An efficient approach to the analysis of rail surface irregularities accounting for dynamic train–track interaction and inelastic deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.     

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.     

Wheel/Rail Non-linear Interactions With Coupling Between Vertical and Lateral Directions

Summary A theoretical model is developed to explore the high frequency wheel/rail interaction with coupling between the vertical and lateral directions. This coupling is introduced through the track dynamics due to the offset of the wheel/rail contact point from the rail centre line. Equivalent models of the railway track in the time domain are developed according to the rail vibration receptances in the frequency domain. The wheel is represented by a mass in each direction with no vertical-lateral coupling. The vertical wheel/rail interaction is generated through a non-linear Hertzian contact stiffness, allowing for the possibility of loss of contact between the wheel and rail. The lateral interaction is represented by a contact spring and a creep force damper in series and their values depend on the vertical contact force. The vibration source is the roughness on the wheel and rail contact surfaces which forms a relative displacement excitation in the vertical direction. Using the combined interaction model with this relative displacement excitation, the wheel/rail interactions with coupling between the vertical and lateral vibrations are simulated. It is found that the lateral interaction force caused by the offset is usually less than thirty percent of the vertical dynamic force. The lateral vibration of the rail is significantly reduced due to the presence of the lateral coupling, whereas the vertical interaction is almost unaffected by the lateral force.     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

A locomotive–track coupled vertical dynamics model with gear transmissions

A gear transmission system is a key element in a locomotive for the transmission of traction or braking forces between the motor and the wheel–rail interface. Its dynamic performance has a direct effect on the operational reliability of the locomotive and its components. This paper proposes a comprehensive locomotive–track coupled vertical dynamics model, in which the locomotive is driven by axle-hung motors. In this coupled dynamics model, the dynamic interactions between the gear transmission system and the other components, e.g. motor and wheelset, are considered based on the detailed analysis of its structural properties and working mechanism. Thus, the mechanical transmission system for power delivery from the motor to the wheelset via gear transmission is coupled with a traditional locomotive–track dynamics system via the wheel–rail contact interface and the gear mesh interface. This developed dynamics model enables investigations of the dynamic performance of the entire dynamics system under the excitations from the wheel–rail contact interface and/or the gear mesh interface. Dynamic interactions are demonstrated by numerical simulations using this dynamics model. The results indicate that both of the excitations from the wheel–rail contact interface and the gear mesh interface have a significant effect on the dynamic responses of the components in this coupled dynamics system.     

Dynamic vehicle–track interaction in switches and crossings and the influence of rail pad stiffness – field measurements and validation of a simulation model

A model for simulation of dynamic interaction between a railway vehicle and a turnout (switch and crossing, S&C) is validated versus field measurements. In particular, the implementation and accuracy of viscously damped track models with different complexities are assessed. The validation data come from full-scale field measurements of dynamic track stiffness and wheel–rail contact forces in a demonstrator turnout that was installed as part of the INNOTRACK project with funding from the European Union Sixth Framework Programme. Vertical track stiffness at nominal wheel loads, in the frequency range up to 20?Hz, was measured using a rolling stiffness measurement vehicle (RSMV). Vertical and lateral wheel–rail contact forces were measured by an instrumented wheel set mounted in a freight car featuring Y25 bogies. The measurements were performed for traffic in both the through and diverging routes, and in the facing and trailing moves. The full set of test runs was repeated with different types of rail pad to investigate the influence of rail pad stiffness on track stiffness and contact forces. It is concluded that impact loads on the crossing can be reduced by using more resilient rail pads. To allow for vehicle dynamics simulations at low computational cost, the track models are discretised space-variant mass–spring–damper models that are moving with each wheel set of the vehicle model. Acceptable agreement between simulated and measured vertical contact forces at the crossing can be obtained when the standard GENSYS track model is extended with one ballast/subgrade mass under each rail. This model can be tuned to capture the large phase delay in dynamic track stiffness at low frequencies, as measured by the RSMV, while remaining sufficiently resilient at higher frequencies.     

