1 Introduction

The carbody sway refers to the lateral, yaw, or roll motion of railway vehicles along the track and is typical in high-speed trains, passenger cars, metro vehicles, and locomotives. This phenomenon can cause discomfort for passengers and wear on both the train and track. Factors contributing to the carbody sway behaviour include hunting motions, aerodynamic effects, track irregularities, and centrifugal forces during curve negotiation. Recent investigations show that the carbody sway with large amplitudes is relevant to the rail alternate side wear. Uneven wear of rails always occurs on opposite sides with specific intervals in tangent or large radius curved tracks.

The hunting instability, tail vortex, wind gusts, track excitation, switch passing, and centrifugal forces are all potential indicators of the carbody swaying behaviour. In Korea, the HEMU-430X high-speed trains experience low-damped carbody oscillations, showing the least damping ratio due to bogie lateral movement coupled with carbody upper sway [1, 2]. In China, reports of the carbody hunting have been made for high-speed trains, metro vehicles, and locomotives due to low effective conicity of wheel–rail contacts resulting from extensive rail grinding or too large constraint stiffness in the yaw direction between the carbody and bogie [3,4,5,6,7]. In Europe, the carbody upper sway issues have been reported in ICE series trains, particularly when adopting the 60E2 grinding rail profile. The combination of the S1002 wheel profile and 60E1 rail profile with the rail cant of 1:20 will experience a low­frequency instability if the wheelset hunting frequency is close to the natural frequency of the vehicle yaw motion [8]. In Japan, Shinkansen trains show greater vibration amplitudes in the tail car when running in tunnel sections [9, 10]. Efforts have been made to optimize head shape, suspension parameters, and semi or full-active control to alleviate the carbody sway in tail vehicles. The aerodynamic effects, such as tunnel aerodynamics, train passing, wind gusts, and transitions in windbreak walls, are main causes of the carbody sway [11,12,13,14,15]. Besides, track irregularities, local defects, and switch passing can directly worsen the train running behaviour [16,17,18]. The centrifugal forces generated during curve negotiations could dramatically increase the secondary lateral stiffness due to stopper contacts [19]. Adding centring control to pull the carbody back to the centre position from the outer side of the curve is effective in attenuating vibrations on curves [20].

Uneven wear patterns in this study do not refer to the conventional rail side wear, but the side wear alternating in the left and right rail. Although the side wear in high or outer rails in curved tracks can be variable, sustained periodic side wear in tangent and shallow curves is atypical in conventional railway tracks [21, 22]. The presence of this issue indicates a poor vehicle–track interaction condition that would typically initiate investigation, rectification and prevention strategies.

The wheel–rail interaction on curved tracks will inevitably increase the wheel and rail wear. This phenomenon can have a significant impact on maintenance costs, as it can cause increased wear on the wheel flange and rail gauge corner. However, the rail alternate side wear refers to the rail wear alternating between two sides of the track with a fixed wavelength. The root cause of rail alternate side wear can be the carbody sway or bogie instability with specific frequencies between the wheel flange and rail corner contact [23,24,25]. The occurrence of initial rail side wear could further aggravate the vehicle running behaviour. However, the interaction between the carbody sway and the rail alternate side wear is rarely studied. Most existing reports focus on the outer rail corner wear in curves, with few cases of fixed-interval wear. The rail alternate side wear can be found in heavy haul line [23,24,25], high-speed railway [26,27,28] and urban transit line [29]. In the early 2000s, only a few instances of this type of wear with fixed intervals were reported. The rail alternate side wear usually occurs in some tangent sections of heavy haul tracks, alternating in the left and right with equal intervals, and is unrelated to the wear depth [23]. The depth of the rail side wear is affected by the lateral force and friction/creep conditions, as well as total weight of passing trains. There exist representative wavelengths of 8–10 m [24] and 18.5–25 m [23], related to the hunting instability of freight cars and locomotives, respectively. The rail alternate side wear is present in China high-speed lines, particularly in ballasted tracks, both in tangent and large radius curved tracks. There are two types of rail side wear in high-speed railway lines. One type with a 20–30 m wavelength is relevant to low-frequency carbody hunting [26, 27], while another with a 7 to 8 m wavelength is relevant to high-frequency bogie instability [28]. Besides, the similar phenomenon of the rail alternate side wear has recently been discovered in various urban rail transit lines [29].

