Effect of rail corrugation on vertical dynamics of railway vehicle coupled with a track

The effect of rail corrugation on the vertical dynamics of railway vehicle coupled with a curved track is investigated in detail with a numerical method when a wheelset is steadily curving. In the calculation of rail corrugation we consider the combination of Kalkers rolling contact theory modified, a model of material loss on rail running surface, and a dynamics model of railway vehicle coupled with a curved track. In the establishment of the dynamic model, for simplicity, one fourth of the freight car without lateral motions, namely a wheelset and the equivalent one fourth freight car body above it, is considered. The Euler beam is used to model the rails and the track structure under the rails is replaced with equivalent springs, dampers and mass bodies. The numerical results show the great influence of the rail corrugation on the vibration of the parts of the vehicle and the track, and the some characters of rail corrugation in development.

Lateral Stability Analysis of Heavy-Haul Vehicle on Curved Track Based on Wheel/Rail Coupled Dynamics

Being viewed from the standpoint of whole system, the hunting stability of a heavy-haul railway vehicle on a curved track is investigated in this paper. First, a model to simulate dynamic performance of the heavy-haul vehicle on the elastic track is developed. Secondly, the reason of the hunting motion is analyzed, and a bifurcation diagram for the vehicle on the curved track is put forward to simulate the nonlinear critical speed. Results show that the hunting motion of the heavy-haul vehicle will appear due to the larger conicity, the initial lateral shift and the wheelset angle of attack. With the hunting motion appearing, the lateral shift and force of the wheelset are changed sharply and periodically with a wave of circa 3.6 m. There is obvious difference in the bifurcation diagram between on a curved track and on a tangent track. Relative to the centerline of the track, each vehicle body on the curved track has two stable cycles. As for the curved track with a radius of 600 m and a superelevation of 55 mm, the nonlinear critical speed of the heavy-haul vehicle is 76.4 km/h.

High-speed tracked vehicle model order reduction for static and dynamic simulations

In this paper, a model order reduction strategy is adopted for the static and dynamic behaviour simulation of a high-speed tracked vehicle. The total number of degree of freedom of the structure is condensed through a selection of interface degrees of freedom and significant global mode shapes, for an approximated description of vehicle dynamic behaviour. The methodology is implemented in a customised open-source software to reduce the computational efforts. The modelled tracked vehicle includes the sprung mass, the unsprung masses, connected by means of torsional bars, and all the track assemblies, composing the track chain. The proposed research activity presents a comprehensive investigation of the influence of the track chain, combined with longitudinal vehicle speed, on statics and vehicle dynamics, focusing on vertical dynamics. The vehicle response has been investigated both in frequency and time domain. In this last case road-wheel displacements are assumed as inputs for the model, under different working conditions, hence considering several road profiles with different amplitudes and characteristic excitation frequencies. Simulation results have proven a high fidelity in model order reduction approach and a significant contribution of the track chain in the global dynamic behaviour of the tracked vehicle.

Multi-Body Dynamics Modeling of Heavy Goods Vehicle-Rail Interaction

Based on the principle of vehicle-track coupling dynamics, SIMPACK multi-body dynamics software is used to establish a C80 wagon line-coupled multi-body dynamics model with 73 degrees of freedom. And the reasonableness of the line-coupled dynamics model is verified by using the maximum residual acceleration, the nonlinear critical speed of the wagon. The experimental results show that the established vehicle line coupling dynamics model meets the requirements of vehicle line coupling dynamics modeling.

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.

Dynamic model of vertical vehicle-subgrade coupled system under secondary suspension

As it is known, track transportation can be divided into track system above and track system below. While the train is moving, the parts above and below are interacted and influenced. Therefore, in fact, the problem of track transportation is the match between the vehicle and the raihvay line system. In this paper, on a basis of dynamic analysis of the vehicle-subgrade model of vertical coupled system under primary suspension, utilizing track maintenance standard and simulating track irregularity excitation, the dynamic interaction of vehicle-track-subgrade system is researched in theory and dynamic model of the vertical vehicle-track-subgrade coupled system under secondary suspension is established by compatibility condition of deformation. Even this model considers the actual structure of a vehicle, also considers vibration characteristic of the substructure of track including subgrade and foundation. All these work want to be benefit for understanding and design about the dynamic characters of subgrade in high speed railway.

