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.     

Indirect method for wheel–rail force measurement and derailment evaluation

Wheel set flange derailment criteria for railway vehicles are derived and the influence of wheel–rail contact parameters is studied. An indirect method for wheel–rail force measurement based on these derailment evaluation criteria is proposed. Laboratory tests for the calibration of strain–force devices on the bearing box are carried out to determine the relationship between the applied force and the measured strain. The simulation package, SIMPACK, is used to develop a passenger car model to generate wheel–rail forces and vibration signals. Different cases are considered in this model to provide an accurate validation of the identified wheel–rail forces. A feasibility test is conducted in the Beijing Loop test line using a passenger car equipped with a set of strain gauges on the wheel set. The comparison of the force time history applied to the instrumented wheel set and that obtained using the indirect method is presented.     

The effect of worn profile on wear progress of rail vehicle steel wheels over curved tracks

Dynamic performance, safety and maintenance costs of railway vehicles strongly depend on wheelset dynamics and particularly on the design of wheelset profile. This paper considers the effect of worn wheel profile on vehicle dynamics and the trend of wear in the wheels as a result of the vehicle movements. ADAMS/RAIL is used to build a multi-body system model of the vehicle. The track model is also configured as an elastic body. Measured new and worn wheel profiles are used to provide boundary conditions for the wheel/rail contacts. The fleet velocity profile taken during its normal braking is also used for the simulation. Wear numbers are calculated for different sets of wheels and the results compared with each other. Outcome of this research can be used for modifying dynamic performance of the vehicle, improving its suspension elements and increasing ride quality. It can also be further processed to reach to a modified wheel profile suitable for the fleet/track combination and for improved maintenance of the wheels. A major advantage of the computer models in this paper is the insertion of the wheel surface properties into the boundary conditions for dynamic modelling of the fleet. This is performed by regularly measuring the worn wheel profiles during their service life and by the calculation of the wear rate for individual wheels.     

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.     

Prediction of Wheel/Rail Profile Wear

The alteration in wheel and rail profiles due to wear involves considerable vehicle and track-maintenance costs, and influences the loading capacity of the rails, as well as the operation safety and riding comfort of the vehicles. In the past twenty years a vehicle dynamics, contact mechanics and tribology based research work has emerged which is also recently continuous in an international scale, and this research is more and more intensive. Parallel to the growing possibilities of computer based analyses, several algorithms and numerical procedures have been elaborated, as well as measurement based experiments have been carried out to establish the reliable prediction of wear-caused wheel and rail profile alterations and to maximise the mileage performance by selecting the optimum vehicle system parameters for running gears operating on a selected railway line or a whole network under specified -in general inherently stochastic - traffic conditions. This paper takes an attempt to introduce the extended sphere of problems of wheel and rail wear prediction, as well as the latest results reflecting the present state of the art.     

Switch Panel wear loading – a parametric study regarding governing train operational factors

The acting forces and resulting material degradation at the running surfaces of wheels and rail are determined by vehicle, track, interface and operational characteristics. To effectively manage the experienced wear, plastic deformation and crack development at wheels and rail, the interaction between vehicle and track demands a system approach both in maintenance and in design. This requires insight into the impact of train operational parameters on rail- and wheel degradation, in particular at switches and crossings due to the complex dynamic behaviour of a railway vehicle at a turnout. A parametric study was carried out by means of vehicle-track simulations within the VAMPIRE® multibody simulation software, performing a sensitivity analysis regarding operational factors and their impact on expected switch panel wear loading. Additionally, theoretical concepts were cross-checked with operational practices by means of a case study in response to a dramatic change in lateral rail wear development at specific switches in Dutch track. Data from train operation, track maintenance and track inspection were analysed, providing further insight into the operational dependencies. From the simulations performed in this study, it was found that switch rail lateral wear loading at the diverging route of a 1:9 type turnout is significantly influenced by the level of wheel–rail friction and to a lesser extent by the direction of travel (facing or trailing). The influence of other investigated parameters, being vehicle speed, traction, gauge widening and track layout is found to be small. Findings from the case study further confirm the simulation outcome. This research clearly demonstrates the contribution flange lubrication can have in preventing abnormal lateral wear at locations where the wheel–rail interface is heavily loaded.     

