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Metro trains often encounter the problem of wheel flange wear when they pass through sharp curves, especially for the poor wheel–rail profile matching or lack of lubrication, evidently increasing t...

A long-term tracking test was performed on a newly designed high-speed train with the nominal speed of 250 km/h. The wheel roughness and structural vibration were both recorded during two re-profil...

High-order polygonal wear wheels have been detected on metro express train operating on one metro line in China, which cause fatigue failures of steel coil springs in the primary suspension. A seri...

Discrete irregularities are a common issue occurring on locomotive wheels. The wheel roughness measured in the field sites indicates that some wheels suffer from discrete wheel irregularities, such...

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 vehi...

The car body structures of modern trains are often formed of extruded aluminium panels. Their acoustic properties, particularly the sound transmission loss, have an important influence on the interior acoustic environment. In order to study the acoustic performance of extruded panels, their Sound Transmission Loss (STL) is studied using the coupled Wavenumber Finite Element method (WFE) and Wavenumber Boundary Element method (WBE). The damping of a typical structure is first measured in the laboratory to give suitable input values for the model. The predicted STL is compared with corresponding measurements of the sample panel, with good agreement above 400 Hz. Based on the validated model, an extensive parametric study is carried out to investigate the effect of different reinforcement rib styles on the STL. The effect of using extruded panels with rectangular, triangular and trapezoidal truss-core sections is studied in detail. Among the parameters studied, the number of bays in a given width has a great influence on the sound insulation. Considering practical use, both the mass and stiffness of each case are also considered. To give increased understanding of the STL behaviour, the dispersion curves are also studied. It is found that structures with better STL usually have fewer free wavenumbers below the acoustic wavenumber. For the same number of structural bays, a panel with triangular stiffening has the highest strength but also the largest mass, whereas a structure with rectangular stiffening has the least strength and lowest mass. In the evaluation, the weighted STL Rw and the spectral adaptation term Ctr are considered. The results are also considered relative to a mass law adjustment of the STL. It is found that the three cases which give the best results are a triangular rib panel with 4 or 5 bays in a 1 m width, and a trapezium case with 5 bays and inclination angle 25°. These have an Rw that is 2–6 dB better than the reference panel, a smaller mass and a higher stiffness.

Rail corrugation is very common in metro systems, and serious noise problems produced by rail corrugation, especially short-wavelength corrugations (25–50 mm), are a common cause of passenger complaints. For metro trains, the wheel-rail interface is the main source of noise, and the wheel-rail roughness, especially in the presence of rail corrugation, is the main excitation source. Rail grinding is a fast, economical, and effective control measure for reducing vibration and noise. However, the existing grinding cycle is not sufficient to meet the requirements of interior noise. There is no rail grinding standard based on interior noise limits for metro trains running on slab tracks in tunnels, which covers the vast majority of situations in China. Therefore, there is an urgent need to understand the effects of rail corrugation on interior noise for metro trains running on slab tracks in tunnels. At the same time, a rail grinding standard based on interior noise limits for such metro trains is very important. In this paper, the characteristics of the serious noise problems caused by rail corrugation are identified and suitable rail grinding controls based on noise limits are presented.

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 me...

Experiments were conducted at field sites to investigate the mechanism of the polygonal wear of electric locomotive wheels. The polygonal wear rule of electric locomotive wheels was obtained. Moreover, two on-track tests have been carried out to investigate the vibration characteristics of the electric locomotive's key components. The measurement results of wheels out-of-round show that most electric locomotive wheels exhibit polygonal wear. The main centre wavelength in the 1/3 octave bands is 200 mm and/or 160 mm. The test results of vibration characteristics indicate that the dominating frequency of the vertical acceleration measured on the axle box is approximately equal to the passing frequency of a polygonal wheel, and does not vary with the locomotive speed during the acceleration course. The wheelset modal analysis using the finite element method (FEM) indicates that the first bending resonant frequency of the wheelset is quite close to the main vibration frequency of the axle box. The FEM...

The resonance vibration of flexible car-bodies greatly affects the dynamics performances of high-speed trains. In this paper, we report a three-dimensional train–track model to capture the flexible vibration features of high-speed train carriages based on the flexible multi-body dynamics approach. The flexible car-body is modelled using both the finite element method (FEM) and the multi-body dynamics (MBD) approach, in which the rigid motions are obtained by using the MBD theory and the structure deformation is calculated by the FEM and the modal superposition method. The proposed model is applied to investigate the influence of the flexible vibration of car-bodies on the dynamics performances of train–track systems. The dynamics performances of a high-speed train running on a slab track, including the car-body vibration behaviour, the ride comfort, and the running safety, calculated by the numerical models with rigid and flexible car-bodies are compared in detail. The results show that the car-bo...

