Experimental and numerical investigation of the effect of rail corrugation on the behaviour of rail fastenings

This paper presents the results of a detailed investigation of the effects of rail corrugation on the dynamic behaviour of metro rail fastenings, obtained from extensive experiments conducted on site and from simulations of train–track dynamics. The results of tests conducted with a metro train operating on corrugated tracks are presented and discussed first. A three-dimensional (3D) model of the metro train and a slab track was developed using multi-body dynamics modelling and the finite element method to simulate the effect of rail corrugation on the dynamic behaviour of rail fastenings. In the model, the metro train is modelled as a multi-rigid body system, and the slab track is modelled as a discrete elastic support system consisting of two Timoshenko beams for the rails, a 3D solid finite element (FE) model for the slabs, periodic discrete viscoelastic elements for the rail fastenings that connect the rails to the slabs, and uniformly viscoelastic elements for the subgrade beneath the slabs. The proposed train–track model was used to investigate the effects of rail corrugation on the dynamic behaviour of the metro track system and fastenings. An FE model for the rail fastenings was also developed and was used to calculate the stresses in the clips, some of which rupture under the excitation of rail corrugation. The results of the field experiments and dynamics simulations provide an insight into the root causes of the fracture of the clips, and several remedies are suggested for mitigating strong vibrations and failure of metro rail fastening systems.     

北京地铁钢轨静态动态测试技术

介绍了地铁钢轨静态、动态测试技术,为了对钢轨波磨损耗进行治理,采用光纤网络和传感器技术对北京地铁几段新、老线路钢轨的应变、位移、加速度进行了动态和静态刚度测试,获得了宝贵的数据与经验。     

Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities

The randomness of track irregularities directly leads to the random vibration of the vehicle–track systems. To assess the dynamic performance of a railway system in more comprehensive and practical ways, a framework for probabilistic assessment of vehicle-curved track systems is developed by effectively integrating a vehicle–track coupled model (VTCM), a track irregularity probabilistic model (TIPM) with a probability density evolution method (PDEM). In VTCM, the railway vehicle and the curved track are coupled by the nonlinear wheel–rail interaction forces, and through TIPM, the ergodic properties of random track irregularities on amplitudes, wavelengths and probabilities can be properly considered in the dynamic calculations. Lastly, PDEM, a newly developed method for solving probabilistic transmissions between stochastic excitations and deterministic dynamic responses, is introduced to this probabilistic assessment model. Numerical examples validate the correctness and practicability of the proposed models. In this paper, the results of probabilistic assessment are presented to illustrate the dynamic behaviours of a high-speed railway vehicle subject to curved tracks with various radii, and to demonstrate the importance of considering the actual status of wheel–rail contacts and curve negotiation effects in vehicle-curved track interactions.     

Rotational vibration absorber for the mitigation of rail rutting corrugation

Torsional vibrations of metro wheel sets are known to be involved in the wavelength-fixing mechanism of the rutting-type rail corrugation. In the first part of this paper, the basic conditions for this type of wear to appear are established using a theory developed in the frequency domain. The efficiency of a dynamic vibration absorber tuned to the first torsional resonance of the wheel set to mitigate rutting corrugation is evaluated numerically. In the second part, the phenomenon is studied on a quarter-scale test bench. The scaling laws for wheel–roller wear predictions are established. The efficiency of the dynamic vibration absorber is evaluated on the scaled bench. The results are compared with theoretical predictions from a linear model. Additionally, the measurements are compared with numerical results from a multi-body model portraying the experiment.     

High-frequency random vibration analysis of a high-speed vehicle–track system with the frequency-dependent dynamic properties of rail pads using a hybrid SEM–SM method