Prediction of Wheel/Rail Profile Wear

SUMMARY

The alteration in wheel and rail profiles due to wear involves considerable vehicle and track-maintenance costs, and influences the loading capacity of the rails, as well as the operation safety and riding comfort of the vehicles. In the past twenty years a vehicle dynamics, contact mechanics and tribology based research work has emerged which is also recently continuous in an international scale, and this research is more and more intensive. Parallel to the growing possibilities of computer based analyses, several algorithms and numerical procedures have been elaborated, as well as measurement based experiments have been carried out to establish the reliable prediction of wear-caused wheel and rail profile alterations and to maximise the mileage performance by selecting the optimum vehicle system parameters for running gears operating on a selected railway line or a whole network under specified -in general inherently stochastic - traffic conditions. This paper takes an attempt to introduce the extended sphere of problems of wheel and rail wear prediction, as well as the latest results reflecting the present state of the art.     

A dynamic wheel–rail impact analysis of railway track under wheel flat by finite element analysis

Wheel–rail interaction is one of the most important research topics in railway engineering. It involves track impact response, track vibration and track safety. Track structure failures caused by wheel–rail impact forces can lead to significant economic loss for track owners through damage to rails and to the sleepers beneath. Wheel–rail impact forces occur because of imperfections in the wheels or rails such as wheel flats, irregular wheel profiles, rail corrugations and differences in the heights of rails connected at a welded joint. A wheel flat can cause a large dynamic impact force as well as a forced vibration with a high frequency, which can cause damage to the track structure. In the present work, a three-dimensional finite element (FE) model for the impact analysis induced by the wheel flat is developed by the use of the FE analysis (FEA) software package ANSYS and validated by another validated simulation. The effect of wheel flats on impact forces is thoroughly investigated. It is found that the presence of a wheel flat will significantly increase the dynamic impact force on both rail and sleeper. The impact force will monotonically increase with the size of wheel flats. The relationships between the impact force and the wheel flat size are explored from this FEA and they are important for track engineers to improve their understanding of the design and maintenance of the track system.     

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.     

Influence of polygonal wear of railway wheels on the wheel set axle stress

The coupled vehicle/track dynamic model with the flexible wheel set was developed to investigate the effects of polygonal wear on the dynamic stresses of the wheel set axle. In the model, the railway vehicle was modelled by the rigid multibody dynamics. The wheel set was established by the finite element method to analyse the high-frequency oscillation and dynamic stress of wheel set axle induced by the polygonal wear based on the modal stress recovery method. The slab track model was taken into account in which the rail was described by the Timoshenko beam and the three-dimensional solid finite element was employed to establish the concrete slab. Furthermore, the modal superposition method was adopted to calculate the dynamic response of the track. The wheel/rail normal forces and the tangent forces were, respectively, determined by the Hertz nonlinear contact theory and the Shen–Hedrick–Elkins model. Using the coupled vehicle/track dynamic model, the dynamic stresses of wheel set axle with consideration of the ideal polygonal wear and measured polygonal wear were investigated. The results show that the amplitude of wheel/rail normal forces and the dynamic stress of wheel set axle increase as the vehicle speeds rise. Moreover, the impact loads induced by the polygonal wear could excite the resonance of wheel set axle. In the resonance region, the amplitude of the dynamic stress for the wheel set axle would increase considerably comparing with the normal conditions.     

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.     

Modelling the Contact Between Wheel and Rail Within Multibody System Simulation

In modern railway industry the simulation of the behaviour of railway vehicles has become an important design method during the last years. Modern simulation packages offer modelling elements that are highly adapted for standard and unusual simulation scenarios. A specific application case is the simulation of a railway vehicle travelling through a switch. It makes high demands on the simulation software due to the inconvenient modelling elements needed: the changing rail profiles on the blade rail and in the crossing vee area as well as the guard rail with its additional contact at the back of the wheel. The article gives an overview over the state of the art in railway vehicle simulation and presents a simulation of a passenger car running through a switch as an application example.     

