Out-of-round railway wheels—a study of wheel polygonalization through simulation of three-dimensional wheel–rail interaction and wear

The objective of this study is to develop a tool for investigation of wheel tread polygonalization with radial irregularities including 1 to 20 wavelengths around the circumference of the wheel. Therefore, an existing multibody system model for simulation of general three-dimensional train–track interaction (accounting for frequencies up to several kHz) is extended with rolling contact mechanics according to FASTSIM. Furthermore, the model is also modified to allow for general wheel–rail profiles. The numerical model uses the concept of an iteration scheme including simulation of dynamic train–track interaction in the time domain coupled with a long-term wear model. A demonstration example including a bogie of a subway train travelling on a straight track is presented. In the example, an initial wheel out-of-roundness (OOR) is applied to the wheels. This irregularity is based on an amplitude spectrum derived from measurements on new wheels. Simulation results show that the most important wavelength-fixing mechanisms of the wheel OOR are (i) the vertical resonance of the coupled train–track system at approximately 40 Hz (the P2 resonance) and (ii) the frequency region including the lowest vertical track antiresonance at 165 Hz, where the dynamic track stiffness is high. Only a straight track is studied, but the model allows for asymmetric train motion on such a track.     

Out-of-round railway wheels—a study of wheel polygonalization through simulation of three-dimensional wheel-rail interaction and wear

The objective of this study is to develop a tool for investigation of wheel tread polygonalization with radial irregularities including 1 to 20 wavelengths around the circumference of the wheel. Therefore, an existing multibody system model for simulation of general three-dimensional train-track interaction (accounting for frequencies up to several kHz) is extended with rolling contact mechanics according to FASTSIM. Furthermore, the model is also modified to allow for general wheel-rail profiles. The numerical model uses the concept of an iteration scheme including simulation of dynamic train-track interaction in the time domain coupled with a long-term wear model. A demonstration example including a bogie of a subway train travelling on a straight track is presented. In the example, an initial wheel out-of-roundness (OOR) is applied to the wheels. This irregularity is based on an amplitude spectrum derived from measurements on new wheels. Simulation results show that the most important wavelength-fixing mechanisms of the wheel OOR are (i) the vertical resonance of the coupled train-track system at approximately 40 Hz (the P2 resonance) and (ii) the frequency region including the lowest vertical track antiresonance at 165 Hz, where the dynamic track stiffness is high. Only a straight track is studied, but the model allows for asymmetric train motion on such a track.     

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

For 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.     

Train–track–bridge dynamic interaction: a state-of-the-art review

ABSTRACT

Train–track–bridge dynamic interaction is a fundamental concern in the field of railway engineering, which plays an extremely important role in the optimal design of railway bridges, especially in high-speed railways and heavy-haul railways. This paper systematically presents a state-of-the-art review of train–track–bridge dynamic interaction. The evolution process of train–bridge dynamic interaction model is described briefly, from the simplest moving constant force model to the sophisticated train–track–bridge dynamic interaction model (TTBDIM). The modelling methodology of the key elements in the TTBDIM is systematically reviewed, including the train, the track, the bridge, the wheel–rail contact, the track–bridge interaction, the system excitation and the solution algorithm. The significance of detailed track modelling in the whole system is highlighted. The experimental research and filed test focusing on modelling validation, safety assessment and long-term performance investigation of the train–track–bridge system are briefly presented. The practical applications of train–track–bridge dynamic interaction theory are comprehensively discussed in terms of the system dynamic performance evaluation, the system safety assessment and train-induced environmental vibration and noise prediction. The guidance is provided on further improvement of the train–track–bridge dynamic interaction model and the challenging research topics in the future.     

Stochastic vibration of the vehicle–bridge system subject to non-uniform ground motions

A study of a train moving along a cable-stayed bridge is performed by considering both the stationary track irregularity and a non-stationary earthquake. A detailed bridge model with 3972 degrees of freedom is established while the train model consists of two locomotives and eight carriages. The equations of motion of the coupled system are obtained by using the displacement continuous condition at the contact, with track irregularities. The earthquake is assumed to occur once the train has entered the bridge. The pseudo-excitation method is used to find the random responses of the coupled system, and the results indicate that the effect of the earthquake is much greater than that of the track irregularities. The paper discusses the influence of the intensity of the earthquake, the wave propagation velocity, the speed of the train, and the dynamic interaction between the vehicles and the bridge.     

Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.     

Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.     

Simulation of Train-Track Interaction with Stochastic Track Properties

A numerical method to simulate vertical dynamic interaction between a moving train and a railway track was extended to account for stochastic properties in the track structure. The numerical simulations are carried out in the time-domain with a moving mass model. Full-scale measurements in the field and laboratory experiments were carried out to obtain data for the stochastic track model. The values of the stochastic variables are thus chosen to correspond to real tracks. To investigate the influence of the randomness of selected stochastic parameters in the track structure, the Latin Hypercube sampling method with correlation control was used to generate stochastic realisations.     

