Research on track vibration characteristics and rail corrugation based on fastener failure

Abstract

Based on the measured rail corrugation data on the curve, a rigid-flexible coupling vehicle-track system dynamic model is established. The stiffness and damping of the fasteners were changed to simulate the failure behavior of the track structure, and the influence of fastener failure on the vibration characteristics of the system was studied to determine the causes of rail corrugation. The research results show that: (1) The number of peaks on wheel-rail vibration significantly increases after fastener failure, which increases the probability of wheel-rail resonance. The fastener failure causes more frequent wheel-rail resonance, leading to severe system vibration and increased wheel-rail wear. (2) The simulated wavelength of 57 mm on the slight radius curve with the highest proportion of corrugation is similar to the measured wavelength of 55 mm. The fastener failure is related to the generation of rail corrugation, which verifies the existence of rail corrugation on site. (3) The smaller the curve radius, the greater the lateral and longitudinal creep forces and wear number, indicating that the degree of rail corrugation on slight radius curve is more severe. When the slight radius curve and fastener failure are satisfied together, the lateral and longitudinal creep forces and wear number reach their maximum values, which further accelerates the generation of rail corrugation.

Keywords

Fastener failure dynamics analysis wheel-rail resonance rail corrugation

Instruction

The fastener serves as a crucial component in the interconnection of the rail and track bed system, which plays a pivotal role in holding track profile, maintaining track structural stability and moderating wheel-rail impact.¹ Fastener failure can result in increased pressure on the adjacent normal fasteners at the failed track. It also leads to a rise in the vibration acceleration of the rails, which exacerbates damages to the surrounding fastener systems and impacts the overall safety of vehicle operation.² Fastener failure has always been a common issue in rail traffic. Fastener failure accounts for 79.5% of metro track failure.³ Fastener failure is not only related to the static and dynamic characteristics but also depends on external excitation such as rail corrugation and wheel polygonization with specific vibration frequency, as well as vibrational fatigue of the track structure. Figure 1(a) to (c)) show common forms of track failure.

Figure 1.

Track failure and fastener structure: (a) gauge apron with displacement; (b) broken fastener clip; (c) rail corrugation under track failure; (d) WJ-8 fastener; (e) SKL15-type fastener clip; (f) e-type fastener clip; (g) ω-type fastener clip.

Several scholars have developed theoretical and experimental studies on fastener failure under static and dynamic loads. Chen et al. set up a FEM(finite element model) of a fastener system and a concrete sleeper. The forces on the sleeper and fastener system under different vertical and lateral loads were analyzed through both simulation and experimental methods.⁴ Xiao et al. developed a system model with elastic fasteners. Based on a comparison with the measured vibration acceleration of the clips, the resonance induced by rail corrugation is a primary cause of clip fracture.⁵ Zhang et al. developed FEMs of the moving wheels to investigate the influence of wheel-rail parameters on the longitudinal force distribution in the fastener system, and the maximum friction force between the rail and the elastic pad.⁶ Noor et al. established a simplified model with fastener systems to analyze the stress, strain, and failure locations of the tie plate induced by train loads.⁷ Gao et al. developed a model with WJ-8 fasteners (see Figure 1(d)) to analyze the vertical nonlinear stiffness behavior of the fastener at different loading stages, and to investigate the impact of different fastener failure types on the response features of the vehicle-track system.⁸

