Wheel-rail Interaction Forces Research Articles

An efficient approach for prediction of subway train-induced ground vibrations considering random track unevenness

In this paper, an efficient and robust approach is presented for the prediction of subway train-induced ground vibrations considering random track unevenness. The proposed approach is developed by a two-step approach. Firstly, the power spectral density functions of the wheel–rail interaction forces are obtained through the combination of the vehicle–track–tunnel–soil theoretical model and the pseudo-excitation method (PEM). Secondly, by assuming the geometry of the track, tunnel, and soil to be homogeneous along the track, the nonstationary random ground vibrations are solved by combining the PEM and the 2.5D finite element–perfectly matched layers method. To improve computational efficiency, an efficient wavenumber sampling scheme is proposed. In the numerical examples, the proposed approach is validated by comparing the results obtained with the published results. The influence of the train speed on the ground vibrations are also investigated, in which two types of track structure, namely the direct fixation track and floating slab track, are considered.

Prediction and Analysis of Structural Noise from a U-beam Using the FE-SEA Hybrid Method

With urban rail transit noise becoming an increasingly serious issue, accurate and quick analysis of the low to medium frequency spectral characteristics of this noise has become important. Based on the FE-SEA (Finite Element - Statistical Energy Analysis) hybrid method, a vibration prediction model of a U-beam was established using a frequency-dividing strategy. The frequency domain and spatial characteristics of the vibration and structural noise of the U-beam within the 1.25-500 Hz frequency range, when subjected to vertical wheel-rail interaction forces, were analyzed. Compared with other methods described in the literature, the proposed FE-SEA hybrid method improves the calculation efficiency while ensuring better accuracy for a wide frequency range of structural noise and vibration. It was found that the excitation frequencies of the wheel-rail force dominate the spectra of the vibration and structural noise of the U-beam. Therefore, the frequency band containing the excitation frequencies should be the target for noise and vibration reduction when implementing strategies. The results show that the bottom plate contributes the most to the sound pressure level at all prediction points, and therefore should be the focus for noise and vibration reduction.

Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities

ABSTRACTThe randomness of track irregularities directly leads to the random vibration of the vehicle–track systems. To assess the dynamic performance of a railway system in more comprehensive and practical ways, a framework for probabilistic assessment of vehicle-curved track systems is developed by effectively integrating a vehicle–track coupled model (VTCM), a track irregularity probabilistic model (TIPM) with a probability density evolution method (PDEM). In VTCM, the railway vehicle and the curved track are coupled by the nonlinear wheel–rail interaction forces, and through TIPM, the ergodic properties of random track irregularities on amplitudes, wavelengths and probabilities can be properly considered in the dynamic calculations. Lastly, PDEM, a newly developed method for solving probabilistic transmissions between stochastic excitations and deterministic dynamic responses, is introduced to this probabilistic assessment model. Numerical examples validate the correctness and practicability of the proposed models. In this paper, the results of probabilistic assessment are presented to illustrate the dynamic behaviours of a high-speed railway vehicle subject to curved tracks with various radii, and to demonstrate the importance of considering the actual status of wheel–rail contacts and curve negotiation effects in vehicle-curved track interactions.

Use of the experimental modal analysis for analytical lifetime estimation of a bogie frame

The fatigue strength validation by tests of the railway bogie frames requires existence of an expensive laboratory and a long time for testing of about 6 to 10 months. Considering these aspects, the European norms admit that fatigue tests can be replaced by finite elements analysis (FEA), with the condition that analytical model to be correctly realized and validated by tests. Experimental modal analysis (EMA) provides a powerful tool for validation of the FEA model by experimental data. The article presents an application for assessment of the fatigue strength of a three-axle locomotive bogie frame. Using Ansys, was carried out the structural analysis of the bogie frame, resulting the modal model characterized by the modal parameters: Eigen frequencies and Eigen shapes. The analytical model was validated by an EMA application carried out on the bogie frame and correlation analysis of the EMA and FEA models. Using a special measuring wheel set, were determined the wheelrail interaction forces for various locomotive running conditions. The analytical structural model, validated through experimental data, and the data files containing the wheel-rail interaction forces, constitutes the input data for the nCode program that evaluates the bogie frame lifetime using appropriate stress curves and a recognized accumulation of damage hypothesis, e.g. the Palmgren-Miner.

