Wheel Rail Contact Model Research Articles

Parallel co-simulation of locomotive wheel wear and rolling contact fatigue in a heavy haul train operational environment

Locomotive wheel wear and rolling contact fatigue simulations that consider both train dynamics and detailed traction control systems have not been reported. This paper developed a parallel co-simulation method to link an in-house longitudinal train dynamics simulator to a commercial software package named GENSYS. An advanced longitudinal train dynamics model, a traction control system model and a wheel–rail contact model were then incorporated into the simulation. Three wear calculation models (T-gamma model, USFD model and Archard model) and two rolling contact fatigue calculation models (T-gamma-based rolling contact fatigue model and shakedown-based rolling contact fatigue model) were implemented. A train with the configuration of 1 locomotive +54 wagons +1 locomotive +54 wagons was simulated. This paper shows that the simulation method is successful and can be used for such more detailed locomotive wheel wear and rolling contact fatigue calculations. Wear and rolling contact fatigue calculation results show that the wear numbers that were calculated using the T-gamma wear model and damage indexes that were calculated using the T-gamma-based rolling contact fatigue model were similar between the leading and remote locomotives. However, wear rates that were calculated using the USFD wear model, wear volumes that were calculated using the Archard model and fatigue indexes that were calculated using the shakedown-based rolling contact fatigue model have evident differences between the leading and remote locomotives. Maximum differences in these results were about 12, 18 and 34%, respectively.

Hunting stability analysis of partially filled tank wagon on curved track using coupled CFD-MBD method

In this study, we develop an innovative numerical method for the investigation of the stability of a partially filled tank wagon moving on a curved track. The calculations are carried out in two subsystems including a dynamic system and fluid sloshing. We analyze the wagon dynamic system the multibody dynamic (MBD) model with 21 degrees of freedom (21-DOFs), which takes into account the lateral, vertical, roll, pitch, and yaw motions. The heuristic creep theory is used for the wheel–rail contact model. We adopt the fourth-order Runge–Kutta method for solving of this model. The transient fluid slosh is simulated by the computational fluid dynamic (CFD) model. The volume of fluid (VOF) technique is used for tracking the free surface of the fluid. This model is validated experimentally using the sloshing test setup. Then the simultaneous interaction between the dynamic system and the transient fluid slosh is analyzed by coupling the CFD model with the MBD model. By the parametric study on the filled-volume and wagon velocity, the critical hunting speed is derived by the Lyapunov indirect method. The results show that a higher filled volume decreases the critical hunting speed. Also, at the instability condition, an increasing trend for the phase trajectory of the wagon components is evident.

Two-way Hertzian spring in numerical analysis of coupled train-track system vibrations

The paper presents and compares two methods for simulation the train-track system vibrations, differing in the wheel-rail contact model used. In the first method, two-way Hertzian spring is used, in the second – a non-deformable constraint. In both methods, a flat computational model is assumed, consisting of an Euler-Bernoulli beam resting on a Winkler-type elastic foundation with damping and a set of rail vehicles modeled by dynamic systems with ten degrees of freedom. The results of numerical analysis are presented, in order to determine an influence of the contact constraints’ deformability on the vibration simulations. It is found that the replacement of non-deformable contact constraints by two-way Hertzian springs has no significant effect on track vibration simulations and has a little effect on vibration simulations of vehicle body and bogie. The developed simulation method can be used for numerical studies of the phenomenon of instantaneous detachments of wheels from rails, after minor modifications directed to introduce one-way Hertzian springs (i.e. not carrying tensile forces) being a more accurate contact model.

A local degraded adhesion model for creep forces evaluation: An approximate approach to the tangential contact problem

The calculation of the creep forces has always been one of the fundamental goals for a wheel-rail contact model. At the same time, a wheel-rail contact model has necessarily to consider the phenomena related to degraded adhesion because they deeply affect both creepages and creep forces. Degraded adhesion is extensively observed at the wheel-rail interface. However, the development of an accurate and efficient adhesion model is quite a challenge due to the complexity of the system and the difficulty in collecting detailed experimental data.In this framework, the paper presents a local degraded adhesion model (based on local slidings/creepages and local pressures inside the contact area) able to provide a more accurate description of the contact phenomena characterizing the wheel-rail degraded adhesion with respect to analogous global models (involving global sliding/creepages and forces). The new model is able to consider important phenomena like the energy dissipated at the contact and the consequent surface cleaning effect leading to an adhesion recovery between wheel and rail. To reach this goal, the Kalker's FASTSIM algorithm has been properly extended and improved to include the previous phenomena.Furthermore, the new model allows the achievement of a good trade-off between accuracy and numerical efficiency. Thank to its efficiency, the model can be implemented inside general railway vehicle multibody models to perform large scale dynamical simulations.The model has been finally validated through experimental data coming from on-field tests and consisting of specific braking maneuvers under degraded adhesion conditions.