Local rolling contact fatigue (LRCF) has occasionally been observed on wheels of high-speed electrical multiple units (EMUs) in recent years in China. It typically propagates to 2.5–8.5 mm deep along shallow angles to the tread surface, leading to large material removal during lathe turning. To reveal the initiation and propagation mechanisms of LRCF, a thorough investigation has been conducted by means of field observations, statistical analyses, and numerical simulations. It is found that 69% of LRCF occurred on the leading axles of leading coaches, and its occurrence rate on the 380 km/h class EMU was 2.87 times that on the 250 km/h class. Records of a 380 km/h class EMU train have shown that LRCF initiated with an occurrence rate of 14.3% from indentations of 2.3–3.0 mm deep and 4 mm in diameter, and the crack depth increased by 0.011–0.031 mm every 1000 km. All these phenomena, among others, suggest that indentations are the main causes of LRCF. The cracks, according to 3D transient and 2D static simulations of wheel–rail rolling contact, probably initiate at the bottom of deep indentations with a characteristic dimension longer than 2–4 mm. Preventive measures against LRCF are recommended at the end.

In this paper, we present a comprehensive model for the prediction of the evolution of high-speed train wheel profiles due to wear. The model consists of four modules: a multi-body model implemented with the commercial multi-body software SIMPACK to evaluate the dynamic response of the vehicle and track; a local contact model based on Hertzian theory and a novel method, named FaStrip (Sichani et al., 2016), to calculate the normal and tangential forces, respectively; a wear model proposed by the University of Sheffield (known as the USFD wear function) to estimate the amount of material removed and its distribution along the wheel profile; and a smoothing and updating strategy. A simulation of the wheel wear of the high-speed train CRH3 in service on the Wuhan-Guangzhou railway line was performed. A virtual railway line based on the statistics of the line was used to represent the entire real track. The model was validated using the wheel wear data of the CRH3 operating on the Wuhan- Guangzhou line, monitored by the authors’ research group. The results of the predictions and measurements were in good agreement.

This paper presents a detailed investigation, via field experiment, into the mechanism of high-order polygonal wear of wheels of a new type of high-speed train. The investigation was carried out during the performance acceptance test of the train and its initial commercial operation. The investigation covered the performance acceptance test of 150 000 km and the commercial operation of about 150 000 km. In the performance acceptance test of the first stage of about 70 000 km, at 200–250 km/h with full loading and sometimes overloading by 30%, the serious polygonal wear of 23-order took place on all the wheels of the train, and was measured and analyzed in detail. All the polygonized wheels were re-profiled because the polygonal wear had caused strong vibration and damage to the train parts. After re-profiling, the vibration of the train and track and the wear status of the wheels were measured and analyzed at different test mileages according to the polygonal wear situation of the wheels. The measured vibration of the train includes the accelerations at different positions of a motor car and a trail car. The vibration modes of the key parts of the bogies of the two cars were calculated. Meanwhile, the track resonant frequencies were investigated at the site. The purpose of the above tests and analysis is try to find the frequency of work mode matching the passing frequency of the high-order wheel polygon. The present investigation shows that one of the working models causes the formation and development of the high-order wheel polygonal wear. The growth of this wear was effectively reduced through the frequent changing of the running speed of the train operating on the way back and forth every day.

A new approach has been developed to determine the dynamic amplification factors of railways. This approach employs a traditional multi-body dynamic model of vehicle–track interaction and a 3D explicit finite element model of wheel–rail rolling contact to treat the low- and high-frequency dynamics, respectively. Excitations are considered by contact surface unevenness and more specifically, by the power spectrum density of track irregularity for the low-frequency analysis and by the critical wheel flat, weld, and rail corrugation for the high frequency. For the 40-tonne axle load heavy haul railway simulated in this work, it has been found that the optimum fastening stiffness should be 150–200 MN/m; the dynamic amplification factors of the wheel–rail contact, fastening, and ballast forces are 1.94, 2.0, and 1.67, respectively, if the fastening stiffness of 200 MN/m is applied. Finally, new dynamic amplification factor formulae that include key parameters such as the fastening stiffness, speed, and axle load are proposed for the heavy haul railway design.

This paper presents a detailed investigation of out-of-round electric locomotive wheels through extensive measurement conducted at field sites. More than 2000 wheels, of seven types of locomotives widely used in China, have been measured since April 2013. The measurement results indicate that two types of freight traffic locomotives suffer serious polygonal wear problems with center wavelengths ranging from 160 to 315 mm. The dominating wavelength is 200 mm. Therefore, the investigations are mainly focused on the two locomotive types. The other types, which are taken for comparison, do not exhibit obvious polygonal wear. However, they exhibited more or less eccentricity. The effect of wheel re-profiling on the wheel polygon is also investigated and discussed. The dominating harmonic orders and center wavelengths after re-profiling are consistent with those before re-profiling at the correct circumstances, if the center wavelength of the polygonal wear is about 200 mm.