Dynamic analysis of vehicle–track interaction due to wheel flat using bond graph

The dynamic response of a railway track under a moving train in the presence of a wheel with flat has been studied over many years. The force at the wheel–rail interface is mainly responsible for vehicle and track components deterioration and adds to the maintenance cost. So, reliable predictions of wheel–rail interaction forces are of prime concern to get the key factors responsible for damage of vehicle and track components. In most of the studies, a symmetrical vehicle–track model with linearity in track components behavior is assumed for simplification. This may lead to incorrect results in some situation. In this paper, wheel–rail impact dynamics is investigated by considering an asymmetrical vehicle–track model with due consideration to nonlinear behavior of track. Some nonlinear factors such as loss of wheel–rail contact, nonlinearity in pad, and ballast behavior are taken into consideration. A combined vehicle–track bond graph model is developed to study the wheel–track interaction dynamics. The rail is modeled as a flexible Euler Bernoulli beam resting on discrete support. The nonlinear Hertzian contact theory is used to accomplish the dynamic interactions between the vehicle and the track. Time response of forces, displacements, velocities, and accelerations of the related components of the vehicle and the track are obtained. It has been found that, though the wheel flat exists on leading right wheels, its effect has also been transferred to other components of the vehicle. The obtained results further lead to provide a better understanding of the interaction dynamics at the wheel–track interface with attention to the nonlinear behavior of pad and ballast.

Calibration and experimental validation of a dynamic model of the train-track system at a culvert transition zone

This article describes the calibration and experimental validation of the dynamic model of the train-track system at a culvert transition zone. The dynamic analyses were performed explicitly using a 3D model in LS-DYNA software and implicitly using a 2D model on ANSYS software. In both programmes, contact algorithms were employed to take the wheel-rail interaction into account. The parameters for the 3D model were calibrated based on the track receptance test. The 3D model was used for the static and dynamic calibration of the 2D model. The damping adopted in the 2D model was significantly amplified to compensate for the radiation damping in the transverse direction of the track, which cannot be incorporated in a plane model. An excellent agreement was obtained between the vertical displacements of the rail, the vertical accelerations of the sleepers and the wheel-rail interaction forces computed by the two models. The computation time of the 2D model is about 25 times lower than the computation time of the 3D model. The 2D model was used to simulate the passage of the Alfa Pendular train at 220 km/h at the transition zone and a very good match between measured and computed responses has been obtained.

Comparative study of 2D and 2.5D responses of long underground tunnels to moving train loads

A comparative study is conducted for the responses of soil-tunnel systems to moving train loads using the 2D and 2.5D finite/infinite element approaches, considering the effects of train speed, rail roughness and floating slab. Focus is placed on the wheel-rail interaction forces in the presence of rail roughness. The following are the major findings of this paper: (1) For all the cases studied, the 2D soil response is always higher than the 2.5D response. (2) The 2D result (with plane strain condition) is the limit of the 2.5D analysis with infinite train speed for smooth rails. (3) The 2D frequency response function (FRF) is contributed by frequencies of the whole range, being less sensitive to variation in roughness frequencies, while the 2.5D FRF is affected seriously by the frequencies of rail roughness. (4) With the floating slab tracks, the velocity and acceleration predicted of the soil are largely reduced for frequencies above the threshold using both approaches. But for frequencies below the threshold, the 2D approach shows higher amplified response. In short, the 2D approach saves tremendous computation time, as the system matrices is relatively smaller. But the 2.5D approach is more realistic, since it can account for various factors of the half space, including rail roughness and wave transmission along the tunnel axis.