The rolling contact research of three dimensional wheel-rail based on finite element analysis

In this paper, wheel-rail contact model was established and analyzed, some useful results were obtained. The results show that In the early stage of wheel-rail contact, the wheel-rail contact pressure increases gradually and the contact point shape changes from regular polygon to irregular polygon in the process of wheel approaching rail joint. The equivalent stress and elastic deformation trend of the rail are basically the same, both of which decrease rapidly and then slowly increase. The plastic deformation of the rail gradually increases and accumulates, and the stress concentration area occurs at the side of the rail joint. When the wheel starts rolling, the equivalent stress of the wheel gradually decreases at first, and then increase. The peak value of the maximum equivalent stress occurs at the joint where the wheel reaches the rail.

On the generation of enhanced lookup tables for wheel-rail contact models

In railway dynamics, the interpolation of lookup tables (LUTs) is a procedure utilized to reduce the computational effort when computing the wheel-rail contact forces. However, the generation of LUTs with multiple inputs and multiple outputs is a challenging task for which aspects such as their minimal size and uniform accuracy over the LUT domain have not been systematically addressed in the literature. Thus, this work presents a comprehensive methodology for a detailed analysis of general LUTs, and identifies ways to improve them. For that, an analysis of the variation of the input parameters is made and the interpolation error is assessed on the cells and edges of the original table, then, based on this analysis, two enhanced LUTs are proposed. The first one is approximately 5 times smaller than the original but holds similar accuracy. The second table exhibits half of the maximum interpolation error of the original LUT but holds an identical size. The methodology is demonstrated here using the recently published Kalker Book of Tables for Non-Hertzian contact (KBTNH) but it can be used by any other LUT approach in order to improve accuracy and/or to reduce size.

Implementation of a non-Hertzian contact model for railway dynamic application

The development of wheel–rail contact models is an active topic of railway research with the dual objective of improving the accuracy of multibody simulations and reducing its computational effort. This paper extends the online Hertzian contact model, proposed by Pombo et al. (Veh. Syst. Dyn. 45: 165–189, 2007) to propose a non-Hertzian contact model. The new methodology presented here includes the following steps: (i) search of the points of contact; (ii) identification of the undeformed distance function; (iii) evaluation of the contact patch; (iv) calculation of the normal and tangential contact forces; (v) application of the contact forces in the multibody vehicle model. Among several contact models available in the literature, this non-Hertzian contact approach uses the Kik–Piotrowski model for the normal contact force, while the tangential forces are obtained from the interpolation of the available Kalker Book of Tables for non-Hertzian (KBTNH) contact. With the purpose to demonstrate the proper implementation and selection of parameters that define this new model, several contact analysis and dynamic simulations are performed in which the wheel S1002 and the rail UIC50 are considered. First, the contact analyses that determine the contact condition of different wheel–rail interactions serve to assess the accuracy of the Hertzian and non-Hertzian models with respect to the software of reference CONTACT. Second, the Hertzian and non-Hertzian models are utilised to perform dynamic simulations of a wheelset, a bogie and a vehicle running in tangent and curved tracks. In short, this work provides, not only a complete description of the implementation of a non-Hertzian contact model in a multibody code, but also suggests for the proper selection of the parameters that promote better accuracy and optimal computational efficiency.

A non-Hertzian wheel-rail contact model considering wheelset yaw and its application in wheel wear prediction

To obtain a relatively accurate wheel-rail contact solution with less time consuming, some so-called fast-accurate methods based on the concept of virtual penetration were provided by researchers. When dealing with the non-Hertzian contact problem with a sharply changing lateral relative curvature, it may be incorrect to calculate the penetration by the Hertzian contact parameters of the initial contact point. This paper proposes a method to get a proper penetration by considering the change of local relative curvature of wheel-rail profiles based on the semi-Hertzian method. Furthermore, the wheelset yaw angle is considered by using the ‘Trace line method’ to get a twisty contact patch which is verified by the program CONTACT. Finally, the proposed method is applied for the wheel wear prediction of a high-speed train. Field tests are carried out to determine the wear coefficient for wheel-rail contact of the high-speed train and to validate the wheel wear prediction model.