Cement asphalt mortar (CAM) softening is a common phenomenon that results from aging and rain soaking when a high-speed railway is in service. CAM softening seriously affects vehicle operation safety and track dynamics. In this paper, a 3D coupling dynamic model of a vehicle and a China railway track system I (CRTS-I) slab track is developed. By using the proposed model, the wheel-rail contact forces, derailment coefficient, wheelset loading reduction ratio, and the track displacements are calculated to study the influences of CAM softening on the dynamic characteristics of a vehicle-track system. A track-subgrade finite difference model is developed to study the effect of CAM softening on track damage. The results show that track interface shear failure develops when the CAM softening coefficients reach 10–100. The CAM softening coefficient should not be less than 1000, otherwise a high-speed running vehicle may risk derailment.

The objective of this paper is to develop a new wheel–rail contact model, which is suitable for considering the effect of wheelset bending deformation on wheel–rail contact behavior at high speeds. Dummies of the two rigid half wheelsets are introduced to describe the spacial positions of the wheels of the deformed wheelset. In modeling the flexible wheelset, the first two wheelset bending modes are considered. Based on the modal synthesis method, these mode values of the wheelset axle are used to solve the motion equations of the flexible wheelset axle modeled as an Euler–Bernoulli beam. The wheel is assumed to be rigid and always perpendicular to the deformed axle at the wheel center. In the vehicle model, two bogies and one car body are modeled as lumped masses. Spring–damper elements are adopted to model the primary and secondary suspension systems. The ballasted track is modeled as a triple-layer discrete elastic supported model. Two high-speed vehicle–track models, one considering rigid wheelset models and the other considering flexible wheelset models, are used to analyze the differences of the numerical results of the two models in both frequency and time domains. In the simulation, a random high-speed railway track irregularity is used as wheel–rail excitations. Wheel–rail forces are calculated and analyzed in the time and frequency domains. The results clarify that this new contact model can characterize very well the influence of the first two bending modes of the wheelset on contact behavior.

A 3D dynamic model of a high-speed train coupled with a flexible ballast track is developed and is presented in this study. In this model, each vehicle is modeled as a 42 degrees of freedom multi-body system, which takes into consideration the nonlinear dynamic characteristics of the suspensions. A detailed inter-vehicle connection model including nonlinear couplers and inter-vehicle dampers, and the linear tight-lock vestibule diaphragm is established to simulate the effect of the end connections of neighboring vehicles on dynamic behavior. The track is modeled as a traditional three-layer discrete elastic support model. The rails are assumed to be Timoshenko beams supported by discrete sleepers. Each sleeper is treated as an Euler beam and the ballast bed is replaced by equivalent rigid ballast bodies. The reliability of the present model is then validated through a detailed numerical simulation comparison with the commercial software SIMPACK, with the effect of the track flexibility on the train/track interaction being analyzed simultaneously. The proposed model is finally applied to investigate the difference between dynamic performances obtained using the entire-train/track model (TTM) and the single-vehicle/track model (VTM). Several key dynamic performances, including vibration frequency response, ride comfort, and curving performance, calculated by the two types of dynamic models are compared and discussed. The numerical results show that there is a significant difference between the dynamic behaviors obtained by VTM and TTM, and that inter-vehicle connections have an important influence on the dynamic behavior of high-speed vehicles.

Short pitch rail corrugations were observed on a recently opened Chinese high-speed line. On the basis of field measurements and observations of corrugations occurred on the high-speed line, a 3D transient rolling contact model is developed using the explicit finite element (FE) method to investigate high-speed vehicle-track interactions in the presence of rail corrugations. The rotational and translational movements of the wheel are introduced as initial conditions in the model. The frictional rolling contact between the wheel and the corrugated rail is solved by a penalty method based surface-to-surface contact algorithm with Coulomb’s law of friction. The contact filter effect is considered automatically by the finite size of the contact patch. Through specifying a time-dependent driving torque applied to the wheel axle, the tangential vehicle-track interaction on the corrugated rail is analyzed in the time domain together with the normal one at different traction levels and at rolling speeds of up to 500 km/h. This analysis focuses on detailed contact solutions, such as distributions of the pressure, surface shear stress, Von Mises (V-M) stress, and frictional work. The corrugation dimensions, traction level, and rolling speed are varied to investigate their influences, building a solid basis for further studying the material damage mechanisms. A theory is proposed based on the simulations to explain the observed phenomenon that the corrugation gradually stabilizes. The traditional multi-body approach is found to overestimate the dynamic wheel-rail interaction on a corrugated rail.

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 prop...

A 3-D explicit finite element model is developed to investigate the transient wheel–rail rolling contact in the presence of rail contamination or short low adhesion zones (LAZs). A transient analysis is required because the wheel passes by a short LAZ very quickly, especially at high speeds. A surface-to-surface contact algorithm (by the penalty method) is employed to solve the frictional rolling contact between the wheel and the rail meshed by solid elements. The LAZ is simulated by a varying coefficient of friction along the rail. Different traction efforts and action of the traction control system triggered by the LAZ are simulated by applying a time-dependent driving torque to the wheel axle. Structural flexibilities of the vehicle–track system are considered properly. Analysis focuses on the contact forces, creepage, contact stresses and the derived frictional work and plastic deformation. It is found that the longitudinal contact force and the maximum surface shear stress in the contact patch become...

