Influence of wheel and rail profile shape on the initiation of rolling contact fatigue cracks at high axle loads

The influence of wheel and rail profile shape features on the initiation of rolling contact fatigue (RCF) cracks is evaluated based on the results of multi-body vehicle dynamics simulations. The damage index and surface fatigue index are used as two damage parameters to assess the influence of the different features. The damage parameters showed good agreement to one another and to in-field observations. The wheel and rail profile shape features showed a correlation to the predicted RCF damage. The RCF damage proved to be most sensitive to the position of hollow wear and thus bogie tracking. RCF initiation and crack growth can be reduced by eliminating unwanted shape features through maintenance and design and by improving bogie tracking.     

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.     

Design of an optimised wheel profile for rail vehicles operating on two-track gauges

This article sets out an optimum synthesis methodology for wheel profiles of railway vehicles in order to secure good dynamic behaviour with different track configurations. Specifically, the optimisation process has been applied to the case of rail wheelsets mounted on double-gauge bogies that move over two different gauges, which also have different types of rail: the Iberian gauge (1668 mm) and the International Union of Railways (UIC) gauge (1435 mm). Optimisation is performed using Genetic Algorithms and traditional optimisation methods in a complementary way. The objective function used is based on an ideal equivalent conicity curve which ensures good stability on straight sections and also proper negotiation of curves. To this end, the curve is constructed in such a way that it is constant with a low value for small lateral wheelset displacements (with regard to stability), and increases as the displacements increase (to facilitate negotiation of curved sections). Using this kind of ideal conicity curve also enables a wheel profile to be secured where the contact points have a larger distribution over the active contact areas, making wear more homogeneous and reducing stresses. The result is a wheel profile with a conicity that is closer to the target conicity for both gauges studied, producing better curve negotiation while maintaining good stability on straight sections of track. The article shows the resultant wheel profile, the contact curves it produces, and a number of dynamic analyses demonstrating better dynamic behaviour of the synthesised wheel on curved sections with respect to the original wheel.     

Modelling of wear and fatigue defect formation in wheel–rail contact

The model for analysing wear and fatigue defect formation is developed based on the approaches of contact and fracture mechanics. The model includes the solution of the contact problem for the wheel and rail to find the shape, size and position of the contact zones and the contact stresses and calculation of the surface wear and the function of damage accumulation in the rail and wheel. The wear rate and the worn-profile evolution of the wheel surface are calculated using both statistic and deterministic approaches to modelling of vehicle dynamics (tribo-dynamic modelling). The influence of the evolution of the wheel–rail profiles due to wear on the damage accumulation process is analysed. It is shown that for some values of the wear rate coefficient, the wear process can prevent the crack initiation under the wheel surface.     

A non-Hertzian method for solving wheel–rail normal contact problem taking into account the effect of yaw

A novel approach is proposed in this paper to deal with non-Hertzian normal contact in wheel–rail interface, extending the widely used Kik–Piotrowski method. The new approach is able to consider the effect of the yaw angle of the wheelset against the rail on the shape of the contact patch and on pressure distribution. Furthermore, the method considers the variation of profile curvature across the contact patch, enhancing the correspondence to CONTACT for highly non-Hertzian contact conditions. The simulation results show that the proposed method can provide more accurate estimation than the original algorithm compared to Kalker’s CONTACT, and that the influence of yaw on the contact results is significant under certain circumstances.     

Carbody elastic vibrations of high-speed vehicles caused by bogie hunting instability

In particular locations of the high-speed track, the worn wheel profile matched up with the worn rail profile will lead to an extremely high-conicity wheel–rail contact. Consequently, the bogie hunting instability arises, which further results in the so-called carbody shaking phenomenon. In this paper, the carbody elastic vibrations of a high-speed vehicle in service are firstly introduced. Modal tests are conducted to identity the elastic modes of the carbody. The ride comfort and running safety indices for the tested vehicle are evaluated. The rigid–flexible coupling dynamic model for the high-speed passenger car is then developed by using the FE and MBS coupling approach. The rail profiles in those particular locations are measured and further integrated into the simulation model to reproduce the bogie hunting and carbody elastic vibrations. The effects of wheel and rail wear on the vehicle system response, e.g. wheelset bifurcation graph and carbody vibrations, are studied. Two improvement measures, including the wheel profile modification and rail grinding, are proposed to provide possible solutions. It is found that the wheel–rail contact conicity can be lowered by decreasing wheel flange thickness or grinding rail corner, which is expected to improve the bogie hunting stability under worn rail and worn wheel conditions. The carbody elastic vibrations caused by bogie hunting instability can be further restrained.     

