Modelling the acoustic performance of slab tracks

Transport is a major contributor to anthropogenic greenhouse gas emissions. Railway transport has a small footprint compared to other means of transport. This is one reason for the construction of new high-speed railway lines world-wide. These lines are often constructed using slab track technology, in which the traditional track configuration of concrete sleepers and ballast is replaced by concrete slabs. In earlier work, it has been found that traffic on slab tracks has higher noise emissions than on ballasted tracks. Rolling noise, radiated from wheels and track, is an important contributor to these noise emissions. To predict the acoustic performance of slab tracks, first, a model for the high-frequency vibration in these tracks is necessary, for which there is currently no standard solution. Further, the effect of the reflective slab track surface on the wheel radiation has not been researched.In this work, a model for the high-frequency vibrations and acoustic radiation of slab tracks has been developed and implemented. The validity of the dynamic model has been tested on a full-scale test rig. The developed model was then used for researching the influence of track parameters on noise emission. In this investigation, the rail pad stiffness was identified to have a major influence. Besides, a model for the sound radiation of railway wheels over hard reflective surfaces was developed, implemented, and validated. The effect of the slab track surface on the radiation efficiency of the vibrating wheel was evaluated and found negligible. The developed models are steps towards predicting the rolling noise generated by rail vehicles on slab tracks, which is significant both for the planning of new lines and the investigation of potential abatement measures

Towards time-domain modelling of wheel/rail noise: Effect of the dynamic track model

Transient events in railway rolling noise, such as the characteristic impulsive noise at switches and crossings, can significantlycontribute to the perceived annoyance, despite being difficult to detect in the standard frequency-domain methods to analyserolling noise. Studying these transient effects and their perception requires predicting the noise in the time domain. Whileseveral time-domain approaches exist for predicting the dynamic interaction of wheel and rail, predicting the associated rollingnoise with adequate accuracy is computationally costly. The lack of a model for transient noise and the need for studying itsperception was recently identified. Aiming for a comprehensive time-domain radiation model that includes the wheel andtrack contributions to rolling noise, this work focuses on the track radiation. The modelling approach taken here is based on a2.5D formulation for the acoustic radiation and moving Green’s functions in the air. The computational cost, which lies mainlyin the 2.5D BE calculations, is addressed by pre-calculating acoustic transfer functions. These transfer functions can becombined with different dynamic track models. Different dynamic track models in turn affect radiated soundfield in differentways. Here, the soundfields produced by six different track models are compared, including different support types andanalytical and numerical rail models. Several descriptors of the soundfield are analysed. In terms of the radiated sound powerand radiation efficiency, modelling the rail as a simple beam leads to similar results as elaborate numerical models up to about5 kHz. In terms of the track-side sound pressure, simple beam models can provide similar results only up to 2.5 kHz. Euler-Bernoulli (E-B) beams seem unfit for time-domain predictions of the radiated noise as they over-estimate the bending wavespeed at high frequencies. The results also show that the standard track decay rate (TDR) and the decay of acoustic soundpressure along the track are comparable

Simulating rolling noise on ballasted and slab tracks: vibration, radiation, and pass-by signals

Shifting to rail-bound freight and passenger traffic is key in Europe\u27s strategy towards transport decarbonisation. However, increasing railway traffic can increase environmental noise pollution. Rolling noise is often the dominant noise source. It originates from the interaction of the rough running surfaces of wheel and rail. Predicting rolling noise and performing acoustic optimisation of existing and new tracks requires validated, flexible, and physics-based prediction tools. This is especially relevant for the different designs of ballastless tracks, which are increasingly used for high-speed lines. Therefore, this thesis aims to develop and implement a modelling approach for rolling noise in the time and frequency domain to increase understanding of sound radiation, investigate noise mitigation measures, and allow research of the perception of transients in rolling noise.To achieve this, models for vibration in wheels and several types of ballasted and slab tracks have been implemented using the Waveguide Finite Element method. This method allows an efficient prediction of the track vibration up to high frequencies. Next, models for the sound radiation from wheel and track were implemented using adaptions of the Boundary Element method (BEM), such as the Fourier series BEM and the wavenumber domain BEM.The computational efficiency was addressed in multiple ways. Finally, an approach to simulate the sound produced at a stationary track-side receiver has been developed and implemented based on moving Green\u27s functions. The simulations were largely implemented in in-house Python code. The ballasted and slab track dynamic models have been tuned and compared with measurements on full-scale tracks.The developed models have been used to analyse the vibrations in track and wheel and the acoustic radiation from these vibrations. This allowed the investigation of noise mitigation measures. Further, the necessary complexity of the dynamic track model for predicting rolling noise in time domain was investigated. Two parameter studies were carried out with a focus on track design with lower noise emission. Slab tracks with booted sleepers showed a potential for noise reduction without increasing loads on the track structure. A continuous rail support lowered the radiated sound power at high frequencies. The contributions of different wheel modes to the radiated sound were investigated considering the directivity of each mode, and dominant modes were identified. The established models produce time signals usable for auralisation, which, among others, has the potential to research human perception of transients in rolling noise