A railway wheel installed with the web-mounted noise shielding and vibration damping assemblies is introduced in this paper. The shielding and damping assemble is alternant constrained to the both ends connecting to the tyre and hub. This design can produce shear strain in periodical variation, and then vibration energy of the shielding plate and the wheel is dissipated effectively. Assembles can also reduce the noise radiation from the wheel web. In order to investigate the vibration and sound radiation reduction of this new type of wheel relevant tests are carried out in a semi-anechoic room. In the test, damping ratio, acceleration, sound energy, sound field and directivity of the damping wheel are given and analyzed. The same tests are conducted for a standard wheel as a comparison. The test results show that the damping ratio of the damping wheel increases significantly compared to the standard one, especially for the damping ratios at the prominent resonance frequencies. The increase of the damping ratio is as much as 44 times. The sound energy levels (SEL) of the damping wheel in the overall range and at a dominant resonance frequency are, respectively, 15 and 40 dB, much less than those of the standard one. By comparing the sound fields and directivities of the two wheels, the sound radiation of the damping wheel is lower in all directions.

Rolling contact fatigue (RCF) was found on wheels of a type of Chinese high speed trains with a designed speed of 250 km/h. To understand its initiation mechanism and isolate the dominant parameters, a statistical analysis was first conducted based on observations of 47 trainsets. Subsequently, a monitoring test covering 2–3 periods of wheel re-profiling was performed in parallel with numerical analyses. This paper mainly presents the results of the statistical analysis and monitoring test. It was found that the RCF was caused by poor geometry match between wheels and low rails on curves, and a mileage of 100,000–150,000 km was often required for its initiation. With existing policies of wheel re-profiling, the RCF cracks can propagate to 0.25–1.2 mm deep. To optimize the re-profiling strategy, periodic re-profiling is proposed at mileages of 180,000, 380,000 and 600,000 km for each factory repair cycle.

This paper presents the results of a detailed experimental investigation of the abnormal vibration of the electric locomotive. A locomotive suffered from serious vibration problem was chosen for the test and its normal operations kept unchanged during the test. The wheel out-of-roundness (OOR) and vibrations of key components including the axle box, the bogie frame and the car body were measured before and after wheel re-profiling. The measured OOR results indicate that the wheels exhibit the OOR with orders 12 to 22 before re-profiling, i.e. with the center wavelengths of 200–315 mm in 1/3 octave bands. The wheel polygonal wear cannot be absolutely removed by the wheel re-profiling. The 16th–19th order OOR becomes to be dominant after re-profiling. The vibration test results show that the axle box, the bogie frame and the car body vibrate with the same dominant frequency before re-profiling. The dominant frequency of the vibration is approximately equal to the passing frequency of a polygonal wheel. The vibrations are significantly reduced after re-profiling. The wheel polygonal wear is the root cause of the abnormal vibration.

The vector form intrinsic finite element (V-5) method and the gap element method are combined to solve the static wheel/rail contact in two-dimensions in this paper to obtain the wheel/rail normal contact pressure, which would be compared with the normal contact pressure of ABAQUS and Hertz theory. The results showed that the contact pressure distribution of V-5 was consistent with ABAQUS and Hertzs, and the mechanical behavior of contact area was reasonable under the circumstance of different axle loads. Besides, it also verified the feasibility of adopting gap elements method to solve the static wheel/rail contact on the basis of vector form finite element method, which with the superiority of large rotation and large deformation, and laid the foundation of rolling wheel-rail contact behavior analysis.

The objective of this study is to investigate the adhesion characteristics of wheel/rail under oil contamination with consideration of surface roughness using a three-dimensional model of wheel/rail in rolling contact. A partial elastohydrodynamic lubrication theory is employed in the model. An under-relaxation revision on the film thickness is used to keep the simulation procedure stable. The dependence of the wheel/rail adhesion coefficient on train speed, surface roughness amplitude, parameter of roughness orientation and axle load is studied under oil contamination. Moreover, the numerical solutions of a two-dimensional model are compared with those of the three-dimensional model. In addition, a good agreement has been found between the numerical results and the experimental results obtained by a JD-1 wheel/rail simulation facility, which consists of a small wheel roller serving as locomotive or rolling stock wheel and a large wheel roller serving as rail.

