Long-term wear and rolling contact fatigue behaviour of a conformal wheel profile designed for large radius curves

There are many reasons to optimise the wheel–rail interface through redesign or maintenance. Minimising wear and rolling contact fatigue (RCF) initiation on wheels and/or rails is often at the forefront of such considerations. This paper covers the design of a conformal wheel profile and its long-term wear and RCF performance to optimise the wheel–rail interface and subsequently reduce the occurrence of surface-initiated RCF on South Africa’s iron ore export line. A comparative study is performed using multibody dynamics simulation together with numerical wheel wear and RCF predictions. The advantages of a conformal wheel profile design are illustrated by evaluating the worn shape and resulting contact conditions of the conformal design. The conformal design has a steadier equivalent conicity progression and a smaller conicity range compared with the current wheel profile design over the wheel’s wear life. The combination of a conformal wheel profile design with 2?mm hollow wear and inadequate adherence to grinding tolerances often result in two-point contact, thereby increasing the probability of RCF initiation. The conformal wheel profile design proved to have wear and potential RCF benefits compared with the current wheel profile design. However, implementation of such a conformal wheel profile must be accompanied by improved rail grinding practices to ensure rail profile compliance.     

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.     

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.     

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

A thorough investigation of wheel–rail impact due to wheel flats is presented, together with a quantitative characterization of the main mechanisms and parameters. A criterion for the speed with respect to contact loss between wheel and rail is derived. In the subcritical speed regime, the magnitude of the impact force is shown to be directly related to the geometry of the flat, whereas in the transcritical speed regime a fictitious or effective flat depth exists, which decreases with the second order of the speed. In this domain, the position of impact shifts towards the end of the flat with increasing speed. The impact force increases with the second order of the speed in the subcritical speed regime and approximately the first order of the speed in the transcritical speed regime. The magnitude of the impact force is inversely proportional to the minimum circumferential curvature of the wheel tread defect in the subcritical speed regime, and to the effective minimum curvature in the transcritical case. The variation with the flat depth is less; the impact varies with the square root of the flat depth. The presented theory is in accordance with measurements reported in the literature and explains characteristic features in them.     

Influence of wheel–rail contact modelling on vehicle dynamic simulation

This paper presents a comparison of four models of rolling contact used for online contact force evaluation in rail vehicle dynamics. Until now only a few wheel–rail contact models have been used for online simulation in multibody software (MBS). Many more models exist and their behaviour has been studied offline, but a comparative study of the mutual influence between the calculation of the creep forces and the simulated vehicle dynamics seems to be missing. Such a comparison would help researchers with the assessment of accuracy and calculation time. The contact methods investigated in this paper are FASTSIM, Linder, Kik–Piotrowski and Stripes. They are compared through a coupling between an MBS for the vehicle simulation and Matlab for the contact models. This way the influence of the creep force calculation on the vehicle simulation is investigated. More specifically this study focuses on the influence of the contact model on the simulation of the hunting motion and on the curving behaviour.     

Modification of the semi-Hertz wheel–rail contact method based on recalculating the virtual penetration value

ABSTRACT

Wheel–rail contact calculation is of vital importance in vehicle system dynamics. In the existing methods of wheel–rail contact calculation, the finite element method and Kalker’s CONTACT program, which are based on the complementary energy principle, are the two methods with accuracy recognised. However, because of its very slow calculation speed, it cannot meet the requirement of online calculation, so a variety of fast non-elliptic algorithms have been proposed. The semi-Hertz method, which is recognised for its great contributions to the fast wheel–rail contact calculation, is based on the concept of virtual penetration. The calculation of virtual penetration is crucial to evaluate the shape and normal pressure distribution of the contact patch. In practice, the virtual penetration is related to the curvature of the whole contact patch; however, the range of the contact patch is determined by the value of penetration. Such an interaction leads the calculation into a dead loop. In the semi-Hertz method, the penetration is calculated by the Hertz parameters of the initial contact point. Thus, the practical range of the method is limited. In this paper, a fast-iterative method for solving virtual penetration is proposed, and a reliable value of virtual penetration can be obtained under any lateral wheel–rail relative curvature variation with good stability and speed. The normal and tangential solutions are analysed with different methods in this paper.     

A fast-simplified wheel–rail contact model consistent with perfect plastic materials

A method is described which is an extension of rolling contact models with respect to plasticity. This new method, which is an extension of the STRIPES semi-Hertzian (SH) model, has been implemented in a multi-body-system (MBS) package and does not result in a longer execution time than the STRIPES SH model [J.B. Ayasse and H. Chollet, Determination of the wheel–rail contact patch in semi-Hertzian conditions, Veh. Syst. Dyn. 43(3) (2005), pp. 161–172]. High speed of computation is obtained by some hypotheses about the plastic law, the shape of stresses, the locus of the maximum stress and the slip. Plasticity does not change the vehicle behaviour but there is a need for an extension of rolling contact models with respect to plasticity as far as fatigue analysis of rail is concerned: rolling contact fatigue may be addressed via the finite element method (FEM) including material non-linearities, where loads are the contact stresses provided by the post-processing of MBS results [K. Dang Van, M.H. Maitournam, Z. Moumni, and F. Roger, A comprehensive approach for modeling fatigue and fracture of rails, Eng. Fract. Mech. 76 (2009), pp. 2626–2636]. In STRIPES, like in other MBS models, contact stresses may exceed the plastic yield criterion, leading to wrong results in the subsequent FEM analysis. With the proposed method, contact stresses are kept consistent with a perfect plastic law, avoiding these problems. The method is benchmarked versus non-linear FEM in Hertzian geometries. As a consequence of taking plasticity into account, contact patch area is bigger than the elastic one. In accordance with FEM results, a different ellipse aspect ratio than the one predicted by Hertz theory was also found and finally pressure does not exceed the threshold prescribed by the plastic law. The method also provides more exact results with non-Hertzian geometries. The new approach is finally compared with non-linear FEM in a tangent case with a unidirectional load and a complete slip: when plasticity is taken into account, and for large adhesion values, friction forces have an influence on the size of the contact patch. The proposed approach enables also to assess extensively the level of plasticity along a track through an indicator associated with a given yield stress.     

