Luis Baeza

High frequency railway vehicle-track dynamics through flexible rotating wheelsets

Some railway problems, such as the corrugation of rails or the impact caused by a wheelflat, are associated with a vehicle–track coupled dynamic phenomenon. Models for the analysis of these problems must account for the structural vibrations of the track components (rails and sleepers), but the most adequate approach for the wheelset has not been sufficiently investigated until present. The wheelset can be considered as an undeformable solid, as an elastic structure where the rotation effects are neglected, or as a rotating flexible solid. In order to fill this gap, this article presents a methodology to use the structural vibrations of a rotating wheelset in high-frequency railway dynamics analyses. The model makes use of Eulerian modal coordinates, a formulation that provides very low computational cost. The method is applied in this article to a wheelflat impact calculation and a vehicle running on a corrugated track. The results show the importance of the more realistic model in the simulations, mainly in certain frequencies.

PACDIN statement of methods

PAntograph–Catenary Dynamic Interaction (PACDIN) is a code developed by the vehicle technology research centre (CITV) of the Universitat Politècnica de València in collaboration with the railway company Talgo S.L. The model of the catenary is a finite element model using absolute nodal coordinates. It is based on a general formulation that can be applied for analysing a wide range of catenary configurations, including stitch wire, transitions or non-straight path tracks. The formulation is fully non-linear and includes large deformations, dropper slackening and contact interaction. The model is linearised when deformations are small, as in the case of the benchmark dynamic analysis. The results of the PACDIN code show a good agreement with the average results of other benchmark codes.

Dynamics of a truss structure and its moving-oscillator exciter with separation and impact-reattachment

The dynamic response of a stationary structure excited by a moving structure is studied in this paper. The stationary structure is in the form of a truss made of a number of rigidly connected Timoshenko beams, while the moving structure consists of two masses linked by a spring and a dashpot (oscillator). To facilitate the mathematical model of the moving-load dynamics of the whole system, the frequencies and modes of the stationary structure are first obtained by the finite-element method and then they are cast in an analytical form within each element through the element shape functions. This is a distinct advantage of this paper. Each component beam of the stationary structure is meshed with an adaptable number of Timoshenko beam elements to allow efficient modelling of the vibration of the structure for a wide range of travelling speeds of the moving oscillator. During the horizontal travel and vertical vibration of the oscillator, it may separate from the vibrating stationary structure and subsequently may reattach to the stationary structure with impact. These two phenomena have been studied in only a few papers for simple moving-load problems in the past and have never been studied for the present problem. It is found through simulated examples that the dynamic response at high speeds can be several times higher than the relevant static response, and separation and reattachment with impact produce a noticeable difference in the dynamic response. Multiple separation and impact events are possible at high speeds. It is also interesting to observe that separation may occur at high subcritical speeds and impact at various values of the coefficient of restitution has mild local influence on the dynamic response after reattachment.

Rail corrugation growth accounting for the flexibility and rotation of the wheel set and the non-Hertzian and non-steady-state effects at contact patch

In this work, a simulation tool is developed to analyse the growth of rail corrugation consisting of several models connected in a feedback loop in order to account for both the short-term dynamic vehicle–track interaction and the long-term damage. The time-domain vehicle–track interaction model comprises a flexible rotating wheel set model, a cyclic track model based on a substructuring technique and a non-Hertzian and non-steady-state three-dimensional wheel–rail contact model, based on the variational theory by Kalker. Wear calculation is performed with Archards wear model by using the contact parameters obtained with the non-Hertzian and non-steady-state three-dimensional contact model. The aim of this paper is to analyse the influence of the excitation of two coinciding resonances of the flexible rotating wheel set on the rail corrugation growth in the frequency range from 20 to 1500 Hz, when contact conditions similar to those that can arise while a wheel set is negotiating a gentle curve are simulated. Numerical results show that rail corrugation grows only on the low rail for two cases in which two different modes of the rotating wheel set coincide in frequency. In the first case, identified by using the Campbell diagram, the excitation of both the backward wheel mode and the forward third bending mode of the wheel set model (B-F modes) promotes the growth of rail corrugation with a wavelength of 110 mm for a vehicle velocity of 142 km/h. In the second case, the excitation of both the backward wheel mode and the backward third bending mode (B-B modes) gives rise to rail corrugation growth at a wavelength of 156 mm when the vehicle velocity is 198 km/h.