In order to investigate the effect of a tangent track buckle on the dynamic derailment of a railway vehicle, a coupled vehicle/track dynamics model is developed, in which the vehicle is modeled as a 35 D.O.F. multibody system and the track is modeled as a 3-layer discrete elastic support model. Rails are assumed to be Timoshenko beams supported by discrete sleepers, and the effects of vertical and lateral motions and rolling of the rail on the wheel/rail creepages are taken into account. The sleepers are treated as Euler beams on elastic foundation for the vertical vibration, while as lumped masses in the lateral direction. A moving sleeper support model is developed to simulate the effect of the periodical discrete sleepers on the vehicle/track interaction. The vehicle and the track are coupled by wheel/rail contacts whereas the normal forces and the creep forces are calculated using the Hertzian contact theory and the nonlinear creep theory by Shen et al., respectively. The equations of motion of the coupled vehicle/track system are solved by means of an explicit integration method. A tangent track buckle is simulated with a cosine function, which describes the misalignment of the track with different lengths due to its buckling. In the analysis the effects of the buckle wavelength and amplitude and of the vehicle speed on the dynamic behavior of the coupled vehicle/track system are considered. The present paper analyzes in detail the conventional derailment coefficients which include the ratio of the wheel/rail lateral force to the vertical force, the wheel load reduction, and the new criteria indicating the wheel/rail contact point traces and the wheel rise with respect to the rail. These criteria are simultaneously used to evaluate the risk of derailment of the whole vehicle. The numerical results obtained indicate that the track misalignment caused by the buckle and the vehicle speed have a great influence on the whole vehicle running safety when the vehicle passes through the buckled tangent track.

A numerical model for dynamic vehicle–track interaction at rail welds with longitudinal surface irregularity is presented. In the model, the vehicle and track, except for the rails, are treated as rigid multi-body systems. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. The model is applied to calculate the dynamic wheel–rail contact forces and the sizes and locations of the contact areas. A three-dimensional finite element model of rail at welds is then built up to investigate the plastic deformation of rail. The contact forces, the sizes and locations of contact areas obtained by the vehicle–track dynamics simulation are utilized as the inputs to finite element model. The influence of different geometries of rail welds on the dynamic wheel–rail contact forces, stresses and deformations of rail is investigated. The analysis reveals that the train speed and the wavelength and wave depth of the irregularities at rail welds have great effects on the wheel–rail contact forces. The dynamic forces due to the welded rail surface irregularity cause increased plastic deformation not only at the rail weld but also at the base metal near the rail weld. The numerical results obtained are very useful in the tolerance design of welded rail surface irregularity.

Some important papers concerning the studies on rail wear and wheel/rail contact stresses are briefly reviewed. The present paper utilizes a numerical method to analyze the effect of railway vehicle curving on the wear and contact stresses of wheel/rail. The numerical method considers a combination of Kalker's non-Hertzian rolling contact theory, a material wear model and a vertical and lateral coupling dynamics model of the vehicle/track. In the analysis, the important factors influencing on the wear and the contact stresses are, respectively, the curving speed, the curved track super-elevation and the rail cant. Compared to the present model, some concerned models and results in the published papers are in detail discussed. Through the detailed numerical analysis, it is found that the difference between the normal loads of the left and right of the wheelset increases linearly with increasing the vehicle curving speed. The material wear volume per length along the rail running surface has a tendency to grow. However, the variation of the maximum normal contact stress has a large fluctuation as the curving speed increases. The increase of the maximum contact stress depends greatly on not only the normal load but also the profiles of the wheel/rail. Increasing the track super elevation efficiently lowers the normal load difference of the left and right of the front wheelset, and the contact stresses and the wear. The rail cant has a great influence on the low rail wear of the curve track. An increase in rail cant results in a great increase in the low rail wear of the curved track, and a decrease in the outside rail wear. These conclusions are very useful in the maintenance of the track.

The paper investigates into the effect of discrete track support by sleepers on the initiation and development of rail corrugation at a curved track when a railway vehicle passes through using a numerical method. The numerical method considers a combination of Kalker's rolling contact theory with non-Hertzian form, a linear frictional work model and a dynamics model of a half railway vehicle coupled with the curved track. The half-vehicle has a two-axle bogie and doubled suspension systems. It is treated as a full dynamic rigid multi-body model. In the track model, an Euler beam is used to model the rail, and the discrete track support by sleepers moving backward with respect to the vehicle running direction is considered to simulate the effect of the discrete sleeper support on the wheels/rails in rolling contact when the vehicle moves on the track. The sleeper is treated as a rigid body and the ballast bed is replaced with equivalent mass bodies. The numerical analysis exams in detail the variations of wheel/rail normal loads, the creepages, and the rail wear volume along the curved track. Their variations are much concerned with the discrete track support. The numerical results show that the discrete track support causes the fluctuating of the normal loads and creepages at a few frequencies. These frequencies comprise the passing frequency of the sleepers and the excited track resonant frequencies, which are higher than the sleeper passing frequency. Consequently, rail corrugation with several wavelengths initiates and develops. Also the results show that the contact vibrating between the curved rails and the four wheels of the same bogie has different frequencies. In this way, the different key frequencies to be excited play an important role in the initiation and development of curved rail corrugation. Therefore, the corrugations caused by the four wheels of the same bogie present different wavelengths. The paper shows and discusses the depths of the initial corrugations caused by the four wheels of the same bogie, at the entering transition curve, the circle curve and the exit transition curve of the curved track, respectively.

