Time-domain modelling of high-frequency wheel/rail interaction

The interaction between wheel and rail is the predominant source of noise emission from railway operations in a wide range of conventional speeds. On the one hand, this wheel/rail noise concerns rolling noise and impact noise caused by the vertical interaction excited by roughness and discrete irregularities of the wheel/rail running surfaces, respectively. On the other hand, it concerns squeal noise generated by the tangential interaction due to frictional instability. The aim of this thesis is to develop a model for the combined vertical and tangential wheel/rail interaction induced by roughness, discrete irregularities or frictional instability. This is the main step in the formulation of a combined prediction model for the three different types of wheel/rail noise, which can be used as a design tool for noise reduction. In order to include the non-linearities in the contact zone, the interaction model presented in this thesis is formulated in the time domain. Wheel and track models are represented by Green’s functions, which leads to a computationally efficient formulation and allows the inclusion of detailed contact models. A two-dimensional (2D) vertical contact model consisting of a bedding of independent springs, and a three-dimensional (3D) vertical and tangential model based on an influence-function method for the elastic half-space, are considered. Non-Hertzian and transient effects are taken into account. In the thesis, the vertical interaction model has been applied for excitation by wheel/rail roughness and by wheel flats. In the former case, the model has been validated against existing established models. In the latter case, encouraging agreement with field measurements has been found. Results from simulations carried out with both the 2D and the 3D contact models for excitation by detailed measured roughness data indicate that significant errors may occur in the calculated contact forces, when the 3D roughness distribution is represented by the roughness on only one longitudinal line. The errors increase with a decrease in roughness correlation across the width of the contact. Frictional instabilities during curve negotiation have been investigated with the combined vertical/tangential interaction model. For both a constant friction law and a friction curve falling with the sliding velocity, stick/slip oscillations were observed. While the model is not yet considered completely reliable in the case of a falling friction curve due to the possibility of multiple solutions, the results in the case of constant friction are in good qualitative agreement with previouslypublished findings on curve squeal

Model-based estimation of rail roughness from axle box acceleration

Monitoring rail roughness in the railway network allows directing grinding actions to where they are needed to reduce rolling noise and large wheel/rail forces. To be able to measure rail roughness on a large scale, indirect measurements onboard railway vehicles have to be carried out. Existing methods use either axle box acceleration (ABA) or under-coach noise measurements to monitor the rail roughness indirectly. The two main challenges with rail roughness estimation from vibroacoustic signals measured onboard vehicles are to separate wheel and rail roughness and to take into account varying track dynamics in the railway network. Both questions have not yet been addressed sufficiently. In this paper, an enhanced method for estimating rail roughness from ABA is presented. In contrast to all existing methods in the literature, the presented method operates in the time domain. A time-domain method has the advantage that the spatial variations of roughness become visible and paves the way for the detection of localized defects such as squats or deteriorated welds. The method is based on a previously developed time-domain model for high-frequency wheel/rail interaction and estimates the time series of the roughness from the time series of ABA. In a first step, the time series of the contact force is calculated from the axle box acceleration using a Least Mean Square algorithm for source identification. In a second step, the combined wheel/rail roughness is obtained from the contact force based on a non-linear Hertzian contact model and a convolutional approach to determine wheel and rail displacement. Separation of wheel and rail roughness is possible by cycle-averaging the contact force over a distance corresponding to the wheel perimeter and performing the second step separately for the part of the contact force originating from the wheel and the rail roughness, respectively. The method was tested for simulated ABA obtained from measured wheel and rail roughness. In the relevant wavelength range from 0.5 m to 5 mm, the rail roughness could be estimated with good accuracy for known track dynamics. Overall, deviations in 1/3-octave bands between estimated and actual roughness were below 1 dB. Only for low rail roughness, higher deviations of less than 2.6 dB occurred around the pinned-pinned resonance frequency. Uncertainties in the track parameters affect the roughness estimation, where the most critical parameter is the rail pad stiffness. A deviation of 20% in rail pad stiffness leads to deviations in the rail roughness of up to 3.5 dB in single 1/3-octave bands. The results illustrate the need to extend the method for the simultaneous extraction of track parameters and roughness from measured axle box acceleration

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 the small-scale roughness of rail and wheel, by parametric excitation on a discretely supported rail and by discrete irregularities of rail and wheel. Here, the model is applied to study the excitation caused by wheel flats by introducing a flat on a rotating wheel whose profile in the contact zone is updated in every time step. To demonstrate the functioning of the model, simulation results are compared to field measurements of impact forces and a brief parameter study is presented

The low-noise potential of low-vibration track

High-speed railway lines worldwide are increasingly built using slab-track technology, in which a reinforced concrete slab replaces the supporting function of traditional ballast and sleepers. The increased use, no longer limited to tunnels and bridges, is partly due to their lower maintenance, compact construction, and potential for effective isolation against ground-borne vibrations. However, rolling noise on slab tracks typically shows higher levels of noise radiation compared to ballasted tracks. There is an apparent conflict between ground-borne vibration and noise: The stiffness of the rail support determines if the vibrational energy is transmitted into the ground, exciting ground-borne vibrations, or stays in the rail, leading to higher noise radiation. In this work, a slab track construction type called low-vibration track is adapted such that both low vibrations and low noise radiation can be achieved without compromising. This is made possible by tuning the inertia of this system\u27s booted sleeper and its surrounding elasticity to provide a low support stiffness at low frequencies and a high stiffness in the range where the rail has a high radiation efficiency. It is found that the track decay rate, an indicator for the radiated noise from the rail, can be increased significantly above 300 Hz