Mathematical modelling of train–turnout interaction

The paper proposes a mathematical model of train–turnout interaction in the mid-frequency range (0–500 Hz). The model accounts for the effects of rail profile variation along the track and of local variation of track flexibility. The proposed approach is able to represent the condition of one wheel being simultaneously in contact with more than one rail, allowing the accurate prediction of the effect of wheels being transferred from one rail to another when passing over the switch toe and the crossing nose. Comprehensive results of train–turnout interaction during the negotiation of the main and the branch lines are presented, including the effect of wear of wheel/rail profiles and presence of track misalignment. In the final part of the paper, comparisons are performed between the results of numerical simulations and line measurements performed on two different turnouts for urban railway lines, showing a good agreement between experimental and numerical results.     

Deterioration mechanisms in the wheel–rail interface with focus on wear prediction: a literature review

Wheel–rail interface management is imperative to railway operation and its maintenance represents a major share of the total maintenance cost. In general, the course of events usually called wear is a complicated process involving several modes of material deterioration and contact surface alteration. Thus material removal or relocation, plastic flow and phase transformation may take place at, just below, or in-between the contacting surfaces. A higher degree of predictability of deterioration mechanisms and a firm basis for optimisation of the wheel–rail system are anticipated to reveal a great potential for cost savings. Wear in the sense of material loss and related wheel–rail profile evolution represents one of several modes of damage. The purpose of this survey is to explore research on wear simulation, to some degree extended to neighbouring disciplines. It is believed that a cross-disciplinary approach involving, for instance, adhesive and abrasive wear, surface plasticity, and rolling contact fatigue opens new perspectives to improved damage prediction procedures.     

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.     

Solving conformal contacts using multi-Hertzian techniques

Recently, publications aiming at wheel–rail contact surveys let readers think that multi-Hertzian methods present severe drawbacks with respect to ‘virtual penetration’ methods. These surveys criticise multi-Hertzian solutions mainly because presenting ‘larger contacts overlaps’ and ‘frequent secondary contacts near the border of the first contact’, both obvious geometric possibilities of which the practical occurrence and eventual inconvenience would remain purely theoretical unless established over definite methods demonstrating poor practical results. Recent surveys all quote Piotrowski–Chollet 2005 survey of wheel–rail contact models that attempted to illustrate defective multi-Hertzian techniques by concentrating on the method initiated by Sauvage in the 1990s and further developed by Pascal. The 2005 paper not only gives no evidence of practical inconveniences of Sauvage’s method but also confuses static geometric contact overlaps with the dynamical overlapping of forces. In reality it mixes Sauvage method up with a quite different technique. Thus a clarification is now necessary by reminding what the proper Sauvage technique really is and by showing some of its practical successful applications. The present paper, focusing on determination of normal contact forces in conformal situations, intends to explain clearly the advantages of the unequivocal localisation of secondary ellipses in that multi-Hertzian method which has been developed in INRETS VOCO codes in the 1990s and successfully used by SNCF and ALSTOM in the INRETS-SNCF code, VOCODYM, and later in Pascal’s online calculation of railway elastic contacts code. It proved its effectiveness for studying freight wagons derailments as well as rail wear and head-check, unrounded wheels wear, high-speed lines’ deformations or TGV comfort. While simulating American ACELA trainsets’ behaviour on the US North-East Corridor tracks, prior to actual tests, as part of the commercial contract. It has been also a major tool for bringing back together French and American Safety Standards.     

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.     

Methodology and verification of calculations for contact stresses in a wheel–rail system

The distribution of contact stresses in the wheel–rail system is a decisive factor for the wear of elements and the safety of rail transport. Analytical calculations of stresses based on the Hertz theory can only be applied to elastic deformation of materials. High dynamic loads leading to plastic deformation (not considered in the Hertz theory) are a predominant cause of problems in the contact vicinity. These problems can be successfully resolved by applying the finite-elements method. Two- and three-dimensional test models were generated to estimate an error in numerical calculations in the MSC.MARC program. We compared the results of numerical calculations with analytical calculations. Based on the obtained results we defined the effect of parameters describing the finite-elements mesh on the calculation error for contact stresses, and adjusted mesh parameters appropriately to achieve as low as possible error in numerical calculations. We also defined the effect of material characteristics on the value of contact stresses on the wheel–rail interface.     

Wear rate estimation of train wheels using dynamic simulations and field measurements

Wheel–rail wear is one of the important problems in the railway industry, especially from the point of safety, maintenance, and replacement cost. To investigate this phenomenon, it is necessary to simulate the wheel–rail interaction. The simulation results and in particular the wear number is not tangible enough to explain the wear condition of the system. For one set of simulation performed on two different railway systems one could obtain the same wear numbers, of say 100, while having two completely different wear rates. In order to have a better understanding of the wear condition, it is proposed to convert the wear numbers to wear rates. In doing so by measuring the wear rate, one determines the rate at which the wheel flange thickness is reduced. In this research, a new approach has been proposed to determine the wheel wear rate through multi-body dynamic analysis and simulation and the field measurements carried out on the fleet of one of Tehran's subway lines. This procedure could also be expanded to determine a wear criterion for specific lines and their fleets. Having this wear criterion would provide a better understanding of the simulation results either prior to the construction of railway lines or for the presently used ones. In other words, designers can simulate a railway line, not being constructed yet, and with a good approximation determine the critical points along the line with high wear rates, and make necessary modifications to decrease the wear.     