Numerical analysis of dynamic response of vehicle–bridge coupled system on long-span continuous girder bridge

To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.

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.

A vertical coupling dynamic analysis method and engineering application of vehicle–track–substructure based on forced vibration

Purpose–This study aims to propose a vertical coupling dynamic analysis method of vehicle–track–substructure based on forced vibration and use this method to analyze the influence on the dynamic response of track and vehicle caused by local fastener failure.Design/methodology/approach–The track and substructure are decomposed into the rail subsystem and substructure subsystem,in which the rail subsystem is composed of two layers of nodes corresponding to the upper rail and the lower fastener.The rail is treated as a continuous beam with elastic discrete point supports,and spring-damping elements are used to simulate the constraints between rail and fastener.Forced displacement and forced velocity are used to deal with the effect of the substructure on the rail system,while the external load is used to deal with the reverse effect.The fastener failure is simulated with the methods that cancel the forced vibration transmission,namely take no account of the substructure–rail interaction at that position.Findings–The dynamic characteristics of the infrastructure with local diseases can be accurately calculated by using the proposed method.Local fastener failure will slightly affect the vibration of substructure and carbody,but it will significantly intensify the vibration response between wheel and rail.The maximum vertical displacement and the maximum vertical vibration acceleration of rail is 2.94 times and 2.97 times the normal value,respectively,under the train speed of 350 km$h
1.At the same time,the maximum wheel–rail force and wheel load reduction rate increase by 22.0 and 50.2%,respectively,from the normal value.Originality/value–This method can better reveal the local vibration conditions of the rail and easily simulate the influence of various defects on the dynamic response of the coupling system.

Numerical Prediction of Ride Comfort of Tracked Vehicle Equipped with Novel Flexible Road Wheels

Enhancing ride comfort has always constituted a crucial focus in the design and research of modern tracked vehicles,heavily reliant on the driving system's performance.While the road wheel is a key component of the driving system,traditional road wheels predominantly adopt a solid structure,exhibiting subpar adhesion performance and damping effects,thereby falling short of meeting the demands for high-speed,stable,and long-distance driving in tracked vehicles.Addressing this issue,this paper proposes a novel type of flexible road wheel(FRW)characterized by a catenary construction.The study investigates the ride comfort of tracked vehicles equipped with flexible road wheels by integrating finite element and vehicle dynamic.First,three-dimensional(3D)finite element(FE)models of both flexible and rigid road wheels are established,considering material and contact nonlinearities.These models are validated through a wheel radial loading test.Based on the validated FE model,the paper uncovers the relationship between load and radial deformation of the road wheel,forming the basis for a nonlinear mathematical model.Subsequently,a half-car model of a tracked vehicle with seven degrees of freedom is established using Newton's second law.A random road model,considering the track effect and employing white noise,is constructed.The study concludes by examining the ride comfort of tracked vehicles equipped with flexible and rigid road wheels under various speeds and road grades.The results demonstrate that,in comparison to the rigid road wheel(RRW),the flexible road wheel enhances the ride comfort of tracked vehicles on randomly uneven roads.This research provides a theoretical foundation for the implementation of flexible road wheels in tracked vehicles.

Dynamic thermo-mechanical responses of road-soft ground system under vehicle load and daily temperature variation

A complete road-soft ground model is established in this paper to study the dynamic responses caused by vehicle loads and/or daily temperature variation.A dynamic thermo-elastic model is applied to capturing the behavior of the rigid pavement,the base course,and the subgrade,while the soft ground is characterized using a dynamic thermo-poroelastic model.Solutions to the road-soft ground system are derived in the Laplace-Hankel transform domain.The time domain solutions are obtained using an integration approach.The temperature,thermal stress,pore water pressure,and displacement responses caused by the vehicle load and the daily temperature variation are presented.Results show that obvious temperature change mainly exists within 0.3 m of the road when subjected to the daily temperature variation,whereas the stress responses can still be found in deeper places because of the thermal swelling/shrinkage deformation within the upper road structures.Moreover,it is important to consider the coupling effects of the vehicle load and the daily temperature variation when calculating the dynamic responses inside the road-soft ground system.

