Solution of the Multiple Wheel and Rail Contact Dynamic Problem

SUMMARY

An unconventional method for calculating the forces developing in the wheel and rail contact patches of a railway vehicle has been implemented at the New Technology Laboratory of INRETS. It takes into account the elastic deformations of the materials in the Hertzian elliptical contact areas; the possibility of having simultaneously several contact patches on each wheel, is introduced in the simulation of the dynamic phenomena.

The theory is applied for a high speed bogie running on a perfectly straight track.     

The Elastic Cross-Influence between Two Quasi-Hertzian Contact Zones

In this paper a type of contact between two bodies is considered, which leads to the formation of two separate contact zones. The contact zones considered are Hertzian ellipses if the distance between them is large. When the distance between the zones is finite it is necessary to take into account the elastic cross-influence of the two zones. In this paper an approximate method is proposed which allows the determination of the actual contact zones as Hertz's ellipses but without disregarding the cross-influence. Numerical results are presented for two, two-humped bodies pressed against each other and for steady state rolling of a flanged wheel along a steel rail.

It is shown that neglecting the cross influence for a flanged wheel leads to a negligible error in the contact forces but the forces are transmitted between wheel and rail through contact patches which are generally more slender than with the cross-influence neglected.     

Energy Dissipation Due to Vehicle/Track Interaction

The effects of track irregularities and wheel profile on the amount of energy dissipated in railroad freight vehicles is examined. A nonlinear computational model is used to determine the average dissipation in the vehicle suspension and the wheel/rail contact patches. This dissipation is a component of the total resistance force acting on the vehicle. Parametric results are presented showing the effects of track geometry, wheel profile, suspension design, and hunting on train resistance. Track geometry studies consider the effects of track quality and curving. The AAR 1:20 wheel profile and the Heumann wheel profile are compared under various operating conditions. Compared with the Heumann profile, the AAR 1:20 profile is shown to have lower average resistance on good quality tangent track, but higher average resistance in steady curves. A trade-off exists between the two profiles when dynamic curve entry is considered.     

The Elastic Cross-Influence between Two Quasi-Hertzian Contact Zones

SUMMARY

In this paper a type of contact between two bodies is considered, which leads to the formation of two separate contact zones. The contact zones considered are Hertzian ellipses if the distance between them is large. When the distance between the zones is finite it is necessary to take into account the elastic cross-influence of the two zones. In this paper an approximate method is proposed which allows the determination of the actual contact zones as Hertz's ellipses but without disregarding the cross-influence. Numerical results are presented for two, two-humped bodies pressed against each other and for steady state rolling of a flanged wheel along a steel rail.

It is shown that neglecting the cross influence for a flanged wheel leads to a negligible error in the contact forces but the forces are transmitted between wheel and rail through contact patches which are generally more slender than with the cross-influence neglected.     

Computation of wheel–rail contact force for non-mapping wheel–rail profile of Translohr tram

Translohr tram has steel wheels, in V-like arrangements, as guide wheels. These operate over the guide rails in inverted-V arrangements. However, the horizontal and vertical coordinates of the guide wheels and guide rails are not always mapped one-to-one. In this study, a simplified elastic method is proposed in order to calculate the contact points between the wheels and the rails. By transforming the coordinates, the non-mapping geometric relationship between wheel and rail is converted into a mapping relationship. Considering the Translohr tram’s multi-point contact between the guide wheel and the guide rail, the elastic-contact hypothesis take into account the existence of contact patches between the bodies, and the location of the contact points is calculated using a simplified elastic method. In order to speed up the calculation, a multi-dimensional contact table is generated, enabling the use of simulation for Translohr tram running on curvatures with different radii.     

Energy Dissipation Due to Vehicle/Track Interaction

SUMMARY

The effects of track irregularities and wheel profile on the amount of energy dissipated in railroad freight vehicles is examined. A nonlinear computational model is used to determine the average dissipation in the vehicle suspension and the wheel/rail contact patches. This dissipation is a component of the total resistance force acting on the vehicle. Parametric results are presented showing the effects of track geometry, wheel profile, suspension design, and hunting on train resistance. Track geometry studies consider the effects of track quality and curving. The AAR 1:20 wheel profile and the Heumann wheel profile are compared under various operating conditions. Compared with the Heumann profile, the AAR 1:20 profile is shown to have lower average resistance on good quality tangent track, but higher average resistance in steady curves. A trade-off exists between the two profiles when dynamic curve entry is considered.     