Impact Loads due to Wheel Flats and Shells

A Finite Element (FE) model of vehicle-track system is employed to duplicate the experiments carried out by British Rail and CP Rail System. The theoretical results of the wheel/rail contact forces, rail-pad forces and strains in the rail showed very good correlation to the experimental data. Extensive results are compared with experimental data in the time domain for through validation of the developed model. The characteristics of the impact loads due to wheel flats and shells are investigated based on the validated FE model. The study shows that the shape and size of flat or shell, axle load, vehicle speed and rail-pad stiffness mainly affect the impact loads. Adding elastomeric shear pads on the wheelset bearing does not reduce the wheel/rail dynamic contact force but it may reduce the dynamic force on the bearing. Reducing rail-pad stiffness to a certain level on a concrete-tie track may significantly reduce the dynamic load and the force transmitted to the concrete tie.     

Estimation of wheel–rail contact conditions and adhesion using the multiple model approach

This paper presents the development of a multiple model estimation approach for the identification of the adhesion limit to overcome the problem of the wheel slip/slide at the rail wheel-rail contact. The contact characteristics at the rail wheel-rail interface are both highly nonlinear and subject to changes due to exposure to external contaminations. The detection of adhesion and its changes is therefore scientifically challenging, but would provide a critical information in the control of trains to avoid undesirable wear of the wheels/track but also the safety compromise of rail operations. This study exploits the variations in the dynamic behaviour of the railway wheelset caused by the contact condition changes and applies a bank of Kalman filters designed at selected operation points for the adhesion estimation. A fuzzy logic system is then developed to identify the contact conditions by examining the residuals from the Kalman filters.     

Numerical analysis of the dynamic interaction between wheel set and turnout crossing using the explicit finite element method

A three-dimensional (3-D) explicit dynamic finite element (FE) model is developed to simulate the impact of the wheel on the crossing nose. The model consists of a wheel set moving over the turnout crossing. Realistic wheel, wing rail and crossing geometries have been used in the model. Using this model the dynamic responses of the system such as the contact forces between the wheel and the crossing, crossing nose displacements and accelerations, stresses in rail material as well as in sleepers and ballast can be obtained. Detailed analysis of the wheel set and crossing interaction using the local contact stress state in the rail is possible as well, which provides a good basis for prediction of the long-term behaviour of the crossing (fatigue analysis). In order to tune and validate the FE model field measurements conducted on several turnouts in the railway network in the Netherlands are used here. The parametric study including variations of the crossing nose geometries performed here demonstrates the capabilities of the developed model. The results of the validation and parametric study are presented and discussed.     

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.     

The vertical and the longitudinal dynamic responses of the vehicle–track system to squat-type short wavelength irregularity

The squat, a kind of rolling contact fatigue occurring on the rail top, can excite the high-frequency vehicle–track interaction effectively due to its geometric deviations with a typical wavelength of 20–40 mm, leading to the accelerated deterioration of a track. In this work, a validated 3D transient finite element model is employed to calculate in the time domain the vertical and the longitudinal dynamic contact forces between the wheel and the rail caused by squats. The vehicle–track structure and the wheel–rail continua are both considered in order to include all the important eigencharacteristics of the system related to squats. By introducing the rotational and translational movements of the wheel, the transient wheel–rail rolling contact is solved in detail by a 3D frictional contact model integrated. The contact filter effect is considered automatically in the simulations by the finite size of the contact patch. The present work focuses on the influences of the length, width and depth of a light squat on the resulted dynamic contact forces, for which idealised defect models are used. The growth of a squat is also modelled to a certain extent by a series of defects with different dimensions. The results show that the system is mainly excited at two frequencies separately in the vertical and the longitudinal dynamics. Their superposition explains the typical appearance of mature squats. As a squat grows up, the magnitude of the excited vibration at the lower frequency increases faster than the one at the higher frequency.     