The application of dither to mitigate curve squeal

Curve squeal is a highly disturbing tonal sound generated by rail vehicles like trains, metros or trams, when negotiating a sharp curve. The probability that squeal occurs increases with reduced curve radius of the track. Curve squeal noise is attributed to self-excited vibrations caused by stick/slip behaviour due to lateral creepage of the wheel tyre on the top of the rail. With respect to the large number of rolling stock units and the long lifetime of vehicles, there is an urgent need for a cheap and simple retrofitting measure to reduce curve squeal. Therefore, main objective of this paper is to investigate the potential to reduce curve squeal by means of active control in the form of dither in an efficient and robust way. Dither control has been applied in the field of mechanical engineering for systems including non-linear components. There it has been shown to suppress self-excited oscillations very efficiently. The control is an open-loop control. It consists in adding a forced vibration to the vibrational system. A time-domain model has been applied to investigate the mechanisms behind self-excited vibrations leading to curve squeal at the squealing noise rig at Chalmers University of Technology. The analysis showed, that in the presence of constant friction, the coupling between lateral and vertical direction is the driving mechanism for building up self-excited vibrations. Based on this insight, the potential of dither has been investigated. For the case considered here dither has the potential to reduce the overall kinetic energy on the wheel by more than 10 dB and on the rail by more than 20 dB. Further optimisation of dither forces with respect to the radiated sound power might increase this potential

The influence of contact modelling on simulated wheel/rail interaction due to wheel flats

Most available wheel/rail interaction models for the prediction of impact forces caused by wheel flats use a Hertzian spring as contact model and do not account for the changes in contact stiffness due to the real three-dimensional wheel flat geometry. In the literature, only little information is available on how this common simplification influences the calculation results. The aim of this paper is to study the influence of contact modelling on simulated impact forces due to wheel flats in order to determine the errors introduced by simplified approaches. For this purpose, the dynamic wheel/rail interaction is investigated with a time-domain model including a three-dimensional (3D) non-Hertzian contact model based on Kalker's variational method. The simulation results are compared with results obtained using a two-dimensional (2D) non-Hertzian contact model consisting of a Winkler bedding of independent springs or alternatively a single non-linear Hertzian contact spring. The relative displacement input to the Hertzian model is either the wheel profile deviation due to the wheel flat or the pre-calculated vertical wheel centre trajectory. Both the 2D model and the Hertzian spring with the wheel centre trajectory as input give rather similar results to the 3D model, the former having the tendency to slightly underestimate the maximum impact force and the latter to slightly overestimate. The Hertzian model with the wheel profile deviation as input can however lead to large errors in the result. Leaving aside this contact model, the correct modelling of the longitudinal geometry of the wheel flat is actually seen to have a larger influence on the maximum impact force than the choice of contact model

Simulation of rail roughness growth on small radius curves using a non-Hertzian and non-steady wheel–rail contact model

A time-domain model for the prediction of long-term growth of rail roughness (corrugation) on small radius curves is presented. Both low-frequency vehicle dynamics due to curving and high-frequency vehicle–track dynamics excited by short-wavelength rail irregularities are accounted for. The influence of non-Hertzian and non-steady effects in the wheel–rail contact model on rail wear is studied. The model features a contact detection method that accounts for wheelset yaw angle as well as surface irregularities and structural flexibilities of wheelset and rail. The development of corrugation on a small radius curve is found to be highly influenced by the wheel–rail friction coefficient. For vehicle speed 25 km/h and friction coefficient 0.3, predictions of long-term roughness growth on the low rail show decreasing magnitudes in the entire studied wavelength interval. For friction coefficient 0.6, roughness growth is found at several wavelengths. The corresponding calculation for the high rail contact of the trailing wheelset indicates no roughness growth independent of friction coefficient. The importance of accounting for the phase between the calculated wear and the present rail irregularity is demonstrated

On the efficient simulation of pass-by noise signals from railway wheels

The article presents an approach for calculating pass-by sound pressure radiated from railway wheels in the time domain using moving Green\u27s functions. The Green\u27s functions are obtained by using Finite Element (FE) and Boundary Element (BE) methods in the frequency domain, subsequent inverse Fourier transform, followed by convolution with a time series of rolling contact forces to obtain the pass-by time signals. However, traditional BE methods are computationally expensive due to the low structural damping of the wheel, necessitating a high frequency resolution. To overcome this issue, a modal approach is introduced in which the pass-by sound radiated by each wheel mode is calculated separately. This approach incorporates the dynamic response of the wheel in the time-domain processing and thus reduces the cost of the BE solution. A modal source signal is introduced to describe the excitation of each mode at each time step. The sound field radiated by unit modal amplitudes is calculated in BE and subsequently approximated by spherical harmonic (SH) equivalent sources, which allows for efficiently calculating acoustic transfer functions for varying relative positions of the wheel and a stationary receiver. Convolution of the source signal with the moving acoustic transfer function produces the pass-by pressure signal. The article investigates the directivity of the radiation from each mode and finds that most modes, including those with dominant radial deflection, radiate in mostly axial direction at high frequencies. Modes that dominate the pass-by pressure level are identified, both in frequency bands and with respect to the relative positioning of the wheel to the receiver. Finally, it is found that an SH expansion order of approximately 30 is required to satisfy the employed error measures, although lower orders may suffice for an auralisation of the signal