Simulation of Bending-Torsional-Lateral Vibrations of the Railway Wheelset-Track System in the Medium Frequency Range

SUMMARY

In the present paper, the dynamic interaction between a wheelset of a high-speed-train car and a railway track is considered with the help of a discrete-continuous mechanical model. This model enables us to investigate the bending-torsional-axial vibrations of the wheelset coupled with the vertical and lateral vibrations of the track through the wheel-rail contact forces. The results of numerical simulations performed for the wheelset motion both on straight and curved tracks demonstrate qualitative similarities of the corresponding dynamic responses of the system and essential quantitative differences of the respective amplitude and average values. Particularly severe interaction between the wheelset and the track is observed in the form of periodic resonances caused by parametric excitation from the track.     

High frequency railway vehicle-track dynamics through flexible rotating wheelsets

Some railway problems, such as the corrugation of rails or the impact caused by a wheelflat, are associated with a vehicle–track coupled dynamic phenomenon. Models for the analysis of these problems must account for the structural vibrations of the track components (rails and sleepers), but the most adequate approach for the wheelset has not been sufficiently investigated until present. The wheelset can be considered as an undeformable solid, as an elastic structure where the rotation effects are neglected, or as a rotating flexible solid. In order to fill this gap, this article presents a methodology to use the structural vibrations of a rotating wheelset in high-frequency railway dynamics analyses. The model makes use of Eulerian modal coordinates, a formulation that provides very low computational cost. The method is applied in this article to a wheelflat impact calculation and a vehicle running on a corrugated track. The results show the importance of the more realistic model in the simulations, mainly in certain frequencies.     

Locomotive dynamic performance under traction/braking conditions considering effect of gear transmissions

Traction or braking operations are usually applied to trains or locomotives for acceleration, speed adjustment, and stopping. During these operations, gear transmission equipment plays a very significant role in the delivery of traction or electrical braking power. Failures of the gear transmissions are likely to cause power loses and even threaten the operation safety of the train. Its dynamic performance is closely related to the normal operation and service safety of the entire train, especially under some emergency braking conditions. In this paper, a locomotive–track coupled vertical–longitudinal dynamics model is employed with considering the dynamic action from the gear transmissions. This dynamics model enables the detailed analysis and more practical simulation on the characteristics of power transmission path, namely motor–gear transmission–wheelset–longitudinal motion of locomotive, especially for traction or braking conditions. Multi-excitation sources, such as time-varying mesh stiffness and nonlinear wheel–rail contact excitations, are considered in this study. This dynamics model is then validated by comparing the simulated results with the experimental test results under braking conditions. The calculated results indicate that involvement of gear transmission could reveal the load reduction of the wheelset due to transmitted forces. Vibrations of the wheelset and the motor are dominated by variation of the gear dynamic mesh forces in the low speed range and by rail geometric irregularity in the higher speed range. Rail vertical geometric irregularity could also cause wheelset longitudinal vibrations, and do modulations to the gear dynamic mesh forces. Besides, the hauling weight has little effect on the locomotive vibrations and the dynamic mesh forces of the gear transmissions for both traction and braking conditions under the same running speed.     

Study on the derailment behaviour of a railway wheelset with solid axles in a railway turnout

ABSTRACT

Dynamic wheel–rail interaction in railway turnouts is more complicated than on ordinary track. In order to evaluate the derailment behaviour of railway wheelsets in railway turnouts, this paper presents a study of dynamic wheel–rail interaction during a wheel flange climbs on the turnout rails, by applying the elasticity positioning wheelset model. A numerical model is established based on a coupled finite element method and multi-body dynamics, and applied to study the derailment behaviour of a railway wheelset in both the facing and trailing directions in a railway turnout, as well as dynamic wheel–turnout rail interaction during the wheel flange climbing on the turnout rails. The influence of the wheel–rail attack angle and the friction coefficient on the dynamic derailment behaviour is investigated through the proposed model. The results show that the derailment safety for a wheelset passing the railway turnout in facing direction is significantly lower than that for the trailing direction and the ordinary track. The possibility of derailment for the wheelset passing the railway turnout in facing and trailing directions at positive wheel–rail attack angles will increase with an increase in the attack angles, and the possibility of derailment can be reduced by decreasing the friction coefficient.     

