Rail Roughness Research Articles

An analytic solution of mathematical expectation for bogie-track interaction problems

This paper presents a frequency-domain analytic solution of mathematical expectation for bogie-track dynamic interaction problems in which a random roughness on the railhead is considered. To achieve this, the Floquet transformation is applied to the coupling system consisting of a bogie and an infinite track. Due to the periodicity of the sleeper spacing, the present problem is reduced to that in a representative track unit. Transformed solutions are expressed by Fourier series in the unit cell. The unknown Fourier coefficients are then obtained from infinite simultaneous equations. In the present formulation the vibration reaction due to the roughness is described in terms of the response function of the bogie-track coupling system and the power spectrum density (PSD) of rail roughness. The track dynamic nature which is independent of the roughness is represented by the former. To validate the derived solution, comparison with time-domain numerical solution is carried out. Furthermore, based on the developed frequency-domain method, two kind of pad damping model given by a constant loss factor and viscous damping are compared through evaluation of the expected value of energy spectrum density (ESD) of rail vibration and the PSD of wheel acceleration. Finally, influence of track structure such as the dynamic equivalent stiffness of rail pad and that of under-sleeper pad on the expectation of ESD of rail vibration and the PSD of wheel acceleration is examined.

Acoustic Roughness Measurement of Railway Tracks: Implementation of a Chord-Based Optical Measurement System on a Train

A large part of the noise emissions from rail traffic originates from rolling noise. This is significantly determined by the surface roughness of the wheel and the rail. To quantitatively assess the noise generation from the wheel–rail contact, it is necessary to measure the surface roughness of the rail network. Direct measurements via trolley devices are usually associated with the need for a free track and limitation in velocity. Indirect measurements of rail roughness, such as measuring axle-box accelerations, enable operation during regular passage but only estimate the acoustic roughness. In this study, the potential of an optical and consequently contact-free measurement method using laser triangulation sensors to measure rail roughness from the train is investigated. The approach can combine the advantage of operation during regular passage with the characteristics of a direct measurement, enabling large-scale monitoring of the rail network. A measurement run with a train was carried out on a meter-gauge track at speeds up to 80 km h−1 The results of the optical measurement approach were compared with a tactile reference measurement on the track. The results show good agreement of the new measurement setup for dry rail surface conditions at 50 km h−1, with a mean deviation of 1.48 dB.

Sources of variability in metro train-induced vibration

In previous in-situ measurements of metro trains it has been found that the velocity level on the track or tunnel wall may vary significantly between different train passages, even though the measuring section, the type of trains and the track and tunnel conditions are identical. An investigation is carried out into the sources of this variability, using a 3D train-track numerical model. This is built using the software SIMPACK and ABAQUS, and is connected through one-way coupling to a finite element model of the tunnel and soil. These models are used to study the influence of various train parameters, including the wheel and rail unevenness, train speed and degree of train loading. For comparison, in-situ measurements were made of the dynamic response of the rail and tunnel wall. The rail roughness at the site as well as the wheel unevenness of all 48 wheels for one train were measured. The results from the model indicate that the wheel unevenness affects the rail velocity level in the frequency region between 25 and 250 Hz and tunnel wall vibration above 5 Hz. The rail velocity level can vary by up to 20 dB due to wheel unevenness, with the largest variations occurring in the frequency bands 50–63 Hz. Variations in passenger loading affect the train-induced vibration by up to 4.5 dB, mainly in the low frequency region. When the train speed varies within a range of ±20% relative to the nominal speed 60 km/h, the frequencies of the peaks are shifted and the level in some frequency bands can change by as much as 10 dB. However, the largest influence is that of the wheel unevenness. It is concluded that the variation in these parameters, especially the wheel and rail unevenness, should be considered to achieve reliable predictions of train-induced vibration.

Rail Roughness Acceptance Criterion Based on Metro Interior Noise

Severe rail roughness leads to a series of problems in metro systems, particularly the vehicle noise problem. To ensure a better acoustic environment, rail roughness control is therefore one of the main concerns for the metro operators. But the existing roughness acceptance criteria are not suitable for metro interior noise control. It is an appropriate method to determine the rail roughness limit based on interior noise. A rail roughness acceptance criterion based on metro interior noise is accordingly proposed in this paper. The relationship between rail roughness and interior noise can be derived with wheel-rail noise as link. With this objective, a combined test and simulation method is adopted. A validated wheel-rfigil noise prediction model is thus established to determine the relationship between rail roughness and wheel-rail noise. Moreover, the transfer function of wheel-rail noise to interior noise is developed based on extensive field test. Using this method, the noise sensitivity to roughness wavelength and acceptance criteria at different speeds and track structures are investigated. Finally, an eclectic rail corrugation acceptance criterion on curved track is suggested in consideration of practical application.