The paper reviews some important published papers on the effects of railway track imperfections on track dynamic behavior, and investigates the effect of unsupported sleepers on the normal load of wheel/rail in detail through a numerical simulation. The numerical simulation is based on a coupling dynamic model of vehicle–track. In the model, the vehicle is modeled as a multi-body system, and the track is considered as a 3-layer model with rails, sleepers, and ballast masses. Each rail of the track is modeled with a Timoshenko beam resting on discrete sleepers. The lateral, vertical, and torsional deformations of the beam are taken into account. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed, and therefore such a track model can consider the effect of the discrete support by sleepers on the coupling dynamic behavior of the vehicle and track in the simulation. In calculating the coupled vehicle and track dynamics, Hertzian contact theory and the theory by Shen et al. are, respectively, used to calculate the normal forces and the creep forces between the wheels and the rails. The motion equations of the vehicle–track are solved by means of an explicit integration method. A nonlinear spring and a nonlinear damper are used to simulate a gap between the unsupported sleeper and the ballast mass. The numerical results obtained indicate that the gaps between the unsupported sleepers and ballast masses have a great influence on the normal load of the wheel and the rail.

A finite element analysis is conducted to study dynamic elastic–plastic stress when a wheel passes a rail joint with height difference between the two sides of a gap. The ANSYS implicit code and LS-DYNA explicit code are coupled to simulate the process of the wheel contacting or impacting the rail joint. Contact elements are used to simulate the interactions between wheel and rails, between rails and joint bars, between joint bars and bolts and between bolts and rails. The effects of train speed, axle load and height difference on the contact forces, stresses and strains at railhead are investigated. Numerical results show that the presence of rail joint with height difference significantly affect the contact force, stress and strains. The results also indicate that the train speed has a larger effect on the contact force, stress and strains than the axle load.

Important published papers on rail wear in the past were reviewed. A numerical method was put forward to predict curved rail wear during a railway vehicle curving. The numerical method was discussed in detail. It considered a combination of Kalker’s non-Hertzian rolling contact theory, rail material wear model, the coupling dynamics of the vehicle and track, and the three-dimensional contact geometry analysis of wheel-rail. In its numerical implementation, the dynamical parameters of all the parts of the vehicle and track, such as normal loads and creepages of the wheels and rails, were firstly obtained through the curving dynamics analysis. The wheel-rail contact geometry calculation gave the wheel-rail contact geometry parameters, which were used in the wheel-rail rolling contact calculation with Kalker’s non-Hertzian rolling contact theory modified. The friction work densities on the contact areas of the wheels and rails were obtained in the rolling contact calculation, and were used to predict the rail running surface wears caused by the multiple wheels of the vehicle simultaneously with the rail material wear model. In the rail material wear model, it was assumed that the mass loss of each unit area was proportional to the frictional work density in the contact area. A numerical example was present to verify the present method. The numerical results of the example are reasonable, and indicate that the high rail wear of the curved track caused by the leading wheelset is much more serious than those caused by the other three wheels of the same bogie.

Research on rail corrugation were briefly reviewed. A rail corrugation model for the whole vehicle and the slab track was developed. It considered a combination of the coupling dynamics model of a whole vehicle and track, the modified Kalker’s non-Hertzian rolling contact model for wheel and rail, a material wear model and an accumulated wear model. It takes not only the effect of wheel/rail transient dynamic interaction on the formation and development of corrugation into account, but also the effect of the accumulated corrugation on the wheel/rail contact and coupling dynamics. That is, this model can take into account a feedback process between the long-term effects of the rail corrugation and the transient coupling dynamic of whole vehicle. This model can be used to study the formation mechanism of rail corrugation. And the initiation and development of the corrugations caused by various track defects, such as track gap, scratch, dent and random geometry irregularities, can be analyzed. A numerical example was presented to verify the procedure. The numerical results of the example are reasonable and indicate the development of corrugation in the initial stage after grinding.

The effect of disabled fastening systems and ballast on railway vehicle derailment is investigated by developing a nonsymmetrical coupled vehicle/track model. In the model a half passenger car is considered, and modeled with a multi-body system with 18 degrees of freedom, which runs on a tangent track at a constant speed. The tangent track is modeled as two elastic beams by discrete nonsymmetrical supporters modeling fastening systems, sleepers, and ballasts. The normal contact forces between wheels and rails are described by Hertzian elastic contact theory, and the tangential forces by the nonlinear creep theory of Shen et al. (Proceedings of the 8th IAVSD Symposium, Cambridge, MA, pp. 591–605). In the numerical analysis, the disabled rail fastening, rail pad, and ballast, on one and two sides of the track are, respectively, considered. Through a detailed analysis, derailment coefficients and the track state variations are obtained. The derailment coefficients are defined as the ratio of the lateral force to the vertical force of the wheel and rail (indicated by L∕V), duration of L∕V, and rate of the wheel load reduction (indicated by ΔV∕V), respectively. The variations of the contact points on the wheel treads, the track gauge, the track cross-level, and rail turnover angle are present in the paper. The numerical results obtained indicate that the failure of rail supports has a great influence on the vehicle running safety.