It is important to address the root cause of rail alternate side wear and propose solutions to prevent the carbody sway phenomenon. The vehicle-related factors of the rail alternate side wear could be the modal vibration [30] of the vehicle system. The modal vibrations are within the acceptable level in normal operations, but aggravate in case of local track impacts. The damping ratio of the natural frequencies could be relatively low. Potential factors that can contribute or influence the rail alternate side wear include friction level [31], surface hardness [32], track stiffness [33, 39], initial defects [34], and wheel–rail contact geometry [35]. The combination of the constant train speed and fixed vibration frequency could result in the rail side wear with fixed wavelengths [36]. For prediction of the alternate wear of rails, the rail side wear can be divided into the rail profile wear in the lateral and longitudinal directions. The numerical calculation of the rail wear formation is a good option to study the mechanism and solutions of the rail alternate side wear [37, 38]. Conventional numerical models can compute the wheel and rail profile wear based on vehicle–track dynamic simulations and a wear module implementing an experimental wear law. The difficulty of simulating the rail alternate side wear lies in the superimposition or reduction effect from different wheelsets at different locations of the track.

This work is originated from the carbody sway phenomenon of metro vehicles which is a common source of complaints from passengers and crews. In the past, the carbody sway behaviour was much investigated from the perspective of wheel–rail contact relationship [2, 3], hunting motion [5,6,7], wind effect [11,12,13], centrifugal forces [20], etc. However, the formation of the alternate side wear issue is more likely the result of the carbody sway in long-term operations. In this work, field tests and numerical investigations were conducted to reveal the effect of the rail alternate side wear on the carbody sway behaviour, with the following highlights:

  • Dynamic characteristics of carbody sway for a railway vehicle are investigated by field testing.

  • The rail alternate side wear phenomenon is found in the track sections suffering from carbody sway.

  • Vehicle system dynamic models considering the rail alternate side wear effect are developed and validated.

  • Parametric studies are conduced to propose potential solutions and reveal the formation mechanism of rail alternate side wear.

The rest of this paper is organized as follows. Section 2 presents the carbody sway behaviour of an urban rail transit train based on full-scale field tests. Section 3 analyses the characteristics of the rail alternate side wear and the formatted track irregularity. In Sect. 4, multibody vehicle dynamic models are developed and verified to replicate the carbody sway phenomenon resulting from the track irregularity caused by rail alternate side wear; the influence of carbody sway on wheel flange and rail gauge corner wear is further studied through creep forces. Finally, Sect. 5 proposes potential solutions, such as improving the damping ratio of the carbody rigid mode and rail grinding, to alleviate this issue.

2 Field investigation of carbody sway for metro vehicles

In this section, the carbody sway phenomenon of metro vehicles in service is introduced. According to the description of train attendants and passengers, a significant lateral movement of the vehicle can be experienced by human perception. The lateral vibrations of the train in most sections are acceptable. However, the carbody sway behaviour always occurred in some particular locations of the track, especially for the tail end of each carbody. Therefore, a full-scale field test was carried out in this work to investigate the dynamic performance and vibration characteristics of metro vehicles. The LM (L and M refer to ‘Liang’ and ‘Mo’ in Chinese, or ‘Vehicle’ and ‘Worn’ in English) wheel profile is used for the test train and the running mileage after reprofiling of the wheel is only 5,000 km. The highest test speed of the train is 80 km/h. The illustration of the test instrument on the tail and adjacent cars is shown in Fig. 1a. Accelerometers are arranged on the carbody floor, bogie frame and axle box to evaluate the ride quality and running behaviour of the metro train. The gyroscope is used to measure the running attitude, e.g. yaw and roll velocities of the carbody. Photoelectric sensors arranged on the bogie frame and reflective sticker on the rotating wheel are applied to measure the train speed. The tested train in the depot is shown in Fig. 1b. The track inspection system with a 2D laser transducer is installed in the tail car to measure the track irregularities.