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.     

Comments on ‘the Kalker book of tables for non-Hertzian contact of wheel and rail’

The ‘simple double-elliptical contact’ (SDEC) approach by Piotrowski et al. [The Kalker book of tables for non-Hertzian contact of wheel and rail. Vehicle Syst Dyn. 2017;55:875–901] generates a-symmetrical contact patches in an elegant way. This allows to extend the table-based approach for the wheel–rail creep force calculation towards non-Hertzian contact geometry. This is an important line of research, because FASTSIM is intricate for non-Hertzian contacts, whereas CONTACT requires long calculation times.

Here, we comment on the further motivation that's provided for the approach. According to the authors, ‘the spin creepage generates longitudinal creep force in non-symmetric, non-elliptical contacts’, which is ‘completely lost’ when using elliptical regularisation. We demonstrate that this mainly depends on the choice of contact origin, and that the interaction is much reduced if different choices are made. This suggests that elliptical regularisation may be viable still, if the details are properly worked out. Furthermore, we introduce the spin center and the free-rolling position as means to extend the table-based approach towards more general non-Hertzian circumstances.     

Systems-on-chip approach for real-time simulation of wheel–rail contact laws

This paper presents the development of a systems-on-chip approach to speed up the simulation of wheel–rail contact laws, which can be used to reduce the requirement for high-performance computers and enable simulation in real time for the use of hardware-in-loop for experimental studies of the latest vehicle dynamic and control technologies. The wheel–rail contact laws are implemented using a field programmable gate array (FPGA) device with a design that substantially outperforms modern general-purpose PC platforms or fixed architecture digital signal processor devices in terms of processing time, configuration flexibility and cost. In order to utilise the FPGA's parallel-processing capability, the operations in the contact laws algorithms are arranged in a parallel manner and multi-contact patches are tackled simultaneously in the design. The interface between the FPGA device and the host PC is achieved by using a high-throughput and low-latency Ethernet link. The development is based on FASTSIM algorithms, although the design can be adapted and expanded for even more computationally demanding tasks.     

Dynamics of an isolated railway wheelset with conformal wheel–rail interactions

ABSTRACT

In multi-body dynamics, we model a non-conformal wheel/rail contact at one centre point since this contact is flat and Hertzian. However, the quasi-conformal contact requires more points since the contact is curved and non-Hertzian. The methodology in solving these points during dynamic simulations is the basis of this development. In this online effort, first, we present a general contact joint and the gutter search method of Pascal and Jourdan [The rigid-multi-Hertzian method as applied to conformal contacts. USA: ASME; 2007] in the context of a multi-body approach. Next, by adopting the non-iterative approach, a subset of these points with positive profile interpenetrations is selected to idealise one curved contact by a set of multi-Hertzian patches for which the Hertz normal contact solution is available. Finally, the feasibility of this multibody approach together with its implementation in two different codes is evaluated by simulating the motion of an isolated wheelset with realistic inertia. On tangent tracks, the wheelset with non-conformal pairing displays self-excited unstable oscillations while it displays a stable behaviour below a critical speed with conformal profiles. A further study reveals the net friction losses at multiple patches within the curved contact being the reason for the stable behavior.     

The Available Methods to Calculate the Wheel/Rail Forces in Non Hertzian Contact Patches and Rail Damaging

In the present paper, the methods used in railway dynamics to take into account the non Hertzian multi contact patches occurring on a wheel, are summarised. Some application cases are presented as well as an explanation of the so called “squat” rail deterioration.     

The Available Methods to Calculate the Wheel/Rail Forces in Non Hertzian Contact Patches and Rail Damaging

Abstract

In the present paper, the methods used in railway dynamics to take into account the non Hertzian multi contact patches occurring on a wheel, are summarised. Some application cases are presented as well as an explanation of the so called “squat” rail deterioration.     

