Train–track coupled dynamics analysis:system spatial variation on geometry,physics and mechanics

This paper aims to clarify the influence of system spatial variability on train–track interaction from perspectives of stochastic analysis and statistics.Considering the spatial randomness of system properties in geometry,physics and mechanics,the primary work is therefore simulating the uncertainties realistically,representatively and efficiently.With regard to the track irregularity simulation,a model is newly developed to obtain random sample sets of track irregularities by transforming its power spectral density function into the equivalent track quality index for representation based on the discrete Parseval theorem,where the correlation between various types of track irregularities is accounted for.To statistically clarify the uncertainty of track properties in physics and mechanics in space,a model combining discrete element method and finite element method is developed to obtain the spatially varied track parametric characteristics,e.g.track stiffness and density,through which the highly expensive experiments in situ can be avoided.Finally a train–track stochastic analysis model is formulated by integrating the system uncertainties into the dynamics model.Numerical examples have validated the accuracy and efficiency of this model and illustrated the effects of system spatial variability on train–track vibrations comprehensively.

Improved Dynamics Model of Locomotive Traction Motor with Elasticity of Rotor Shaft and Supporting Bearings

The locomotive traction motor is described as a rotor-bearing system coupling the kinetic equations of the traction shaft and its support bearings with the determination of their elastic deformations in this study.Under the effect of excitations induced by the dynamic rotor eccentric distance and time-varying mesh stiffness,the elastic structure deformations of the shaft and support bearings are formulated in the vibration environment of the locomotive.In addition,the nonlinear contact forces between the components of the rolling bearing,the lubricating oil film,and radial clearance are comprehensively considered in this study.The results indicate that the elastic deformations of the shaft and bearings can change the dynamic responses of the traction motor and its support bearings.There are large differences between the ranges of the rotor motion calculated by the rigid and the flexible traction motor models when the intensified wheel-rail interaction is considered.With the increase of the rotor eccentricity,the results underscore the role of the elasticity of traction shaft and support bearings in dynamic researches of the traction motor.The critical value of the initial eccentric distance for the rub-impact phenomenon decreases from 1.23 mm to 1.15 mm considering the flexible effect of the shaft and bearings.This dynamics model of the traction motor can provide more accurate and reasonable simulation results for correlational dynamic researches.

Influence of railway wheel tread damage on wheel-rail impact loads and the durability of wheelsets

Dynamic wheel-rail contact forces induced by a severe form of wheel tread damage have been measured by a wheel impact load detector during full-scale field tests at different vehicle speeds.Based on laser scanning,the measured three-dimensional damage geometry is employed in simulations of dynamic vehicle-track interaction to calibrate and verify a simulation model.The relation between the magnitude of the impact load and various operational parameters,such as vehicle speed,lateral position of wheel-rail contact,track stiffness and position of impact within a sleeper bay,is investigated.The calibrated model is later employed in simulations featuring other forms of tread damage;their effects on impact load and subsequent fatigue impact on bearings,wheel webs and subsurface initiated rolling contact fatigue of the wheel tread are assessed.The results quantify the effects of wheel tread defects and are valuable in a shift towards condition-based maintenance of running gear,and for general assessment of the severity of different types of railway wheel tread damage.

Dynamic analysis of traction motor in a locomotive considering surface waviness on races of a motor bearing

The traction motor is the power source of the locomotive.If the surface waviness occurs on the races of the motor bearing,it will cause abnormal vibration and noise,accelerate fatigue and wear,and seriously affect the stability and safety of the traction power transmission.In this paper,an excitation model coupling the time-varying displacement and contact stiffness excitations is adopted to investigate the effect of the surface waviness of the motor bearing on the traction motor under the excitation from the locomotive-track coupled system.The detailed mechanical power transmission path and the internal/external excitations(e.g.,wheel–rail interaction,gear mesh,and internal interactions of the rolling bearing)of the locomotive are comprehensively considered to provide accurate dynamic loads for the traction motor.Effects of the wavenumber and amplitude of the surface waviness on the traction motor and its neighbor components of the locomotive are investigated.The results indicate that controlling the amplitude of the waviness and avoiding the wavenumber being an integer multiple of the number of the rollers are helpful for reducing the abnormal vibration and noise of the traction motor.

Interaction of subway LIM vehicle with ballasted track in polygonal wheel wear development

This paper develops a coupled dynamics model for a linear induction motor （LIM） vehicle and a subway track to investigate the influence of polygonal wheels of the vehicle on the dynamic behavior of the system. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom. A Timoshenko beam is used to model the rails which are discretely supported by sleepers. The sleepers are modeled as rigid bodies with their vertical, lateral, and rolling motions being considered. In order to simulate the vehicle running along the track, a moving sleeper support model is introduced to simulate the excitation by the discrete sleeper supporters, in which the sleepers are assumed to move backward at a constant speed that is the same as the train speed. The Hertzian contact theory and the Shen– Hedrick–Elkins’ model are utilized to deal with the normal dynamic forces and the tangential forces between wheels and rails, respectively. In order to better characterize the linear metro system （LMS）, Euler beam theory based on modal superposition method is used to model LIM and RP. The vertical electric magnetic force and the lateral restoring force between the LIM and RP are also taken into consideration. The former has gap-varying nonlinear characteristics, whilst the latter is considered as a constant restoring force of 1 kN. The numerical analysis considers the effect of the excitation due to polygonal wheels on the dynamic behavior of the system at different wear stages, in which the used data regarding the polygonal wear on the wheel tread are directly measured at the subway site.