The fatigue properties of the fastener will change with changes in the dynamic properties of the fastener. Based on a vehicle-track coupling system model and a detailed fastener analysis model, Xin et al. obtained the dynamic stress time-domain curve of the rail clips and analyzed its fatigue life.⁹ Liu created a mid-high frequency dynamic model and a vibration model of the fastener system. The multi-directional stress analysis method was adopted to study the effect of rail corrugation on the fatigue lifespan of clips.¹⁰ Xiang et al. built a FEM of a fastener system and concluded that wheel polygonization, curve conditions, and increasing speed all elevate the stress value of the fastener clips, which reduces the lifespan of the clips. The fastener fatigue calculation method is applicable to diverse research objects, including crack initiation, crack expansion, and fatigue life quantification.¹¹ In a study conducted by Park et al., the strain and displacement of rail fastener clips undergoing fatigue cracking were tested with two types of installed fastener clips. The results indicated that the stress amplitude of SKL15 fastener clips (see Figure 1(e)) exceeded the allowable stress amplitude, suggesting the potential for fatigue cracking.¹² Liu et al. developed implicit and explicit FEMs for fastener clips and experimentally measured the fatigue properties of the material. The strain-life relationship was determined through fatigue loading tests.¹³ In the microscopic analysis of fastener failure, Hasap et al. conducted fatigue tests, finite element analysis, and failure analysis on e-type fastener clips (see Figure 1(f)).¹⁴ Using a spectrometer and scanning electron microscope, they found that the severity of fatigue crack fronts increased with the crack length until overload fracture occurred. Xiao et al. combined the cumulative damage theory and fatigue analysis methods to discuss the influence of wheel-rail impact on the lifespan of the WJ-8 fasteners. They concluded that fasteners in the rail joint area experienced the most severe fatigue damage and had the shortest lifespan.¹⁵

Rail corrugation is a long-standing unresolved problem of the vehicle-track system. With the substantial increase of the vehicle speed and load, the frequency range of wheel-rail excitation is increased, and the resonance of vehicle and track components appears in different degrees, which seriously has an impact on the security and stability of the vehicle, reduces the service life of structural components of the vehicle-track system. In terms of the impact of rail corrugation and vibration on the fastener system, Zhu et al. investigated the vibration features of ω-type fastener clips (see Figure 1(g)) under static and dynamic loads. The vibration acceleration of the rail clips increased by approximately 10 times after considering rail corrugation, leading to excessive vibration energy in the fastener clips and subsequently exacerbating fatigue damage.¹⁶ Xiao et al. found that the vibration features of the fastener clips on the outer rail of the circular curve were excited by the corrugation with a wavelength of 30-50 mm, while those on the inner rail were excited by a wavelength of 40-60 mm. The resonance frequency of the clips matched the wheel-rail excitation frequency, leading to resonance fatigue fractures.¹⁷ Du analyzed fastener clip fractures from various aspects, including track vibration, clip design, installation conditions, track irregularities, and rail corrugation. It was found that rail corrugation induces high-frequency vibration in the rail, making the fasteners prone to fracture under high-frequency loads.¹⁸ Lin et al. studied the impact of rail corrugation on the lifespan of fastener clips in high-speed railways by simulating. They concluded that the fluctuation frequency of the buckling pressure and the vertical displacement of the rail matched the excitation frequency of the corrugation, leading to increased dynamic stress in the clips and reduced fatigue life.¹⁹ Wang et al. investigated fastener clip fractures in rail corrugation lines. Based on experimental and conceptual analysis of the clip’s dynamic performance, they found a correlation between the mode frequency of the clips and the frequency of rail corrugation.²⁰

Currently, research and analysis on fastener failure primarily focus on vehicle safety, interactions between fasteners, and track vibration. Research on wheel-rail resonance caused by fastener failure and the resulting rail corrugation is relatively scarce. Based on the measured rail corrugation data from curved tracks, a rigid-flexible coupling vehicle-track dynamic model is established. By changing the parameters of the fasteners to simulate the failure behavior of the track structure, the influence of track failure on the vibration characteristics of the system is studied, and the causes of rail corrugation on the curve are identified.

Model establishment and parameter selection

The track structure is mainly composed of rails, fasteners, sleepers, and track beds, which play a role in supporting vehicle operation and stability. Under wheel-rail contact conditions, the wheels apply pressure to the rails, which is then transmitted step-by-step to the track bed. Multiple layers of vibration isolation devices are incorporated to ensure smooth vehicle operation and to reduce vibration and noise.