Wheel/Rail Non-linear Interactions With Coupling Between Vertical and Lateral Directions

Summary A theoretical model is developed to explore the high frequency wheel/rail interaction with coupling between the vertical and lateral directions. This coupling is introduced through the track dynamics due to the offset of the wheel/rail contact point from the rail centre line. Equivalent models of the railway track in the time domain are developed according to the rail vibration receptances in the frequency domain. The wheel is represented by a mass in each direction with no vertical-lateral coupling. The vertical wheel/rail interaction is generated through a non-linear Hertzian contact stiffness, allowing for the possibility of loss of contact between the wheel and rail. The lateral interaction is represented by a contact spring and a creep force damper in series and their values depend on the vertical contact force. The vibration source is the roughness on the wheel and rail contact surfaces which forms a relative displacement excitation in the vertical direction. Using the combined interaction model with this relative displacement excitation, the wheel/rail interactions with coupling between the vertical and lateral vibrations are simulated. It is found that the lateral interaction force caused by the offset is usually less than thirty percent of the vertical dynamic force. The lateral vibration of the rail is significantly reduced due to the presence of the lateral coupling, whereas the vertical interaction is almost unaffected by the lateral force.     

Research into the problem of wheel tread spalling caused by wheelset longitudinal vibration

This study mainly focuses on the mechanism of wheel tread spalling through wheelset longitudinal vibration that has been often neglected. Analysis of two actual cases of the wheel tread spalling problem leads to the conclusion that the wheel tread spalling is closely related to the wheelset longitudinal vibration in some locomotives, and many of these problems can be reasonably explained if the wheelset longitudinal vibration is considered. For better understanding of some abnormal wheel spalling problems, the formations of the wheelset longitudinal vibration and the wheel/rail contact parameters were analysed in the initial wheel tread spalling. With the preliminary analytical results, the wheelset longitudinal dynamic behaviour, the characteristics of wheel/rail contact and the mechanics in the condition of the wheelset longitudinal vibration were further studied quantitatively. The results showed that the wheelset longitudinal vibration changed not only the limit of these parameters and the position of principal stress, but also the direction of the principal stress on the surface of wheel/rail contact patch. It is likely that the significant stress changes provoke too much stress on the surface of wheel/rail contact patch, cause fatigue in wheel/rail contact patch and eventually lead to wheel tread spalling. The results of these studies suggest that the suppression of the wheelset longitudinal vibration extends wheel/rail life and the addition of a vertical damper with an ahead angle provides a possible solution to the wheel spalling problem.     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

A New Wheel/Rail Spatially Dynamic Coupling Model and its Verification

Based on the theory of vehicle-track coupling dynamics, a new wheel/rail spatially dynamic coupling model is established in this paper. In consideration of rail lateral, vertical and torsion vibrations and track irregularities, the wheel/rail contact geometry, the wheel/rail normal contact force and the wheel/rail tangential creep force are solved in detail. In the new wheel/rail model, the assumption that wheel contacts rail rigidly and wheel always contacts rail is eliminated. Finally, by numeric simulation comparison with international well-known software NUCARS, comparison with vehicle-track vertical coupling model, and comparison with running test results by China Academy of Railway Sciences, the new wheel/rail spatially dynamic coupling model is shown to be correct and effective.     

Railway ground vibrations induced by wheel and rail singular defects

Railway local irregularities are a growing source of ground-borne vibration and can cause negative environmental impacts, particularly in urban areas. Therefore, this paper analyses the effect of railway track singular defects (discontinuities) on ground vibration generation and propagation. A vehicle/track/soil numerical railway model is presented, capable of accurately predicting vibration levels. The prediction model is composed of a multibody vehicle model, a flexible track model and a finite/infinite element soil model. Firstly, analysis is undertaken to assess the ability of wheel/rail contact models to accurately simulate the force generation at the wheel/rail contact, in the presence of a singular defect. It is found that, although linear contact models are sufficient for modelling ground vibration on smooth tracks, when singular defects are present higher accuracy wheel/rail models are required. Furthermore, it is found that the variation in wheel/rail force during the singular defect contact depends on the track flexibility, and thus requires a fully coupled vehicle/track/foundation model. Next, a parametric study of ground vibrations generated by singular rail and wheel defects is undertaken. Six shapes of discontinuity are modelled, representing various defect types such as transition zones, switches, crossings, rail joints and wheel flats. The vehicle is modelled as an AM96 train set and it is found that ground vibration levels are highly sensitive to defect height, length and shape.     

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.     

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.