Wheel-rail Forces Research Articles

A frequency-domain simulation method for the evolution of rail corrugation in curves

Rail corrugation remains a major problem in many railways and metros, leading to high noise and vibration levels as well as potential damage to the track and vehicle. A frequency domain simulation method is proposed for the evolution of the rail surface roughness, which can simulate the formation and development of rail corrugation in curves. A coupled vehicle-track dynamic model is established in the frequency domain to calculate the dynamic vertical and lateral wheel-rail contact forces and the associated vibration. The wheel-rail contact state is determined by using a multi-body dynamics model. The frictional-work wear model is used to calculate the roughness change caused by wheel-rail dynamic interaction. The method is verified by comparing the results with those of on-site testing on a 300 m radius curve of a metro line. It is shown that the main causes of rail corrugation are associated with the peaks in the vertical wheel-rail forces in the frequency domain, generated by the interaction between the wheel and rail. At short wavelengths the corrugation is associated with the wave reflections in the rail between adjacent axles. The phase relationship between the vertical wheel-rail force and the initial roughness has a strong influence on the roughness growth trend, leading to preferential growth in certain wavelength bands. The wheel-rail contact state and friction parameters affect the rate of development of the corrugation. Finally, a corrugation index is proposed to allow quick evaluation of the wavelength and growth rate of corrugation.

3D rolling contact finite element analysis of high-speed railway turnout considering ratchetting effect

The present work introduces a three-dimensional finite element model for the wheel-turnout-sleeper system, incorporating a cyclic constitutive model that accurately captures the nonlinear hardening behavior of rail steel under cyclic loadings. At the same time, a mixed implicit-explicit finite element method is employed to investigate the transient rolling contact behavior of wheel-turnout. Through dynamic analysis, the transient rolling contact status of the wheel-turnout, stress and strain responses of the turnout, and wheel-rail forces are investigated under varying crossing speeds and number of cycles. It is found that during the wheelset crossing, the contact stress remains relatively stable on the stock rail, and multi-point contact occurs at the wing rail and long point rail, and the contact stress on the surface of the long point rail is more significant. With an increase in crossing speed in the same cycle, there is a gradual rise in contact stress on the long point rail face. At the same crossing speed, with the increase in the number of cycles, the contact position between the wheelset and the long point rail gradually moves back, and the top width of the contact position gradually expands. Meanwhile, the fluctuation range of vertical displacement of the wheel center diminishes, and the wheel flange moves away from the long point rail. Additionally, a progressive accumulation of ratcheting strain is observed on the rail, and the ratcheting strain on the long point rail significantly exceeds that on the stock rail. The research results will help to provide a reference for the optimization and design of the critical cross-section profile of the long point rail and will have guiding significance for the maintenance and repair of turnouts.

Visual measurement of lateral relative displacement of wheel-rail of high-speed train under earthquake

When an earthquake causes the wheel-rail detachment of a high-speed train, the derailment evaluation criteria based on wheel-rail force faces failure. At this time, the lateral relative displacement of the wheel-rail (LRDWR) is more intuitive and continuous to assess the running safety of a high-speed train. In the past, many experimental studies have been conducted on measuring the LRDWR of trains. However, there is still a lack of effective measurement methods to solve the problem of LRDWR measurement in complex texture and high-speed dynamic scenes. Therefore, a lateral relative wheel-rail displacement measurement method based on machine vision and the improved Hourglass network (LRWRDVH) is proposed in this paper to determine the LRDWR by predicting the pixel coordinates of a few wheel-rail keypoints. The scaled-down bridge running test of the high-speed train is designed for validation, and then the LRDWR measurement of high-speed train under earthquake is carried out using the LRWRDVH method to evaluate the running safety of high-speed train. The test results show that the LRWRDVH method is effective and accurate and can be further used to study the running safety of high-speed trains under earthquakes.

