Dynamic Wheel-rail Force Research Articles

Dynamic interactions of tram-turnout coupling system in embedded turnout area

Embedded turnout is one of the key facilities in the embedded track network of modern tram systems. In this study, the damping performance and track stiffness of an embedded turnout are tested on site. A multi-rigid body dynamics model of the tram and a finite-element dynamics model of the embedded turnout are established, and the two models are coupled based on the wheel-rail contact theory for the turnout area. Next, the dynamic responses of the tram passing through the embedded turnout are analyzed. The results show that the embedded turnout has favorable damping performance. The high stiffness of variable section rails at the switch and frog would lead to an increase in the wheel-rail dynamic force. When the tram passes through the embedded turnout, the wheel-rail vertical force reaches maximum values of 106.3 and 35.2 kN at the frog and switch, respectively; the maximum wheel derailment coefficient and wheel weight reduction rate are 0.49 and 0.57, respectively, which are within the safety limit specified in the Standards; the maximum lateral and vertical vibration accelerations of the tram body are 0.38 and 0.71 m/s2, respectively, satisfying the comfort requirements; the wheel–rail wear work at the switch is greater than that at the frog.

Study on corrugated wear on high-speed railways based on an improved finite element model of wheel-rail rolling contact

An improved method for simulation of the transient wheel-rail rolling contact (WRRC) was proposed. A 3D implicit/explicit finite element (FE) model was established to calculate the transient response of the wheel-rail system (WRS). The dynamic wheel-rail forces excited by rail weld joints were investigated to reveal the causes of corrugated wear on high-speed lines. The results show that the wheel-rail forces obtained by the proposed method can quickly converge to the steady-state values without obvious initial disturbance, and the convergence rate is almost independent of the wheel speed. The vibration in vertical direction of the track at 655.6 Hz excited by the weld joint is identified as the main cause for the corrugated wear in 125–160 mm on high-speed lines.

Study on heat treatment and strengthening process of titanium alloy spring for railway vehicle

Lightweight can not only reduce the running energy consumption of the railway vehicle, but also reduce the running wheel-rail dynamic force, and unsprung mass lightweight has a more significant impact. Titanium alloy is very suitable for spring railway vehicle manufacturing. Titanium alloy spring can reduce its own weight and stress, and it has the capability of anticorrosion. But there is no experience in titanium alloy spring material heat treatment and strengthening process for reference. In this paper, the research is carried out, and the heat treatment method and strengthening process suitable for the titanium alloy spring manufacture is summarized. And the observation of the microstructure and mechanical properties test of the spring show that the titanium alloy spring can meet the technical requirement by adopting appropriate heat treatment method and strengthening process.

Effect of uncertainty of fastening systems properties on wheel/rail dynamic force

In this paper, effect of uncertainty of fastening system properties on the wheel/rail dynamic force (WRDF) was investigated. For this purpose, two deterministic and epistemic models of vehicle/track interaction were developed, using the finite element method. Validity of the results obtained from the models was shown through comparison between the model results and those obtained from field tests. The effects of uncertainty of fastening system properties on the WRDF in different axle loads, vehicle speeds, rail irregularities and various track maintenance conditions were derived through probability and sensitivity analyses. Using the results obtained, some contours were developed to obtain the amplification of WRDF (due the uncertainty of fastening system properties) as a function of vehicle axle load, vehicle speed and track maintenance conditions.

Dynamic behavior of resilient wheels at a rail weld joint

The aim of this paper is to investigate the dynamic response of the resilient wheel equipped on the intercity train at the rail weld. A vehicle-track coupling dynamics model with resilient wheels is developed. A rigid multi-body system with 55 degrees of freedom is utilized to model the vehicle system. The rubber layer of the resilient wheel is modeled as a three-directional spring-damper unit between the wheel rim and the wheel core. For the track sub-model, the rails were modelled as Euler Beam and supported by concrete sleepers modelled as mass block. The vehicle and track motion equations are represented as mass-stiffness-damping matrixes. The accuracy of this modeling method at low frequencies is verified via the comparison between the field measured data and numerical results. The dynamic results of the rigid wheel are compared with those of the resilient wheel. Results show that the dynamic wheel-rail force of the rigid wheel is slightly higher than that of the resilient wheel. Furthermore, the mass factor is introduced to investigate the effect of the rubber layer position on the tire acceleration and the wheel-rail impact force. The numerical simulation results are expected to provide references for resilient wheel application into the intercity train.