A rail-borne piezoelectric transducer for energy harvesting of railway vibration

This paper investigates design, modelling, and test issues related to piezoelectric energy transducer. The model analyzes a rail-borne “seismic” energy harvester that is designed to generate electrical energy from local variations in rail acceleration. The energy harvester analyzed in this model consists of a piezoelectric PZT film clamped at one end to the rail with a tip mass mounted on its other end. It includes two sub-models in this paper: a vehicle-track interaction model considering vehicle travelling load; and a cantilevered piezoelectric beam model for the visualization of voltage and power profile and frequency response. Four rail irregularities (American 6th grade track spectrum, Chinese track spectrum, German high and low-disturbance track spectrum) are compared and implemented into the calculation script. The calculated results indicate a rail displacement of 0.2 mm to 0.8 mm. Vibration tests of the proposed rail-borne device are conducted; a hydraulic driven system with excitation force up to 140 kN is exploited to generate the realistic wheel-rail interaction force. The proposed rail-borne energy harvester is capable of energy harvesting at low-frequency (5 Hz to 7 Hz) and small railway vibration (0.2 mm to 0.4 mm rail displacement). The output power of 4.9 mW with a load impedance of 100 kOhm is achieved. The open circuit peak-peak voltage reaches 24.4 V at 0.2 mm/7 Hz/5 g wheel-rail excitation. A DC-DC buck converter is designed, which works at the resonance frequency of 23 Hz/5 g on a lab vibration rig, providing a 3.3 VDC output.

Establishment and verification of three-dimensional dynamic model for heavy-haul train–track coupled system

ABSTRACTFor the long heavy-haul train, the basic principles of the inter-vehicle interaction and train–track dynamic interaction are analysed firstly. Based on the theories of train longitudinal dynamics and vehicle–track coupled dynamics, a three-dimensional (3-D) dynamic model of the heavy-haul train–track coupled system is established through a modularised method. Specifically, this model includes the subsystems such as the train control, the vehicle, the wheel–rail relation and the line geometries. And for the calculation of the wheel–rail interaction force under the driving or braking conditions, the large creep phenomenon that may occur within the wheel–rail contact patch is considered. For the coupler and draft gear system, the coupler forces in three directions and the coupler lateral tilt angles in curves are calculated. Then, according to the characteristics of the long heavy-haul train, an efficient solving method is developed to improve the computational efficiency for such a large system. Some basic principles which should be followed in order to meet the requirement of calculation accuracy are determined. Finally, the 3-D train–track coupled model is verified by comparing the calculated results with the running test results. It is indicated that the proposed dynamic model could simulate the dynamic performance of the heavy-haul train well.

Modelling of nonlinear hunting instability for a high-speed railway vehicle equipped by hollow worn wheels

One of the reasons for frequent vibrations of coaches and hunting instability are hollow worn wheels. The main purpose of this paper is to investigate the effect of the wheel surface hollowing on the inconstancy and vibrations of a wagon. Considering the nonlinearity of the hollow surface, as well as both single and double point wheel-rail contacts are the significant points of this study. In order to do this, 800 wheel profiles of 100 coaches were measured in a controlled manner in a period of six months as an infield study. Statistical methods were used to categorize the measured hollow wheel profiles and select eight of the most observed ones. Then, a nonlinear mathematical model of a high-speed railway vehicle with 21 degrees of freedom was used for dynamic analysis of a wagon equipped by the hollow worn wheels on a tangent track. In order to model the effect of hollowing on the dynamic behaviour of the vehicle, the nonlinearity of wheel profile was taken into account. Also, both single and double point wheel-rail contacts were considered for accurate modelling of the wheel-rail interaction forces. Based on the results of the study, the tread hollowing must be considered as an independent dimensional parameter in periodic inspections. Also, it was concluded that worn wheels should be inspected regularly and re-profiled before their false flanges exceed a limit of 2 mm, in order to prevent the hunting phenomenon, and ensure being away from derailment of a passenger railway vehicle. Validation of the mathematical modelling was performed through the modelling of vehicle in ADAMS/Rail and comparing the results.