Fig. 1
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Test illustration: a test instrument; b tested train in the depot; c track inspection system

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2.1 Dynamic evaluation of the carbody sway for metro vehicles

The mileage history (Fig. 2a, upper) and the short-time Fourier transform (STFT) spectrum (Fig. 2a, middle) are applied to analyse the vibration characteristics of the tested vehicles. The window length of the STFT spectrum is set up to 10 s with a 1-s sliding interval for better resolution. The lateral axis represents the running mileage and the vertical axis indicates the vibration frequency. The colour map depth shows the amplitude of vibration at each mileage and frequency. As Fig. 2a shows, vibrations with a frequency of around 1.4 Hz are present throughout the entire trip. This frequency remains constant at different speeds and is considered to be that of the carbody rigid mode. Large amplitude hotspots are observed in certain sections of the track, indicating significant oscillation frequencies known as the carbody sway. The track structure types are also illustrated in Fig. 2a (lower). Typical track structures include low damping tracks with DTVI2 fasteners, middle damping tracks with the type III or tow-layer damper fasteners, and high damping tracks with floating slabs. It is shown the worst carbody sway phenomenon occurs in the section with the track structure of type III fasteners. The stiffness of this type of fasteners is around 10 MN/m, which is softer than conventional fasteners. The mechanism of influence of the track structure parameters on the carbody hunting behaviour and rail alternate side wear should be further studied in future works.

Fig. 2
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Evaluation and analyses of measured lateral vibrations on the carbody floor: a STFT spectrum; b lateral and vertical ride index; c amplitude of harmonic vibration and ride comfort

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The field-tested results in those sections are evaluated using the Sperling ride indices defined by the standard GB 5599, as shown in Fig. 2b. In the section where the carbody sway occurs, the vertical ride indices (Wz) are at an excellent level, but the lateral ride indices (Wy) go beyond the excellent limit, which is illustrated by red dashed line in Fig. 2b. Herein, the limit values of the excellent level for lateral and vertical ride indices are both 2.5. However, in normal sections, both the lateral and vertical ride indices remain within the excellent level. The riding comfort coefficient could be calculated based on the amplitude and frequency of vibrations. Figure 2c shows harmonic vibrations in the frequency range of 1–2 Hz. The transient vibration amplitude in the lateral direction reaches a level considered poor in terms of riding comfort, suggesting that the occurrence of the carbody sway has significant effect on the ride quality of passengers.

2.2 Vibration characteristics of the carbody and bogie

The vibration characteristics of the vehicle system is analysed using test data from the accelerometers and gyroscope. The mileage history signals undergo processing with a 10 Hz low-pass filter. Significant yaw motions of the carbody can be observed in Fig. 3a, while the roll and pitch motions remain at a relatively lower level. The dominant frequency of the carbody yaw and roll motions is around 1.4 Hz. It reflects that the rigid modal vibration as illustrated in Fig. 2 is related to the yaw mode. Besides, the mileage history of vibrations of the vehicle system and frequency spectra in three directions are shown in Fig. 3b. The vibration analysis shows that the harmonic vibration with a frequency of 1.4 Hz exists in the lateral direction of the vehicle system, as well as in the vertical direction of the carbody, and the lateral vibration of the bogie is similar to that of the carbody. Although some frequency peaks in the spectrum can be observed, the high-frequency vibrations induced by carbody elastic modes are not discussed in this work.