A rail roughness growth model for a wheelset with non-steady,non-Hertzian contact

This paper presents a model simulating rail roughness growth in which the interaction of a wheelset with the track is considered. The aim is to investigate any possible mechanism for roughness growth due to the coupling between the vertical dynamics, the torsional vibration across the axle of the wheelset and the non-steady contact mechanics. The time-domain simulations are carried out for a driven wheelset on tangent track. Both rigid and flexible are considered with parameter variations for moments of the wheelset, vehicle speeds and wavelengths of initial roughnesses. The 2D non-Hertzian and non-steady contact model used in simulations are based on influence coefficients obtained from a boundary element model. The nonlinear development of the rail roughnesses after millions of wheelset passages is also presented.     

High-speed wheel/rail contact determining method with rotating flexible wheelset and validation under wheel polygon excitation

A rotating flexible wheelset model is developed and integrated into a vehicle/track dynamic model. Flexible wheelset modes with natural frequencies less than 1000?Hz are considered in the wheelset modelling. An innovation of the paper is that wheel/rail rolling contact calculation considers the effect of the wheelset flexibility and the rotating effect. By introducing two half dummy rigid wheelsets the rolling contact between the flexible wheelset and the two rails can be transformed to that between a rigid wheelset and the rails. As an extension application, the wheel OOR (Out-Of-Round) wears with the 11th, 15th, and 17th orders are used to the vehicle system dynamic model with rigid, flexible and rotating-flexible wheelset model. The results of the three models are compared to study the influence of wheelset flexibility and rotation. The ‘online searching contact method’ developed in this paper is compared with the traditional contact method with considering the rotating flexible wheelset. And then a measured OOR is used to excite the rotating flexible wheelset, the response of which is analysed and verified.     

Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.     

Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.     

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.     

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.     

Effect of vehicle vibration environment of high-speed train on dynamic performance of axle box bearing

In this study, we developed a comprehensive three-dimensional vehicle–track coupled dynamics model considering the traction drive system and axle box bearing. In this model, dynamic interactions between the axle box bearing and other components, such as the wheelset and bogie frame, are considered based on a detailed analysis of the structural properties and working mechanism of the axle box bearing. A few complicated dynamic excitations, such as the time-varying mesh stiffness of gears, time-varying stiffness of bearing, bearing gaps and track irregularities, are considered. Then, the dynamic responses of the vehicle–track system are demonstrated via numerical simulations based on the established dynamics model. The results indicate that the traction drive system and track irregularities can significantly influence the dynamic interactions of the axle box bearing. The necessity of considering the excitation caused by gear meshing and track irregularities when assessing the dynamic performance of the axle box bearing is demonstrated.     

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.     

A locomotive–track coupled vertical dynamics model with gear transmissions

A gear transmission system is a key element in a locomotive for the transmission of traction or braking forces between the motor and the wheel–rail interface. Its dynamic performance has a direct effect on the operational reliability of the locomotive and its components. This paper proposes a comprehensive locomotive–track coupled vertical dynamics model, in which the locomotive is driven by axle-hung motors. In this coupled dynamics model, the dynamic interactions between the gear transmission system and the other components, e.g. motor and wheelset, are considered based on the detailed analysis of its structural properties and working mechanism. Thus, the mechanical transmission system for power delivery from the motor to the wheelset via gear transmission is coupled with a traditional locomotive–track dynamics system via the wheel–rail contact interface and the gear mesh interface. This developed dynamics model enables investigations of the dynamic performance of the entire dynamics system under the excitations from the wheel–rail contact interface and/or the gear mesh interface. Dynamic interactions are demonstrated by numerical simulations using this dynamics model. The results indicate that both of the excitations from the wheel–rail contact interface and the gear mesh interface have a significant effect on the dynamic responses of the components in this coupled dynamics system.     

Dynamic response of the train–track–bridge system subjected to derailment impacts

Derailments on bridges, although not frequent, when occurs due to a complex dynamic interaction of the train–track–bridge structural system, are very severe. Furthermore, the forced vibration induced by the post-derailment impacts can toss out the derailed wagons from the bridge deck with severe consequences to the traffic underneath and the safety of the occupants of the wagons. This paper presents a study of the train–track–bridge interaction during a heavy freight train crossing a concrete box girder bridge from a normal operation to a derailed state. A numerical model that considers the bridge vibration, train–track interaction and the train post-derailment behaviour is formulated based on a coupled finite-element – multi-body dynamics (FE-MBD) theory. The model is applied to predict the post-derailment behaviour of a freight train composed of one locomotive and several wagons, as well as the dynamic response of a straight single-span simply supported bridge containing ballast track subjected to derailment impacts. For this purpose, a typical derailment scenario of a heavy freight train passing over a severe track geometry defect is introduced. The dynamic derailment behaviour of the heavy freight train and the dynamic responses of the rail bridge are illustrated through numerical examples. The results exhibit the potential for tossing out of the derailed trains from the unstable increase in the yaw angle signature and a lower rate of increase of the bridge deck bending moment compared to the increase in the static axle load of the derailed wheelset.     

