figure 1.Installation position of the axle-box hanger and the failure crack location.

Figure 2 .
Figure 2. Field investigation on the metro: (a) measuring points of the axle-box and the hanger and (b) data acquisition system.

Figure 3 .
Figure 3. Lateral vibration performance of the axle-box hanger: (a) time-domain analysis, (b) time-frequency analysis, and (c) frequency-domain analysis.

Figure 5 .
Figure 5. Field investigation on rail corrugation: (a) tested section of the visible rail corrugation, (b) amplitude of the rail corrugation, and (c) roughness level of the rail corrugation.
The three newly designed hangers are named newly designed structure A (Structure A), newly designed structure B (Structure B), and newly designed structure C (Structure C).In comparison to the original structure, Structure A features optimized external profiles with increased thickness.Both the external profile and internal profile of Structure C have been optimized.The external profile and internal profile of Structure B is optimized and the thickness is slowly changed.

Figure 6 .
Figure 6.Structure modal test: (a) schematic diagram of the modal test with impact hammer and (b) frequency-domain analysis.

Figure 7 .
Figure 7. Lateral vibration performance of the newly designed axle-box hanger: (a) time-domain analysis, (b) time-frequency analysis, and (c) frequency-domain analysis.

Table 1 .
Modal analysis of the axle-box hanger.