Qualitative Prediction Model for Dynamic Behavior of Ballasted Tracks

Theoretical, experimental, analytical, and statistical evaluations were performed to predict and assess the dynamic behavior of a ballasted track, such as the track support stiffness, track impact factor, or dynamic wheel–rail forces. Field measurements were then performed to evaluate the dynamic behavior of the ballasted track and its components. A qualitative prediction model was then developed to predict and assess track performance as a function of dynamic wheel-rail force and variation in track support stiffness. The developed two-degree-of-freedom dynamic track model can define the rail pad and ballast stiffness ranges based on designed and measured values. Using the proposed model, qualitative analysis results are presented as a discrete space of various track responses and parameters, rather than as single values. The proposed model was then validated using field measurements, which demonstrated that the proposed model predicted the vertical rail displacement and rail bending stress within approximately 2–5% of the obtained field measurements. Overall, the developed qualitative prediction model allows the dynamic response of in-service ballasted tracks to be estimated as a function of the rail pad and ballast stiffness using only a simple field measurement.

A framework combining pseudo-excitation method and two-and-a-half-dimensional finite element method for random ground vibrations induced by high-speed trains

A framework is developed in this article to predict the nonstationary random ground vibrations induced by high-speed trains, by combining the pseudo-excitation method with the two-and-a-half-dimensional finite element method. This development contains two steps. First, the power spectral density of the wheel–rail dynamic force is accurately obtained through the combination of the pseudo-excitation method and a vehicle–slab-track–ground theoretical model. Second, the nonstationary random ground vibrations are efficiently solved by combining the pseudo-excitation method and the two-and-a-half-dimensional finite element method, where the power spectral density of the wheel–rail dynamic force obtained in the former step is used to constitute the pseudo-loads. In the numerical examples, the accuracy and efficiency of the proposed approach are validated through the comparison to the fast three-dimensional random method for train–track–soil system developed previously. The results show that the proposed approach can predict the train-induced random ground vibrations with sufficient accuracy and has three-to-five times increase in efficiency in comparison to the fast three-dimensional random method.

Residual stresses in thermite welded rails: significance of additional forging

The aluminothermic welding (ATW) process is the most commonly used welding process for welding rails (track) in the field. The large amount of weld metal added in the ATW process may result in a wide uneven surface zone on the rail head, which may, in rare cases, lead to irregularities in wear and plastic deformation due to high dynamic wheel-rail forces as wheels pass. The present paper studies the introduction of additional forging to the ATW process, intended to reduce the width of the zone affected by the heat input, while not creating a more detrimental residual stress field. Simulations using a novel thermo-mechanical FE model of the ATW process show that addition of a forging pressure leads to a somewhat smaller width of the zone affected by heat. This is also found in a metallurgical examination, showing that this zone (weld metal and heat-affected zone) is fully pearlitic. Only marginal differences are found in the residual stress field when additional forging is applied. In both cases, large tensile residual stresses are found in the rail web at the weld. Additional forging may increase the risk of hot cracking due to an increase in plastic strains within the welded area.