Method for obtaining the wheel–rail contact location and its application to the normal problem calculation through ‘CONTACT’

This work presents a robust methodology for calculating inter-penetration areas between railway wheel and rail surfaces, the profiles of which are defined by a series of points. The method allows general three-dimensional displacements of the wheelset to be considered, and its characteristics make it especially suitable for dynamic simulations where the wheel–rail contact is assumed to be flexible. The technique is based on the discretisation of the geometries of the surfaces in contact, considering the wheel as a set of truncated cones and the rail as points. By means of this approach, it is possible to reduce the problem to the calculation of the intersections between cones and lines, the solution for which has a closed-form expression. The method has been used in conjunction with the CONTACT algorithm in order to solve the static normal contact problem when the lateral displacement of the wheelset, its yaw angle and the vertical force applied in the wheelset centroid are prescribed. The results consist of smooth functions when the dependent coordinates are represented as a function of the independent ones, lacking the jump discontinuities that are present when a rigid contact model is adopted. Example results are shown and assessed for the normal contact problem for different lateral and yaw positions of the wheelset on the track.     

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.     

Carbody elastic vibrations of high-speed vehicles caused by bogie hunting instability

In particular locations of the high-speed track, the worn wheel profile matched up with the worn rail profile will lead to an extremely high-conicity wheel–rail contact. Consequently, the bogie hunting instability arises, which further results in the so-called carbody shaking phenomenon. In this paper, the carbody elastic vibrations of a high-speed vehicle in service are firstly introduced. Modal tests are conducted to identity the elastic modes of the carbody. The ride comfort and running safety indices for the tested vehicle are evaluated. The rigid–flexible coupling dynamic model for the high-speed passenger car is then developed by using the FE and MBS coupling approach. The rail profiles in those particular locations are measured and further integrated into the simulation model to reproduce the bogie hunting and carbody elastic vibrations. The effects of wheel and rail wear on the vehicle system response, e.g. wheelset bifurcation graph and carbody vibrations, are studied. Two improvement measures, including the wheel profile modification and rail grinding, are proposed to provide possible solutions. It is found that the wheel–rail contact conicity can be lowered by decreasing wheel flange thickness or grinding rail corner, which is expected to improve the bogie hunting stability under worn rail and worn wheel conditions. The carbody elastic vibrations caused by bogie hunting instability can be further restrained.     

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

Abstract

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.     

Dynamic responses of a high-speed railway car due to wheel polygonalisation

The polygonal wear around the wheel circumference could pose highly adverse influences on the wheel/rail interactions and thereby the performance of the vehicle system. In this study, the effects of wheel polygonalisation on the dynamic responses of a high-speed rail vehicle are investigated through development and simulations of a comprehensive coupled vehicle/track dynamic model. The model integrates flexible slab track, wheelsets and axle boxes subsystem models so as to account for elastic deformations caused by impact loads induced by the wheel polygonalisation. A field-test programme was undertaken to acquire the polygonal wear profile and axle box acceleration response of a high-speed train, and the data are used to demonstrate the validity of the coupled vehicle/track system model. Subsequently, the effects of wheel polygonalisation are evaluated in terms of wheel/rail impact forces, axle box vertical acceleration and dynamic stress developed in the axle considering different amplitudes and harmonic orders of the polygonal wear. The results suggest that the high-order wheel polygonalisation can give rise to high-frequency impact loads at the wheel/rail interface, and excite some of the vibration modes of the wheelset and the axle box leading to high-magnitude axle box acceleration and dynamic stress in the wheelset axle.     

A contact-area model for rail-pads connections in 2-D simulations: sensitivity analysis of train-induced vibrations

A numerical model to predict train-induced vibrations is presented. The dynamic computation considers mutual interactions in vehicle/track coupled systems by means of a finite and discrete elements method. The rail defects and the case of out-of-round wheels are considered. The dynamic interaction between the wheel-sets and the rail is accomplished by using the non-linear Hertzian model with hysteresis damping. A sensitivity analysis is done to evaluate the variables affecting more the maintenance costs. The rail–sleeper contact is assumed extended to an area-defined contact zone, rather than a single-point assumption which fits better real case studies. Experimental validations show how prediction fits well experimental data.