Dynamic Simulation of Tracked Vehicle Using the DADS Software

The track model used in the dynamic analysis and design system software is investigated. A home made tank is taken as an example to illustrate the method for modeling an integral tracked vehicle and perform the dynamic simulation. The obtained results have demonstrated that the simulation method has the advantage of high efficiency, more convenience and more insight into the dynamical behavior of the system.

Trajectory tracking control for underactuated unmanned surface vehicles with dynamic uncertainties

The trajectory tracking control problem for underactuated unmanned surface vehicles(USV) was addressed, and the control system took account of the uncertain influences induced by model perturbation, external disturbance, etc. By introducing the reference, trajectory was generated by a virtual USV, and the error equation of trajectory tracking for USV was obtained, which transformed the tracking problem of underactuated USV into the stabilization problem of the trajectory tracking error equation. A backstepping adaptive sliding mode controller was proposed based on backstepping technology and method of dynamic slide model control. By means of theoretical analysis, it is proved that the proposed controller ensures that the solutions of closed loop system have the ultimate boundedness property. Simulation results are presented to illustrate the effectiveness of the proposed controller.

A Study on the Dynamic Analysis of A Tracked Vehicle for Ocean Mining on the Deep Seabed

A study is presented on the dynamic analysis of a tracked vehicle for mining on the deep seabed of very soft soil. Equations for the interaction between the track and extremely soft seabed are employed to develop a track/soil interaction module called TVAS. The vehicle is modeled as a multibody dynamic system by the use of a multibody dynamic analysis program. The module developed is cooperated with the multibody dynamic analysis program with a user-defined subroutine. The dynamic behavior and the conceptual design of the mining vehicle on the deep seabed are investigated.

Influence of vehicle-road coupled vibration on tire adhesion based on nonlinear foundation

The influence of pavement vibration on tire adhesion is of great significance to the structure design of vehicle and pavement.The adhesion between tire and road is the key to studying vehicle dynamics,and the precise description of tire adhesion affects the accuracy of dynamic vehicle responses.However,in most models,only road roughness is considered,and the pavement vibration caused by vehicle-road interaction is ignored.In this paper,a vehicle is simplified as a spring-mass-damper oscillator,and the vehicle-pavement system is modeled as a vehicle moving along an Euler-Bernoulli beam with finite length on a nonlinear foundation.The road roughness is considered as a sine wave,and the shear stress is ignored on the pavement.According to the contact form between tire and road,the LuGre tire model is established to calculate the tire adhesion force.The Galerkin method is used to simplify the partial differential equations of beam vibration into finite ordinary differential equations.A product-to-sum formula and a Dirac delt function are used to deal with the nonlinear term caused by the nonlinear foundation,which realizes the fast and accurate calculation of super-high dimensional nonlinear ordinary differential equations.In addition,the dynamic responses between the coupled system and the traditional uncoupled system are compared with each other.The obtained results provide an important theoretical basis for research on the influence of vehicle-road coupled vibration on tire adhesion.

Rigid-Flexible Coupling Dynamic Analysis of Sub-Launched Vehicle During the Vertical Tube-Exit Stage

During the launching stage,hydrodynamic pressure and adapters' reaction loads can influence the vehicle's rigid motion as well as cause its structural vibration,which is a typical rigid-flexible coupling dynamic problem. This paper presents a 2-D rigid-flexible coupling model to calculate the vehicle's dynamic responses in that period.The vehicle was equivalent to a flexure beam with axial deformation. Hybrid coordinate and modal superposition methods were used to describe its large rigid displacement and small deformation. By the second Lagrange equation,the vehicle centroid's displacements,rotational angle and modal coordinates were chosen as generalized coordinates and then the vehicle 's rigid-flexible coupling dynamic equations were obtained. By numerical simulation,the results of vehicle's motion parameters and transverse internal loads were acquired.The calculation results showed that differences of the vehicle's motion parameters between the rigid-flexible coupling model and the rigid body assumption are noticeable and the peak magnitude of the vehicle's transverse internal loads in the rigid-flexible coupling model is higher remarkably than that in the rigid body assumption.

