Correlation between rolling noise generation and rail roughness of tangent tracks and curves in time and frequency domains

Despite considerable advantages of the railway track over other means of transportation, noise pollution is the main adverse consequence of railway transportation. The basic cause of railway noise is rail corrugation. Although characteristics of railway noise have been considerably studied in the literature, rail corrugation effects on rolling noise generation in tangent tracks and the curves have not been sufficiently investigated. This research addresses the limitations of the current understanding of the rolling noise generation by investigating rail corrugation effects on rolling noise in tangent tracks and curves. This research was made based on the results obtained form a thorough field investigation carried out in a railway line which includes tangents tracks and sharp curves. A track geometry recording car was used to measure rail corrugations. For this purpose, an indirect method was developed in this research to obtain rail corrugation patterns from the data recorded by the track recording car. The effectiveness of the new method was shown. The induced noises were recorded using two particular types of microphones and implementing the method suggested by the ISO 3095 Standard. The rolling noise signal was distinguished from the total noise, using Butterworth Band-Pass Filtering. The role of rail corrugations in the rolling noise was discussed. Correlations were made between various types of corrugations and the induced noises. The results were presented and discussed in the spatial and frequency scales. Results obtained have led to new findings in rail corrugation effects on rolling noise generation. This research paves a way toward a better understanding of rolling noise sources and the parameters influencing the noise.     

A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset-track system

The present work proposes friction coupling at the wheel-rail interface as the mechanism for formation of rail corrugation. Stability of a wheelset-track system is studied using the finite element complex eigenvalue method. Two models for a wheelset-track system on a tight curved track and on a straight track are established. In these two models, motion of the wheelset is coupled with that of the rail by friction. Creep force at the interface is assumed to become saturated and approximately equal to friction force, which is equal to the normal contact force multiplied by dynamic coefficient of friction. The rail is supported by vertical and lateral springs and dampers at the positions of sleepers. Numerical results show that there is a strong propensity of self-excited vibration of the wheelset-track system when the friction coefficient is larger than 0.21. Some unstable frequencies fall in the range 60-1200 Hz, which correspond to frequencies of rail corrugation. Parameter sensitivity analysis shows that the dynamic coefficient of friction, spring stiffness and damping of the sleeper supports all have important influences on the rail corrugation formation. Bringing the friction coefficient below a certain level can suppress or eliminate rail corrugation.     

Numerical prediction of rail roughness growth on tangent railway tracks

Growth of railhead roughness (irregularities, waviness) is predicted through numerical simulation of dynamic train-track interaction on tangent track. The hypothesis is that wear is caused by longitudinal slip due to driven wheelsets, and that wear is proportional to the longitudinal frictional power in the contact patch. Emanating from an initial roughness spectrum corresponding to a new or a recent ground rail, an initial roughness profile is determined. Wheel-rail contact forces, creepages and wear for one wheelset passage are calculated in relation to location along a discretely supported track model. The calculated wear is scaled by a chosen number of wheelset passages, and is then added to the initial roughness profile. Field observations of rail corrugation on a Dutch track are used to validate the simulation model. Results from the simulations predict a large roughness growth rate for wavelengths around 30-40 mm. The large growth in this wavelength interval is explained by a low track receptance near the sleepers around the pinned-pinned resonance frequency, in combination with a large number of driven passenger wheelset passages at uniform speed. The agreement between simulations and field measurements is good with respect to dominating roughness wavelength and annual wear rate. Remedies for reducing roughness growth are discussed.     

Wheel/rail noise generation due to nonlinear effects and parametric excitation

Two models are developed, one in the time domain and another in the frequency domain, to explain when a wheel/rail noise generation model requires the inclusion of discrete supports, parametric excitation, and the nonlinear contact spring. Numerical simulations indicate the inclusion of discrete supports to describe low frequency response, and also at higher frequencies, especially where the rail is very smooth or has a corrugation/wavelength corresponding to the pinned-pinned frequency. With a corrugation, it may become essential to include the nonlinear contact spring, as contact loss occurs at high corrugation amplitudes. As nonlinearity causes force generation over a broad frequency range, some contributions excite wheel resonances, resulting in high radiation levels, that require the inclusion of wheel/rail nonlinear effects and parametric excitation for accurate prediction.     

Prediction of rail corrugation using a rotating flexible wheelset coupled with a flexible track model and a non-Hertzian/non-steady contact model

This paper presents a model for simulating vehicle–track interaction at high frequencies for investigations of rail roughness growth. The dynamic interaction model developed employs a substructuring technique and the whole system consists of a number of substructures that can be modelled independently. The systems are coupled through the forces at the wheel–rail contact and the railpad. A coupled, rotating flexible wheelset, a flexible track model and a non-Hertzian/non-steady contact model have been implemented and results are presented here for a free wheelset on a symmetrical track system with initial random and sinusoidal roughness. Both rigid and flexible wheelsets are considered.     

