Elsevier

Journal of Sound and Vibration

Volume 331, Issue 19, 10 September 2012, Pages 4246-4258
Journal of Sound and Vibration

The influence of track modelling options on the simulation of rail vehicle dynamics

https://doi.org/10.1016/j.jsv.2012.04.024Get rights and content

Abstract

This paper investigates the effect of different models for track flexibility on the simulation of railway vehicle running dynamics on tangent and curved track. To this end, a multi-body model of the rail vehicle is defined including track flexibility effects on three levels of detail: a perfectly rigid pair of rails, a sectional track model and a three-dimensional finite element track model. The influence of the track model on the calculation of the nonlinear critical speed is pointed out and it is shown that neglecting the effect of track flexibility results in an overestimation of the critical speed by more than 10%. Vehicle response to stochastic excitation from track irregularity is also investigated, analysing the effect of track flexibility models on the vertical and lateral wheel–rail contact forces. Finally, the effect of the track model on the calculation of dynamic forces produced by wheel out-of-roundness is analysed, showing that peak dynamic loads are very sensitive to the track model used in the simulation.

Highlights

► We study the influence of track modelling options on rail vehicle dynamics simulation. ► Results obtained using different modelling options are compared. ► The use of a sectional track model may result in significant modelling inaccuracy. ► Simulation results of railway dynamics are highly sensitive to the track model.

Introduction

In modern railway engineering, the numerical simulation of running dynamics has become a major tool for ensuring appropriate vehicle performance in terms of vehicle stability and running safety, damage and irregular wear of the wheel and rail surfaces, and estimation of the vehicle’s load collectives [1]. This is normally based on the definition of detailed multi-body vehicle models [2], [3] representing to a fine level of detail the whole vehicle or even the entire train set (particularly in the case of articulated trains).

Although track flexibility is usually recognised to have an important effect on vehicle dynamics [3], simple track models are often used in vehicle dynamics studies. However, the implications of using a simplified track model in terms of its ability accurately to reproduce vehicle dynamics and wheel–rail contact forces are often left unaddressed or treated on a qualitative basis.

The aim of this paper is therefore to investigate the effect of different track models in train–track interaction modelling and simulations, and to clarify the implications of simplifying assumptions in modelling track flexibility. Defining the “correct model” for a given analysis would require extensive comparison with measurements, but this is not an easy task. Often this comparison is hampered by insufficient knowledge of model input data (particularly, rail profiles, track irregularity, suspension parameters, see [3]) and also by the limited bandwidth of the existing methods used to measure wheel–rail contact forces: these measurements in a frequency range up to 2 kHz are reported e.g., in [4], [5], but to the Authors’ knowledge no results were published showing the correct calibration of an instrumented wheelset in this frequency range. For these reasons, the approach followed in this paper is to compare numerical results obtained using track models with different levels of detail and analyse the sensitivity of simulation results to the track model adopted.

An examination of the state-of-the-art reveals a number of different approaches to representing track flexibility in vehicle dynamics calculations. Many papers deal with the coupled vibration of the train and of the railway track, usually referred to as “train–track interaction”, see the classical reviews [6], [7]: it is customary in these studies to use detailed track models, often based on the finite element method, coupled to simple vehicle models, normally neglecting the details of the vehicle’s suspension system or only considering the unsprung masses [5], [8], [9].

On the other hand, in vehicle dynamics studies the effect of track flexibility is either neglected or considered in a simplified way. Typically, simple sectional models are used in which the track under each wheelset is represented by lumped parameter systems travelling with the same speed as the vehicle, see e.g., Iwnicki et al. [10] and Chaar and Berg [11], [4], so that elasticity and inertia effects are accounted for in first approximation but the coupling of rail displacements under the different wheelsets and high-frequency track dynamics are neglected.

In [11] a hierarchy of lumped parameter models is proposed for the track and the implications of fitting calculated track receptance to measured receptance are analysed, while [4] proposes the use of space-dependent track stiffness and damping parameters approximately to reproduce the sleeper passing effect.

In this paper, three different levels of detail are considered for the track model: a perfectly rigid track, a simplified sectional model and a detailed three-dimensional finite element model. The effect of these track modelling options on vehicle dynamics is investigated with respect to the nonlinear critical speed of the vehicle, to the dynamic fluctuations of wheel–rail contact forces in tangent track and in curve, and to the effect of wheel out-of-roundness.

Despite the usual range of frequency for vehicle dynamics studies is 0–20 Hz, the vehicle+track model defined in this paper addresses a wider frequency range up to 300 Hz, to analyse the effect of intermediate and high frequency effects on wheel–rail contact forces which are of interest in the study of damage/wear phenomena and in the definition of vehicle load collectives. To this end, the vehicle model incorporates wheelset flexibility, including all the flexible wheelset modes falling at least in the 0–300 Hz frequency range.

The vehicle considered in this analysis is a distributed power EMU with maximum service speed of 250 km/h. The results obtained are shown to be highly sensitive to the degree of detail of the track model used, showing that the use of simplified assumptions on track modelling should be carefully considered and justified in the framework of train–track interaction analyses.

Section snippets

The mathematical model

In this study, a mathematical model is used to describe the vibration in the vertical and horizontal planes of a single railway vehicle running over a flexible track. The model is defined in the time domain to consider the nonlinear effects related to wheel–rail contact and nonlinear components in the vehicle suspensions. Two different sets of equations are written for the vehicle and for the track, coupled by the contact forces at the wheel–rail interface, which are expressed as function of

Vehicle critical speed

Rail vehicles may suffer from a self-excited vibration mechanism know as “hunting” and consisting of the combination of a lateral and yaw oscillation of the bogies [19]. The minimum vehicle speed at which the hunting vibration onsets is known as the “critical speed” of the vehicle.

Critical speed calculations are part of the design process of a railway vehicle and are performed either based on a linear stability analysis [19] or on nonlinear vehicle dynamic simulations performed in the time

Response to random track irregularity

This section presents the results of simulations in the presence of rail irregularity, pointing out the influence of different track modelling options on wheel–rail contact forces, which are important not only in terms of wear and damage phenomena in the rolling surfaces, but also for calculating the vehicle’s load collectives [1]. The two cases of tangent track running and curve negotiation are considered in subsections 4.1 and 4.2, respectively.

Track irregularity is introduced in the analysis

Effect of out-of-round wheels

Several causes have been identified for wheel out-of-roundness such as incorrect behaviour of the braking system or inhomogeneous tread material properties [26]. In this section the effect of wheel defects on wheel–rail contact forces is considered analysing the effect of different modelling options for both the wheelset and the track. Deviations from circularity can either be of a continuous nature, i.e., occurring along the entire wheel circumference, or localised, in which case they are

Conclusions

In this paper the effect of track modelling on rail vehicle dynamics simulations was analysed, focusing on stability analysis, on the vehicle’s response to stochastic excitation due to track irregularity and on the effect of wheel out-of-roundness.

As far as vehicle stability is concerned, it is shown that both the vehicle critical speed and the dominant frequency of the hunting motion are highly influenced by the degree of detail used in modelling track flexibility. Neglecting or considering a

References (26)

  • N. Chaar et al.

    Simulation of vehicle–track interaction with flexible wheelsets, moving track models and field test

    Vehicle System Dynamics

    (2006)
  • A.A. Shabana

    Vibration of Discrete and Continuous Systems

    (1996)
  • S. Bruni et al.

    A time domain model for the study of high frequency train–track interaction

    7th International Conference on Railway Bogies and Running Gears

    (2007)
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