Establishment of the elastic track model

In the rigid-flexible coupling dynamics model, the introduction of elasticity will significantly add degrees of freedom to the vehicle-track system, which poses higher requirements for simulation calculations. The substructure analysis method can solve the computational problems of the dynamics model. The elastomers can be modeled dynamically through the FEMBS interface module of the finite element analysis software ANSYS and the dynamics analysis software Simpack. The specific process of the system elasticisation is shown in Figure 2(a).²¹ FEM of the elastomers is developed and the result files from the substructure analysis are obtained. A standard file for the elastomers in the FEMBS interface module is generated using the file containing information on nodes, elements, materials, etc. of the FEM and the substructure analysis results. This standard file is imported into the vehicle-track system and replaces the corresponding multi-rigid-body. The characteristic modes of the elastomers are selected and marker points are generated at the main nodes. The connection relationships on the original rigid body are defined on the corresponding elastic body marker points, completing the elasticization process of the component.

Figure 2.

Elasticization process of system structure modeling.

Due to the elastic track bed sleeper being embedded in the concrete structure of the track system, the sleeper and the bed can be considered as an entity. The vibration damping effect of the beds can be neglected, so the model is simplified. The dynamic vibration response of the track obtained is closer to the real situation. In this model, only the vertical vibration of the system is considered, and the fasteners are modeled using spring-damping force elements directly connected to the ground, as shown in Figure 2(b). In addition, the wheelset is one of the key components affecting vehicle safety and stability. Its elastic deformation directly influences the calculation of wheel-rail creep and wear. Considering the vibration characteristics and inherent modes after wheel-rail excitation, the system in Figure 2(c) is treated as elastomers. The elastic wheelset is designed with a hollow shaft to closely match the real modal shapes. Wheel-rail contact is the foundation of normal operation and the cause of many vehicle-track system-related issues. An elastic model is used for accurately reflecting the actual contact state.

Simulation parameters on the curve

Elastic track models with various curve radii are developed to conduct dynamic simulations of the vehicle-track system. The impact of fastener failure on track vibration features and rail corrugation is studied. Table 1 presents the statistical results for rail corrugation length and mileage proportion on a specific metro line, with rail corrugation observed at curve radii of 500m, 800m, and 2500m. The highest proportion (48.31%) is found at 500m. Curve radii of 500m, 800m, and 2500m are selected for the analysis of the relationship between fastener failure, track vibration characteristics and rail corrugation.

Table 1.

Length and proportion of rail corrugation.

Curve radius (m)	Corrugation conditions	Values	Curve radius (m)	Corrugation conditions	Values
400	Length/m	0	1200	Length/m	0
	Mileage/m	618.5		Mileage/m	1208.8
	Proportion/%	0		Proportion/%	0
500	Length/m	889.6	2500	Length/m	121.4
	Mileage/m	1814.9		Mileage/m	478.9
	Proportion/%	48.31		Proportion/%	25.34
800	Length/m	653.9	3000	Length/m	0
	Mileage/m	1371.3		Mileage/m	347.7
	Proportion/%	47.69		Proportion/%	0

To meet the engineering accuracy and maximum calculation requirements, the length of elastic track is set to 40 times the sleeper spacing.²² The selected sleeper spacing in the simulation is 0.625 m.

The track excitation is set to the A5 spectrum, and the DTVI2 fastener is applied to the elastic track. The horizontal and vertical stiffness of the fasteners are 8.79 MN/m and 40 MN/m respectively, and the vertical damping is 9.898 kN·s/m.

During the operation, when fasteners fracture, loosen, or completely fail, rail vibration intensifies, causing the vibration acceleration to increase by more than 30%. Additionally, the response of curve decays slowly, leading to a sharp increase in wheel-rail forces and a reduction in wheel load. It is detrimental to the rail’s fatigue lifespan and safety while operating.²³ Different fastener parameters are set to simulate various forms of fastener failure, and the effect of fastener failure on rail vibration characteristics and rail corrugation is studied.