Fig. 3
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Measured vibrations of vehicle system in mileage history and the frequency spectrum: a carbody angular velocities; b carbody accelerations; c bogie accelerations

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3 Analysis of track irregularity due to rail alternate side wear

3.1 Rail alternate side wear

The carbody sway always occurs in some particular locations of the track, where on-track investigations were conducted on the wear conditions to provide a more intuitive observation of this issue. Visual inspections showed that a new phenomenon of rail corner wear exists in abnormal sections, as illustrated in Fig. 4a. The rail corner wear exists on either the left or right sides of the rail, displaying in sinusoidal forms with a wavelength of around 15 m. The largest side wear depth of the rail corner in the lateral coordinate shifts with certain intervals, as shown in Fig. 4b. The wavelength of the rail side wear is 15–20 m. It seems that the sinusoidal wear was periodically branded by the wheel–rail interactions in vehicle motions. The initial reason for the formation of the rail alternate side wear could be complicated. For instance, the damping ratio of the carbody rigid mode is not high enough to prevent the vehicle from swaying due to large or sudden impacts from the track. The poor wheel–rail contact relationship could also bring out the carbody hunting or bogie hunting instability in local parts. In general, the vehicle behaviour and the rail alternate side wear are interactive with each other.

Fig. 4
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Illustration of rail alternate side wear: a observation; b measurement

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3.2 Track irregularity analysis

The test train is equipped with a track inspection system to measure track irregularities. The system analyses the mileage–wavelength spectrum to identify common types of irregularities, such as long wavelength alignment irregularities, illustrated in Fig. 5a. The vertical axis shows the wavelength while the lateral axis represents the running mileage, and the colour map indicates the power spectrum density (PSD) which measures the irregularity amplitude at each mileage and wavelength. The spectrum analysis reveals that specific wavelengths of track alignment irregularities occur at certain locations on the track, coinciding with the carbody sway sections. Figure 5b displays the mileage history curve for track alignment irregularities on one side rail, where the quasi-static component results from the track curvature while the harmonic component indicates a fixed wavelength from the rail alternate side wear. Based on the power spectrum density analysis in Fig. 5c, it has been determined that the predominant wavelength of the track alignment irregularity measures 15.75 m. Assuming a train speed of 80 km/h, the associated frequency generated by this wavelength component is 1.41 Hz. It is evident that the frequency of vibration resulting from specific wavelength excitations will augment in proportion to the train speed. In the mileage history, Fig. 5d compares the carbody lateral accelerations of the train at various speeds. The quasi-static lateral accelerations are a result of the combination of train speed and cant deficiency on curved tracks. Figure 5e demonstrates a local enlargement of carbody lateral vibrations at different operation modes, i.e. automatic train operation (ATO) and restriction management (RM). The train speeds at this section for two modes are 80 km/h and 20 km/h, respectively. Although the vertical ranges at two vertical axes are different in Fig. 5e, it can be observed that the carbody vibration trajectory are similar under the same track alignment irregularity.

Fig. 5
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Track irregularity analysis: a mileage–wavelength spectrum; b mileage history curve; c power spectrum analysis; d effect of train speed on carbody lateral accelerations; e local enlargement. ATO and RM stand for automatic train operation and restriction management, respectively