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

A new method is proposed as a solution for the large-scale coupled vehicle–track dynamic model with nonlinear wheel–rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle–track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.     

Dynamic instability of a wheel moving on a discretely supported infinite rail

The parametric instability of a wheel moving on a discretely supported rail is discussed. To achieve this, an analysis method is developed for a quasi-steady-state problem which can represent an exponential growth of oscillation. The temporal Fourier transform of the rail motion is expanded by a Fourier series with respect to the longitudinal coordinate, and then the response of the rail deflection due to a quasi-harmonic moving load is derived. The wheel/track interaction is formulated by the aid of this function and reduced to an infinite system of linear equations for the Fourier coefficients of the contact force. The critical velocities between the stable and unstable states are calculated based on the nontrivial condition of the homogeneous matrix equation. Through these analyses the influences of the modeling of rail and rail support on the unstable speed range are examined. Moreover, not only the first instability zone but also other zones are evaluated.     

A rational fraction polynomials model to study vertical dynamic wheel–rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel–rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel–rail contact passing over a welding defect at different speeds.     

The influence of track modelling options on the simulation of rail vehicle dynamics

This paper investigates the effect of different models for track flexibility on the simulation of railway vehicle running dynamics on tangent and curved track. To this end, a multi-body model of the rail vehicle is defined including track flexibility effects on three levels of detail: a perfectly rigid pair of rails, a sectional track model and a three-dimensional finite element track model. The influence of the track model on the calculation of the nonlinear critical speed is pointed out and it is shown that neglecting the effect of track flexibility results in an overestimation of the critical speed by more than 10%. Vehicle response to stochastic excitation from track irregularity is also investigated, analysing the effect of track flexibility models on the vertical and lateral wheel–rail contact forces. Finally, the effect of the track model on the calculation of dynamic forces produced by wheel out-of-roundness is analysed, showing that peak dynamic loads are very sensitive to the track model used in the simulation.     

A dynamic model for an asymmetrical vehicle/track system

A finite element model to simulate an asymmetrical vehicle/track dynamic system is proposed in this paper. This model consists of a 10-degree-of-freedom (d.o.f.) vehicle model, a track model with two rails, and an adaptive wheel/rail contact model. The surface defects of wheels and rails can be simulated with their geometry and an endless track model is adopted in the model. All time histories of forces, displacements, velocities and accelerations of all components of the vehicle and track can be obtained simultaneously. By using this model, one can study the effect that wheel/rail interaction from one side of the model has on the other. This can be done for many asymmetrical cases that are common in railway practice such as a wheel flat, wheel shelling, out-of-round wheel, fatigued rail, corrugated rail, head-crushed rail, rail joints, wheel/rail roughness, etc. Only two solutions are reported in this paper: steady state interaction and a wheel flat.     

Stimulation of the local growth of aligned carbon nanotubes by pulse laser exposure of the substrate

The local stimulation of carbon nanotubes (CNT) growth at the laser-modified sites that have been obtained by excimer laser irradiation at 248 nm causing a local surface modification has been investigated by two different processing methods. The influence of the laser processing parameters on the CNT growth is compared for the irradiation of thin spin-coated iron nitrate films on silicon substrates and the backside irradiation of a fused silica substrate being in contact with an iron nitrate solution. Both techniques cause the formation of catalytic surface sites either by decomposition of the film or by deposition from the solution. For both laser modification approaches the local growth of vertical aligned nanotubes has been observed. In the case of spin-coated film the laser irradiation conditions have only a small influence on the CNT growth whereas at backside modification by means of a solution a strong dependence on the laser processing parameters has been found.     

The effects on noise of changes in wheel/rail system parameters

An analytical model has been developed that simulates the generation and propagation of wheel/rail noise. In the model, wheel/rail vibrations are induced by running surface roughness. The vibration responses are determined from considering contact stiffness effects and wheel/rail impedance interactions. Near field sound power levels are then calculated by combining the responses with radiation efficiencies, space-averaging the velocity squared on the wheel, and accounting for the decay of vibration along the rail. Finally, the noise levels predicted for the wayside are obtained from an analysis of the propagation that includes the effect of finite ground impedance. Good agreement exists between the analytical model and a series of validation measurements taken at DOT's Transportation Test Center in Pueblo, Colorado. A sensitivity analysis conducted for the parameters of a typical baseline system achieved significant changes in rolling noise only for reductions in wheel/rail contact stiffness, increases in wheel/rail contact area, and decreases in wheel/rail roughness through wheel truing and rail grinding.     