Modelling the Contact Between Wheel and Rail Within Multibody System Simulation

In modern railway industry the simulation of the behaviour of railway vehicles has become an important design method during the last years. Modern simulation packages offer modelling elements that are highly adapted for standard and unusual simulation scenarios. A specific application case is the simulation of a railway vehicle travelling through a switch. It makes high demands on the simulation software due to the inconvenient modelling elements needed: the changing rail profiles on the blade rail and in the crossing vee area as well as the guard rail with its additional contact at the back of the wheel. The article gives an overview over the state of the art in railway vehicle simulation and presents a simulation of a passenger car running through a switch as an application example.     

Stochastic analysis of dynamic interaction between train and railway turnout

The performance of a railway turnout (switch and crossing) is influenced by a large number of input parameters of the complex train–turnout system. To reach a robust design that performs well for different traffic situations, random distributions (scatter) of these inputs need to be accounted for in the design process. Stochastic analysis methods are integrated with a simulation model of the dynamic interaction between train and turnout. For a given nominal layout of the turnout, using design of experiments methodology and a two-level fractional factorial screening design, four parameters (axle load, wheel–rail friction coefficient, and wheel and rail profiles) are identified to be the most significant. These parameters are further investigated using a three-level full factorial design and stochastic analysis. The random distributions of transverse wheel profile and set of transverse rail profiles along the switch panel are accounted for by the Karhunen–Loève expansion technique. The influence of the random distributions of the input parameters on the statistical outputs of wheel–rail contact forces, wear and rolling contact fatigue is assessed using Latin hypercube sampling to generate a number of stochastic load realizations.     

Optimisation of railway crossing geometry considering a representative set of wheel profiles

A numerical method for robust geometry optimisation of railway crossings is presented. The robustness is achieved by optimising the crossing geometry for a representative set of wheel profiles. As a basis for the optimisation, a crossing geometry is created where rail cross-sectional profiles and longitudinal height profiles of both wing rails and crossing nose are parameterised. Based on the approximation that the two problems are decoupled, separate optimisations are performed for the cross-sectional rail profiles and the longitudinal height profiles. The rail cross sections are optimised to minimise the maximum Hertzian wheel–rail contact pressure. The longitudinal height profiles are optimised to minimise the accumulated damage in the wing rail to crossing nose transition zone. The accumulated damage is approximated using an objective criterion that accounts for the angle of the wheel trajectory reversal during the transition from the wing rail to the crossing nose as well as the distribution of transition points for the utilised wheel profile set. It is found that small nonlinear height deviations from a linear longitudinal wing rail profile in the transition zone can reduce the objective compared to the nominal design. It is further demonstrated that the variation in wheel profile shapes, lateral wheel displacements and the feasible transition zone length of the crossing will determine the longitudinal height profiles of the wing rail and crossing nose if all wheel profiles are to make their transition within the transition zone.     

Numerical investigation on effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout

In railway turnout, the stock rail and switch rail are separated to enable the vehicle changing among the tracks, and they are provided with different rail resilience level on the baseplate. Therefore, there will be vertical relative motion between stock/switch rails under the wheel loads, and the relative motion will affect consequentially the wheel–rail contact conditions. A method is developed to investigate the effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout. First, the rigid wheel–rail contact points of stock/switch rails are calculated based on the trace line method, and then the contact status is determined by the presented equations, finally, the distribution of wheel–rail contact forces of stock/switch rails is obtained based on the continuity of interface displacements and forces which using an approximate surface deformation method. Some parametric studies have been performed, such as the lateral displacement of wheel set, the vertical contact forces, the wheel profiles and the vertical stiffness of rail pad. The results of the parametric study are presented and discussed.     

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 simulation of railway vehicles: wheel/rail contact analysis

The multibody simulation of railway vehicle dynamics needs a reliable and efficient method to evaluate the contact points between wheel and rail, because their positions have a considerable influence on the direction and intensity of the contact forces. In this work, an innovative semi-analytic procedure for the detection of the wheel/rail contact points (named the DIFF method) is presented. This method considers the wheel and the rail as two surfaces whose analytic expressions are known and is based on the idea that in the contact points the difference between the surfaces has local minima and is equivalent to solving an algebraic two-dimensional system. The original problem can be reduced analytically to a simple scalar equation that can be easily solved numerically (since the problem dimension is one, even elementary non-iterative algorithms can be efficient).