A hybrid Spectral Element Method (SEM)–Symplectic Method(SM) method for high-efficiency computation of the high-frequency random vibrations of a high-speed vehicle–track system with the frequency-dependent dynamic properties of rail pads is presented. First, the Williams-Landel-Ferry (WLF) formula and Fractional Derivative Zener (FDZ) model were, respectively, applied for prediction and representation of the frequency-dependent dynamic properties of Vossloh 300 rail pads frequently used in China's high-speed railway. Then, the proposed hybrid SEM–SM method was used to investigate the influence of the frequency-dependent dynamic performance of Vossloh 300 rail pads on the high-frequency random vibrations of high-speed vehicle–track systems at various train speeds or different levels of rail surface roughness. The experimental results indicate that the storage stiffness and loss factors of Vossloh 300 rail pad increase with the decrease in dynamic loads or the increase in preloads within 0.1–10,000?Hz at 20°C, and basically linearly increase with frequency in a logarithmic coordinate system. The results computed by the hybrid SEM–SM method demonstrate that the frequency-dependent viscous damping of Vossloh 300 rail pads, compared with its constant viscous damping and frequency-dependent stiffness, has a much more conspicuous influence on the medium-frequency (i.e. 20–63?Hz) random vibrations of car bodies and rail fasteners, and on the mid- (i.e. 20–63?Hz) and high-frequency (i.e. 630–1250?Hz) random vibrations of bogies, wheels and rails, especially with the increase in train speeds or the deterioration of rail surface roughness. The two sensitive frequency bands can also be validated by frequency response function (FRF) analysis of the proposed infinite rail–fastener model. The mid and high frequencies influenced by the frequency-dependent viscous damping of rail pads are exactly the dominant frequencies of ground vibration acceleration and wheel rolling noise caused by high-speed railways, respectively. Even though the existing time-domain (or frequency-domain) finite track models associated with the time-domain (or frequency-domain) fractional derivative viscoelastic (FDV) models of rail pads can also be used to reach the same conclusions, the hybrid SEM–SM method in which only one element is required to compute the high-order vibration modes of infinite rail is more appropriate for high-efficiency analysis of the high-frequency random vibrations of high-speed vehicle–track systems.     

减振型双块式无砟轨道合理刚度匹配研究

为研究城际铁路减振型双块式无砟轨道的合理刚度匹配,基于轮轨系统耦合动力学理论,结合我国城际铁路的运营特点,建立了城际铁路车辆-减振型双块式无砟轨道耦合动力分析模型,分析了列车在时速200 km和160 km时的轮轨动力响应。结果表明:对列车最高运行速度为200 km/h的城际客运专线,建议钢轨允许垂向位移控制在2 mm以内,减振垫的垂向位移应控制在1 mm左右;支点反力、钢轨位移受扣件刚度的影响显著,减振垫刚度是决定底座板加速度及道床板位移的决定性因素。城际铁路“在大站停”列车时速200 km、“站站停”列车最高时速160 km时,扣件合理刚度可取为42~49 kN/mm,减振垫的合理刚度可取为0.036~0.044 N/mm3。     

Investigation on the sensitive and insensitive zones of the rail support stiffness for the dynamic response of a vehicle system under low excitation frequencies

The variation of the rail support stiffness is an inherent issue of railway tracks. There is still no consensus on the influence of the rail support stiffness variation on the dynamic response of the vehicle–track system. One view indicates that changes of the support stiffness do not have considerable influence on the vehicle dynamic response. The main influence factor is the rail deflection. However, the opposite view presents that the influence of the support stiffness on the system dynamic response is obvious. Reasons that lead to the dispute of previous studies are the neglect of the influence of the excitation frequencies and a lack of understanding of stiffness sensitive zones. In this study a vehicle–track coupling model with equivalent overall support stiffness is employed to investigate the response of the vehicle to changes of the track stiffness and excitation frequencies. Results show that for each of frequencies (1–40?Hz) the dynamic response of the vehicle is only sensitive to a certain range of the support stiffness. A stiffness sensitive zone for each excitation frequency can be observed. In order to further study the influence of the subgrade on the vehicle system dynamic response a vehicle–track-subgrade model is utilised. The subgrade stiffness belonging to the stiffness sensitive zone has a significant influence on vehicle vibrations. For overall support stiffness of the rail higher than 20?kN/mm, the stiffness sensitive zones of low excitation frequencies can be avoided.     

An investigation into the mechanism of the polygonal wear of metro train wheels and its effect on the dynamic behaviour of a wheel/rail system

This paper presents a detailed investigation conducted into the mechanism of the polygonal wear of metro train wheels through extensive experiments conducted at the sites. The purpose of the experimental investigation is to determine from where the resonant frequency that causes the polygonal wear of the metro train wheels originates. The experiments include the model tests of a vehicle and its parts and the tracks, the dynamic behaviour test of the vehicle in operation and the observation test of the polygonal wear development of the wheels. The tracks tested include the viaducts and the tunnel tracks. The structure model tests show that the average passing frequency of a polygonal wheel is approximately close to the first bending resonant frequency of the wheelset that is found by the wheelset model test and verified by the finite element analysis of the wheelset. Also, the dynamic behaviour test of the vehicle in operation indicates the main frequencies of the vertical acceleration vibration of the axle boxes, which are dominant in the vertical acceleration vibration of the axle boxes and close to the passing frequency of a polygonal wheel, which shows that the first bending resonant frequency of the wheelset is very exciting in the wheelset operation. The observation test of the polygonal wear development of the wheels indicates an increase in the rate of the polygonal wear of the wheels after their re-profiling. This paper also describes the dynamic models used for the metro vehicle coupled with the ballasted track and the slab track to analyse the effect of the polygonal wear of the wheels on the wheel/rail normal forces.     