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4 Modelling and simulations

4.1 Vehicle system dynamic models

This section presents numerical simulations aimed at providing insights into the mechanism and effects of the carbody sway behaviour due to the rail alternate side wear. The train speed in the simulation is set up to 80 km/h. The vehicle system scheme is depicted in Fig. 6a and comprises four conventional wheelsets, eight axle boxes, two pairs of bogie frames, and one carbody. Each bogie frame and carbody possess six independent degrees of freedom (DoFs), enabling unrestricted movements or rotations in the lateral, vertical, and longitudinal directions. The wheelset has four independent and two dependent DoFs, with the vertical and roll motions dependent on the lateral and yaw motions. There exist eight axle boxes in the vehicle. Each axle box located between the wheelset and bogie frame is considered with the pitching DoF relative to the free rotating wheelset. The model accounts for a total of 50 independent DoFs of rigid motions. The nonlinearity of the suspension system significantly impacts the vehicle behaviour in the vehicle dynamic model. The primary rubber spring is represented as a force element connecting the non-rotating axle box and bogie frame. The secondary lateral damper is a crucial component in preventing the sway behaviour of vehicles. Therefore, this paper fully considers the actual characteristics of the lateral damper and adopts the Maxwell model in simulations. The measured damping of the lateral damper at one end of the vehicles is smaller than the designed value, as shown in Fig. 6b. The nonlinear force–displacement characteristic of the secondary lateral stopper is also considered in the simulation.

Fig. 6
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Vehicle dynamic models: a scheme; b suspension nonlinearity; c wheel–rail contact conicity

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The wheel–rail modelling is a crucial part in simulation of rail vehicle dynamics. Here, we apply the Hertz model to solve the wheel–rail contact patch normal forceand solve the tangential force using the simplified Kalker theory. The wheel–rail profiles also have a substantial impact on the carbody sway behaviour. The equivalent wheel–rail contact conicity is around 0.1 for the standard and measured new wheel profiles matched up with the new rail with a rail inclination of 1:40. The low wheel–rail contact conicity around 0.06 is also considered in the simulation by combination of the standard wheel profile and the grinding rail profile. The extreme wheel–rail contact conicity is as high as 0.68 for the measured worn wheel profiles. An indicator for the wear in simulation is the Tγ value, calculated as the product of creepage (γ) and corresponding creep force (T). The measuring accuracy of the rail profiles by the track inspection system is not high enough for wheel–rail contact and creep force calculation. In the future work, it is meaningful to use the rail profiles measured by handle devices for numerical simulations by considering the variation of the rail profile in the dynamic analysis.

Previous work [39] proved that the hunting critical speed of a train will be decreased slightly as the track vertical and lateral stiffness decreases. In this work, the track structure flexibility is not fully considered. According to field experience, however, it is found that the rail alternate side wear is also relevant to the soft tracks, e.g. damper fastener, floating slab, ballast track and bridges. Therefore, the relationship between the rail side wear and the track structure should be further studied in the future.

4.2 Model verification

The time- and frequency-domain analyses are carried out based on the developed dynamic model. The time history and frequency spectrum of the vehicle lateral vibrations by simulations are compared with those by field testing, as shown in Fig. 7. The model verification is conducted on the tangent tracks with a speed of 80 km/h. It is indicated that the calculated carbody lateral accelerations and secondary lateral displacements show good agreement with those obtained by the on-track testing, and that a significant harmonic motion in the vehicle system occurs with an oscillation frequency of around 1.4 Hz. This verifies that the developed dynamic model can well reproduce the low-frequency carbody sway phenomenon due to the track excitation with a particular wavelength.

Fig. 7
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Comparison of the time histories and frequency spectra of the vehicle lateral vibrations between testing and simulation: a carbody lateral accelerations; b lateral damper displacement

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4.3 Parametric studies

It is critical to improve the performance of the vehicle subjected to poor track excitations. Based on the occurring mechanism of this issue, several potential solutions are proposed and verified by simulations using the dynamic model. The potential solutions include but are not limited to the following scenarios:

  • Increasing the wheel–rail contact conicity. The equivalent conicity of wheel–rail contact is ranging from 0.06 to 0.6 with consideration of wheel profiles at various wear periods. It is seen from Fig. 6c that the wheel–rail contact conicity for the wheel profiles with a large running mileage is higher than that for the new wheel profiles. The increase of the wheel–rail contact conicity can decrease the carbody lateral accelerations, while the vibration frequency remains constant, as shown in Fig. 8a. This phenomenon has also been proved by the tested results from the car adjacent to the tail car with worn wheel profiles. In the scenario of high wheel–rail contact conicity, the wheel lateral displacement is relatively small. As the carbody modal vibration frequency is invariant, the induced vibration of the carbody could be lower.

