Modelling railway rolling noise

Abstract

Railways are a vital component of modern transportation systems and play a crucial role in achieving climate goals as an environmentally friendly means of travel. One key challenge for a shift to rail is railway noise. It arises from various sources, with rolling noise being the most significant at conventional train speeds. Existing prediction tools rely on various simplifications that potentially limit their accuracy. This thesis therefore aims to overcome this by developing a comprehensive simulation tool for rolling noise predictions by combining state-of-the-art numerical models of the wheel and the track, capable of accurate calculations up to high frequencies. Neglecting wheel rotation or simplifying it as a moving load is a commonly found modelling assumption. To investigate this effect, a rotating axisymmetric Finite Element model of the wheel has been developed. Results show that resonances in the frequency response of the rotating wheel split into two distinct peaks, with the separation depending on the mode type and train speed. These peaks correspond to co- and counter-rotating waves that do not have fixed nodal lines around the wheel circumference. In contrast, in a non-rotating wheel, these peaks do not separate, leading to standing waves with fixed nodal lines and partial decoupling of vibrations. Simplifying rotation by a moving load approximation only partially captures the peak separation.Using a Timoshenko beam to model the rail neglects cross-section deformation, which may be important, particularly at high frequencies. Therefore, a 2.5D Finite Element rail model has been implemented and coupled to an equivalent continuous support. The track frequency responses are analysed for different forcing conditions. It is shown that the vibration transmitted along the rail consists of several waves that dominate at different frequencies and distances from the excitation position, depending on the forcing location on the rail and the direction of the force. These waves include cross-section deformation as frequency increases and introduce vertical/lateral coupling due to torsion, which is not seen in a Timoshenko beam model. The 2.5D FE track model showed a good agreement with measurements in terms of the frequency responses and track decay rates.The rotating wheel model was coupled to an analytical model to calculate the sound radiation, while a 2.5D Boundary Element model of the track has been implemented for accurate high-frequency calculations that capture the effects of rail cross-section deformation. By introducing an interpolation method, calculation times are reduced by a factor of over 100, enabling efficient calculations of rail and sleeper sound power. It is shown that cross-section deformation can increase the sound power by over 10 dB for excitation with a vertical force. Larger differences occur for lateral forcing conditions, as the Timoshenko beam model does not account for rail torsion and foundation eccentricity. The sound radiation from the sleepers is modelled as a discrete set of radiators, showing that, in comparison with a rigidly vibrating sleeper, a flexible sleeper can increase sound power around the sleeper resonance frequencies. This is more relevant in a track with a stiffer rail pad, that increases the rail-on-pad resonance beyond the first few modal sleeper frequencies.The developed wheel and track models are coupled in an interaction model for roughness excitation, allowing for the vertical, lateral, longitudinal and spin degrees of freedom, and used to calculate rolling noise in terms of sound power in the frequency domain. The effects of some common modelling assumptions are quantified by comparing the current model with simplified track, wheel, and interaction models. The rolling noise calculations show that rail cross-section deformation increases the rail sound power by up to 6 dB at high frequencies in one-third octave band resolution. This increase is more relevant in a track with a soft rail pad, where the rail contribution remains significant in comparison with the wheel, even at high frequencies. A Timoshenko beam is therefore less suitable, in general, to predict rail sound radiation accurately. The sound power of the rotating wheel has up to 8 dB difference in one-third octave bands compared with the non-rotating wheel. The overall wheel sound power is increased by 2-3 dB at common train speeds if rotation is included. A moving load approximation reduces this difference to about 0.5 dB, making this a reasonable modelling simplification. Further, it is found that including coupling in the interaction model in longitudinal and spin direction yields small changes of up to 0.5 dB in wheel or rail sound power compared with only including vertical and lateral coupling.Finally, a sound propagation model has been introduced which allows the pass-by synthesis of rolling noise produced by a set of wheels moving along the track above a ground represented by an acoustic impedance. This enabled a comparison with measured pass-by noise to validate the model. The comparison showed the model can accurately predict the temporal evolution of rolling noise. The overall A-weighted level is predicted within up to 1 dB accuracy. In the one-third octave bands from 400 Hz to 8 kHz, the noise was underestimated by 2.6 dB and 2.2 dB on average for train speeds of 160 km/h and 80 km/h. Further validations of the full rolling noise model are desirable to determine the range of its applicability and confirm its robustness.

More information

Identifiers

ORCID for Christopher Knuth: orcid.org/0000-0003-4995-2179

ORCID for Giacomo Squicciarini: orcid.org/0000-0003-2437-6398

ORCID for David Thompson: orcid.org/0000-0002-7964-5906

Catalogue record

Export record