Composite embedded track structure considering temperature dependent characteristics for rolling noise reduction of inter-city railway system

Intercity railway will generate strong noise when passing through the surrounding residents, among which rolling noise is the main noise source and is difficult to control. A composite embedded track structure containing polymer material was fabricated to analyze its damping and rolling noise reduction characteristics. The damping characteristics of polymer materials of embedded track were tested by dynamic thermo-mechanical analyzer (DMA Q800). The frequency response function (FRF) of the embedded track system is tested by force hammer percussion method. The vibration of the embedded track is simulated by the the 2.5-dimensional finite element method (2.5D FEM) considering damping characteristics obtained by material test of DMA Q800. The sound radiation model of embedded track is developed by using 2.5-dimensional sound boundary element method (2.5D BEM). The model is verified by the test. The FRF, track decay rate, and wheel-rail force at different temperatures are analyzed. With the decrease of temperature, the elastic modulus and loss factor of polymer material of embedded track increase, which will affect the above results. Sound directivity and effect on wheel-rail noise reduction of embedded track have been studied. The results show that the composite embedded track has good damping characteristics and noise reduction performance. Sound sensitivity analysis of loss factors of the three polymer materials of embedded track is carried out to improve embedded track noise reduction capability.

Research on inversion of wheel-rail force based on neural network framework

Wheel-rail force is a critical parameter for vehicle-track-bridge (VTB) structure system, playing a pivotal role in ensuring the safe operation of trains and service performance of track and bridge structures. This paper proposes a methodological framework for efficient and accurate prediction of wheel-rail force, that bidirectional gated recurrent unit (Bi-GRU) neural network is developed and the hyperparameters of networks are optimized through grey wolf optimization (GWO). Based on the developed VTB system model, numerical experiments are carried out to produce datasets which are verified through field test. In order to make the data more universal and comprehensive, Latin hypercube sampling (LHS) is introduced to randomize the parameters of VTB model. The datasets generated from VTB system, with rail seat force as input and wheel-rail force as output, serve as the training data for framework. Additionally, the inversion effects under various working conditions are examined and discussed. The results indicate that the model can precisely inverse continuous wheel-rail forces from the moment the wheels enter the first test rail seat until leave the last test point of rail seat. When the neural network learns from the features of at least three or more rail seats on each track slab (with intervals not exceeding 2 rail seats), it can accurately inverse the time history curve of wheel-rail forces. The framework presents a viable alternative for the wheel-rail force analysis, and promising potential for the realization of online monitoring of wheel-rail force.

Dynamic Receptance Analysis Combined with Hybrid FE-SEA Method to Predict Structural Noise from Long-Span Cable-Stayed Bridge in Urban Rail Transit

In this study, dynamic receptance analysis (DRA) is proposed and combined with hybrid finite element (FE)-statistical energy analysis (SEA) method to accurately predict structural noise from long-span cable-stayed bridge (LSCB) with steel box composite girder (SBCG) in urban rail transit (URT). To begin with, a vertical vehicle–track coupling model in frequency domain is established based on DRA, in which the rail is represented by an infinite Timoshenko beam supported by a series of fasteners that are regarded as springs with complex stiffness. The floating slab is regarded as the Euler beam with both ends free supported by steel springs. Using this model, the spectrums of the wheel–rail force and the forces transferred to the bridge can be efficiently obtained by taking rail roughness as the excitation. Due to the low modal density of the concrete deck, the hybrid FE-SEA method is introduced to establish the noise prediction model, in which the discontinuity caused by using distinct models for different frequency bands is avoided. Then the on-site noise tests of a LSCB with SBCG in URT are carried out to verify of the proposed method. Finally, based on the prediction method, the acoustic contributions of the bridge components are analyzed in detail. The force transfer characteristics as well as the noise reduction effects of different track structures are thoroughly investigated, so as to provide reference for the future research on bridge-borne noise control.