Simulation of Train-Track Interaction with Stochastic Track Properties

A numerical method to simulate vertical dynamic interaction between a moving train and a railway track was extended to account for stochastic properties in the track structure. The numerical simulations are carried out in the time-domain with a moving mass model. Full-scale measurements in the field and laboratory experiments were carried out to obtain data for the stochastic track model. The values of the stochastic variables are thus chosen to correspond to real tracks. To investigate the influence of the randomness of selected stochastic parameters in the track structure, the Latin Hypercube sampling method with correlation control was used to generate stochastic realisations.     

A linear complementarity method for the solution of vertical vehicle–track interaction

A new method is proposed for the solution of the vertical vehicle–track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel–rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel–rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel–rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle–track interaction including a separation between wheel and rail.     

Dynamic Interaction between Wheel and Track - A Parametric Search towards an Optimal Design of Rail Structures

The dynamic vertical interaction between a moving rigid wheel and a flexible railway track is investigated. A round and smooth wheel tread and an initially straight and noncorrugated rail surface are assumed in the present optimization study. A symmetric linear three-dimensional beam structure model of a finite portion of the track is suggested including rail, pads, sleepers and ballast with spatially nonproportional damping. The full interaction problem is numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the track. Transient bending stresses in sleepers and rail are calculated. The influence of seven selected track parameters on the dynamic behaviour of the track is investigated. A two-level fractional factorial design method is used in the search for a combination of numerical levels of these parameters making the maximum bending stresses a minimum.     

On the overriding issue of train front end collision in rail vehicle dynamics

A three-dimensional dynamic model of crashed vehicles coupled with moving tracks is developed to research the dynamic behaviour of the train front end collision on tangent tracks. The three-dimensional dynamic model consists of a crashed vehicle model, moving track models, a simple wheel–rail contact model, a velocity-based coupler model and the model of energy absorption and anti-climbing devices. The vector method dealing with the nonlinear wheel–rail geometry is put forward in the paper. The developed model is applicable in the scope that central collisions occur on tangent tracks at low speeds. The examples of the vehicle impacting with a rigid wall and the train front end collision are carried out to obtain the dynamic responses of vehicles. The overriding issue is studied on the basis of the wheel rise in train collisions. The results show that the second bogie of the first colliding vehicle possesses the maximal wheel rise. The wheel rise increases with the increase of vehicles. However, the number of vehicles has tiny influence on the overriding in train collisions at low speeds. On the contrary, the impact speed has significant influence on the overriding in train collisions. The wheel rise increases rapidly if the impact speed is close to the critical speed of overriding. The large wheel rise is principally generated by the great coupler force related to the rigid impact in the axial direction.     

Simulation of dynamic interaction between train and railway turnout

Dynamic train–track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel–rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel–rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.     

Dynamic Interaction between Wheel and Track - A Parametric Search towards an Optimal Design of Rail Structures

SUMMARY

The dynamic vertical interaction between a moving rigid wheel and a flexible railway track is investigated. A round and smooth wheel tread and an initially straight and noncorrugated rail surface are assumed in the present optimization study. A symmetric linear three-dimensional beam structure model of a finite portion of the track is suggested including rail, pads, sleepers and ballast with spatially nonproportional damping. The full interaction problem is numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the track. Transient bending stresses in sleepers and rail are calculated. The influence of seven selected track parameters on the dynamic behaviour of the track is investigated. A two-level fractional factorial design method is used in the search for a combination of numerical levels of these parameters making the maximum bending stresses a minimum.     

Modelling,validation and analysis of a three-dimensional railway vehicle–track system model with linear and nonlinear track properties in the presence of wheel flats

This paper presents dynamic contact loads at wheel–rail contact point in a three-dimensional railway vehicle–track model as well as dynamic response at vehicle–track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel–rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle–track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel–rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel–rail impact forces that arise in the wheel–rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.     

Sensitivity of train stochastic dynamics to long-term evolution of track irregularities

The influence of the track geometry on the dynamic response of the train is of great concern for the railway companies, because they have to guarantee the safety of the train passengers in ensuring the stability of the train. In this paper, the long-term evolution of the dynamic response of the train on a stretch of the railway track is studied with respect to the long-term evolution of the track geometry. The characterisation of the long-term evolution of the train response allows the railway companies to start off maintenance operations of the track at the best moment. The study is performed using measurements of the track geometry, which are carried out very regularly by a measuring train. A stochastic model of the studied stretch of track is created in order to take into account the measurement uncertainties in the track geometry. The dynamic response of the train is simulated with a multibody software. A noise is added in output of the simulation to consider the uncertainties in the computational model of the train dynamics. Indicators on the dynamic response of the train are defined, allowing to visualize the long-term evolution of the stability and the comfort of the train, when the track geometry deteriorates.     

Simulation of Bending-Torsional-Lateral Vibrations of the Railway Wheelset-Track System in the Medium Frequency Range

In the present paper, the dynamic interaction between a wheelset of a high-speed-train car and a railway track is considered with the help of a discrete-continuous mechanical model. This model enables us to investigate the bending-torsional-axial vibrations of the wheelset coupled with the vertical and lateral vibrations of the track through the wheel-rail contact forces. The results of numerical simulations performed for the wheelset motion both on straight and curved tracks demonstrate qualitative similarities of the corresponding dynamic responses of the system and essential quantitative differences of the respective amplitude and average values. Particularly severe interaction between the wheelset and the track is observed in the form of periodic resonances caused by parametric excitation from the track.