A third-order approximation method for three-dimensional wheel–rail contact

Multibody train analysis is used increasingly by railway operators whenever a reliable and time-efficient method to evaluate the contact between wheel and rail is needed; particularly, the wheel–rail contact is one of the most important aspects that affects a reliable and time-efficient vehicle dynamics computation. The focus of the approach proposed here is to carry out such tasks by means of online wheel–rail elastic contact detection. In order to improve efficiency and save time, a main analytical approach is used for the definition of wheel and rail surfaces as well as for contact detection, then a final numerical evaluation is used to locate contact. The final numerical procedure consists in finding the zeros of a nonlinear function in a single variable. The overall method is based on the approximation of the wheel surface, which does not influence the contact location significantly, as shown in the paper.     

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.     

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.     

The Kalker book of tables for non-Hertzian contact of wheel and rail

A new regularisation of non-elliptical contact patches has been introduced, which enables building the look-up table called by us the Kalker book of tables for non-Hertzian contact (KBTNH), which is a fast creep force generator that can be used by multibody dynamics system simulation programs. The non-elliptical contact patch is regularised by a simple double-elliptical contact region (SDEC). The SDEC region is especially suitable for regularisation of contact patches obtained with approximate non-Hertzian methods for solving the normal contact problem of wheel and rail. The new regularisation is suitable for wheels and rails with any profiles, including worn profiles.

The paper describes the new procedure of regularisation of the non-elliptical contact patch, the structure of the Kalker book of tables, and parameterisation of the independent variables of the tables and creep forces.

A moderate volume Kalker book of tables for SDEC region suitable for simulation of modern running gears has been computed in co-simulation of Matlab and program CONTACT.

To access the creep forces of the Kalker book of tables, the linear interpolation has been applied.

The creep forces obtained from KBTNH have been compared to those obtained by program CONTACT and FASTSIM algorithm. FASTSIM has been applied on both the contact ellipse and the SDEC contact patch. The comparison shows that KBTNH is in good agreement with CONTACT for a wide range of creepage condition and shapes of the contact patch, whereas the use of FASTSIM on the elliptical patch and SDEC may lead to significant deviations from the reference CONTACT solutions.

The computational cost of calling creep forces from KBTNH has been estimated by comparing CPU time of FASTSIM and KBTNH. The KBTNH is 7.8–51 times faster than FASTSIM working on 36–256 discretisation elements, respectively.

In the example of application, the KBTNH has been applied for curving simulations and results compared with those obtained with the creep force generator employing the elliptical regularisation. The results significantly differ, especially in predicted creepages, because the elliptical regularisation neglects generation of the longitudinal creep force by spin creepage.     

Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem

ABSTRACT

In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached.     

Non-steady state modelling of wheel–rail contact problem

Among all the algorithms to solve the wheel–rail contact problem, Kalker's FastSim has become the most useful computation tool since it combines a low computational cost and enough precision for most of the typical railway dynamics problems. However, some types of dynamic problems require the use of a non-steady state analysis. Alonso and Giménez developed a non-stationary method based on FastSim, which provides both, sufficiently accurate results and a low computational cost. However, it presents some limitations; the method is developed for one time-dependent creepage and its accuracy for varying normal forces has not been checked. This article presents the required changes in order to deal with both problems and compares its results with those given by Kalker's Variational Method for rolling contact.     

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.     

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.     

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.     

Short wavelength rail corrugation and non-steady-state contact mechanics

J. J. Kalker has been the first to consider non-steady-state or transient contact mechanics. Based on Kalker the second author developed a linear contact model for the non-steady-state rolling contact of a wheel running over slightly corrugated rails. The theoretical investigations are concentrated on linear, non-steady-state contact mechanics superimposed to a nonlinear reference state. The reference state is given by the running behaviour of a wheelset due to traction, curving or hunting. For the linear, non-steady-state analysis Kalker's theory has to be modified to predict wear rates in dependency of the corrugation wavelengths. As a result corrugations are only amplified in the range between 2 and 10 cm. Therefore, non-steady-state contact mechanics and wear are responsible for a wavelength fixing mechanism. Structural mechanics of the rail indicate that wavelength in this range is predominantly amplified.     

Influence of the track quality and of the properties of the wheel–rail rolling contact on vehicle dynamics

This work describes an analytical approach to determine what degree of accuracy is required in the definition of the rail vehicle models used for dynamic simulations. This way it would be possible to know in advance how the results of simulations may be altered due to the existence of errors in the creation of rolling stock models, whilst also identifying their critical parameters. This would make it possible to maximise the time available to enhance dynamic analysis and focus efforts on factors that are strictly necessary. In particular, the parameters related both to the track quality and to the rolling contact were considered in this study. With this aim, a sensitivity analysis was performed to assess their influence on the vehicle dynamic behaviour. To do this, 72 dynamic simulations were performed modifying, one at a time, the track quality, the wheel–rail friction coefficient and the equivalent conicity of both new and worn wheels. Three values were assigned to each parameter, and two wear states were considered for each type of wheel, one for new wheels and another one for reprofiled wheels. After processing the results of these simulations, it was concluded that all the parameters considered show very high influence, though the friction coefficient shows the highest influence. Therefore, it is recommended to undertake any future simulation job with measured track geometry and track irregularities, measured wheel profiles and normative values of the wheel–rail friction coefficient.