Numerical simulation of wheel wear evolution for heavy haul railway

The prediction of the wheel wear is a fundamental problem in heavy haul railway. A numerical methodology is introduced to simulate the wheel wear evolution of heavy haul freight car. The methodology includes the spatial coupling dynamics of vehicle and track, the three-dimensional rolling contact analysis of wheel-rail, the Specht's material wear model, and the strategy for reproducing the actual operation conditions of railway. The freight vehicle is treated as a full 3D rigid multi-body model. Every component is built detailedly and various contact interactions between parts are accurately simulated, taking into account the real clearances. The wheel-rail rolling contact calculation is carried out based on Hertz's theory and Kalker's FASTSIM algorithm. The track model is built based on field measurements. The material loss due to wear is evaluated according to the Specht's model in which the wear coefficient varies with the wear intensity. In order to exactly reproduce the actual operating conditions of railway,dynamic simulations are performed separately for all possible track conditions and running velocities in each iterative step.Dimensionless weight coefficients are introduced that determine the ratios of different cases and are obtained through site survey. For the wheel profile updating, an adaptive step strategy based on the wear depth is introduced, which can effectively improve the reliability and stability of numerical calculation. At last, the wear evolution laws are studied by the numerical model for different wheels of heavy haul freight vehicle running in curves. The results show that the wear of the front wheelset is more serious than that of the rear wheelset for one bogie, and the difference is more obvious for the outer wheels. The wear of the outer wheels is severer than that of the inner wheels. The wear of outer wheels mainly distributes near the flange and the root; while the wear of inner wheels mainly distributes around the nominal rolling circle. For the outer wheel of front wheelset of each bogie, the development of wear is gradually concentrated on the flange and the developing speed increases continually with the increase of traveled distance.

Research on rail wear of small radius curve in EMU depot

Purpose–With the help of multi-body dynamics software UM,the paper uses Kik–Piotrowski model to simulate wheel-rail contact and Archard wear model for rail wear.Design/methodology/approach–The CRH5 vehicle-track coupling dynamics model is constructed for the wear study of rails of small radius curves,namely 200 and 350 m in Guangzhou East EMU Depot and those 250 and 300 m radius in Taiyuan South EMU Depot.Findings–Results show that the rail wear at the straight-circle point,the curve center point and the circlestraight point follows the order of center point>the circle-straight point>the straight-circle point.The wear on rail of small radius curves intensifies with the rise of running speed,and the wearing trend tends to fasten as the curve radius declines.The maximum rail wear of the inner rail can reach 2.29 mm,while that of the outer rail,10.11 mm.Originality/value–With the increase of the train passing number,the wear range tends to expand.The rail wear decreases with the increase of the curve radius.The dynamic response of vehicle increases with the increase of rail wear,among which the derailment coefficient is affected the most.When the number of passing vehicles reaches 1 million,the derailment coefficient exceeds the limit value,which poses a risk of derailment.

Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Employing theory on vehicle-track coupled dynamics, the equation of motion of a vehicle-track vertical coupled system was established by combining frequency analysis and symplectic mathematics. The frequency response of the vehicle-track vertical coupled system was calculated under the excitation of the German low-interfer- ence spectrum, and the effects of the vehicle speed, vehicle suspension parameters, and track support parameters on the frequency response of the coupled system were studied. Results show that, under the excitation of the German low- interference spectrum, the vertical vibration of the car body is mainly concentrated in the low-frequency band, while that of the bogie has a wide frequency distribution, being strong from several Hertz to dozens of Hertz. The vertical vibrations of the wheel-rail force, wheelset, and track structure mainly occur at a frequency of dozens of Hertz. In general, the vertical vibration of the vehicle-track coupled system increases with vehicle speed, and the vertical vibrations of the car body and bogie obviously shift to higher frequency. Increasing the vehicle suspension stiffness increases the low- frequency vibrations of the vehicle system and track struc- ture. With an increase in vehicle suspension damping, the low-frequency vibrations of the car body and bogie and the vibrations of the wheel-rail vertical force and track structure decrease at 50-80 Hz, while the mid-frequency and high- frequency vibrations of the car body and bogie increase. Similarly, an increase in track stiffness amplifies the vertical vibrations of the wheel-rail force and track structure, while an increase in track damping effectively reduces the vertical vibrations of the wheel-rail vertical force and track structure.