Safety evaluation for railway vehicles using an improved indirect measurement method of wheel–rail forces

The wheel–rail force measurement is of great importance to the condition monitoring and safety evaluation of railway vehicles. In this paper, an improved indirect method for wheel–rail force measurement is proposed to evaluate the running safety of railway vehicles. In this method, the equilibrium equations of a suspended wheelset are derived and the wheel–rail forces are then be obtained from measured suspension and inertia forces. This indirect method avoids structural modifications to the wheelset and is applicable to the long-term operation of railway vehicles. As the wheel–rail lateral forces at two sides of the wheelset are difficult to separate, a new derailment criterion by combined use of wheelset derailment coefficient and wheel unloading ratio is proposed. To illustrate its effectiveness, the indirect method is applied to safety evaluation of railway vehicles in different scenarios, such as the cross wind safety of a high-speed train and the safety of a metro vehicle with hunting motions. Then, the feasibility of using this method to identify wheel–rail forces for low-floor light rail vehicles with resilient wheels is discussed. The values identified by this method is compared with that by Simpack simulation for the same low-floor vehicle, which shows a good coincidence between them in the time domain of the wheelset lateral force and the wheel–rail vertical force. In addition, use of the method to determine the high-frequency wheel–rail interaction forces reveals that it is possible to identify the high-frequency wheel–rail forces through the accelerations on the axle box.

A case study of interior low-frequency noise from box-shaped bridge girders induced by running trains: Its mechanism, prediction and countermeasures

A side effect of high-speed railway and urban rail transit systems is the associated vibration and noise. Since the use of concrete viaducts is predominant in railway construction due to scarce land resources, low-frequency (20–200Hz) structure-radiated noise from concrete bridges is a principal concern. Although it is the most commonly used bridge type, the mechanism of noise emission from box-shaped bridge girders when subjected to impact forces from moving trains, which sounds like beating a drum, has not been well studied. In this study, a field measurement was first made on a simply-supported box-shaped bridge to record the acceleration of the slabs and the associated sound pressures induced by running trains. These data indicated that a significant beat-wave noise occurred in the box-shaped cavity when the train speed was around 340km/h, which arose from the interference between two sound waves of 75.0Hz and 78.8Hz. The noise leakage from the bridge expansion joint was serious and resulted in obvious noise pollution near the bridge once the beat-wave noise was generated in the cavity. The dominant frequency of the interior noise at 75.0Hz was confirmed from the spectrum of the data and the modal analysis results, and originated from the peak vibration of the top slab due to resonance and the first-order vertical acoustic mode, which led to cavity resonance, amplifying the corresponding noise. The three-dimensional acoustic modes and local vibration modes of the slab were calculated by using the finite element method. A simplified vehicle–track–bridge coupling vibration model was then developed to calculate the wheel–rail interaction force in a frequency range of 20–200Hz. Numerical simulations using the boundary element method confirmed the cavity resonance effect and the numerical results agreed well with the data. Based on the calibrated numerical model, three noise reduction measures, i.e., adding a horizontal baffle in the interior cavity, narrowing the width of top slab by reducing the inclination angle of the webs, and using a softer fastener on the track, were found to be effective and practical for reducing the noise generated by high-speed trains.

Reference Values for Railway Sidings Track Geometry

Railway sidings are operated at speeds much lower than those used on national railway lines; a typical speed is 6km/h. In establishing reference values for maintenance of railway infrastructure in terms of the geometry for such operating conditions, it is noted that both national and European regulations do not provide specific information regarding railway sidings.The overall objective of the research is, therefore, the definition of possible reference values for track geometry, based on those adopted by European rail networks (European and national standards), which can guarantee the appropriate security level for low speed operation typical of railway sidings connected to the national network.The basic principle in defining these values is the maximization of technical-economic efficiency and the maintenance of the acceptability of the risk associated to railway operation. The research results can therefore provide useful information about the cost-effective management of maintenance and safe operation for railway sidings.For this purpose, the approach was inspired to that of Regulation 402/2013, which defines at European level a common safety method for risk analysis. Quantification of probabilities and damages should be based on simulation models because the available statistics do not allow significant results to be inferred. However, the research sector has not yet produced a consolidated modelling. For these reasons, and since it is not possible to quantify probabilities reliably, the proposals resulting from this research are based on the identification of situations where it can be shown that the hazard probability remains unchanged.The approach used to formulate possible reference values valid outside of national networks (railway sidings) is based on an understanding of the underlying principles of the codes of good practice, on the formulation of hypotheses conform to the same principles, and the proposals about mitigative measures of risk associated to the use of different reference values, such as to keep the risk of the railway within the limits of acceptability, acting conservatively so as to keep unchanged, or reduce, the probability of hazardous events.The assessment parameters, object of the first phase of the research referred to in this work and used here as an example, are longitudinal level and alignment of railway track. In the case of vehicles running at low speed, the study was conducted by varying the magnitude of the reference values by using values that belong to external intervals with respect to those in accordance with European and national codes of good practice, examining the corresponding effects on the physical quantities related to safety. The effects of their variations on the wheel-rail interaction forces were studied using a simple dynamic model (with one degree of freedom) and a random generated excitation given by track defectiveness and the corresponding random response in terms of vertical and lateral contact forces (Q and Y).