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.

Calibration of a finite element model of Prescale film for wheel-rail normal contact area measurements

This article presents the latest of a series of research activities aimed to determine the deviation originated when Prescale pressure measurement film is used to measure the size and shape of the wheel-rail contact area. Despite being an attractive solution due to the simplicity of the measurement procedure, it is well known that the contact interaction is altered by the presence of the film. Consequently, characterizing and filtering out the systematic measurement error is a fundamental requirement for accurate quantitative assessments. Nevertheless, the complexity of the wheel-rail contact problem, which lacks an analytical solution, hinders the direct determination of correction values. The approach presented here builds on error corrections for simpler Hertzian geometries to calibrate a film model for further use in the wheel-rail contact scenario. The results highlight the marked dependency of the measurement error on wheel and rail roughness and underline the importance of including the film into finite element models that are validated by comparison with experimental observations.

A multifunctional electromagnetic device for vibration energy harvesting and rail corrugation sensing

A multifunctional electromagnetic device for harvesting rail vibration energy and sensing rail corrugation is proposed. Firstly, the optimal coil position is investigated theoretically and verified through experiments. Then, experimental frequency-sweeping tests are carried out to understand the response characteristics of the harvester. Two sections of a metro line with/without rail corrugations are selected to measure rail roughness and vibration. Using the field-measured rail vibration as excitations, the response characteristics of the harvester are investigated through indoor experiments. Experimental results demonstrate that occurrences of corrugation can be identified through time-frequency analysis of the electromotive forces of the harvester. Besides, electrical load tests under normal rail vibration demonstrate that this harvester will yield its maximum power of 18.6 mW (average power: 1.5 mW) when the resistance of the external electrical load is close to the internal resistance of the coil. The capability to energise small commercial electronic devices is verified by charging a supercapacitor, and driving LEDs, a digital clock, and a thermo-hygrometer to work, respectively. The capabilities of the harvester for powering low-power electronics and sensing rail corrugation pave the wave for designing a self-powered sensing node for rail corrugation monitoring.

Railway wheel tread damage and axle bending stress – Instrumented wheelset measurements and numerical simulations

ABSTRACT A combination of instrumented wheelset measurements and numerical simulations of axle bending stresses is used to investigate the consequences of evolving rolling contact fatigue (RCF) damage on a passenger train wheelset. In a field test campaign, stresses have been monitored using a wheelset with four strain gauges mounted on the axle, while the evolution of wheel tread damage (out-of-roundness) has been measured on regular occasions. The strain signals are post-processed in real time and stress variations are computed. Based on a convolution integral approach, the measured wheel out-of-roundness has been used as input to numerical simulations of vertical dynamic wheelset–track interaction and axle stresses. Simulated and measured axle stresses are compared for cases involving combinations of low or high levels of rail roughness and the measured levels of RCF damage. The study enhances the understanding of how wheel tread damage and track quality influence axle stress amplitudes.

Numerical evaluation of approach slab influence on transition zone behavior in high-speed railway track

Some issues concerning railway routes are related to avoiding uneven deformations, rail roughness, and increased dynamic loads. Lack of transition zones at the entrance and exit of bridges intensifies the above-mentioned failures due to sudden changes in track stiffness. The main objective of this article is to investigate the effects of approach slab length, thickness, and travel speed on the transition zone. On this basis, one attempts to study the dynamic behavior of a track in a transition zone between a slab track and bridge as well as dynamic responses of sensitivity analysis to the approach slab length and thickness under various vehicle speeds. Dynamic analysis is conducted using a three-dimensional finite element model (FEM) of a track and the China Star train. Results show that an increase in the cruising speed from 120 to 300 km/h exacerbates deformation by 25% and the approach slab thickness reduces the deformation of the transition zone by 42%. Moreover, it is observed that the increase in the length of the transition zone, significantly affects the regulation of deformation intensity and the behavior of the transition zone is a function of the length and thickness of the slab.