基于仿形门台架试验的滑移门动力学分析方法

准确分析滑移门系统的动力学特性,对车用滑移门的工程开发具有重要意义。文章基于仿形门试验台进行滚轮力试验测量,采用联合仿真的DOE方法,对滑移门动力学模型中的滚轮导轨接触模型进行两因素、多水平组合寻优,获取满足滚轮力误差要求的最优接触力参数组合,并对滑移门动力学模型进行开启、关闭的仿真分析。研究表明,基于此方法建立的滑移门动力学模型具有较高的分析精度,中导轨前导向轮峰值力最大误差为7.52%,能够准确地模拟滑移门的滑动过程;0 °导轨滚轮力比带倾角的滚轮力显著增大,与试验现象完全一致。文章所建立的仿形门试验、动力学建模、参数识别以及动力学分析等流程,可支持滑移门多参数影响分析和平顺性评估,为滑移门正向开发提供有效的理论分析依据。     

Influence of uneven rail irregularities on the dynamic response of the railway track using a three-dimensional model of the vehicle–track system

A mathematical model of the vehicle–track interaction is developed to investigate the coupled behaviour of vehicle–track system, in the presence of uneven irregularities at left/right rails. The railway vehicle is simplified as a 3D multi-rigid-body model, and the track is treated as the two parallel beams on a layered discrete support system. Besides the car-body, the bogies and the wheel sets, the sleepers are assumed to have roll degree of freedom, in order to simulate the in-plane rotation of the components. The wheel–rail interface is treated using a nonlinear Hertzian contact model, coupling the mathematical equations of the vehicle–track systems. The dynamic interaction of the entire system is numerically studied in time domain, employing Newmark's integration method. The track irregularity spectra of both the left/right rails are taken into account, as the inputs of dynamic excitations. The dynamic responses of the track system induced by such irregularities are obtained, particularly in terms of the vertical (bounce) and roll displacements. The numerical model of the present research is validated using several benchmark models reported in the literature, for both the smooth and unsmooth track conditions. Four sample profiles of the measured rail irregularities are considered as the case studies of excitation sources, examining their influences on the dynamic behaviour of the coupled system. The results of numerical simulations demonstrate that the motion of track system is significantly influenced by the presence of uneven irregularities in left/right rails. Dynamic response of the sleepers in the roll direction becomes more sensitive to the rail irregularities, as the unevenness severity of the parallel profiles (quantitative difference between left and right rail spectra) is increased. The severe geometric deformation of the track in the bounce–pitch–roll directions is mainly related to such profile unevenness (cross-level) in left/right rails.     

The role of the contact geometry in wheel–rail impact due to wheel flats: Part II

A classification of wheel flats according to the different stages of their growth is given, along with the characteristic features of the dynamic wheel–rail interaction for each category. Mathematical expressions and frequency spectra of the corresponding wheel mass trajectories are derived. Difference is made between the subcritical and the transcritical speed regime. A criterion is derived for contact loss for worn flats. Simulations show that the dynamic wheel–rail interaction is governed by the track stiffness for low train speeds or long flat lengths; for high speeds and/or short flat lengths the interaction is governed by the inertial properties of the wheel and the rail. For a given flat geometry, nonlinearities in the relationship between the impact magnitude and the train speed occur in the stiffness-dominated speed domain, whereas this relationship is approximately linear in the inertia-governed domain. In the latter domain, the impact magnitude is found to be linearly dependent upon the maximum trajectorial curvature or inversely linearly dependent on the minimum circumferential wheel tread curvature. The above relationships are valid for the subcritical speed regime, in which no contact loss occurs. Different contributions from the literature are compared with respect to the established relationship between impact magnitude and speed. Significant differences are found, due to insufficiently defined parameters and conditions. Conditions are derived for a consistent application of the so-called equivalent rail indentation in experiments with wheel flats, and the indirect strain registration method for measuring dynamic wheel–rail contact forces is reviewed.     