A hybrid model for the prediction of low–frequency noise emanating from a concrete box-girder railway bridge

Concrete box-girder bridges are widely used on high-speed railway and urban rail transit lines; however, the low-frequency noise generated by these systems has not been intensively studied. The prediction of bridge-radiated noise is a complicated procedure and can require prohibitively long computational times. This paper presents a hybrid finite element and statistical energy analysis (hybrid FE–SEA) procedure for the prediction of bridge-radiated noise, with the aim of reducing computational time while still guaranteeing accuracy. A simplified train–bridge coupling model is first introduced and solved in the frequency range 20–200 Hz; the wheel–rail interaction force is calculated and taken as the vibration excitation. The hybrid FE–SEA model is then constructed, in which the rail and ballastless track are modeled as the SEA subsystems and the bridge girder components as the FE subsystems. The bridge-radiated noise is finally estimated by considering each vibrating component of the bridge as a flat plate. The procedure is applied to predict the vibration and noise emanating from a simply supported concrete box-girder bridge with a standard span of 32 m, and the computed results are compared with those obtained from in-situ measurements. The numerical results are in good agreement with measured data, and comparisons between computed and measured results reveal that the noise radiation from adjacent spans needs to be considered at a perpendicular distance of 25 m from the track’s centerline. Furthermore, the vibration transmission mechanism and the acoustic contribution performance are investigated, based on the validated numerical model. The results show that the vibrational energy of the top slab has the highest value; however, the vibration of the flange cannot be ignored. Therefore, the top slab and the flange, which may respectively account for 50% and 25% of the overall noise contribution at far-field points, should be given priority when formulating noise-mitigation measures.

Track and ground vibrations generated by high-speed train running on ballastless railway with excitation of vertical track irregularities

Track irregularities generated during the running service of high-speed railways aggravate vibrations of the track and the surrounding ground environment. To better understand the propagation of vibrations induced by high-speed train running on irregular tracks, a 2.5-dimensional (2.5D) finite element model combining with thin-layer elements was applied to establish a vehicle–track–foundation coupled dynamic analysis model. A quarter-car model was used to derive the equation for wheel–rail interaction force considering track irregularity. The track structure and the underlying foundation were simulated using the 2.5D finite element model, and the subsoil boundary was simulated using thin-layer elements. Compared with the field measurements of the Beijing–Shanghai high-speed railway, the reliability of the established numerical model in analyzing vibration response was verified. A spectrum analysis of the response data obtained from the field measurements reveals that for a newly constructed high-speed railway, track alignment is in good condition due to the operation of grinding and leveling, and vehicle parameters dominate the vibration response of the track structure. Then influences of track irregularities of four typical wavelengths on the vibrations of the track and the surrounding ground environment were investigated. It is found that track irregularities of smaller wavelengths induce higher vibration frequencies and significantly higher vibration responses from the track and the ground compared to track irregularities of longer wavelengths. However, the low-frequency vibrations induced by the latter propagate to a longer distance compared to the former. The critical velocity of the ballastless slab track–ground system is greater than the Rayleigh wave velocity of the soft layer of the subsoil. When train speed is lower than the critical velocity, track irregularity substantially affects the vibrations of the track and the surrounding ground. When the train speed exceeds that critical velocity, the ground vibration is determined by the train wheel weight.