Assessment of non-Hertzian wheel-rail contact models for numerical simulation of rail damages in switch panel of railway turnout

Rail damages in railway turnout switch panels are closely related to the complicated wheel-rail contact conditions in the turnouts. In order to assess the applicability of different non-Hertzian contact models for simulating rail damages in railway turnout switch panel, three engineering approaches, i.e. Kik-Piotrowski, Ayasse-Chollet and Sichani, are adopted to simulate rail wear and surface initiated rolling contact fatigue (RCF) damages by studying a Chinese CN60-1100-1:18 high-speed turnout switch panel. A comparison is then carried out taking into account the results calculated by Kalker’s three-dimensional (3D) theory and an elastic-plastic FEM (Finite Element Method) model. The analyzed results show that the computational efficiencies of the three engineering approaches are all quite high for simulating rail damages in switch panel. Under elastic conditions, the calculation accuracy of the Sichani approach is found to be the highest, meaning that this would appear to be the preferred method for simulating rail damages in railway turnout switch panel. The research findings can be taken as theoretical guidance for selecting wheel-rail contact models and analyzing these types of damages in railway turnout switch panels.

Wheel–rail impact loads and noise generated at railway crossings – Influence of vehicle speed and crossing dip angle

Wheel–rail impact loads and noise at railway crossings are calculated by applying a hybrid prediction model. It combines the simulation of non-linear vertical dynamic vehicle‒track interaction in the time domain and the prediction of sound pressure level using a linear frequency-domain model. The two models are coupled based on the concept of an equivalent roughness spectrum. The time-domain model uses moving Green's functions for the linear vehicle and track models, accounting for wheel structural flexibility and a discretely supported rail with spatially-varying beam properties, and a non-Hertzian wheel–rail contact model. Three-dimensional surface geometry of the wheel and crossing is accounted for in the solution of the wheel–rail contact. The hybrid model is compared against field measurements and is demonstrated by investigating the influence of vehicle speed and crossing geometry on the radiated impact noise. Based on simulation results, it is concluded that the impact loads and noise can be mitigated by reducing the effective dip angle at the crossing, which is determined by the vertical trajectory of the wheel when making the transition between wing rail and crossing nose.

Numerical Investigation into the Effect of Geometric Gap Idealisation on Wheel-Rail Rolling Contact in Presence of Yaw Angle

For a fast calculation of vehicle-track dynamics and wheel-rail contact mechanics, wheel-rail contact geometric gap is usually idealised in elliptic or nonelliptic form. These two idealisations deviate from the actual one if the lateral combined curvature within the contact patch is not constant or the yaw angle of wheelset exists. The influence of these idealisations on contact solution has not yet been deeply understood, and thus the accuracy of simplified contact modelling applied to vehicle-track dynamics and wheel-rail contact mechanics remains uncertain. This paper presents a numerical methodology to treat 3D wheel-rail rolling contact, in which the asymmetric geometric gap due to yaw angle is fully taken into account. The attention of this work is placed on investigating the effect of geometric gap idealisation on wheel-rail contact force, rolling contact solution, and wear distribution. It can help with the effective wheel-rail contact modelling on the computation of both vehicle-track dynamics and wheel-rail contact mechanics.

Determination of the Vertical Vibration of a Ballasted Railway Track to Be Used in the Experimental Detection of Wheel Flats in Metropolitan Railways

This paper presents a mathematical model used to obtain the vertical vibration of a ballasted railway track when a wheel is passing at a certain speed over a fixed location of the rail. The aim of this simulation is to compare calculated root-mean-square (RMS) values of the vertical vibration velocity with measured RMS values. This comparison is the basis for a proposed time domain methodology for detecting potential wheel flats or any other singular defect on the wheel rolling bands of metropolitan trains. In order to reach this goal, a wheel–rail contact model is proposed; this model is described by the track vertical impulse response and the vertical impulse response of the wheel with the primary suspension, both linked through a Hertz nonlinear stiffness. To solve the model for obtaining the wheel–rail contact force, a double convolution method is applied. Several kinds of wheel flats are analyzed, from theoretical round edged wheel flats to different real wheel profile irregularities. Afterward, the vertical vibration velocity at a fixed point on the rail is obtained using a variable kernel convolution method. Running different simulations for different wheel flats, a study of the vertical vibration attenuation along the rail is carried out. Finally, it is proceeded to obtain the temporary evolution of the RMS value for the rail vertical vibration velocity in order to be used as a reference for detecting wheel flats or any other defect. This last aspect will be presented in more detail in a second paper.