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

A time-domain model for railway rolling noise

The poster presents a modelling approach for railway rolling noise prediction developed at Chalmers during a recent PhD project. Rolling noise, which is caused by the roughness-excited vibration of the wheel and the track, is the dominant noise source in a wide range of vehicle speeds. The presented modelling approach is based on the time-domain, non-linear contact model WERAN. The model has been extended with a numerically efficient description of the structural vibration of the wheel and the track based on moving Green\u27s functions. Further, efficient models for the sound radiation from the wheel and track were developed and implemented, again using a Green\u27s functions approach. The Green\u27s functions are computed using combinations of the Waveguide Finite Element method (2.5D FE), the Wavenumber domain Boundary Element Method (WBEM / 2.5D BE), the Fourier domain BEM (FBEM), and spherical harmonics equivalent sources. This model provides a physics-based, time-domain description of the radiated sound based on the combined roughness between the wheel and the rail. There are several possible applications for a time-domain rolling noise model, for example in component design, condition monitoring, and, by auralising the noise, as an effective tool for communication with a broader public

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

Sound Radiation from Railway Wheels including Ground Reflections: A half-space formulation for the Fourier Boundary Element Method

Current models for the acoustic radiation from railway wheels assume free field radiation. However, slab tracks are increasingly used for new railway lines. The acoustically hard surface of those tracks makes a re-evaluation of the free field assumption relevant, as such a surface can affect the radiation efficiency of an acoustic radiator. The wheel as the acoustic radiator is most conveniently described in a cylindrical coordinate system, thus making use of its axisymmetry. While this is a viable solution for the structural vibrations, for instance by using the curved Waveguide Finite Element formulation, the axisymmetry breaks when including a reflective plane in the calculation of the acoustic radiation. A convenient method to include an infinitely large, reflective plane is by using half-space Green’s functions in combination with the Boundary Element method. This method can be formulated in cylindrical coordinates using the Fourier series BEM (FBEM). However, the FBEM has not yet been combined with half-space Green’s functions. This paper provides a half-space formulation for the FBEM, which enables e.g. the evaluation of sound radiation of railway wheels over reflective surfaces. Finally, it is shown that the assumption of free field radiation for railway wheels is valid, as there is no major contribution of the reflective plane to the radiation efficiency of the wheel. The developed method is validated against laboratory measurements as well as analytical models

Calibration and validation of the dynamic response of two slab track models using data from a full-scale test rig

For the development of accurate and reliable simulation models, the procedure of calibration and validation against measurement data is essential. In this paper, a finite element model and a waveguide finite element model of a slab track are calibrated and validated against hammer impact measurement data from a full-scale test rig. The finite element model is three-dimensional, where the rails are modelled as Rayleigh–Timoshenko beams and the concrete slab and support layer are modelled using linear shell elements. In the waveguide finite element model, a constant track cross-section described by two-dimensional finite elements is assumed, and the vibration in the direction perpendicular to the cross-section is described by propagating waves that are decaying exponentially. Measured frequency response functions (FRFs) are compared with the corresponding calculated FRFs from the two modelling approaches. The calibration is conducted in two steps using (i) a parameter study and (ii) a genetic algorithm. For multiple excitation positions and sensor locations, both calibrated models capture the trend of the Single-Input Multiple-Output measurements with rather small deviations compared to the overall dynamic range. This implies that both models can successfully represent the dynamic response of the test rig and can be considered as validated

TOWARDS TIME-DOMAIN MODELLING OF WHEEL/RAIL NOISE: EFFECT OF THE DYNAMIC TRACK MODEL

Transient events in railway rolling noise, such as the characteristic impulsive noise at switches and crossings, can significantly contribute to the perceived annoyance, despite being difficult to detect in the standard frequency-domain methods to analyse rolling noise. Studying these transient effects and their perception requires predicting the noise in time-domain. While several time-domain approaches exist for predicting the dynamic interaction of wheel and rail, predicting the associated rolling noise with adequate accuracy is computationally costly. The lack of a model for transient noise and the need for studying its perception were recently identified. Aiming for a comprehensive time-domain radiation model that includes the wheel and track contributions to rolling noise, this work focusses on the track radiation. The modelling approach taken here is based on a 2.5D formulation for the acoustic radiation and moving Green\u27s functions in air. The computational cost, which lies mainly in the 2.5D BE calculations, is addressed by pre-calculating acoustic transfer functions. These transfer functions can be combined with different dynamic track models. Different dynamic track models in turn affect radiated sound field in different ways. Here, the sound fields produced by six different track models are compared, including different support types and analytical and numerical rail models. Several descriptors of the sound field are analysed. In terms of the radiated sound power and radiation efficiency, modelling the rail as a simple beam leads to similar results as elaborate numerical models up to about 5 kHz. In terms of the track-side sound pressure, simple beam models can provide similar results only up to 2.5 kHz. Euler-Bernoulli beams seem unfit for time-domain predictions of the radiated noise as they overestimate the bending wave speed at high frequencies. The results also show that the standard track decay rate and the decay of acoustic sound pressure along the track are comparable