Risk assessment of flange climb derailment of a rail vehicle

We study the wheel flange climb onto the railhead, which is one of the most dangerous regimes of motion and can lead to derailment. The tangential components of the wheel-rail interaction forces are described by the creep model with small slips taken into account. We pass to the limit of infinite rigidity of the interacting bodies (zero slip velocities). It is shown that, in the actual service conditions of rail vehicle motion, neglecting the wheel-rail slip is not justified; namely, the limit model is determined by the primary Dirac constraints, i.e., finite relations between coordinates and momenta arising owing to the system Lagrangian degeneration. The obtained nonclassical model allows one to study the efficiency of some railway motion safety criteria and analytically estimate derailment conditions, which depend on the flange shape, the track curvature radius, the height of the vehicle center of mass, the wheel-rail interaction forces, the coefficients of friction of the interacting surfaces, and the external perturbation forces and moments.

Application of Polyurethane Polymer and Assistant Rails to Settling the Abnormal Vehicle-Track Dynamic Effects in Transition Zone between Ballastless and Ballasted Track

This paper describes tests on a transition section between ballasted and ballastless tracks in the Liupanshui-Zhanyi railway in China. The originally unsettled transition zone is exposed to sudden car shaking and a series of track transition problems during train passage. As an example, the influences of polyurethane polymer and a combination of polyurethane and assistant rails to increase track stiffness distribution and track transition decay rates on the dynamic vehicle and track behaviour were investigated. The measured results indicate using only polyurethane and using both polyurethane and assistant rails not only effectively makes the track stiffness change more even but also increases the track decay rate at the target frequencies. These positive effects further reduce the wheel-rail interaction forces and vehicle and rail vertical acceleration, which decreases more when combining polyurethane and assistant rails than when using only polyurethane because the former outperforms the latter for smoothing the track stiffness distribution and increasing the track decay rate. Based on abating wheel-rail impact during the transition from ballasted to ballastless track and improving traffic operation and passenger comfort, combining polyurethane and assistant rails had the greatest effect and may be an effective remedy.

Dynamic analysis of fatigue check load for ballastless track in high-speed railway

The dynamic response of wheel-rail system is analyzed and validated with field measured results based on vehicle-track coupled dynamic theory and the simulation software. Further, the effect of ballastless track irregularity spectra of high-speed railway on wheel-rail interaction forces and statistical characteristics is investigated systematically using a typical Chinese high-speed train and a ballastless track. Research results show that the vehicle-track coupled dynamic method can well simulate the wheel-rail interaction under high-speed driving conditions. The ballastless track spectra of the percentile 75 can be adopted as excitation inputs for evaluating the wheel-rail interaction, and the riding safety and comfort under high-speed driving conditions. The reasonable fatigue check load of ballastless tracks in high-speed railway is 1.5 times as large as static wheel load.

Dynamic Characteristic Analysis of Irregularity under Turnout by Vehicle-Turnout Rigid-Flexible Coupling Model

Finite element model of track in frog zone is built by vehicle-turnout system dynamics. Considering variation of rail section and elastic support, bending deformation of turnout sleeper, spacer block and sharing pad effects, the track integral rigidity distribution in longitudinal direction is calculated in the model. Vehicle-turnout rigid-flexible coupling model is built by finite element method (FEM), multi-body system (MBS) dynamics and Hertz contact theory. With the regularity solution that different stiffness is applied for rubber pad under sharing pad of different turnout sleeper zone, analysis the variation of vertical acceleration of bogie and wheelset, rail vertical displacement and wheel-rail interaction force, this paper proves that setting reasonable rubber pad stiffness is an efficient method to solve rigidity irregularity problem.

Fully Coupled Three-Dimensional Train-Track-Soil Model for High-Speed Rail

With the increase of train speed, track modeling has faced great challenges as traditional static or quasi-static analyses become insufficient. Many track models have not had a train model and defined the wheel–rail interaction force as a stationary, independent, and empirical loading profile. In fact, the wheel–rail contact force is a function of train–track interaction and is difficult to predetermine. Another limitation of two-dimensional track models is the lack of sophisticated three-dimensional soil parts; this deficiency becomes critical when train speed is high enough to cause significant wave motion in the subgrade soil. A fully coupled three-dimensional train-track-soil model is developed and verified by a benchmark finite element program. Case studies are then described to demonstrate the capability of this track model.