Investigation on rail corrugation grinding criterion based on coupled vehicle–track dynamics and rolling contact fatigue model

Based on the measured spectra of rail roughness and track structures longitudinal roughness, the rail grinding limit is studied with the help of an established coupled dynamic metro vehicle–track model and a rolling contact fatigue model. The results indicate that metro rail grinding control should be regulated according to corrugation wavelength range and operating speed. Based on the rolling contact fatigue model, longer wavelength of rail corrugation has less influence on the wheel rolling contact fatigue. For the metro lines with a maximum operating speed of 80 km/h, the average levels of rail corrugation in the wavelength ranges of 30–65 mm, 65–125 mm, and 125–250 mm should be less than 5.4, 24.8, and 33.8 dB re 1 μm, respectively; for the ones with the operating speed of 80–120 km/h, the corresponding average corrugation levels in the three wavelength ranges should be less than 4.4, 9.8, and 29.8 dB re 1 μm, respectively.

Complex eigenvalue analysis and parameters analysis to investigate the formation of railhead corrugation in sharp curves

Rail corrugation, a quasi-sinusoidal irregularity of the rail head, is a common issue experienced throughout the railway networks worldwide. It generally leads to high wheel-rail dynamic loads, increased noise emission, and poor ride comfort. Most commonly, rail corrugation is likely to develop on sharp curves. This paper aims to study the numerical feasibility of the prediction of self-excited vibrations for the study of rutting corrugation formation without excitation from initial rail roughness. A finite element model for the prediction of the self-excited vibrations of the leading wheelset-rails system in a sharp curve has been developed in ABAQUS. The friction coupling between the wheel and rail is taken into account. It is assumed that the lateral creep forces between wheel and rail are quasi-saturated. The proposed model is applied to investigate the effect of several structural factors on self-excited vibrations occurrence. The obtained numerical results match closely with the typical wavelength of rutting corrugation observed in the field sites and the experimental evidence on rutting corrugation. It has been found out that the interaction effect of the wheelset cross-section and the track gauge has a significant influence on self-excited vibrations. For a typical European wheelset cross-section, self-excited vibrations only occurred under the widened track gauge. For the studied Chinese wheelset, self-excited vibrations occurred, however, only under the standard track gauge. Therefore, following the assumptions underlying the analysis, wheelset cross-section might be an inhibitor factor at a particular track gauge. A parameter sensitivity analysis shows that the friction coefficient is linearly correlated with the system's instability and the frequency of the unstable modes of vibration.

Validation of a dynamic wheel load factor and the influence of various track irregularities on the dynamic response of prestressed concrete sleepers

Prestressed concrete sleepers are generally designed taking into account the influence of the dynamic wheel load. In Japan, the dynamic wheel load factor of 2.0 has been typically used for the serviceability limit state since the 1950s. However, there are few examples that have proved its validity. In this study, field measurement tests and three-dimensional numerical analysis were conducted for prestressed concrete sleepers laid on a straight section of a railway track with continuously welded rails. According to the results of the field tests, the measured dynamic wheel load factor was less than the conventionally used dynamic wheel load factor of 2.0, and the bending moments exceeding the full prestress condition, i.e. the compressive stress on all sections, were generated in some cases. Furthermore, even with the prestressed concrete sleepers of the same type laid continuously, the bending moment was increased more than three times due to the support conditions of the prestressed concrete sleepers and the rail roughness. Results of the numerical analyses also revealed that the bending moment was increased more than two times because of the hanging (unsupported) sleepers, and the tensile stress of the prestressed concrete sleeper exceeded 3 N/mm2 when the rail roughness was approximately 2 mm or more. Based on this investigation, the validity of the dynamic wheel load factor of 2.0 was proved.

Vehicle-track-soil interaction and train-induced ground vibration – Theory and measurements in Germany, Switzerland and France

Three measurement campaigns of train-induced ground vibrations are evaluated for the vehicle-track-soil interaction. Ground vibrations, track vibrations and vehicle vibrations have been measured for train passages and impulse excitation and compared with theoretical results. The soil and the track-soil system are calculated by wavenumber integrals. The influence of the vehicle is introduced by a substructure method. By comparing theory and measurement the different components of excitation force and ground vibration can be analysed, the quasi-static excitation, track-alignment errors, the out-of-roundness of wheels, the wheel and rail roughness, and moreover, scattered axle impulses and ineffective high-frequency parts of the wheelset accelerations and forces.