Rail corrugation is a main factor causing the vibration and noise from the structures of railway vehicles and tracks. A calculation model is put forward to analyse the effect of rail corrugation with different depths and wavelengths on the dynamical behaviour of a passenger car and a curved track in detail. Also the evolution of initial corrugation with different wavelengths is investigated. In the numerical analysis, Kalker's non-Hertzian rolling contact theory is modified and used to calculate the frictional work density on the contact area of the wheel and rail in rolling contact. The material loss per unit area is assumed to be proportional to the frictional work density to determine the wear depth of the contact surfaces of the curved rails. The combined influences of the corrugation development and the vertical and lateral coupled dynamics of the passenger car and the curved track are taken into account. The numerical results indicate that: (1) the corrugation with high passing frequencies has a great influence on the dynamical performance of the wheelset and track, but little on the car-body and the bogie frame; (2) the deeper the corrugation depth is, the greater the influence and the rail material wear are; but the longer the corrugation wavelength is, the smaller the influence and the wear are; and (3) the initial corrugation with a fixed wavelength on the rail running surface decreases with increasing number of the passenger car passages.

The effects of track vibration with its natural frequency in the vertical and lateral directions on the formation and development of rail corrugation are analysed in detail in the present study. Kalker's rolling contact theory with non-Hertzian form is modified and then used to calculate the frictional work density on the contact area of the wheel and rail in rolling when a wheelset is steadily curving. A model presenting the material loss of unit area proportional to the frictional work density is used to determine the wear of contact surface material of the rail. Due to the continuous and repeated rolling/slip contact of the wheel and rail the accumulation of the wear obtained by calculation reveals a periodical change in the rolling direction of the wheel. The numerical results also show that the track vibration with its natural frequencies can cause the formation of initial corrugation on the smooth contact surface of rail during the first passage of wheelset. The occurring wavelength of the corrugation depends on the frequencies and the rolling speed of the wheelset, and the depth and growth speed of corrugation depend on the vibration amplitude of the contact normal load and the lateral vibration of track.

The effect of track irregularities on rail corrugation is investigated in detail with the numerical method when a wheelset is steadily curving. The irregularities considered in the analysis include initial running surface of rail with periodically varying and different wave length, stochastic roughness on the rail running surface, and vertical uneven support stiffness of the rail due to the discrete sleeper supports. The numerical method considers a combination of Kalker's rolling contact theory with non-Hertzian to be modified, a linear frictional work model and a vertical dynamics model of railway vehicle coupled with a curved track. The model is also validated by an experiment with a full scale facility. The influence of different speeds of wheelset curving on the development of the corrugation is taken into account in the calculation. The numerical results indicate that (1) for existing of the initial corrugation of new rail with any wavelength the depth from the peak to trough of it decreases gradually with an increase of wheelset passage, but the initial corrugation evolved has a tendency to move in the rolling direction, (2) the amplitude of the initial stochastic roughness of new rail is gradually leveled out and but a corrugation with very small depth and a few fixed passing frequencies is initiated, the passing frequencies are the same as the natural frequencies of the track, and (3) the discrete rail supports by sleepers have a great influence on the formation of the corrugation.

The effect of a scratch formed on the running surface of a curved rail, due to the slide of a locomotive wheel, on the formation and evolution of rail corrugation is investigated in detail with numerical methods when a wheelset is steadily and repeatedly curving. In the calculation we consider a combination of Kalker’s rolling contact theory with non-Hertzian to be modified, a linear frictional work model and a vertical dynamics model of railway vehicle coupled with a curved track. Also the influence of different speeds of wheelset curving through the scratch on the development of the corrugation is taken into account. The numerical results indicate that a scratch causes strong contact vibration between the wheel and rail, and initiation and development of rail corrugation under the condition of steady creepage occurring between the wheel and curved rail. The wave-length of the corrugation depends on the speed of wheelset curving and the natural frequencies of the track.

The first-order bending deformation of wheelset is considered in the modeling vehicle/track coupling dynamic system to investigate its effect on wheel/rail contact behavior. In considering the effect of the first-order bending resonance on the rolling contact of wheel/rail, a new wheel/rail contact model is derived in detail in the modeling vehicle/track coupling dynamic system, in which the many intermediate coordinate systems and complex coordinate system transformations are used. The bending mode shape and its corresponding frequency of the wheelset are obtained through the modal analysis by using commercial software ANSYS. The modal superposition method is used to solve the differential equations of wheelset motion considering its flexible deformation due to the first-order bending resonance. In order to verify the present model and clarify the influence of the first-order bending deformation of wheelset on wheel/track contact behavior, a harmonic track irregularity with a fixed wavelength and a white-noise roughness are, respectively used as the excitations in the two models of vehicle-rail coupling dynamic system, one considers the effect of wheelset bending deformation, and the other does not. The numerical results indicate that the wheelset first-order bending deformation has an influence on wheel/rail rolling contact behavior and is easily excited under wheel/rail roughness excitation.