Influence of the wheel-rail contact instationary process on contact parameters

The rapid convergence of the tangential rolling contact parameters to their stationary values, combined with the high computational cost associated with calculations using instationary models, has meant that stationary models are usually employed in railway dynamics. However, the validity of stationary models when the applied contact conditions are subjected to rapid changes has not been sufficiently investigated. With the objective of deducing the effects of the evolution of the instationary process on the contact parameters, the tangential contact problem is solved for a set of reference conditions. For this purpose a calculation model is adapted, from which it is possible to analyse the evolution of the contact parameters when the forces exerted between rail and wheel are subjected to rapid changes. From the calculations made, situations impossible to simulate by means of stationary theories are obtained according to the frequency of variation in the forces, such as slip zones in the leading edge of the contact area and reverse contact (locally, the traction field is opposite to the direction of the external force transmitted to the contact).

Error estimation and h-adaptive refinement in the analysis of natural frequencies

This paper deals with the estimation of the discretization error and the definition of an optimum h-adaptive process in the finite element analysis of natural frequencies and modes. Consistent and lumped mass matrices are considered. In the first case, the discretization error essentially proceeds from the stiffness modelization, so it is possible to apply the same error estimators than those considered in static problems. On the other hand, the error associated with the modelization of the inertial properties must be taken into account if lumped mass matrices are used. As far as h-adaptivity is concerned, it is usually interesting to obtain meshes with a specified error for each mode. However, traditional criteria for static problems consider only one load case. Defining the optimum mesh as the one that gets the desired error with the minimum number of elements, a method is proposed for the h-adaptive process taking into account a set of natural modes simultaneously. The proposed methods have been validated by applying them to bi-dimensional test problems.

Non-steady state modelling of wheel–rail contact problem

Among all the algorithms to solve the wheel–rail contact problem, Kalkers 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 Kalkers Variational Method for rolling contact.

A State-of-the-Art Review of Curve Squeal Noise: Phenomena, Mechanisms, Modelling and Mitigation

Curve squeal is an intense tonal noise occurring when a rail vehicle negotiates a sharp curve. The phenomenon can be considered to be chaotic, with a widely differing likelihood of occurrence on different days or even times of day. The term curve squeal may include several different phenomena with a wide range of dominant frequencies and potentially different excitation mechanisms. This review addresses the different squeal phenomena and the approaches used to model squeal noise; both time-domain and frequency-domain approaches are discussed and compared. Supporting measurements using test rigs and field tests are also summarised. A particular aspect that is addressed is the excitation mechanism. Two mechanisms have mainly been considered in previous publications. In many early papers the squeal was supposed to be generated by the so-called falling friction characteristic in which the friction coefficient reduces with increasing sliding velocity. More recently the mode coupling mechanism has been raised as an alternative. These two mechanisms are explained and compared and the evidence for each is discussed. Finally, a short review is given of mitigation measures and some suggestions are offered for why these are not always successful.

Modelling of railway curve squeal including effects of wheel rotation

Railway vehicles negotiating tight curves may emit an intense high-pitch noise. The underlying mechanisms of this squeal noise are still a subject of research. Simulation models are complex since they have to consider the non-linear, transient and high-frequency interaction between wheel and rail. Often simplified models are used for wheel and rail to reduce computational effort, which involves the risk of over-simplifications. This paper focuses on the importance to include a rotating wheel instead of a stationary wheel in the simulation models. Two formulations for a rotating wheel are implemented in a previously published wheel/rail interaction model: a realistic model based on an Eulerian modal coordinate approach and a simplified model based on a rotating load and moving Green’s functions. The simulation results for different friction coefficients and values of lateral creepage are compared with results obtained for the stationary wheel. Both approaches for the rotating wheel give almost identical results for the rolling speed considered. Furthermore, it can be concluded that a model of a stationary flexible wheel is sufficient for both capturing the tendency to squeal and predicting the resulting wheel/rail contact forces.

Simulation of the evolution of rail corrugation using a rotating flexible wheelset model

This paper presents a simulation tool designed for predicting the wear pattern on the running surface of the rails and for studying the evolution of rail corrugation after thousands of wheelset passages. This simulation tool implements a cyclic track model, a rotating flexible wheelset model, a wheel–rail contact model and a wear model. The vehicle–track system is modelled by using a substructuring technique, by which the vehicle, the rails and the sleepers are treated independently of each other and are coupled by the forces transmitted through the wheel–rail contact and the railpad. The vehicle model takes only account of the wheelset since the sprung masses of the vehicle are not relevant in the frequency range analysed. The wheelset model considers the flexibility of the wheelset and the effects associated with rotation. By using the Campbell diagram, two cases have been identified in which the combined effect of two different modes may give rise to higher wheel–rail contact forces and wear.