Application of MetaRail railway noise measurement methodology: comparison of three track systems

Within the fourth RTD Framework Programme, the European Union has supported a research project dealing with the improvement of railway noise (emission) measurement methodologies. This project was called MetaRail and proposed a number of procedures and methods to decrease systematic measurement errors and to increase reproducibility. In 1999 the Austrian Federal Railways installed 1000 m of test track to explore the long-term behaviour of three different ballast track systems. This test included track stability, rail forces and ballast forces, as well as vibration transmission and noise emission. The noise study was carried out using the experience and methods developed within MetaRail. This includes rail roughness measurements as well as measurements of vertical railhead, sleeper and ballast vibration in parallel with the noise emission measurement with a single microphone at a distance of 7.5 m from the track. Using a test train with block- and disc-braked vehicles helped to control operational conditions and indicated the influence of different wheel roughness.It has been shown that the parallel recording of several vibration signals together with the noise signal makes it possible to evaluate the contributions of car body, sleeper, track and wheel sources to the overall noise emission. It must be stressed that this method is not focused as is a microphone-array. However, this methodology is far easier to apply and thus cheaper. Within this study, noise emission was allocated to the different elements to answer questions such as whether the sleeper eigenfrequency is transmitted into the rail.     

Gravitational Instability of a Thermally Conducting Plasma in an Oblique Magnetic Field

The combined influence of the effects of Hall currents, magnetic resistivity and viscosity have been studied on the gravitational instability of a thermally conducting homogeneous unbounded plasma in an oblique magnetic field. The solution has been obtained through the normal mode technique and the dispersion relation has been derived. It is shown that the Jeans' criterion for gravitational instability remains unchanged. Solving numerically the dispersion relation, the dependence of the growth rate of the gravitational unstable mode on the considered physical effects has been obtained for an astrophysical situation. For conditions prevailing in the magnetized collapsing clouds, the numerical calculations for the plot of growth rate against wave number has been obtained for several values of the parameters characterizing Hall currents magnetic resistivity viscosity thermal conductivity. It is found that magnetic resistivity and thermal conductivity have destabilizing influence while viscosity has stabilizing influence on the instability of the plasma of disturbance m(ϱ) = 9 × 10⁻³ kg.     

A full-scale test rig for railway rolling noise: simulation and measurement of dynamic wheelset-track interaction

A new outdoor rolling-noise test rig on a 25 m stretch of full-scale track will enable the study of vibrations of wheel and rail and of the pertinent noise emission under controlled conditions. The arrangement can be seen as a physical realization of the Track-Wheel Interaction Noise Software (TWINS) computer software. The track and wheel, which are not in mechanical contact, are excited in vertical and lateral directions using electrodynamic actuators. The track can be statically pre-loaded by up to 30 tonnes. The use of the rig is presently under development. The aim is that the radiated noise from separate railway components could be found as the wheel and the track can be excited both together and separately. Amplitude and phase of the applied forces are predetermined by use of an algorithm taking into account the real wheel-rail interaction properties. In that way different wheel-rail contact conditions can be simulated. Eight partners have co-operated in the development and operation of the CHARMEC/Lucchini Railway Noise Test Rig in Surahammar, Sweden.In ongoing experiments, the dynamics of both the wheel and rail have been examined in the frequency domain. For the track, comparisons have been made between data obtained from the rig and those from field measurements on a standard Swedish line. Both dynamic response and spatial decay rates have been studied. The performance of the rig has also been compared to results from TWINS and to results from the literature. Good agreement was obtained in the frequency range from 100 to 5000 Hz. Some results from preliminary measurements of noise emission will be given.     

Effect on vehicle and track interaction of installation faults in the concrete bearing surface of a direct-fixation track

Various installation faults can occur in fasteners in the construction of a direct-fixation track using the top-down method. In extreme cases, these faults may cause excessive interaction between the train and track, compromise the running safety of the train, and cause damage to the track components. Therefore, these faults need to be kept within the allowable level through an investigation of their effects on the interactions between the train and track. In this study, the vertical dynamic stiffness of fasteners in installation faults was measured based on a dynamic stiffness test by means of an experimental apparatus that was devised to feasibly reproduce installation faults with an arbitrary shape. This study proposes an effective analytical model for a train–track interaction system in which most elements, except the nonlinear wheel–rail contact and some components that behave bilinearly, exhibit linear behavior. To investigate the effect of the behavior of fasteners in installation faults in a direct-fixation track on the vehicle and track, vehicle–track interaction analyses were carried out, targeting key review parameters such as the wheel load reduction factor, vertical rail displacement, wheel load, and mean stress of the elastomer. From the results, it was noted that it is more important for the installation faults in the concrete bearing surface of a direct-fixation track to be limited for the sake of the long-term durability of the elastomer rather than for the running safety of the train or the structural safety of the track.     