Efficient decoupling technique applied to the numerical time integration of advanced interaction models for railway dynamics

Railway interaction is characterised by the coupling between the train and the track introduced through the wheel/rail contact. The introduction of the flexibility in the wheelset and the track through the finite element (FE) method in the last four decades has permitted to study high‐frequency phenomena such as rolling noise and squeal, whose origin lies in the strongly non‐steady state and non‐linear behaviour of the contact forces that arise from the small contact area. In order to address models with a large number of degrees of freedom, innovative Eulerian‐modal models for wheelsets with rotation and cyclic tracks have been developed in recent years. The aim of this paper is to extend the resulting formulation to an uncoupled linear matrix equation of motion that allows solving each equation independently for each time step, considerably reducing the associated computational cost. The decoupling integration method proposed is compared in terms of computational performance with Newmark and Runge‐Kutta schemes, commonly used in vehicle dynamics, for simulations with the leading wheelset negotiating a tangent track and accounting the rail roughness.

Derivation of network-wide surface condition corrections for rail noise modelling

Noise modelling and mapping techniques are increasingly being used to understand noise impacts to communities across large geographic areas. Rail transit noise around a network can vary considerably with factors such as track type, train speed, rail roughness/surface condition, among others. Reference source levels for a particular rolling stock type are normally derived by measurement at a particular location or locations, and applied around the network. When modelling noise network wide, it is important to understand how variable rail roughness can affect predicted noise levels at locations other than those used for measurements. With elevated guideway, it can also be difficult to access appropriate external measurement locations. This study describes a study undertaken for the Vancouver SkyTrain network using the Nord2000 rail noise prediction algorithm. Variations in rolling noise level of the order of 15 dB were identified and attributed to rail surface condition. Noise measurements inside a test train were used to determine frequency dependent train speed coefficients and corrections to apply for rail condition around the network. This paper describes the approach used and the outcomes in relation to this city-wide rail noise mapping project.

Measuring method and analysis of rail roughness in high-speed railway

The indirect method and direct method are employed to measure and analyze the rail roughness of ballastless tracks in high-speed railway, respectively. The indirect method deduces the one-third octave band spectrum of the rail roughness by using the field tested rail acceleration, longitudinal decay rate of rail vibration, and the transfer function between the rail roughness and rail acceleration obtained by wheel-rail dynamic calculation. The direct method employs the rail roughness measurement instrument to directly measure the rail surface in high-speed railway, and then the one-third octave band spectrum of the rail roughness is acquired after the trend term removal, the outlier removal and the time-frequency transformation of the measured data. The rail roughness spectra obtained by the two methods are compared with European roughness limit spectrum. Results show that reliable results can be obtained by both the indirect and direct methods, the measured rail roughness of the tested high-speed railway is smaller than the European spectrum limit when the wavelength is larger than 0.05 m, whereas it exceeds the European spectrum limit when the wavelength is smaller than 0.05 m, which should be controlled.

Assessment of measurement-based methods for separating wheel and track contributions to railway rolling noise

The noise produced during a train pass-by originates from several different sources such as propulsion noise, noise from auxiliary equipment, aerodynamic noise and rolling noise. The rolling noise is radiated by the wheels and the track and is excited by the wheel and rail unevenness, usually referred to as roughness. The current TSI Noise certification method, which must be satisfied by all new mainline trains in Europe, relies on the use of a reference track to quantify the noise from new vehicles. The reference track is defined by an upper limit of the rail roughness and a lower limit of the track decay rate (TDR). However, since neither the rail roughness nor the track radiation can be completely neglected, the result cannot be taken as representing only the vehicle noise and the measurement does not allow separate identification of the noise radiated by wheel and track. It is even likely that further reductions in the limit values for new rolling stock cannot be achieved on current tracks. There is therefore a need for a method to separate the noise into these two components reliably and cheaply. The purpose of the current study is to assess existing and new methods for rolling noise separation. Field tests have been carried out under controlled conditions, allowing the different methods to be compared. The TWINS model is used with measured vibration data to give reference estimates of the wheel and track noise components. Six different methods are then considered that can be used to estimate the track component. It is found that most of these methods can obtain the track component of noise with acceptable accuracy. However, apart from the TWINS model, the wheel noise component could only be estimated directly using three methods and unfortunately these did not give satisfactory results in the current tests.