A coupled model for train-track-bridge stochastic analysis with consideration of spatial variation and temporal evolution

• A model is developed to assess the dynamic performance of train-track-bridge systems in temporal-spatial random fields. • A MCM-KLE unification method is presented to characterize the random field of track-bridge systems. • Extensive cases are illustrated from aspects of random vibration, statistical analysis, long-term prediction, etc. Due to random characteristics of system parameters and excitations, the dynamic assessment and prediction for the train-track-bridge interaction systems become rather complex issues needing to be addressed, especially considering the longitudinal inhomogeneity and uncertainty of dynamic properties in physics and correspondingly their temporal evolutions. In this paper, a temporal-spatial coupled model is developed to fully deal with the deterministically/non-deterministically computational and analytical matters in the train-track-bridge interactions with a novelty, where a train-track-bridge interaction model is newly developed by effectively coupling the three-dimensional nonlinear wheel-rail contact model and the finite element theory, moreover, the Monte-Carlo method (MCM) and Karhunen–Loève expansion (KLE) are effectively united to model the random field of track-bridge systems, and a spectral evolution method accompanied by a track irregularity probabilistic model are introduced to select the most representative track irregularity sets and to characterize their random evolutions in temporal dimension. In terms of random vibration analysis, the high-efficiency and effectiveness of this developed model is validated by comparing to a robust method, i.e., MCM. Apart from validations, multi-applications of the temporal-spatial coupled model from aspects of deterministic computation, random vibration, resonant analysis and long-term dynamic prediction, etc., have been fully presented to illustrate the universality of the proposed model.

Differential wear modelling – Effect of weld-induced material inhomogeneity on rail surface quality

A methodology is introduced to enable prediction of differential wear along the rail due to the presence of geometrical imperfections and microstructural inhomogeneities. The method incorporates vehicle-track dynamic interaction, wheel-rail contact and wear modelling in order to predict long-term longitudinal rail profile evolution. The effect of different contact and wear modelling features on the results is investigated. As a case study, the differential rail wear due to material inhomogeneity caused by rail head weld repairs is considered. It is concluded that, regardless of the magnitude of hardness variation within the heat affected zone, the long-term surface degradation can be minimized by limiting the length over which the variation occurs.

An iterative methodology for the prediction of dynamic vehicle–track interaction and long-term periodic rail wear

In this study, a versatile numerical method for the prediction of long-term growth of rail roughness is presented and its functionality is demonstrated for the development of rail corrugation on small radius curves. The procedure includes two sub-modules: (1) a time-domain model for the simulation of dynamic vehicle–track interaction in a wide range of frequencies by using a commercial software for multibody dynamics and (2) a post-calculation of sliding wear based on the Archard’s model in combination with a non-Hertzian and transient wheel–rail contact model. The structural flexibility of the wheelset is accounted for by using the finite element method. The rail wear generated by a large number of passing trains is assessed by recurrently updating the rail surface based on the wear depth calculated in each post-processing step. The current work sets out from a previous study in which a model for the prediction of long-term growth of rail roughness on small radius curves was developed in a general-purpose programming language. By transferring the model into a commercial software, the aim is to develop an engineering tool that is more applicable for different operational conditions, such as various vehicle and track designs and track alignments. The proposed method is verified by comparing the simulation results against those obtained with the pre-existing software. Conditions similar to a 120 m radius curve on the Stockholm metro exposed to corrugation growth on the low rail are considered. The corrugation is found to be generated by the leading wheelsets. The prevailing wavelength-fixing mechanisms are identified and discussed.

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

ABSTRACTA 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.

Nonlinear Dynamic Characteristics of the Railway Vehicle

AbstractThe nonlinear dynamic characteristics of a railway vehicle are checked into thoroughly by applying two different wheel-rail contact model: a heuristic nonlinear friction creepage model derived by using Kalker ’s theory and Polach model including dead-zone clearance. This two models are matched with the quasi-static form of the LuGre model to obtain more realistic wheel-rail contact model. LuGre model parameters are determined using nonlinear optimization method, which it’s objective is to minimize the error between the output of the Polach and Kalker model and quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation attitude and stable/unstable motion of the railway vehicle in the presence of nonlinearities which are yaw damping forces in the longitudinal suspension system are analyzed in great detail by changing the vehicle speed. Phase portraits of the lateral displacement of the leading wheelset of the railway vehicle are drawn below and on the critical speeds, where sub-critical Hopf bifurcation take place, for two wheel-rail contact model. Asymmetric periodic motions have been observed during the simulation in the lateral displacement of the wheelset under different vehicle speed range. The coexistence of multiple steady states cause bounces in the amplitude of vibrations, resulting instability problems of the railway vehicle. By using Lyapunov’s indirect method, the critical hunting speeds are calculated with respect to the radius of the curved track parameter changes. Hunting, which is defined as the oscillation of the lateral displacement of wheelset with a large domain, is described by a limit cycle-type oscillation nature. The evaluated accuracy of the LuGre model adopted from Kalker’s model results for prediction of critical speed is higher than the results of the LuGre model adopted from Polach’s model. From the results of the analysis, the critical hunting speed must be resolved by investigating the track tests under various kind of excitations.