Modelling Ambient Vibration Responses Induced by Operation of Metro Train on Curved Rail Segment with Small Curvature Radius

The torsional effect of the tracks on curved segment intensifies the ambient vibration response induced by Metro operation. This paper studies the ambient vibration responses induced by the operation of the Metro train on curved rail segments. By taking the curved segment of Hangzhou Metro Line 1 of China as an example, the wheel-rail model employing the multibody dynamics is demonstrated; the dynamic wheel-rail force of a B-type vehicle passing through a 350 m radius curved segment is also calculated. A finite element method model of the track-tunnel-soil-building is developed and verified by comparing the measured results with the simulated ones. Then, we analyzed the ambient vibration responses induced by the Metro operation. The results show that the horizontal vibration induced by the Metro train, on curved segments, cannot be ignored. When propagating on the ground, the variation trend of the horizontal vibration acceleration is greater than that of the vertical vibration. The horizontal vibration attenuates faster than the vertical vibration. The secondary vibration along the horizontal direction yields a significant amplifying effect upon the building. The vibration level increases with the height of the building, along the horizontal direction, but the vertical vibration level changes negligibly. The insight exhibits the influence level of the horizontal action of the Metro train wheels to the tracks, which can be referred by the practitioners for the planning and operation.

Structure-borne noise from long-span steel truss cable-stayed bridge under damping pad floating slab: Experimental and numerical analysis

This study investigates the structure-borne noise characteristics and a control measure of the long-span steel truss cable-stayed bridge (LSTCB) which are induced by running trains in urban rail transit. A frequency-domain theoretical model of a vehicle–track coupling interaction system, in which the vibration reduction track structure of damping pad floating slab (DPFS) are taken into account, is firstly established, from which the wheel–rail dynamic force, the force transmission rate, and the force transmitted to the bridge can be obtained. After that, a vibration model of the LSTCB and a noise model of the steel truss girder are established, which are based on the refined finite element method (FEM) and statistical energy analysis (SEA) method respectively, to predict the structure-borne noise of the LSTCB. Next, the near-field noise test of an LSTCB under DPFS at an urban rail transit line, are analyzed and used to validate the prediction model. Then, the structure-borne noise characteristics of the LSTCB and noise reduction effect of DPFS are studied. It is found that the wheel-rail transfer to the track slab and bridge are influenced by the track structure system; the attenuation rate of the near-field sound pressure level (SPL) is relatively slow in the range of 20–100 Hz, fast after 100 Hz, and faster than the far-field SPL; the vibration energies that input to the LSTCB are mainly distributed in the bridge deck, longitudinal web, and transverse web; the sound radiation capability of the bridge deck is stronger than that of other subsystems; compared with the common track structure (embedded sleeper), the track structure of DPFS can reduce the overall sound pressure level of the LSTCB by 10–13 dB(A).

차륜-레일 상호작용력을 고려한 고속철도의 레일연마효과 분석에 관한 연구

본 연구에서는 고속철도 운영선에서 레일연마에 따른 레일표면요철의 변화수준을 계측하고 레일연마횟수에 따른 연마효과 및 연마품질의 수준을 국제규정과 비교하여 적정연마횟수를 검토하였다. 또한 레일표면요철이 동적 차륜/레일 상호작용력에 미치는 영향을 차륜-레일의 동역학 모델을 이용하여 검토하고 이를 선행 연구결과와 비교분석하였다. 본 연구결과를 이용하여 차륜/레일 상호작용력의 발생수준에 근거한 적정 레일연마방안(레일표면요철관리방안)을 도출하였다.

EXPERIMENTAL INVESTIGATION ON DYNAMIC BEHAVIOUR OF HEAVY-HAUL RAILWAY TRACK INDUCED BY HEAVY AXLE LOAD

The damage to the track structure and the influence to the line deformation have greatly deteriorated with the increase of the axle load compared with that of the ordinary trains. However, there is a paucity of experimental research on the dynamic influence of the heavier haul freight trains on the railway tracks. The objective of this study is to investigate the dynamic behaviour of heavy-haul railway track induced by heavy axle load by field experimental tests. The wheel–rail dynamic force, the track structure dynamic deformation and the track vibration behaviour are measured and analysed when the train operates in the speed range from 10 to 75 km/h and the axle load of vehicles varies from 21 to 30 t. Comparisons between the results for the axle conditions of 25 and 30 t are made in this paper to reveal the axle load effects. It is demonstrated that part of the indicators reflecting the dynamic behaviour of the railway track increases approximately linearly with the train running speed and axle load, while others are influenced negligibly