Rail surface spot irregularity effects in vehicle-track interaction simulations of train-track-bridge interaction

The presence of rail surface damage leads to increased vibrations on railway bridges as wheels cross the localized irregularities. These short wavelength irregularities appear frequently on the top of rail in railway tracks and, along with the increased axle loading, fatigue failure accelerates, and ultimately, serviceability decreases. Compromised bridge safety and reliability is countered by an increase in inspections as bridge structures continue to age and deteriorate. In recent years, the effects of rail surface spot irregularities on the condition of railway bridges have attracted the attention of the industry and the research community. This study has two objectives. Firstly, it introduces the methodology, algorithms, and models for Vehicle Track Interaction (VTI) simulations developed to study the effects of Rail Surface Spot Irregularities (RSSI) on system response. The proposed VTI simulator solves the wheel-rail interaction problem in a Staggered Time Marching (STM) form. Long- and short-wave surface irregularities are accounted for. A multi-point wheel-rail contact algorithm is developed and implemented for properly capturing the wheel contact points in view of the relative size of the wheel and the rail surface irregularities. The proposed method is verified analytically. Subsequently, this paper investigates and quantifies the effects of the shape and location of RSSI on the vibrations of the bridge structure and the train for different train speeds. It is shown that RSSI affects wheel-rail interactions forces significantly and the induced vibrations substantially stimulate bridge velocity and acceleration. The effects are more pronounced for specific RSSI locations and train speeds.

Postearthquake train operation safety assessment model based on machine learning

Abstract Assessing the seismic risk to high-speed rail systems with limited structural damage data is a challenging task. This study employs machine learning algorithms to predict the wheel–rail forces of high-speed trains operating under postearthquake conditions, particularly when infrastructure along the railway is damaged. By developing a postearthquake train operation safety assessment model, this article effectively predicts the impact of track irregularities induced by different earthquake intensities on wheel–rail interactions. The results obtained through feature selection and regression analysis using the Random Forest algorithm provide valuable insights into key safety indicators for postearthquake train operations. Compared to traditional multibody dynamic models, this approach significantly improves the efficiency of analysis and computation. An analysis of the results across multiple speed levels reveals that trains operating at 250 km/h face derailment risks when subjected to high-intensity earthquakes (PGA > 0.6 g). The proposed predictive safety assessment model demonstrates that adjusting train speeds according to seismic intensity can effectively enhance operational safety, offering critical support for postearthquake emergency recovery efforts.

A hybrid reliability assessment method for slab track with changing structural parameters

Changes in the dynamic properties of high-speed rail (HSR) slab track structures can have a great impact on train safety and ride quality. However, the dynamic response of wheel–rail systems, which is related to operational safety, has rarely been considered in existing service reliability assessments of track structures. To solve this problem, a hybrid method was developed, with the serviceability limit state (SLS) first defined with respect to the derailment coefficient (DC) and wheel unloading rate (WUR). In calculating the reliability index, the response surface method and the first-order reliability method were used to solve the implicit expression of wheel–rail force in the SLS equation. To reduce the computation cost, a surrogate model expressing the non-linear mapping of the wheel–rail interaction is proposed. The computation efficiency and accuracy of the hybrid method were compared with Monte Carlo simulation and a back-propagation neural network (BPNN). The computation time of the hybrid method was only 1/8.4 of the BPNN method, while the accuracy of the reliability index was 98% for the DC and 97% for the WUR. The hybrid method was used to assess the reliability of a typical slab track structure under changing stiffness and damping coefficients of the fasteners, cement asphalt mortar and foundation. The stiffness and damping of the fasteners had the most impact on wheel–rail dynamics and track reliability. This research provides new insights into reliability assessments for HSR slab track with respect to train operational safety.

A new methodology for pre-camber design of a long-span bridge considering dynamic train load and complex environmental effects

This work aims to develop a reasonable pre-camber design method for long-span cable-stayed bridges by investigating the high-speed train-bridge interaction under complex environmental loads, including ambient temperature, concrete creep, and concrete shrinkage (CCCS). First, an integrated dynamic model of the train-track-cable stayed bridge system (TTCSBS) is established using multibody dynamics and finite element theory and validated through field test. Then, the temperature change features at several key positions on the long-span bridge are investigated using long-term monitoring data. Temperature-induced bridge deformation is calculated by applying the established bridge finite element model (FEM) and compared with test results. CCCS-induced bridge deformation is determined through numerical calculations that consider the bridge's structural and material properties. On this basis, the effects of bridge deformation caused by environmental loads on vehicle-bridge dynamic interaction are investigated in detail, and a new bridge pre-camber design method is proposed to counteract the effects of both environmental and train dynamic loads. Results indicate that the proposed model's simulations align well with field test data. The long-span bridge deformation induced by the environmental loads intensifies the dynamic responses of a running vehicle, particularly the wheel-rail vertical force and car-body vertical vibration. However, it has slight influence on train-induced bridge vibration. The proposed pre-camber design method for long-span bridges, which accounts for long-term environmental load action, effectively ensures good vehicle service performance. The research results could provide useful guidance for the design of long-span bridge systems.