Derailment mechanism of trains running over bridges during strong earthquakes

This paper examines the seismic safety of high-speed railway (HSR) trains running over bridges during strong earthquakes. It develops an original seismic vehicle-bridge interaction (SVBI) analysis scheme to investigate the response of both the vehicle system and the bridge system. The study models the train vehicles as three-dimensional (3D) multibody assemblies. All components of a vehicle are assumed rigid bodies connected with springs and dashpots, representing the vehicle suspension system. The 3D bridge is simulated using the finite element method (FEM). To determine the contact point and the direction of the contact forces it considers the practical nonlinear profiles of wheels and rails. The normal contact forces are derived from kinematic constraints as Lagrange multipliers. Detachment occurs when a normal contact force becomes zero. The study formulates the contact-detachment transition along the normal direction of contact as a linear complementarity problem (LCP) and assumes impact follows Newton’s law. The calculation of the tangential creep forces due to the rolling contact is based on a nonlinear Shen-Hedrick-Euristic creep model. The proposed wheel-rail contact model can capture directly different contact phenomena, including flange contact, detachment, uplifting, climbing, derailment, and re-contact. The results underline the importance of a realistic analysis of the SVBI during seismic shaking. They show that seismic induced vibration of the bridge reduces both the comfort and the safety of the vehicles travelling over the bridge, compared to same vehicles travelling on the ground. For most examined cases with different wheelsets, the detachment of a wheel happens when the other wheel belonging to the same wheelset is in flange contact. The derailment of the wheel takes place when the wheel rolls over the rail head.

Effect of vertical ground motion on earthquake-induced derailment of railway vehicles over simply-supported bridges

The running safety of railway vehicles on bridges can be negatively affected by earthquake events. This phenomenon has traditionally been investigated with only the lateral ground excitation component considered. This paper presented results from a numerical investigation on the contribution of vertical ground motion component to the derailment of vehicles on simply-supported bridges. A full nonlinear wheel–rail contact model was used in the investigation together with the Hertzian contact theory and nonlinear creepage theory, which allows the wheel to jump vertically and separate from the rail. The wheel–rail relative displacement was used as the criterion for derailment events. A total of 18 ground motion records were used in the analysis to account for the uncertainty of ground motions. The results showed that inclusion of vertical ground motion will likely increase the chance of derailment. It is recommended to include vertical ground motion component in earthquake induced derailment analysis to ensure conservative estimations. The derailment event on bridges was found to be more closely related to the deck acceleration rather than the ground acceleration.

Comparison of calculation methods for wheel–switch rail normal and tangential contact

Wheel–rail contact is more complex in railway a turnout than in ordinary track and, thus, necessitates an advanced model to simulate dynamic interaction and predict rail wear. The main aim of the present work is to assess the application of several wheel–rail rolling contact models in railway turnout. For normal contact problems, wheel–rail contact models based on four different methods are compared: Hertz theory, the semi-Hertzian method, CONTACT, and the finite element method. The assessment is based on the results of contact patch shape and size and contact pressure for several wheelset lateral displacements. The load is set to a constant and equal to static wheel load. Calculations are performed at the section of switch rail head with width 35 mm in CN60-1100-1:18 turnout; both standard and worn rail profiles are accounted for. For tangential contact problems, four corresponding methods are assessed, based on the calculation of creep forces, distribution of the stick/slide region and computational efficiency: Shen–Hedrick–Elkins theory, FASTSIM, improved FASTSIM based on semi-Hertzian method, and CONTACT. It is found that the normal contact problems solved by the semi-Hertzian method and CONTACT correlate well with the finite element method, and the tangential contact problems solved by improved FASTSIM and CONTACT are quite favorable. The conclusions of this work can provide some guidance for contact model selection in the dynamic simulation and wear prediction of railway turnout.