Vibration characteristics of damping pad floating slab on the long-span steel truss cable-stayed bridge in urban rail transit

With the development of urban rail transit, long-span steel truss cable-stayed bridges have become increasingly favored. Therefore, train-induced bridge-borne vibration and noise are occurring more often. The damping pad floating slab (DPFS) has been widely used as an effective vibration damping track structure; however, there is a lack of research on the vibration mechanism and effects of the DPFS for long-span steel truss cable-stayed bridges. This study focuses on the steel truss cable-stayed bridge in urban rail transit. First, the theoretical model of the train-track-bridge coupling interaction is established in the frequency-domain (the track structure is DPFS, and the interaction of multiple wheels is considered). Using this model, the wheel–rail dynamic force, force transmission rate of the track, and the force transmitted to the bridge are calculated. Then, the vibration prediction model of the long-span steel truss cable-stayed bridge is established using the plate-beam finite element (FE) method and statistical energy method. The force transmitted to the bridge is applied to the vibration prediction model to obtain the vibration transmission characteristics of the typical plate of the bridge. The prediction model is verified by comparing the obtained results with the field test of a long-span steel truss cable-stayed bridge, and the damping mechanism of DPFS track is discussed. Finally, the force transmitted to the bridge is calculated based on the embedded-sleeper (ES) track structure (the ES has no vibration damping facilities). The values of the overall vibration level are calculated from the prediction models using ES and DPFS, and the vibration reduction effect of DPFS is studied by comparison with the ES.

차륜-레일 상호작용력과 레일연마의 상관관계 분석

차륜-레일 상호작용력과 레일연마의 상관관계 분석

On the stick-slip vibration in the suspension of a freight wagon

Damping based on the dry friction is frequently in suspensions of the freight wagons. The paper presents some aspects of vertical vibration of freight wagons. It uses a simple model considering that the vehicle was reduced to a mass suspended on a wheel, moving at constant speed on a rigid track with harmonic irregularity. Stick-slip vibration can occur due to the friction and it is characterized by sudden changes in the wheel acceleration affecting the ride quality. The paper shows the influence of stick-slip vibration on the wheel-rail dynamic force.

Investigation of rail irregularity effects on wheel/rail dynamic force in slab track: Comparison of two and three dimensional models

Rail irregularity is one of the most significant load amplification factors in railway track systems. In this paper, the capability and effectiveness of the two main railway slab tracks modeling techniques in prediction of the influences of rail irregularities on the Wheel/Rail Dynamic Force (WRDF) were investigated. For this purpose, two 2D and 3D numerical models of vehicle/discontinuous slab track interaction were developed. The validation of the numerical models was made by comparing the results of the models with those obtained from comprehensive field tests carried out in this research. The effects of the harmonic and non-harmonic rail irregularities on the WRDF obtained from 3D and 2D models were investigated. The results indicate that the difference between WRDF obtained from 2D and 3D models is negligible when the irregularities on the right and left rails are the same. However, as the difference between irregularities of the right and left rails increases, the results obtained from 2D and 3D models are considerably different. The results indicate that 2D models have limitations in prediction of WRDF; that is, a 3D modeling technique is required to predict WRDF when there is uneven or non-harmonic irregularity with large amplitudes. The size and extent of the influences of rail irregularities on the wheel/rail forces were discussed leading to provide a better understanding of the rail-wheel contact behavior and the required techniques for predicting WRDF.

Evaluation of High-Speed Track Quality Using Dynamic Simulation of Vehicle-Track Interaction

Track quality is a determinant factor for evaluating the overall performance of vehicle track interaction with respect to safety, ride quality and maintenance. Important parameters specifying the general quality of the track include track geometry (undamped) and track stiffness (damped), which can be evaluated by measurements taken along with track sections. A new co-simulation model based on Finite Element Method (FEM) and Multi Body Simulation (MBS) is built for the detailed description of track quality and its contribution to vehicle track interaction without simplifying the track structure as interconnected single elements. The simulation models and tools have been validated with the help of measured track geometry, track stiffness and dynamic wheel rail forces along the track sections of high speed lines. A comparative study between high speed lines using conventional ballasted track and ballastless track showed a significantly better quality in ballastless track sections. The dynamic forces which were determined by simulations and verified by measurements along the ballastless track section were comparatively less than the specified limits by German regulations for ballastless track design. Lower levels of dynamic forces can be utilized for optimization of track design and installation procedures with respect to lower initial costs.