Design and optimisation of wheel–rail profiles for adhesion improvement

This paper describes a study for the optimisation of the wheel profile in the wheel–rail system to increase the overall level of adhesion available at the contact interface, in particular to investigate how the wheel and rail profile combination may be designed to ensure the improved delivery of tractive/braking forces even in poor contact conditions. The research focuses on the geometric combination of both wheel and rail profiles to establish how the contact interface may be optimised to increase the adhesion level, but also to investigate how the change in the property of the contact mechanics at the wheel–rail interface may also lead to changes in the vehicle dynamic behaviour.     

Dynamic model for the wheel–rail contact friction

Accurately estimating the coefficient of friction (CoF) is essential in modelling railroad dynamics, reducing maintenance costs, and increasing safety in rail operations. The typical assumption of a constant CoF is widely used in theoretical studies; however, it has been noticed that the CoF is not constant, but rather depends on various dynamic parameters and instantaneous conditions. In this paper, we present a newly developed three-dimensional nonlinear CoF model for the dry rail condition and test the CoF variation using this model with estimated dynamic parameters. The wheel–rail is modelled as a mass–spring–damper system to simulate the basic wheel–rail dynamics. Although relatively simple, this model is considered sufficient for the purpose of this study. Simulations are performed at a train speed of 20 m/s using rail roughness as an excitation source. The model captures the CoF extremes and illustrates its nonlinear behaviour and instantaneous dependence on several structural and dynamic parameters.     

A novel method to model wheel–rail normal contact in vehicle dynamics simulation

An approximate analytical method is proposed for calculating the contact patch and pressure distribution in the wheel–rail interface. The deformation of the surfaces in contact is approximated using the separation between them. This makes it possible to estimate the contact patch analytically. The contact pressure distribution in the rolling direction is assumed to be elliptic with its maximum calculated by applying Hertz' solution locally. The results are identical to Hertz's for elliptic cases. In non-elliptic cases good agreement is achieved in comparison to the more accurate but computationally expensive Kalker's variational method (CONTACT code). Compared to simplified non-elliptic contact methods based on virtual penetration, the calculated contact patch and pressure distribution are markedly improved. The computational cost of the proposed method is significantly lower than the more detailed methods, making it worthwhile to be applied to rolling contact in rail vehicle dynamics simulation. Such fast and accurate estimation of contact patch and pressure paves the way for on-line modelling of damage phenomena in dynamics simulation packages.     

Improvement of vehicle–turnout interaction by optimising the shape of crossing nose

Proper rail geometry in the crossing part is essential for reducing damage on the nose rail. To improve the dynamic behaviour of turnout crossings, a numerical optimisation approach to minimise rolling contact fatigue (RCF) damage and wear in the crossing panel by varying the nose rail shape is presented in the paper. The rail geometry is parameterised by defining several control cross-sections along the crossing. The dynamic vehicle–turnout interaction as a function of crossing geometry is analysed using the VI-Rail package. In formulation of the optimisation problem a combined weighted objective function is used consisting of the normal contact pressure and the energy dissipation along the crossing responsible for RCF and wear, respectively. The multi-objective optimisation problem is solved by adapting the multipoint approximation method and a number of compromised solutions have been found for various sets of weight coefficients. Dynamic behaviour of the crossing has been significantly improved after optimisations. Comparing with the reference design, the heights of the nose rail are notably increased in the beginning of the crossing; the nominal thicknesses of the nose rail are also changed. All the optimum designs work well under different track conditions.     

A method to determine the two-point contact zone and transfer of wheel–rail forces in a turnout

A practical method to determine the zone of two contact points and the transfer of wheel–rail forces between two rails in a turnout is presented in this paper. The method is based on a wheel–rail elastic penetration assumption and used to study a turnout system for a 200 km/h high-speed railway in China. Rail profiles in a number of key sections in the turnout are identified first, and profiles in other sections are then obtained by interpolation between key sections. The track is modelled as flexible with rails and sleepers represented by beams and the interaction between the vehicle and turnout is simulated for cases of the vehicle passing the turnout. Results are mainly presented for two-point contact positions and the characteristics of the wheel–rail forces transference. It is found that the heights of the switch and crossing rail top have significant effects on the wheel–rail contact forces. Finally, the optimised top height for the crossing rails is proposed to reduce the system dynamic force in the turnout system.