  • Optimising secondary suspension parameters. As mentioned above, the damping deficiency of secondary lateral dampers in operations could be more dominant, especially in the end 1 of the rail car, as shown in Fig. 6b. An increase in the secondary lateral damping can avoid the resonance between the carbody modal vibration and the track excitations from the rail alternate side wear, and further suppress the carbody lateral accelerations, as shown in Fig. 8b. The carbody lateral accelerations reach a certain level when the secondary lateral damping is higher than 20 kN∙s/m. The frequency of carbody lateral vibrations will not change with the increase of the secondary lateral damping. Decreasing the secondary lateral stiffness can also alleviate the carbody lateral acceleration of the vehicle subjected to track excitations from the rail alternate side wear, as shown in Fig. 8c.

  • Limiting the train speed and track irregularities. It has been proved in the field test that the amplitude and frequency of the vibrations resulting from the specific wavelength track excitations can be decreased by limiting the train speed. Similar results can be obtained by numerical simulations, as shown in Fig. 8d. Slightly sacrificing the operation schedule by limiting the train speed to 40–60 km/h can achieve a trade-off between the dynamic performance and operation schedule. Besides, the vibration level of the carbody sway can also be suppressed by either changing the wavelength or controlling the level of track irregularities. Figure 8e shows that the carbody lateral acceleration under the American class 5 track irregularity (Nu5) is lower than that under measured track excitations. However, the vibration frequency of around 1.4 Hz still exists in the vehicle system as the carbody modal vibration occurs under random track irregularities.

Fig. 8
figure 8figure 8

Effect of key parameters on carbody lateral vibrations of the vehicle subjected to track irregularities due to rail alternate side wear: a wheel–rail contact conicity; b secondary lateral damping (csy); c secondary lateral stiffness (ksy); d train speed; e track irregularity

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5 Formation mechanism of rail alternate side wear

This section discusses the initial formation mechanism of rail alternate side wear, which involves the distribution of contact points as well as creep forces in the left and right wheel–rail contact interface. The lateral position of the contact points on the wheel profile is depicted in Fig. 9a, where a harmonic trajectory can be observed along the longitudinal direction. The left and right contact points exhibit a lateral distribution that alternates between the wheel flange and tread area. When the contact point on the left wheel is near the wheel flange, the one on the right wheel is located on the wheel tread area. The contact points on the wheel tread area are focussed on the nominal contact position, with a certain lateral shift of the wheel without flange contact. Figure 9b illustrates the lateral position of contact points on the rail profile, where the left and right contact point distributions display an alternating shift between the rail inner and outer sides. The interval between peak values of lateral contact positions corresponds to that of the rail alternate side wear. It is worth noting that the contact between the wheel flange and rail corner increases the wheel–rail creep force, resulting in peak values of wheel–rail tangential forces in phase with the contact point distribution. Figure 9c shows the vertical position of contact points on the rail profile, with vertical displacements of contact points on the rail being less than 2 mm and smaller than the lateral shifts.

Fig. 9
figure 9

Distribution of contact points in the wheel–rail interface: a lateral contact position on the wheel; b lateral contact position on the rail; c vertical contact position on the rail

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The primary reason for the formation of rail alternate side wear may be due to the low-frequency modal vibration of the carbody with a low damping ratio. These vibrations can be triggered by significant disturbances at specific locations such as rail discontinuities, switch passing, sudden changes in track stiffness, low wheel–rail friction coefficient, or contact conicity. Here. the creep forces and wear indices of two typical scenarios are analysed to explain the mechanism of rail alternate side wear. In the first scenario, the vehicle system is simulated under fixed-wavelength track irregularities, while the second scenario is under random track irregularities.