Development and validation of a wear model for the analysis of the wheel profile evolution in railway vehicles

The numerical wheel wear prediction in railway applications is of great importance for different aspects, such as the safety against vehicle instability and derailment, the planning of wheelset maintenance interventions and the design of an optimal wheel profile from the wear point of view. For these reasons, this paper presents a complete model aimed at the evaluation of the wheel wear and the wheel profile evolution by means of dynamic simulations, organised in two parts which interact with each other mutually: a vehicle's dynamic model and a model for the wear estimation. The first is a 3D multibody model of a railway vehicle implemented in SIMPACK?, a commercial software for the analysis of mechanical systems, where the wheel–rail interaction is entrusted to a C/C++user routine external to SIMPACK, in which the global contact model is implemented. In this regard, the research on the contact points between the wheel and the rail is based on an innovative algorithm developed by the authors in previous works, while normal and tangential forces in the contact patches are calculated according to Hertz's theory and Kalker's global theory, respectively. Due to the numerical efficiency of the global contact model, the multibody vehicle and the contact model interact directly online during the dynamic simulations.

The second is the wear model, written in the MATLAB® environment, mainly based on an experimental relationship between the frictional power developed at the wheel–rail interface and the amount of material removed by wear. Starting from a few outputs of the multibody simulations (position of contact points, contact forces and rigid creepages), it evaluates the local variables, such as the contact pressures and local creepages, using a local contact model (Kalker's FASTSIM algorithm). These data are then passed to another subsystem which evaluates, by means of the considered experimental relationship, both the material to be removed and its distribution along the wheel profile, obtaining the correspondent worn wheel geometry.

The wheel wear evolution is reproduced by dividing the overall chosen mileage to be simulated in discrete spatial steps: at each step, the dynamic simulations are performed by means of the 3D multibody model keeping the wheel profile constant, while the wheel geometry is updated through the wear model only at the end of the discrete step. Thus, the two parts of the whole model work alternately until the completion of the whole established mileage. Clearly, the choice of an appropriate step length is one of the most important aspects of the procedure and it directly affects the result accuracy and the required computational time to complete the analysis.

The whole model has been validated using experimental data relative to tests performed with the ALn 501 ‘Minuetto’ vehicle in service on the Aosta–Pre Saint Didier track; this work has been carried out thanks to a collaboration with Trenitalia S.p.A and Rete Ferroviaria Italiana, which have provided the necessary technical data and experimental results.     

Extended applications of track irregularity probabilistic model and vehicle–slab track coupled model on dynamics of railway systems

Track irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel–rail interactions. For depicting the dynamic behaviours of vehicle–track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle–track coupled model by properly considering the wheel–rail nonlinear contact mechanisms. In the present study, the vehicle–track coupled model is programmed by combining finite element method with wheel–rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.     

A study on high-speed rolling contact between a wheel and a contaminated rail

A 3-D explicit finite element model is developed to investigate the transient wheel–rail rolling contact in the presence of rail contamination or short low adhesion zones (LAZs). A transient analysis is required because the wheel passes by a short LAZ very quickly, especially at high speeds. A surface-to-surface contact algorithm (by the penalty method) is employed to solve the frictional rolling contact between the wheel and the rail meshed by solid elements. The LAZ is simulated by a varying coefficient of friction along the rail. Different traction efforts and action of the traction control system triggered by the LAZ are simulated by applying a time-dependent driving torque to the wheel axle. Structural flexibilities of the vehicle–track system are considered properly. Analysis focuses on the contact forces, creepage, contact stresses and the derived frictional work and plastic deformation. It is found that the longitudinal contact force and the maximum surface shear stress in the contact patch become obviously lower in the LAZ and much higher as the wheel re-enters the dry rail section. Consequently, a higher wear rate and larger plastic flow are expected at the location where the dry contact starts to be rebuilt. In other words, contact surface damages such as wheel flats and rail burns may come into being because of the LAZ. Length of the LAZ, the traction level, etc. are varied. The results also show that local contact surface damages may still occur as the traction control system acts.     

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.