Creep force modelling for rail traction vehicles based on the Fastsim algorithm

The evaluation of creep forces is a complex task and their calculation is a time-consuming process for multibody simulation (MBS). A methodology of creep forces modelling at large traction creepages has been proposed by Polach [Creep forces in simulations of traction vehicles running on adhesion limit. Wear. 2005;258:992–1000; Influence of locomotive tractive effort on the forces between wheel and rail. Veh Syst Dyn. 2001(Suppl);35:7–22] adapting his previously published algorithm [Polach O. A fast wheel–rail forces calculation computer code. Veh Syst Dyn. 1999(Suppl);33:728–739]. The most common method for creep force modelling used by software packages for MBS of running dynamics is the Fastsim algorithm by Kalker [A fast algorithm for the simplified theory of rolling contact. Veh Syst Dyn. 1982;11:1–13]. However, the Fastsim code has some limitations which do not allow modelling the creep force – creep characteristic in agreement with measurements for locomotives and other high-power traction vehicles, mainly for large traction creep at low-adhesion conditions. This paper describes a newly developed methodology based on a variable contact flexibility increasing with the ratio of the slip area to the area of adhesion. This variable contact flexibility is introduced in a modification of Kalker's code Fastsim by replacing the constant Kalker's reduction factor, widely used in MBS, by a variable reduction factor together with a slip-velocity-dependent friction coefficient decreasing with increasing global creepage. The proposed methodology is presented in this work and compared with measurements for different locomotives. The modification allows use of the well recognised Fastsim code for simulation of creep forces at large creepages in agreement with measurements without modifying the proven modelling methodology at small creepages.     

A survey of wheel–rail contact models for rail vehicles

Accurate and efficient contact models for wheel–rail interaction are essential for the study of the dynamic behaviour of a railway vehicle. Assessment of the contact forces and moments, as well as contact geometry provide a fundamental foundation for such tasks as design of braking and traction control systems, prediction of wheel and rail wear, and evaluation of ride safety and comfort. This paper discusses the evolution and the current state of the theories for solving the wheel–rail contact problem for rolling stock. The well-known theories for modelling both normal contact (Hertzian and non-Hertzian) and tangential contact (Kalker's linear theory, FASTSIM, CONTACT, Polach's theory, etc.) are reviewed. The paper discusses the simplifying assumptions for developing these models and compares their functionality. The experimental studies for evaluation of contact models are also reviewed. This paper concludes with discussing open areas in contact mechanics that require further research for developing better models to represent the wheel–rail interaction.     

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.     

Dynamic responses of a high-speed railway car due to wheel polygonalisation

The polygonal wear around the wheel circumference could pose highly adverse influences on the wheel/rail interactions and thereby the performance of the vehicle system. In this study, the effects of wheel polygonalisation on the dynamic responses of a high-speed rail vehicle are investigated through development and simulations of a comprehensive coupled vehicle/track dynamic model. The model integrates flexible slab track, wheelsets and axle boxes subsystem models so as to account for elastic deformations caused by impact loads induced by the wheel polygonalisation. A field-test programme was undertaken to acquire the polygonal wear profile and axle box acceleration response of a high-speed train, and the data are used to demonstrate the validity of the coupled vehicle/track system model. Subsequently, the effects of wheel polygonalisation are evaluated in terms of wheel/rail impact forces, axle box vertical acceleration and dynamic stress developed in the axle considering different amplitudes and harmonic orders of the polygonal wear. The results suggest that the high-order wheel polygonalisation can give rise to high-frequency impact loads at the wheel/rail interface, and excite some of the vibration modes of the wheelset and the axle box leading to high-magnitude axle box acceleration and dynamic stress in the wheelset axle.     

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.     

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.     

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

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.     

An alternative to FASTSIM for tangential solution of the wheel–rail contact

In most rail vehicle dynamics simulation packages, tangential solution of the wheel–rail contact is gained by means of Kalker's FASTSIM algorithm. While 5–25% error is expected for creep force estimation, the errors of shear stress distribution, needed for wheel–rail damage analysis, may rise above 30% due to the parabolic traction bound. Therefore, a novel algorithm named FaStrip is proposed as an alternative to FASTSIM. It is based on the strip theory which extends the two-dimensional rolling contact solution to three-dimensional contacts. To form FaStrip, the original strip theory is amended to obtain accurate estimations for any contact ellipse size and it is combined by a numerical algorithm to handle spin. The comparison between the two algorithms shows that using FaStrip improves the accuracy of the estimated shear stress distribution and the creep force estimation in all studied cases. In combined lateral creepage and spin cases, for instance, the error in force estimation reduces from 18% to less than 2%. The estimation of the slip velocities in the slip zone, needed for wear analysis, is also studied. Since FaStrip is as fast as FASTSIM, it can be an alternative for tangential solution of the wheel–rail contact in simulation packages.     

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.     

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.     

Determination of the wheel rail contact patch in semi-Hertzian conditions

This paper deals with the subject of the semi-Hertzian contact, which is a way to represent the wheel rail contact in railways or roller bearing applications. The method is based on the interpenetration of the two underformed bodies' profiles. The first step deals with the problem of the shape ratio; it is proposed to compensate the two main curvatures to obtain the good ratio in Hertzian conditions. Then, Hertz and Kalker's equations are used to establish the stresses at the level of a strip. These stresses expressions are used directly in a contact model discretized in strips and tabulated as a function of the lateral displacement between the wheel and the rail. The validation is made by comparison to the previous multi-Hertzian model of the VOCOLIN software. A first test shows identical results in Hertzian conditions; a second one shows only a small difference in semi-Hertzian conditions like S1002/UIC60 1:40.     

Simulation of dynamic interaction between train and railway turnout

Dynamic train–track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel–rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel–rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.     

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

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

A new method for determining wheel–rail multi-point contact

A new method for wheel–rail multi-point contact is presented in this paper. In this method, the first- and the second-order derivatives of the wheel–rail interpolation distance function and the elastic wheel–rail virtual penetration are used to determine multiple contact points. The method takes account of the yaw angle of the wheelset and allows the identification of all possible points of contact between wheel and rail surfaces with an arbitrary geometry. Static contact geometry calculations are first carried out using the developed method for both new and worn wheel profiles and with a new rail profile. The validity of the method is then verified by simulations of a coupled vehicle and track system dynamics over a small radius curve. The simulation results show that the developed method for multi-point contact is efficient and reliable enough to be implemented online for simulations of vehicle–track system dynamics.     

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 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.