The analyses of creep forces and wear indices for the two scenarios are shown in Fig. 10. We can see that the longitudinal creep force at the left side (Tx_L) of the wheel–rail interface are opposite to the one at the right side (Tx_R), while the lateral creep forces at the left (Ty_R) and right (Ty_R) sides are in-phase. However, the wheel–rail lateral creep force at one side is consistently lower or higher than that on the other side. The wear index is calculated by summation of the creepage multiplied by creep force in the longitudinal and lateral directions as Txvx + Tyvy, where vx and vy are creepage, and Tx and Ty are creep forces, in the longitudinal and lateral directions, respectively. Observations indicate that the wear index of the left rail side is higher than that of the right rail side during the first peak but significantly decreases during the second peak. The distance between consecutive peaks of the wear index is half the characteristic wavelength. Hence, the wavelength of track gauge irregularity is half the wavelength of track alignment irregularity on either side. In the scenario of the measured track irregularity, the wheel–rail creep forces undergo harmonic motion due to the resonance between fixed-wavelength track excitations and carbody modal vibrations. However, in the case of random track irregularities, the harmonic motion results only from carbody natural modes. This distinction clarifies the initial cause of the formation of alternate side rail wear.

Fig. 10
figure 10

Creep forces and wear indices under a measured and b random track irregularities

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In this work, the wavelength of the rail alternate wear is around 15 to 20 m, which is relevant to a low vibration frequency of 1.1 to 1.5 Hz at the speed of 80 km/h. Therefore, the study is focussed on the low frequency vibrations in the vehicle–track system. Normally, the natural frequencies of the track system are high, which contributes to the formation of the wheel–rail short-pitch roughness; in contrast, the natural frequencies of the vehicle system are lower and are considered as a potential indicator to the regular rail alternate side wear.

According to field observations, the rail alternate side wear on the ballast track or bridges is more common than on the unballasted track. Therefore, the influence of the track stiffness and plastic deformation on the rail side wear should be further studied in future work using a track model consisted of sleepers and fasteners simulated as spring–damper systems. Besides, the numerical prediction of the rail alternate side wear is also necessary to be conducted in the future.

6 Conclusions

The carbody sway behaviour due to the track irregularity from the rail alternate side wear was investigated using field tests and numerical simulations, and some conclusions can be drawn as follows:

  1. 1.

    Track irregularities caused by rail alternate side wear can result in carbody sway behaviour of railway vehicles, bringing significant influence on the ride comfort of passengers. The harmonic vibration with a frequency of 1.4 Hz exists in the whole trip at both the lateral and vertical directions of the vehicle system.

  2. 2.

    Visual inspections show that a new phenomenon of rail corner wear exists in the carbody sway sections. The track inspection system shows that the track alignment irregularities with a wavelength of 15–20 m occur at the same locations. The corresponding frequency due to this type of track excitation is coincident with the natural frequency. Limiting the train speed can decrease the forced vibration frequency, but will not change the waveform along the track.

  3. 3.

    A vehicle dynamic model was developed to address the carbody sway, and the simulation results show a good agreement with the test results. Increasing the wheel–rail conicity can reduce lateral acceleration, while vibration frequency remains unchanged. Properly increasing the lateral damping or decreasing the lateral stiffness of secondary suspensions can alleviate the carbody sway behaviour. To slightly limit the train speed to 40–60 km/h can suppress the carbody oscillation without sacrificing the operation schedule.

  4. 4.

    The contact positions on the wheel and rail profiles show a harmonic trajectory along the track. The left and right contact points exhibit a lateral or vertical distribution that alternates between the wheel flange and tread area, as well as the rail inner and outer sides. The wear index at one side of the wheel–rail interface is consistently lower or higher than on the other side. The initial cause of the formation of the alternate side rail wear could be the low-frequency modal vibration of the carbody with a low damping ratio.