A 2.5D finite element and boundary element model for the ground vibration from trains in tunnels and validation using measurement data

A numerical model is presented for the ground-borne vibration produced by trains running in tunnels. The model makes use of the assumption that the geometry and material properties are invariant in the axial direction. It is based on the so-called two-and-a-half dimensional (2.5D) coupled Finite Element and Boundary Element methodology, in which a two-dimensional cross-section is discretised into finite elements and boundary elements and the third dimension is represented by a Fourier transform over wavenumbers. The model is applied to a particular case of a metro line built with a cast-iron tunnel lining. An equivalent continuous model of the tunnel is developed to allow it to be readily implemented in the 2.5D framework. The tunnel structure and the track are modelled using solid and beam finite elements while the ground is modelled using boundary elements. The 2.5D track-tunnel-ground model is coupled with a train consisting of several vehicles, which are represented by multi-body models. The response caused by the passage of a train is calculated as the sum of the dynamic component, excited by the combined rail and wheel roughness, and the quasi-static component, induced by the constant moving axle loads. Field measurements have been carried out to provide experimental validation of the model. These include measurements of the vibration of the rail, the tunnel invert and the tunnel wall. In addition, simultaneous measurements were made on the ground surface above the tunnel. Rail roughness and track characterisation measurements were also made. The prediction results are compared with measured vibration obtained during train passages, with good agreement.

An iterative methodology for the prediction of dynamic vehicle–track interaction and long-term periodic rail wear

In this study, a versatile numerical method for the prediction of long-term growth of rail roughness is presented and its functionality is demonstrated for the development of rail corrugation on small radius curves. The procedure includes two sub-modules: (1) a time-domain model for the simulation of dynamic vehicle–track interaction in a wide range of frequencies by using a commercial software for multibody dynamics and (2) a post-calculation of sliding wear based on the Archard’s model in combination with a non-Hertzian and transient wheel–rail contact model. The structural flexibility of the wheelset is accounted for by using the finite element method. The rail wear generated by a large number of passing trains is assessed by recurrently updating the rail surface based on the wear depth calculated in each post-processing step. The current work sets out from a previous study in which a model for the prediction of long-term growth of rail roughness on small radius curves was developed in a general-purpose programming language. By transferring the model into a commercial software, the aim is to develop an engineering tool that is more applicable for different operational conditions, such as various vehicle and track designs and track alignments. The proposed method is verified by comparing the simulation results against those obtained with the pre-existing software. Conditions similar to a 120 m radius curve on the Stockholm metro exposed to corrugation growth on the low rail are considered. The corrugation is found to be generated by the leading wheelsets. The prevailing wavelength-fixing mechanisms are identified and discussed.

Experimental study of the treatment measures for rail corrugation on tracks with Egg fasteners in the Beijing metro

Rail corrugation occurring on tracks fitted with Egg fasteners has become a serious problem on the newly operated lines of the Beijing metro in recent years. Investigations and field measurements show that the dominant wavelengths of corrugation are 63–100 mm, inducing dominant frequencies of vibration on the rail in the frequency range of 160–310 Hz for train speeds at 60–70 km/h. Due to the influence of the dynamic behaviour of tracks on the formation of rail corrugation, various options for changing the dynamic behaviour of the track structure can be considered as possible solutions to treat corrugation. Four treatment measures have been considered: rail grinding, adding a rubber pad within the fastener, replacing the fastener with a compression-type fastener, and installing rail dampers on the rail. Field experiments have been carried out to evaluate the effectiveness of these rail corrugation treatment measures on two lines of the Beijing metro. Frequency response functions, track decay rates, and pass-by acceleration on the rail were measured, and the development of rail roughness was monitored. Experimental results show that all the four measures are effective to control or at least slow down the development of rail corrugation on tracks with Egg fastener. Rail grinding is mostly used to limit the effects of corrugation; here, it was noted that low-amplitude corrugation on some straight lines did not reappear after rail grinding. After adding a rubber pad within the fastener, the existing corrugation reduced in amplitude, while corrugation did not reappear on a newly ground rail. Replacing the fastener with a compression-type fastener and installing rail dampers on the rail were found to slow down the development of corrugation.