A new mesh-type rail pad with second-order stiffness

In this paper, a novel mesh-type rail pad with second-order stiffness (MTRPSOS) is proposed, which is comprised of a mesh-type rail pad (MTRP) and multiple filled blocks. By adjusting the height of the filled blocks, the stiffness curves of the MTRPSOS exhibit pronounced second-order stiffness (SOS) characteristics. A finite element (FE) model of the MTRPSOS and a dynamic model were established to investigate the SOS characteristics and their impact on various dynamic indices. The FE calculations reveal that both static and dynamic stiffness of the MTRPSOS increase as the height of the filled blocks decreases. Moreover, as the height of the filled blocks increases, stress distribution becomes more uniform. The dynamic calculations demonstrate that the SOS characteristics of the MTRPSOS significantly affect various dynamic indices. As the SOS of the MTRPSOS decreases, rail displacement correspondingly increases, while vibration acceleration, wheel-rail forces, fastener reaction forces, and derailment coefficient all decrease. This indicates that the MTRPSOS offers superior vibration reduction under the SOS conditions compared to the first-order stiffness conditions. Additionally, a comparative study was conducted to assess the vibration reduction effect of the MTRPSOS in contrast to traditional rail pad, and the results show that the MTRPSOS consistently exhibits lower vibration levels under the same operating conditions, underscoring its superior capacity for vibration reduction.

On use of train-track-subgrade dynamic model for investigating the train-induced cumulative deformation of subgrade and its dynamic effects

This work focuses on two research projects. The first project deals with the prediction of the train-induced cumulative deformation of the high-speed railway subgrade based on the train-track-subgrade dynamic model, and the second project deals with the long-term performance of the train-track-subgrade interaction system subject to the permanent deformation of the subgrade. The train-track-subgrade interaction is established as the model fundament, and the empirical model of soil cumulative deformation prediction is introduced to realize the joint analysis of the train-induced cumulative deformation of the subgrade and its effect on the performance of the time-varying dynamic system. From the numerical results, the train-induced cumulative deformation of subgrade shows a fast and then slow trend, and the deformation has periodic distribution in the longitudinal direction. Although the cumulative deformation of the subgrade for the ballastless track is small compared with that of ballasted track, its effect on the vertical response of the train-track-subgrade interaction system is obvious. With the development of cumulative deformation of subgrade, the vibrations of the car body are excited in the frequency band of 0∼100 Hz. Furthermore, the maximum car body vertical accelerations, the wheel-rail vertical forces, and the vertical accelerations of track and subgrade increase by about 34∼48.4%, 125 %, 400 %, and 66.7 %, respectively.

A fast hybrid algorithm for the random vibration analysis of train-bridge systems under crosswinds

In this study, a fast hybrid algorithm based on surrogate and theoretical models is proposed. It solves surrogate model failure with too many inputs to the system and improves the computational efficiency in random vibration analysis of train-bridge systems under crosswinds. First, the surrogate model to rapidly predict the wheel-rail force time history and the theoretical model (finite element model) of the bridge are established. Then, a large number of samples of fluctuating wind speeds and track irregularities are generated based on the Monte Carlo method. Next, the wheel-rail force and the dynamic response of the bridge are calculated using the surrogate and theoretical models, respectively, and the coupling of the train and bridge subsystems is realized through iteration. Finally, the random vibrations of the train-bridge system under crosswinds are analyzed based on the calculation results of all samples. The results of the hybrid algorithm agree well with those of the traditional calculation method. The maximum normalized mean square error (NMSE) is only 0.0105, and the computational efficiency of the hybrid algorithm is nearly 4 times higher than that of traditional calculation methods. When the train is in the midspan of the bridge, the bridge dynamic response has a large mean and standard deviation. Under crosswinds, wheels on the windward side determine the safe running of the entire train. Under the wind speed of 15 m/s and Chinese high-speed railway track irregularities, the train operation reliability on the bridge is 98 %.