Vibration characteristics and modal analysis of the wheel-rail system

The primary cause of vibration in the coupling system is the wheel-rail contact. The relationship between the force transmission at the wheel-rail interface and structural vibration characteristics is studied. It is significant for preventing wheel-rail resonance, wear and track damage. Different fastener parameters are selected (stiffness of 40 MN/m and damping of 9.898 kN·s/m, stiffness of 40 MN/m and damping of 0N·s/m, stiffness of 0 MN/m and damping of 9.898 kN·s/m, stiffness of 0 MN/m and damping of 0N·s/m) to simulate and compare four forms of fastener failure. Individual track nodes exhibit high randomness, making them unsuitable for overall analysis. Therefore, four consecutive fastener nodes (A, B, C, and D) on the curved track are selected to represent the vibration characteristics of the entire track.

Analysis of vibration characteristics on wheel-rail system

Wheel-rail vibration is an inevitable phenomenon during the operation, and resonance remains a potential threat in mechanical structures. When frequency resonance occurs between mechanical structures, it can lead to structural damage and failure, making resonance a critical consideration in structural design. Vibration primarily originates from the wheel-rail contact. Wheel-rail vibration is studied for beneficially addressing the causes of vibration in the vehicle-track system. Figure 3 shows the variation in vibration frequencies of the two rails and wheelsets on a curve with a radius of 500m. At the low-frequency range of 54 Hz, both rails and wheelsets exhibit peaks. In the mid-high frequency range, peaks can be observed at 251 Hz and 270 Hz for both sides. The rails and wheelsets exhibit resonance at this frequency, and the inner resonance is more pronounced.

Figure 3.

Vertical vibration spectrum of fasteners under normal performance (R500 m).

Figure 4 shows the variation in vibration frequencies on an 800m radius curve. At the low-frequency range of 93 Hz, peaks can be viewed in both the rails and wheelsets. In the mid-high frequency range, peaks are observed at 208 Hz and 268 Hz for both sides of the rails and wheelsets. Resonance phenomena occur in the rails and wheelsets at frequencies of 93 Hz, 208 Hz, and 268 Hz. The peak energy at the outer rail is higher, making the resonance in the outer wheel-rail vibration more pronounced.

Figure 4.

Vertical vibration spectrum of fasteners under normal performance (R800 m).

Figure 5 shows the variation in vibration frequencies on a 2500m radius curve. There are no peaks in the low-frequency range for the two rails, with peaks mainly concentrated in the mid-high frequency range. At vibration frequencies of 230 Hz, 255 Hz and 275 Hz, significant resonance phenomena are observed on both sides of the rails and wheelsets. The inner rail exhibits more pronounced resonance due to the higher energy at its peaks.

Figure 5.

Vertical vibration spectrum of fasteners under normal performance (R2500 m).

In summary, the vibration frequencies of the wheelsets do not show significant changes with varying curve radii. However, as the curve radius increases, the peaks of the rails shift towards the mid-high frequency range, and the quantity of peaks on two rails increases. In the mid-high frequency range, the wheel-rail system exhibits the same peaks at multiple vibration frequencies. Due to differences in peak energy between two sides, more pronounced resonance is observed on one side of the rail and wheelset.

Analysis of wheel-rail vibration characteristics under track failure

In the case of complete failure of fastener stiffness and damping, the relationship between the vibration frequencies of the two rails and wheelsets is analyzed to explore the impact of track failure on wheel-rail vibration characteristics.

Figure 6 shows the vibration spectrum of a wheel-rail system on the 500m radius curve. At a low-frequency range of 49 Hz, resonance is indicated in both the rails and wheelsets. Peaks are also observed at frequencies of 138 Hz, 237 Hz and 262 Hz for both sides. The rails and wheelsets exhibit resonance phenomena at these frequencies, with more pronounced inner wheel rail resonance.

Figure 6.

Vertical vibration spectrum under fastener failure (R500 m).

Figure 7 shows the vibration characteristics on an 800m radius curve under conditions of fastener failure. At low frequencies of 48 Hz and 78 Hz, peaks are observed in both the rails and wheelsets. Peaks occur at 207 Hz and 270 Hz for both sides in the mid-high frequency range. The rails and wheelsets exhibit resonance phenomena at these frequencies, with the inner rail exhibiting more pronounced resonance due to higher peak energy.