Dynamic Characteristics of Tracked Vehicle Power Train Considering Road Random Torsional Excitation

The road random torsional excitation is one type of torque rooted from the road roughness and vehicle drive system. This paper aims to study how the road random torsional excitation affects the dynamic characteristics of vehicle power train. The method of simulating the random torsional excitation of tracked vehicle is explored at first. Secondly,the road random torsional excitations under different road roughness,vehicle speeds and pre-tensions are obtained. Thirdly,the dynamic analysis model of tracked vehicle power train is constructed with the consideration of the road random torsional excitation. Eventually,the influences of this excitation on output torque,bearing support force,vibration acceleration and dynamic shear stress of transmission shafts are intensively studied.The research conclusions are helpful to correct and refine the present virtual prototype of tracked vehicle power train.

Dynamic Motion Resistance for Tracked Vehicle

Based on previous achievements,a dynamic pressure-sinkage equation for saturated clay is established.First,aquasi-static penetration rate is selected,and the ratio of the dynamic penetration rate to the quasi-static rate is used to characterize the degree of dynamic effect,then theβth power of the ratio is used to quantify the dynamic effect of sinkage.The dynamic effect exponentβis obtained using penetration tests with different penetration rates.Then,a dynamic motion resistance equation for a tracked vehicle is established based on the dynamic pressure-sinkage equation.The equation incorporates both penetration and bulldozing resistance.Finally,a series of simulation experiments with varying travel speeds and slip rates is carried out.The results show that an increase in the speed leads to stronger terrain stiffness,resulting in a decrease in sinkage and motion resistance.However,the enhancement effect becomes weaker with an increase in the travel speed.

GPU-Based Simulation of Dynamic Characteristics of Ballasted Railway Track with Coupled Discrete-Finite Element Method

Considering the interaction between a sleeper,ballast layer,and substructure,a three-dimensional coupled discrete-finite element method for a ballasted railway track is proposed in this study.Ballast granules with irregular shapes are constructed using a clump model using the discrete element method.Meanwhile,concrete sleepers,embankments,and foundations are modelled using 20-node hexahedron solid elements using the finite element method.To improve computational efficiency,a GPU-based(Graphics Processing Unit)parallel framework is applied in the discrete element simulation.Additionally,an algorithm containing contact search and transfer parameters at the contact interface of discrete particles and finite elements is developed in the GPU parallel environment accordingly.A benchmark case is selected to verify the accuracy of the coupling algorithm.The dynamic response of the ballasted rail track is analysed under different train speeds and loads.Meanwhile,the dynamic stress on the substructure surface obtained by the established DEM-FEM model is compared with the in situ experimental results.Finally,stress and displacement contours in the cross-section of the model are constructed to further visualise the response of the ballasted railway.This proposed coupling model can provide important insights into high-performance coupling algorithms and the dynamic characteristics of full scale ballasted rail tracks.

Evaluation of High-Speed Track Quality Using Dynamic Simulation of Vehicle-Track Interaction

Track quality is a determinant factor for evaluating the overall performance of vehicle track interaction with respect to safety, ride quality and maintenance. Important parameters specifying the general quality of the track include track geometry (undamped) and track stiffness (damped), which can be evaluated by measurements taken along with track sections. A new co-simulation model based on Finite Element Method (FEM) and Multi Body Simulation (MBS) is built for the detailed description of track quality and its contribution to vehicle track interaction without simplifying the track structure as interconnected single elements. The simulation models and tools have been validated with the help of measured track geometry, track stiffness and dynamic wheel rail forces along the track sections of high speed lines. A comparative study between high speed lines using conventional ballasted track and ballastless track showed a significantly better quality in ballastless track sections. The dynamic forces which were determined by simulations and verified by measurements along the ballastless track section were comparatively less than the specified limits by German regulations for ballastless track design. Lower levels of dynamic forces can be utilized for optimization of track design and installation procedures with respect to lower initial costs.