The window is one of the main components of the high speed train car body structure through which noise can be transmitted. To study the windows’ acoustic properties, the vibration of one window of a high speed train has been measured for a running speed of 250 km/h. The corresponding interior noise and the noise in the wheel-rail area have been measured simultaneously. The experimental results show that the window vibration velocity has a similar spectral shape to the interior noise. Interior noise source identification further indicates that the window makes a contribution to the interior noise. Improvement of the window’s Sound Transmission Loss (STL) can reduce the interior noise from this transmission path. An STL model of the window is built based on wave propagation and modal superposition methods. From the theoretical results, the window’s STL property is studied and several factors affecting it are investigated, which provide indications for future low noise design of high speed train windows.

The effect of track irregularities on the initiation and evolution of rail corrugation due to cyclic plastic deformation is investigated through a numerical method. The track irregularities studied in the analysis include an isolated irregularity (such as rail joint, scratch, squat) and periodically varying running surface of the rail. In the numerical method, the Hertz contact theory, an elastic-plastic finite element model and a vertical dynamics model for the railway vehicle coupled with the track are considered. An advanced cyclic plasticity model is used for the deformation analysis. The combined influences of the plastic deformation and the vertical coupling dynamics of the car and the track are taken into account in the corrugation development. The residual stresses and strains below the trough and crest of corrugation are obtained. The numerical results indicate that: (1) when a vehicle runs on rails with an isolated irregularity the contact vibration between the wheel and rail occurs at a large amplitude, and rail corrugation due to plastic deformation can be easily initiated and developed; (2) the passing frequencies of the plastic deformation induced rail corrugation are the same as the natural frequencies of the track; (3) the corrugation caused by the isolated irregularity and the periodically varying rail profile has a tendency to move along the running direction and its evolution rate decays with an increase in the wheelset passage; and, (4) the residual stresses stabilize after a limited number of rolling passes, and the residual strains increase at a reduced rate with increasing wheelset passages.

The present paper reviews the vibro-acoustic modelling of extruded aluminium train floor structures including the state-of-the-art of its industrial applications, as well as the most recent developments on mid-frequency modelling techniques in general. With the common purpose to predict mid-frequency vibro-acoustic responses of stiffened panel structures to an acceptable accuracy at a reasonable computational cost, relevant techniques are mainly based on one of the following three types of mid-frequency vibro-acoustic modelling principles: (1) enhanced deterministic methods, (2) enhanced statistical methods, and (3) hybrid deterministic/statistical methods. It is shown that, although recent developments have led to a significant step forward in industrial applicability, mature and adequate prediction techniques, however, are still very much required for solving sound transmission through, and radiation from, extruded aluminium panels used on high-speed trains. Due to their great potentials for predicting mid-frequency vibro-acoustics of stiffened panel structures, two of recently developed mid-frequency modelling approaches, i.e. the so-called hybrid finite element-statistical energy analysis (FE-SEA) and hybrid wave-based method-statistical energy analysis (WBM-SEA), are then recapitulated.

A calculation model is put forward to analyze the effect of a scratch on the running surface of a curved rail on initiation and growth of plastic deformation induced rail corrugation when a wheelset is steadily and repeatedly curving. The numerical method considers a combination of Carter’s two-dimensional contact theory, a two-dimensional elastic–plastic finite element model and a vertical dynamics model of railway vehicle coupled with a curved track. A concept of feedback between the corrugation development and the vertical coupling dynamics of the wheelset and track is involved. The cyclic ratchetting effect of the rail material under repeated contact loadings is taken into account. The numerical results indicate that when a vehicle runs on rails with a scratch the contact vibration between the wheel and rail occurs at large amplitude, and rail corrugation due to plastic deformation initiates and develops. The corrugation has a tendency to move along the running direction and its evolution rate decays as wheelset passages increase. The passing frequencies of the plastic deformation induced corrugation depend on the natural frequencies of the track. The residual stresses stabilize after a limited number of wheelset passages. The residual strains increase at a reduced rate with increasing wheelset passages.

When a railway vehicle passes through a track with different weld irregularities at high speed, the impact loading of the vehicle coupled with the track is investigated in detail using a coupled vehicle/track model. In this model, a half vehicle is considered and modeled as a multi-body system. In the track model, a Timoshenko beam resting on discrete sleepers is applied to model each rail. Each sleeper is modeled as a rigid body accounting for its vertical, lateral, roll motions. A moving sleeper support model is used to simulate the interaction of the vehicle and the track. The ballast bed is replaced with equivalent masses. The equivalent dampers and springs are used to replace the connections between the parts of the vehicle and track. In calculating the coupled vehicle and track dynamics, Hertzian contact theory and the creep force theory by Shen et al. are, respectively, used to calculate the normal forces and the creep forces between the wheels and the rails. The motion equations of the vehicle-track are solved by means of an explicit integration method. The weld rail irregularity is modeled by setting a local track vertical deviation at a rail weld joint, which is described with a simplified cosine function. In the numerical analysis the effect of the different wavelength, depth, the position of the welded joint in a sleeper span, and vehicle speed is taken into account. The numerical results obtained are greatly useful in the tolerance design of welded rail profile irregularity caused by damage and hand-grinding after rail welding.Copyright © 2008 by ASME