Figure 7.

Vertical vibration spectrum under fastener failure (R800 m).

In the case of fastener failure, frequency domain analysis of the 2500 m radius curve reveals the vibration characteristics shown in Figure 8. At a low-frequency range of 47 Hz, peaks can be observed in both the rails and wheelsets. In the mid-high frequency range, peaks are present at 139 Hz, 230 Hz and 245 Hz for both sides. The rails and wheelsets exhibit resonance phenomena at these frequencies. The peak energy of the inner steel rail is relatively high, so the inner wheel rail resonance is more pronounced.

Figure 8.

Vertical vibration spectrum under fastener failure (R2500 m).

In summary, when the track structure fails, the wheel-rail resonance frequencies in the low-frequency range are around 48 Hz for all three curve radii. The failure features of the track structure conceal the curve radius parameter characteristics, and the track vibration characteristics in this case are only affected by the failure of the track structure. Additionally, compared to normal fastener, the number of peaks in the wheel-rail vibration region significantly increases after fastener failure, which raises the probability of wheel-rail resonance. The fastener failure leads to more frequent wheel-rail resonance, which is not conducive to the normal operation of vehicles and tracks.

Modal analysis of wheel-rail system

The natural frequencies and modes of the elastic track can be obtained, and their relationship and variation are analyzed to avoid structural damage caused by the wheel-rail resonance. In terms of complete fastener failure, the resonance frequencies of the wheel-rail with a curve radius of 500m are 49 Hz, 138 Hz, 237, and 262 Hz, the resonance frequencies of the curve radius of 800m are 48 Hz, 78 Hz, 207, and 270 Hz, as well as the resonance frequencies of the curve radius of 2500m are 47 Hz, 139 Hz, 203, and 245 Hz. The vibration modes corresponding to these frequencies are shown in Table 2. The natural modes of the track are selected to be as close as possible to the resonance frequencies, with the rails exhibiting vertical bending vibration of varying degrees, typically between the 7th and 17th modes relative to the ground.

Table 2.

Wheel-Rail vibration modes.

The natural modes of the rail in the low-frequency range at 45 Hz are close to the resonance frequencies of 47 Hz (R2500 m), 48 Hz (R800 m) and 49 Hz (R500 m), while 71 Hz is close to the frequency of 78 Hz. In the mid-high frequency range, 142 Hz and 143 Hz are close to the resonance frequencies of 138 Hz (R500 m) and 139 Hz (R2500 m), 212 Hz is close to the resonance frequencies of 207 Hz (R800 m) and 203 Hz (R2500 m), as well as 262 Hz and 245 Hz are equal to the resonance frequencies of 262 Hz (R500 m) and 245 Hz (R2500 m). Additionally, the natural modes of the wheelset at 128 Hz are close to the resonance frequencies of 138 Hz (R500 m) and 139 Hz (R2500 m), while 201 Hz is close to the resonance frequencies of 207 Hz (R800 m) and 203 Hz (R2500 m). Corresponding natural modes can be found for all resonance frequencies, with resonance occurring as multi-order vertical bending vibration of the wheel-rail system.

Research on rail corrugation under track failure

As the vehicle operates on the track, the wheel-rail contact surface gradually wears down. This abnormal wear affects the vibration features of the track. Wheel-rail wear reduces contact area, increases contact stress, and deteriorates the dynamics performance of the system, leading to changes in the vibration features.

Due to space constraints, the 500m curve with the highest rail corrugation proportion in Table 1 was selected for analysis. The operational speed is 54 km/h. The measured rail corrugation wavelength is 55 mm. According to equation (1), the rail corrugation wavelengths corresponding to resonance frequencies of 49 Hz, 138 Hz, 237 Hz and 262 Hz are 306 mm, 109 mm, 63 mm, and 57 mm, respectively. The simulated rail corrugation wavelength of 57 mm (at 262 Hz) is close to the measured wavelength of 55 mm. A correlation between track failure and rail corrugation is indicated, and the presence of this rail corrugation’s wavelength in the field is presented. In equation (1): λ is the rail corrugation wavelength, v is the operating speed, and f is the passing frequency.