Effect of periodic corrugation,reinforcement, heterogeneity and initial stress on Love wave propagation

This paper investigates the impact of corrugated boundary surfaces, reinforcement on the propagation of Love-type wave in prestressed corrugated heterogeneous fiber-reinforced layer resting over a void pores half-space. The heterogeneity in the upper corrugated layer is caused due to exponential variation in the elastic constants with respect to the space variable pointing positively downwards. The dispersion equation in the complex form has been derived using method of separation of variables. The real and imaginary parts of the complex dispersion equation were separated and found in well agreement with the classical Love wave equation. Also, the attenuation of the Love waves has been discussed. The study reveals that such a medium transmits two fronts of Love waves. The first front depends upon the change in volume fraction of the pores and the second front depends upon the modulus of rigidity of the elastic matrix of the medium. The substantial influence of corrugation parameters, reinforcement, undulatory parameter, initial stress, heterogeneity parameter and position parameter on the phase velocity, and attenuation of Love-type wave have been observed and depicted by means of graph. It has been observed that the phase velocity decreases with the increase in initial stress parameters, heterogeneity, and reinforcement in upper layer.     

On the dynamics of interaction between a moving mass and an infinite one-dimensional elastic structure at the stability limit

The paper herein deals with the study of the dynamic behaviour generated by the instability of the vibration of a loaded mass, uniformly moving along an Euler-Bernoulli beam on a viscoelastic foundation, induced by the anomalous Doppler waves excited in the beam. This issue is relevant for the case of modern trains travelling along a track with soft soil when the trains speed exceeds the phase velocity of the waves induced in the track. The model corresponds to a railway vehicle reduced to a loaded wheel running along a (half) track. The beam takes account of the bending stiffness of the rail and the mass of the track, including the mass of the rail, semi-sleepers and half of the ballast layer, where the viscoelastic foundation represents the subgrade. The model includes the wheel/rail Hertzian contact and it allows the simulation of the possibility of contact loss. The nonlinear equations of motion are integrated using a numerical approach based on the Green’s function method. When the vibration becomes unstable, the system evolution is a limit cycle characterised by a succession of shocks, due to the action of two opposite factors: the anomalous Doppler waves that pump energy at the interface between the moving mass and the beam, thus forcing the mass to take off, and the static load that push the mass downwards. The frequency of the shocks increases at higher velocity and the magnitude of the impact force decreases; the most dangerous velocity is the critical one, which represents the stability limit of the linear approximation of the motion equations. The transient behaviour that precedes the limit cycle appearance is being analysed. The Hertzian contact influences the time history of the limit cycle and the magnitude of the impact force and, therefore, it is essential to be included in the model. To the authors’ knowledge, this problem has never been dealt with.     

Experimental characterization of novel SiC foam corrugated structured packing with varied pore size and corrugation angle

In our study, SiC foam material has been applied to produce corrugated structured packing in distillation. Three kinds of novel packing with different pore size and corrugation angle have been developed and tested in pilot scale, respectively, to investigate the influence of structural parameters on the performance of SiC foam corrugated structured packing. Hydraulic parameters including pressure drop for dry and wet packing and flooding velocity are determined in an organic glass tower of 600 mm internal diameter, using gas–water. Mass transfer efficiency (HETP) is measured by total reflux experiments in a column with a 310 mm diameter at atmospheric pressure, using a mixture of n-heptane and cyclohexane. The experimental results indicate that SFP-500YD3 with a smaller pore size has higher dry and wet pressure drop, lower flooding velocity and higher mass transfer efficiency compared with SFP-500Y-D5. SFP-500X-D3 with a 30° corrugation angle exhibits lowest pressure drop and highest separation efficiency among all three packings. This study reveals the influence of structural characteristics of SiC foam corrugated structured packing on its performance.     

Measuring,modelling and optimising an embedded rail track

A finite element (FE) model and a boundary element (BE) model have been developed to predict the decay rate, vibration and noise responses of an embedded rail track. These models are validated using measured results. The optimisation of the embedded rail track is conducted using these calculated models. The results indicate that the optimised cross-section of the gutter for the embedding rail can significantly reduce the radiated noise of the embedded rail track. The embedded rail track using the I-shaped cross-section gutter reduces the radiated noise of the track by at least by 3 dB(A). Furthermore, combining the material parameter optimisation with the gutter cross-section optimisation can further reduce the radiated noise of the embedded rail track. Increasing the Young’s modulus of the rail pad in the embedded rail track with the I-shaped cross-section gutter can result in a radiated noise reduction of 4 dB(A).