An investigation into the mechanism of the out-of-round wheels of metro train and its mitigation measures

This paper presents an investigation into the mechanism of polygonal wear of metro train wheels through experiments conducted at field sites. The experiments comprise dynamic behaviour test of vehicle and track system, the wheel transverse wear and polygonal wear measurements, rail corrugation and rail weld joint irregularities’ measurements. Moreover, the numerical modal analysis of the wheelset is also performed. The wheel measurement results show that most wheels exhibit obvious eccentricity and polygonal wear with 5–8 harmonics. The investigation results indicate that the wavelength-fixing mechanism of the wheel out-of-roundness with 5–8 harmonics is the P2 resonance. Four measures have been proposed to mitigate the formation of wheel polygonal wear based on the field measurement results.     

Thermal buckling and post-buckling behaviour of continuous welded rail track

Because thermal expansions are constrained within continuous welded rail track, the track can buckle, and does so mainly in the horizontal plane. In this paper, a parametric finite element model of railway track is presented, and its sensitivity to the variations of the main parameters that characterise the scenario has been investigated and discussed. Comparison with existing literature shows good agreement. It is found that curved tracks suffer from thermal buckling more than tangent tracks do. To simulate a track misalignment defect, a new methodology has been utilised that does not introduce, as is usual, geometrical discontinuities near the same defect, because it takes into account – in a natural way – the bending stiffness of the whole railway track in the horizontal plane. To contribute to a better understanding of the safe utilisation of raw experimental data obtained from in situ tests, a deep analysis of the effects on the thermal track buckling response produced by each parameter characterising the sleeper–ballast lateral resistance curve is presented and discussed. It is found that for current ballasted railway tracks, the minimum buckling temperature depends only on the limit lateral resistance, whereas a high value of the initial stiffness can lead to overestimation of the maximum buckling temperature, also taking into account the ‘natural’ decrease in the maximum buckling temperature due to an increase in the railway-traffic-induced defect amplitude.     

Vertical random vibration analysis of vehicle–track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.     

Effect of temperature- and frequency-dependent dynamic properties of rail pads on high-speed vehicle–track coupled vibrations

The soft under baseplate pad of WJ-8 rail fastener frequently used in China’s high-speed railways was taken as the study subject, and a laboratory test was performed to measure its temperature and frequency-dependent dynamic performance at 0.3?Hz and at ?60°C to 20°C with intervals of 2.5°C. Its higher frequency-dependent results at different temperatures were then further predicted based on the time–temperature superposition (TTS) and Williams–Landel–Ferry (WLF) formula. The fractional derivative Kelvin–Voigt (FDKV) model was used to represent the temperature- and frequency-dependent dynamic properties of the tested rail pad. By means of the FDKV model for rail pads and vehicle–track coupled dynamic theory, high-speed vehicle–track coupled vibrations due to temperature- and frequency-dependent dynamic properties of rail pads was investigated. Finally, further combining with the measured frequency-dependent dynamic performance of vehicle’s rubber primary suspension, the high-speed vehicle–track coupled vibration responses were discussed. It is found that the storage stiffness and loss factor of the tested rail pad are sensitive to low temperatures or high frequencies. The proposed FDKV model for the frequency-dependent storage stiffness and loss factors of the tested rail pad can basically meet the fitting precision, especially at ordinary temperatures. The numerical simulation results indicate that the vertical vibration levels of high-speed vehicle–track coupled systems calculated with the FDKV model for rail pads in time domain are higher than those calculated with the ordinary Kelvin–Voigt (KV) model for rail pads. Additionally, the temperature- and frequency-dependent dynamic properties of the tested rail pads would alter the vertical vibration acceleration levels (VALs) of the car body and bogie in 1/3 octave frequencies above 31.5?Hz, especially enlarge the vertical VALs of the wheel set and rail in 1/3 octave frequencies of 31.5–100?Hz and above 315?Hz, which are the dominant frequencies of ground vibration acceleration and rolling noise (or bridge noise) caused by high-speed railways respectively. Since the fractional derivative value of the adopted rubber primary suspension, unlike the tested rail pad, is very close to 1, its frequency-dependent dynamic performance has little effect on high-speed vehicle–track coupled vibration responses.     