Investigation of dynamic gauge widening in small radius curves and its impact on lateral wheel-rail contact forces

In this paper, the lateral interaction between a rail vehicle and the track is investigated during cases of an occurrence of dynamic gauge widening. This is composed of the nominal track gauge, wear of the rail profiles and track widening due to wheel-rail forces on sections of curved track. A multibody simulation model is used to investigate the various influencing parameters. This model not only analyses the single rail’s lateral displacement but also tilting. Furthermore, the simulation of rail pads with adjustable stiffnesses is enabled. The resulting different contact points between the wheel and rail are represented, affecting the wheel-rail contact forces. The results reveal that changes in contact geometry caused by rail tilting depend strongly on the specific wheel and rail profiles. This is illustrated by comparing a new rail profile with a heavily worn rail profile. Particular attention is also paid to the distinction between leading and trailing wheelsets. Finally, the model is validated using measured wheel-rail forces and rail head movement, as measured on the track. A better understanding of dynamic track widening can improve the running behaviour of the wheelset on small radius curves, help protect against derailment and reduce wear on the wheel and rail.

The effect of hydraulic anti-kink system on the safety performance of a four-module single-type tram

The effect of the hydraulic anti-kink system on the longitudinal-yaw stability and small radius curve passing safety of the four-module single-type tram is studied. Firstly, the dynamics model of the anti-kink system is established based on the working principle of the anti-kink system, and the dynamic response of the system is analysed. Secondly, the influence of the anti-kink system on the longitudinal-yaw stability is analysed based on the longitudinal-yaw dynamics model of the four-module single-type tram. Finally, a virtual prototype of the anti-kink system and the four-module single-type low-floor tram with independent rotating wheels is established to test the longitudinal-yaw stability of the vehicle, and the curve passing safety. The results show that: the double-hinged device increases the longitudinal-yaw instability of the vehicle and is more likely to produce jackknifing phenomenon, so the stiffness of the anti-kink system should be set as much as possible to prevent the jackknifing phenomenon and ensure the safe operation of the train. By reducing the stiffness of the anti-kink system properly, the wheel-rail force during curve passing can be reduced, and thus improving vehicle safety.

Dynamic Response and Running Safety of High-Speed Railway Train–Track–Bridge System Under Near-Fault Pulse-Type Ground Motion

The pulse effect of near-fault ground motion has asevere threat to high-speed railway train running on bridge. Current research generally relies on numerical simulation and lacks physical test data. In this paper, a scale indoor physical test of high-speed train running on bridge is conducted and dynamic characteristics of high-speed railway train–track–bridge system under near-fault pulse-type ground motion are explored. The bridge of the physical test is excited by shaking table with lateral inputs of near-fault pulse-type ground motion, pulse-free ground motion and far-field ground motion. A corresponding numerical model is established and validated by the test data. Then, the influence regularities of pulse effect on system dynamic response and running safety indexes are explored under different peak ground acceleration (PGA) and train speeds using data of the physical tests and the numerical simulation comprehensively. Results suggest that compared to the near-fault pulse-free ground motion and the far-field ground motion, the near-fault pulse-type ground motion leads to larger lateral beam displacement, lateral train acceleration, and running safety indexes in different degrees. And from the data results of this paper, its lateral wheel–rail force and derailment coefficient are the first to break through the limit values. By studying the parameter sensitivity of lateral train acceleration, it was found that under the near-fault pulse-type ground motion, the lateral train acceleration is significantly more sensitive to changes of train speed and PGA. From the perspective of energy, the near-fault pulse-type ground motion results in spectrum intensity (SI) indexes which are larger and improve faster with the increase of PGA than other ground motions. This indicates that it inputs significantly more energy into the high-speed railway train–track–bridge system, although it may not excite larger lateral beam acceleration.