3D dynamic model of the railway wagon to obtain the wheel–rail forces under track irregularities

Employing a dynamic model of the railway wagon in three dimensions, this paper presents the results of dynamic wheel–rail forces under the presence of track irregularities. A mathematical model of the wagon system is developed using dynamic equations of the components, taking into account the vertical (bounce), pitch and roll motions of the system. The model examines the dynamics of the wagon system under arbitrary rail irregularities. The spectra of rail surface irregularities are fed into the vehicle model to extract the time histories of dynamic forces between the wheel and the rail. Using the irregularity spectra of left/right rails, vibration of the wheelsets is studied for the bounce–roll motions. The dynamic contact forces between wheels and rails are determined for three examples of the measured irregularities. Moreover, three V-shape defects are modelled as examples of the singular defects on rail surface. The results of dynamic simulations confirm the large amounts of impact forces due to the presence of rail irregularities, particularly for the cases with much unevenness between the left/right profiles.

Stress intensity factors evaluation for through-transverse crack in slab track system under vehicle dynamic load

The stress intensity factors (SIFs) for through-transverse crack in the China Railway Track System (CRTS II) slab track system under vehicle dynamic load are evaluated in this paper. A coupled dynamic model of a half-vehicle and the slab track is presented in which the half-vehicle is treated as a 18-degree-of-freedom multi-body system. The slab track is modeled as two continuous Bernoulli–Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The model is applied to calculate the vertical and lateral dynamic wheel–rail forces. A three-dimensional finite element model of the slab track system is then established in which the through-transverse crack at the bottom of concrete base is created by using extended finite element method (XFEM). The wheel–rail forces obtained by the vehicle-track dynamics calculation are utilized as the inputs to finite element model, and then the values of dynamic SIFs at the crack-tip are extracted from the XFEM solution by domain based interaction integral approach. The influences of subgrade modulus, crack length, crack angle, friction coefficient between cracked surfaces, and friction coefficient between faces of concrete base and subgrade on dynamic SIFs are investigated in detail. The analysis indicates that the subgrade modulus, crack length and crack angle have great effects on dynamic SIFs at the crack-tip, while both of the friction coefficients have negligible influences on variations of dynamic SIFs. Also the statistical characteristics of varying SIFs due to random wheel–rail forces are studied and results reveal that the distributions of dynamic SIFs follow an approximately Gaussian distribution with different mean values and standard deviations. The numerical results obtained are very useful in the maintenance of the slab track system.

Influence of Track Support Stiffness of Ballasted Track on Dynamic Wheel-Rail Forces

Dynamic wheel-rail force can be limited to high-frequency components owing to imperfections in the wheel-rail contact surface (P1) and may also contain low-frequency components owing to coupled wheel-rail vibrations in phase on the ballast (P2). Previous studies on dynamic wheel-rail forces have focused on the quality index of surface roughness (QI) of only rail welds. In this study, the influences of rail surface roughness and track stiffness of a ballasted track on dynamic wheel-rail forces currently employed in high-speed lines were assessed by performing field measurements using actual vehicles running along the service lines. The theoretical dynamic wheel-rail force determined using a previous theory was compared with the dynamic wheel-rail force determined through field measurements. At a constant QI, an increase in the vertical track stiffness caused an increase in P2. Therefore, the vertical track stiffness affects P2 more strongly than P1. Hence, P1 is more affected by QI and train velocity than is P2. Further, it is inferred that the results of multiple regression analysis obtained using measured data such as QI, vertical track stiffness, and P2 can be used to predict the peak dynamic forces acting on ballasted tracks.