Simulation of dynamic interaction between train and railway turnout

Dynamic train–track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel–rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel–rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.     

Train-Track Interaction and Mechanisms of Irregular Wear on Wheel and Rail Surfaces

Summary High-frequency train-track interaction and mechanisms of wheel/rail wear that is non-uniform in magnitude around/along the running surface are surveyed. Causes, consequences and suggested remedies to relieve the problems are discussed for three types of irregular wheel/rail wear: (1) short-pitch rail corrugation on tangent tracks and large radius curves, (2) wheel corrugation as caused by tread braking, and (3) wheel polygonalisation. The state-of-the-art in modelling of dynamic train-track interaction in conjunction with prediction of irregular wear is reviewed.     

Train-Track Interaction and Mechanisms of Irregular Wear on Wheel and Rail Surfaces

Summary High-frequency train-track interaction and mechanisms of wheel/rail wear that is non-uniform in magnitude around/along the running surface are surveyed. Causes, consequences and suggested remedies to relieve the problems are discussed for three types of irregular wheel/rail wear: (1) short-pitch rail corrugation on tangent tracks and large radius curves, (2) wheel corrugation as caused by tread braking, and (3) wheel polygonalisation. The state-of-the-art in modelling of dynamic train-track interaction in conjunction with prediction of irregular wear is reviewed.     

Effects of rail thermal stress on the dynamic response of vehicle and track

A new method is proposed to obtain the dynamic responses of the vehicle–track coupling system under the conditions of rail thermal stress changes in high-speed railways. Exact models are established with different rail longitudinal forces, in which multibody dynamic models are used for vehicles and the direct stiffness method for structures. In order to provide a general, simple and flexible formulation to express longitudinal stress distribution, the accurate model of long slab track consists of many small units with parameters which can be initialised separately. The exact analytical equation of track frequency and modal function was obtained by the transition matrix method, which can be used in calculating the dynamic response of wheel–rail coupling model. The proposed model is verified through comparisons with other classical solutions. Under the influence of train velocities and track irregularities, the specific vibration performances that frequency shifted and amplitude peak enhanced with thermal force are demonstrated through examples. The results show that the response analyses of vehicle and track have great application potentiality for fast estimation of the rail longitudinal stress.     

Fundamentals of vehicle–track coupled dynamics

This paper presents a framework to investigate the dynamics of overall vehicle–track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle–track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel–rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time–frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle–track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing–Qinhuangdao line and the high-speed running test on the Qinhuangdao–Shenyang line. Differences in the dynamic responses analysed by the vehicle–track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.     

The dynamic response of rail support

This research reviews principles behind the dynamic response of rail supports, and introduces a method of analysis to find the maximum response in a realistic setting. Assuming a time-dependent, moving mass with massive wheels is essential, because the ratio of the moving mass to the rail mass is significant. However, the dynamic response of the track is not affected by dynamic properties of the train other than its unsprung mass, because the natural frequencies of the train suspension and track are significantly different. A numerical method is developed to model the dynamic response based on these principles, and applied to the Korean urban transit. The dynamic response includes multiple peaks with a large amplitude range, creating noise while the wheel passes the support. The dynamic impact factor (DIF) for the rail support depends mainly on the stiffness and damping of the rail support. The DIF for the rail moment is below the code value, whether this value is based on numerical analysis or on-site measurements. However, our numerical analysis results in a DIF for support settlement that is greater than the code value, if the damping is less than 3%.     

Simulation of dynamic interaction between train and railway turnout

Dynamic train-track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel-rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel-rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.     

Prediction of the interaction between a simple moving vehicle and an infinite periodically supported rail – Green's functions approach

This paper herein describes the interaction between a simple moving vehicle and an infinite periodically supported rail, in order to signalise the basic features of the vehicle/track vibration behaviour in general, and wheel/rail vibration, in particular. The rail is modelled as an infinite Timoshenko beam resting on semi-sleepers via three-directional rail pads and ballast. The time-domain analysis was performed applying Green's matrix of the track method. This method allows taking into account the nonlinearities of the wheel/rail contact and the Doppler effect. The numerical analysis is dedicated to the wheel/rail response due to two types of excitation: the steady-state interaction and rail irregularities. The study points out to certain aspects regarding the parametric resonance, the amplitude-modulated vibration due to corrugation and the Doppler effect.