Influence of the friction modelling decisions on the acceptance of the running behaviour of a friction-damped locomotive

Multibody simulations are widely used for the dynamic analysis of railway vehicles, including the acceptance of vehicle running behaviour. Among these, the freight vehicles have, generally, friction damped suspensions for which numerical modelling is particularly challenging due to the contacting geometries, the intermittent contact, and the frequent stick-slip transitions. The impact of modelling decisions of friction-damped suspensions on the acceptance quantities for vehicle behaviour is the focus of this work. The selection of friction models and tuning of their parameters is challenging. In particular, the selection of friction coefficients is not straight forward, as friction conditions vary during operation and over time. This work aims to address both problems. A model of a friction-damped freight locomotive is used to simulate the dynamic response of the vehicle under realistic operation conditions and assess the impact of the friction modelling decisions. The results show that the use of different friction models provides similar results if the parameters are appropriately tuned. In contrast, the selection of friction coefficients significantly impacts the acceptance quantities, with emphasis on the wheel-rail forces at small radius curve transitions. The results recommend that the standard should include variations of the friction coefficients used for the friction-damped suspensions.

Optimisation of rail profile and grinding pattern in the curve section of a subway

During routine rail maintenance, rail grinding of sharp curves is challenging. In particular, setting up the grinding pattern is essential. A rail-grinding pattern optimisation method is proposed based on the mathematical relationship between the grinding pattern parameters and geometric parameters of the rail grinding profile. In this method, the design variables and constraints are reasonably selected, and a multi-objective optimisation function considering the wheel-rail contact stress, wheel-rail lateral force, and rail grinding amount is established. The optimisation model is solved using a chaotic microvariation adaptive genetic algorithm. The optimisation method is applied to the repairable grinding of a worn rail in a metro curve section. The results demonstrate that using this method can realise an ideal grinding pattern with the expected grinding effect in addition to high accuracy and high optimisation speed. The wheel-rail contact characteristics, wear characteristics, and train dynamic performance are significantly improved after rail grinding; this is significant for conducting grinding operations and improving the train’s curve-passing ability. Therefore, this study provides theoretical guidance for formulating rail-grinding patterns.

Vold–Kalman filter order tracking of axle box accelerations for track stiffness assessment

Intelligent data-driven monitoring procedures hold enormous potential for ensuring safe operation and optimal management of railway infrastructure in the face of increasing demands on cost and operations efficiency. Numerous studies have highlighted track stiffness as a main parameter influencing the evolution of degradation that drives maintenance processes. As such, the measurement of track stiffness is fundamental for characterizing the performance of the track in terms of deterioration rate and noise emission. In this work, we propose a rail stiffness assessment scheme relying on low-cost, on board monitoring sensors, namely axle-box accelerometers, that are mounted on in-service trains and enable frequent, real-time monitoring of the railway infrastructure network. A Vold–Kalman filter is proposed for decomposing the signal into periodic wheel and track related excitation–response pair functions. We demonstrate that these components are in turn correlated to operational conditions, such as wheel out-of-roundness and the rail type. We further illustrate the relationship between the track stiffness, the measured wheel-rail forces and the sleeper passage amplitude, which can ultimately serve as an indicator for predictive track maintenance and prediction of track durability.

Connection Between Track Geometry Quality and Dynamic Vehicle Response at Various Speeds

Track geometry measurements are widely used for describing track quality. However, derailments and track deterioration are caused by forces arising in vehicle-track system. This research focuses on two types of vehicle response. Firstly, the influence of the longitudinal level irregularities on the vertical wheel-rail forces was examined. Secondly, the correlation between the lateral axle box acceleration and the cross level irregularities was investigated. Track geometry and vehicle response data were acquired simultaneously by a track recording car, formed from a passenger car, at various speeds up to 130 km/h. Vehicle-track forces were calculated based on accelerometers mounted on the car body, bogies and axle boxes, considering mass and moment of inertia. Non-linear regressions resulted in vertical vehicle-track force estimation functions. It was proven that the use of second spatial derivatives of the longitudinal level gave a better estimation than the use of reference TQIs according to European Standard EN 13848-6. A linear relationship was found between the speed and standard deviation of vertical vehicle-track forces. On straight sections with constant speed, correlation coefficients of around 0.8 were found between second spatial derivatives of cross level and lateral axle box acceleration.