Evolution and formation mechanism of rail corrugation in high-speed railways involving the longitudinal wheel-track coupling relationship

Rail corrugation poses a significant threat to train running safety in the field of railway engineering.Therefore,this study employs numerical analysis to investigate the evolution and formation mechanism of rail corrugation in high-speed railways(HSR).Firstly,a three-dimensional(3D)vehicle-track coupled dynamics(VTCD)model is established,which considers the longitudinal wheel-rail(WR)coupling relationship more adequately.Then,by integrating the USFD wear model into this 3D VTCD model,a long-term iterative wear model is developed to reproduce the corrugation evolution process.The predicted corrugation exhibits two distinct wavelength components and closely matches the sample obtained from China's HSR,validating the established model in terms of reliability.Furthermore,the formation mechanism of these two wavelength components is investigated by analyzing the harmonic behavior of vehicle-track coupled systems(VTCS)and the evolution law of rail corrugation under different calculation conditions.The findings reveal that the 3rd-order vertical rail local bending mode(RLBM)between two wheelsets of a bogie(TW-B)is the primary factor contributing to the formation of the long-wavelength component of rail corrugation.The discrete supports of the fasteners do not affect the 3rd-order vertical RLBM,which can be stably excited.Moreover,the vertical rail vibration has a substantial coupled effect on the longitudinal WR creep.When the 3rd-order vertical RLBM is excited,the coupled effect and the negative longitudinal WR creepage together evidently promote the formation of the short-wavelength component of rail corrugation.

Damage evolution and dynamic response of cement asphalt mortar layer of slab track under vehicle dynamic load

The damage evolution and dynamic performance of a cement asphalt(CA)mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper.Initially,a statistical damage constitutive model for the CA mortar layer is developed using continuous damage mechanics and probability theory.In this model,the strength of the CA mortar elements is treated as a random variable,which follows the Weibull distribution.The inclusion of strain rate dependence affords considering its influence on the damage development and the transition between viscosity and elasticity.Comparisons with experimental data support the reliability of the model.A three-dimensional finite element(FE)model of a slab track is then created with the commercial software ABAQUS,where the devised model for the CA mortar is implemented as a user-defined material subroutine.Finally,a vertical vehicle model is coupled with the FE model of the slab track,through the wheel-rail contact forces,based on the nonlinear Hertzian contact theory.The evolution of the damage and of the dynamic performance of the CA mortar layer with various initial damage is investigated under the train and track interaction.The analysis indicates that the proposed model is capable of predicting the damage evolution of the CA mortar layer exposed to vehicle dynamic load.The dynamic compressive strain,the strain rate,and the induced damage increase significantly with an increase in the initial damage,whereas the dynamic compressive stress exhibits a sharp decrease with the increasing initial damage.Also,it is found that the strain rate dependence significantly influences the damage evolution and the dynamic behavior of the CA mortar layer.

A frequency and amplitude dependent model of rail pads for the dynamic analysis of train-track interaction

A frequency and amplitude dependent model is used to describe the complex behavior of rail pads. It is implemented into the dynamic analysis of three dimensional coupled vehicle-slab track （3D-CVST） systems. The vehicle is treated as a 35-degree- of-freedom multi-body system, and the slab track is represented by two continuous Bernoulli-Euler beams supported by a se- ries of elastic rectangle plates on a viscoelastic foundation. The rail pad model takes into account the influences of the excita- tion frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, re- spectively. The Granwald representation of the fractional derivatives is employed to numerically solve the fractional and non- linear equations of motion of the 3D-CVST system by means of an explicit integration algorithm. A dynamic analysis of the 3D-CVST system exposed to excitations of rail harmonic irregularities is primarily carried out, which reveals the dependence of stiffness and damping on excitation frequency and displacement amplitude. Subsequently, sensitive analyses of the model parameters are investigated by conducting the dynamic analysis of the 3D-CVST system subjected to excitations of welded rail joint irregularities. Following this, parameters of the rail pad model are optimized with respect to experimental values. For elu- cidation, the 3D-CVST dynamic model incorporated with the rail pads model is used to calculate the wheel/rail forces induced by excitations of measured random track irregularities. Further, the numerical results are compared with experimental data, demonstrating the reliability of the proposed model.

Time-domain model for wheel-rail noise analysis at high operation speed

This paper develops a numerical model for wheel-rail noise analysis in the time-domain. This model for wheel-rail noise is based on vehicle-track coupling dynamics considering the effect of flexible wheelsets and track, and a transient wheel-rail noise prediction method. This model can approximatively characterize the components of vibration and noise in the frequency range up to 3.5 kHz. The wheel-rail forces are calculated and shown in both time and frequency domains by using the vehicle- track coupling dynamic model. Then the vibration and sound of the flexible wheelset are calculated by the transient finite element- boundary element （FE-BE） prediction model at 300 kin/h, in which the effects of random irregularity and discrete supporting excitation are considered. The numerical results calculated by using the present model are discussed. The present model is also used to calculate the effect of corrugation with wavelengths of 40 mm to 300 mm on wheel-rail noise. The numerical results can be useful for academic research and engineering application to railway noise and vibration.