Astrid Pieringer

A fast time‐domain model for wheel/rail interaction demonstrated for the case of impact forces caused by wheel flats

The prediction of impact forces caused by wheel flats requires the application of time‐domain models that are generally more computationally demanding than are frequency‐domain models. In this paper, a fast time‐domain model is presented to simulate the dynamic interaction between wheel and rail, taking into account the non‐linear processes in the contact zone. Track and wheel are described as linear systems using impulse‐response functions that can be precalculated. The contact zone is modelled by non‐linear contact springs, allowing for loss of contact. This general model enables the calculation of the vertical contact forces generated by any kind of roughness excitation between wheel and rail. Here, the model is adapted to the excitation caused by wheel flats by introducing the irregular wheel shape as a form of extreme roughness. A brief parameter study is presented to demonstrate the functioning of the model. The results from the model are discussed and compared with results from literature.

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.

Towards an engineering model for curve squeal

Curve squeal is a strong tonal noise that may arise when a railway vehicle negotiates a curve. The wheel/rail contact model is the central part of prediction models, describing the frictional instability occurring in the contact during squeal. A previously developed time-domain squeal model considers the wheel and rail dynamics, and the wheel/rail contact is solved using Kalker’s nonlinear transient CONTACT algorithm with Coulomb friction. In this paper, contact models with different degree of simplification are compared to CONTACT within the previously developed squeal model in order to determine a suitable contact algorithm for an engineering curve squeal model. Kalker’s steady-state FASTSIM is evaluated, and, without further modification, shows unsatisfying results. An alternative transient single-point contact algorithm named SPOINT is formulated with the friction model derived from CONTACT. Compared to the original model results, the SPOINT implementation results are promising and similar to results from CONTACT.

A Time Domain Model for Wheel/Rail Interaction Aiming to Include Non-linear Contact Stiffness and Tangential Friction

A time domain model is presented for the dynamic interaction between a railway wheel and rail, which takes into account the non-linear processes in the contact zone and aims at predicting both normal and tangential contact forces. The model follows an approach that has been used successfully, for instance for the modelling of the interaction between road and tyre. Track and wheel are described as linear systems by the means of impulse response functions. The contact zone is modelled by non-linear contact springs with stiffnesses depending on the roughness of rail and wheel. Here, the method of the area of real contact is applied in order to obtain the required spring characteristics. For the tangential contact, a characteristic function for the friction coefficient is applied. In a first stage, the approach is demonstrated for the calculation of normal contact forces. For validation, the results from the model are compared with an existing time domain model that itself has been validated by field testing. Very good agreement is found for different types of roughness excitation.

A time-domain model for coupled vertical and tangential wheel/rail interaction - a contribution to the modelling of curve squeal

Lateral forces due to frictional instability are seen as the main reason for the occurrence of curve squeal. Predicting squeal requires thus to describe the high-frequency wheel/rail interaction during curving including the coupling between vertical and lateral directions. In this article, a time-domain approach is presented which includes both vertical and lateral forces and takes into account the non-linear processes in the contact zone. Track and wheel are described as linear systems using pre-calculated impulse response functions. The non-linear, non-steady state contact model is based on an influence function method for the elastic half-space, includes a velocity-dependent friction coefficient and accounts for surface roughness. First results from the interaction model demonstrate the functioning of the approach.

Investigation of railway curve squeal using a combination of frequency- and time-domain models

Railway curve squeal arises from self-excited vibrations during curving. In this paper, a frequency- and a time-domain approach for curve squeal are compared. In particular, the capability of the frequency-domain model to predict the onset of squeal and the squeal frequencies is studied. In the frequency-domain model, linear stability is investigated through complex eigenvalue analysis. The time-domain model is based on a Green’s function approach and uses a convolution procedure to obtain the system response. To ensure comparability, the same submodels are implemented in both squeal models. The structural flexibility of a rotating wheel is modelled by adopting Eulerian coordinates. To account for the moving wheel–rail contact load, the so-called moving element method is used to model the track. The local friction characteristics in the contact zone are modelled in accordance with Coulomb’s law with a constant friction coefficient. The frictional instability arises due to geometrical coupling. In the time-domain model, Kalker’s non-linear, non-steady state rolling contact model including the algorithms NORM and TANG for normal and tangential contact, respectively, is solved in each time step. In the frequency-domain model, the normal wheel/rail contact is modelled by a linearization of the force-displacement relation obtained with NORM around the quasi-static state and full-slip conditions are considered in the tangential direction. Conditions similar to those of a curve on the Stockholm metro exposed to severe curve squeal are studied with both squeal models. The influence of the wheel-rail friction coefficient and the direction of the resulting creep force on the occurrence of squeal is investigated for vanishing train speed. Results from both models are similar in terms of the instability range in the parameter space and the predicted squeal frequencies.