λ = \frac{v}{3.6 f}

(1)

Considering the wheel-rail contact under track vibration, the wear issue is analyzed by using dynamic evaluation indicators such as lateral and longitudinal creep forces and wear number. The tangential contact is analyzed based on Kalker’s simplified theory. And the wheel-rail creep forces are calculated using the FASTSIM algorithm. The wear number incorporates spin creep force and spin creep rate to more accurately reflect their impact on rail wear, as shown in equation (2). Where T_x and T_y are the longitudinal and lateral creep forces, v_x and v_y are the longitudinal and lateral creep rates.

W I = T_{x} v_{x} + T_{y} v_{y} + M z

(2)

Table 3 shows the wheel-rail contact stress for different failure modes. On small-radius curves, stress concentration often occurs between the wheel flange and the rail gauge, with the maximum contact stress concentrated near the wheel flange, leading to increased wear. This explains why the measured rail corrugation is often centered on the rail crown. Stress remains relatively unchanged when only fastener stiffness or damping fails. However, with complete fastener failure, the area of maximum contact stress increases, leading to greater wear and accelerated rail corrugation.

Table 3.

Vertical contact stress of wheel-rail.

Four failure forms of fasteners are simulated: normal (I), stiffness failure (II), damping failure (III), and complete failure (IV). Figure 9 shows that fastener failure causes varying degrees of fluctuation in dynamic performance indicators. Smaller curve radii result in higher lateral and longitudinal creep forces and wear numbers. The small curve radius line is indicated to have severe rail corrugation. When fasteners fail completely, the lateral and longitudinal creep forces and wear number reach their maximum, accelerating the formation of rail corrugation.

Figure 9.

Wheel-rail wear conditions: (a) wear number; (b) lateral creep force; (c) longitudinal creep force.

Conclusion

A rigid-flexible coupling vehicle-track system dynamic model is established based on measured rail corrugation data. By changing the stiffness and damping parameters of the fasteners, the failure behavior of the structure is simulated. The effects of track failure on the vibration characteristics of the vehicle-track system are studied, and the reasons for rail corrugation on curved lines are identified. The main conclusions are as follows:

(1) When a track has structural failure, the wheel-rail resonance frequencies of the three curve radii are all around 48 Hz in the low-frequency range. Track failure overshadows the parameter characteristics of the curve radius. The vibration features of the track in this case are only influenced by the failure of the track structure. Track failure increases peaks in wheel-rail vibration, heightening resonance probability. Fastener failure leads to more frequent wheel-rail resonance, which makes the vibration more severe and exacerbates wear.

(2) For the curve with the highest rail corrugation proportion, resonance frequencies of 49 Hz, 138 Hz, 237 Hz, and 262 Hz correspond to wavelengths of 306 mm, 109 mm, 63 mm, and 57 mm. The simulated wavelength of 57 mm (resonance frequency 262 Hz) closely matches the measured 55 mm. A link between track failure and rail corrugation is indicated, and the presence of corrugation at this wavelength in the field is confirmed.

(3) Complete fastener failure increases the area of maximum wheel-rail contact stress, leading to greater wear and accelerated rail corrugation. Smaller curve radii result in higher lateral and longitudinal creep forces and wear numbers. The level of rail corrugation on a small radius curve is more severe. When this curve results in complete track failure, both the lateral and longitudinal creep forces and wear number reach their maximum, which further accelerates the generation of rail corrugation.

Footnotes

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.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Natural Science Foundation of Jiangsu Province (No. BK20231173), Science and Technology Planning Project in Xuzhou (No. KC22293), Jiangsu Province College Student Innovation Training Program (202310320108Y), Innovative Training Project for College Students in China (202410320025Z).

ORCID iD

Li Xiang

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