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.

COUPLING VIBRATION OF VEHICLE-BRIDGE SYSTEM

By applying the sinusoidal wave mode to simulate the rugged surface of bridge deck,accounting for vehicle-bridge interaction and using Euler-Bernoulli beam theory, a coupling vibration model of vehicle-bridge system was developed. The model was solved by mode analyzing method and Runge-Kutta method, and the dynamic response and the resonance curve of the bridge were obtained. It is found that there are two resonance regions, one represents the main resonance while the other the minor resonance, in the resonance curve. The influence due to the rugged surface, the vibration mode of bridge, and the interaction between vehicle and bridge on vibration of the system were discussed. Numerical results show that the influence due to these parameters is so significant that the effect of roughness of the bridge deck and the mode shape of the bridge can't be ignored and the vehicle velocity should be kept away from the critical speed of the vehicle.

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.

Experimental investigation on vibration characteristics of the medium-low-speed maglev vehicle-turnout coupled system

The steel turnout is one of the key components in the medium–low-speed maglev line system.However,the vehicle under active control is prone to vehicle–turnout coupled vibration,and thus,it is necessary to identify the vibration characteristics of this coupled system through field tests.To this end,dynamic performance tests were conducted on a vehicle–turnout coupled system in a medium–low-speed maglev test line.Firstly,the dynamic response data of the coupled system under various operating conditions were obtained.Then,the natural vibration characteristics of the turnout were analysed using the free attenuation method and the finite element method,indicating a good agreement between the simulation results and the measured results;the acceleration response characteristics of the coupled system were analysed in detail,and the ride quality of the vehicle was assessed by Sperling index.Finally,the frequency distribution characteristics of the coupled system were discussed.All these test results could provide references for model validation and optimized design of medium–low-speed maglev transport systems.

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.

Flight Dynamic Analysis of Hypersonic Vehicle Considering Liquid-Solid Coupling

With the liquid propellant making up 60%—70% of the takeoff weight of the hypersonic vehicle,the dynamic load caused by great propellant sloshing interacts with the flexible structure of the aircraft.Therefore,the dynamic model displays characteristics of strong coupling with structure/control and nonlinearity.Based on the sloshing mass dynamic simplified as a spring-mass-damping model,a rigid-flexible-sloshing model is constructed.Moreover,the effect on the dynamic performance of the coupled model is analyzed with changing frequency and damping.The results show that propellant sloshing dynamics significantly affects the rigid body motion modes,especially flexible mode and short mode.The right half plane pole(RHP)moves far from the imaginary axis with the consumption of the propellant.The flexible mode attenuates with the increase of the sloshing damping,and the coupling becomes stronger when sloshing frequency is close to the short mode frequency or the flexible frequency of the beam.

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.

Turning traction force of tracked mining vehicle based on rheological property of deep-sea sediment

Based on main physical and mechanical properties of deep-sea sediment from C-C poly-metallic nodule mining area in the Pacific Ocean, the best sediment simulant was successfully prepared by mixing bentonite with a certain content of water. Compression-shear coupling rheological constitutive model of the sediment simulant was established by endochronic theory and the coupling rheological parameters were obtained by compressive and compression-shear creep tests. A new calculation formula of turning traction force of the tracked mining vehicle was first derived based on the coupling rheological model and consideration of pushing resistance and sinkage of the tracked mining vehicle. Effects of the turning velocity, crawler spacing and contacting length of crawler with deep-sea sediment on the turning traction force were analyzed. Research results can provide theoretical foundation for operation safety and optimal design of the tracked mining vehicle.

Frost heave analysis of ballasted track above box culvert and its influence on train vibration

The uneven frost heave of frost-susceptible subgrade soil causes track irregularity,which highly enhances train vibration and affects the comfort and safety of railway transportation.This paper presents a coupled thermo-hydro-mechanical(THM)analysis for the freezing behavior of railway located above a box culvert.The vertical acceleration of the vehicle,an indicator of riding comfort,is predicted through a vehicle dynamic model.The results reveal that the existence of a box culvert changes the subgrade thermal pattern,leading to a deeper frost penetration depth.The frost heave amount above the box culvert is larger than the adjacent section,resulting in uneven track structure upheave and track irregularity.This frostinduced track irregularity highly affects train vibration.

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.

Simple and fast prediction of train-induced track forces,ground and building vibrations

A simple and fast prediction scheme is presented for train-induced ground and building vibrations.Simple models such as(one-dimensional)transfer matrices are used for the vehicle–track–soil interaction and for the building–soil interaction.The wave propagation through layered soils is approximated by a frequency-dependent homogeneous half-space.The prediction is divided into the parts“emission”(excitation by railway traffic),“transmission”(wave propagation through the soil)and“immission”(transfer into a building).The link between the modules is made by the excitation force between emission and transmission,and by the free-field vibration between transmission and immission.All formula for the simple vehicle–track,soil and building models are given in this article.The behaviour of the models is demonstrated by typical examples,including the mitigation of train vibrations by elastic track elements,the low-and high-frequency cut-offs characteristic for layered soils,and the interacting soil,wall and floor resonances of multi-storey buildings.It is shown that the results of the simple prediction models can well represent the behaviour of the more time-consuming detailed models,the finite-element boundary-element models of the track,the wavenumber integrals for the soil and the three-dimensional finite-element models of the building.In addition,measurement examples are given for each part of the prediction,confirming that the methods provide reasonable results.As the prediction models are fast in calculation,many predictions can be done,for example to assess the environmental effect along a new railway line.The simple models have the additional advantage that the user needs to know only a minimum of parameters.So,the prediction is fast and user-friendly,but also theoretically and experimentally well-founded.

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.

Analyses and Simulation of Fuzzy Logic Control for Suspension System of a Track Vehicle

The vibration caused by terrible road excitation affects the ride quality and safety of track vehicles. The vibration control of suspension systems is a very important factor for modern track vehicles. A fuzzy logic control for suspension system of a track vehicle is presented. A mechanical model and a system of difft, rential equations of motion taking account of the mass of loading wheel are established. Then the fuzzy logic control is applied to control the vibration of suspension system of track vehicles for sine signal and random road surfaces. Numerical simulation shows that the maximum acceleration of suspension system can be reduced to 44 % of the original value for sine signal road surface, and the mean square root of acceleration of suspension system can be reduced to 21% for random road surface. Therefore, the proposed fuzzy logic control is an efficient method for the suspension systems of track vehicles.

Fuzzy Logic Control for Suspension Systems of Tracked Vehicles

A scheme of fuzzy logic control for the suspension system of a tracked vehicle is presented. A mechanical model for the whole body of a tracked vehicle, which is totally a fifteen-degree-of-freedom system, is established. The model includes the vertical motion, the pitch motion as well as the roll motion of the tracked vehicle. In contrast to most previous studies, the coupling effect among the vertical, the pitch and the roll motions of the suspension system of a tracked vehicle is considered simultaneously. The simulation of fuzzy logic control under road surface with random excitation shows that the acceleration, pitch angle and roll angle of suspension system can be efficiently controlled.

Prediction of vibrations from underground trains on Beijing metro line 15

The impact of vibrations due to underground trains on Beijing metro line 15 on sensitive equipment in the Institute of Microelectronics of Tsinghua University was discussed to propose a viable solution to mitigate the vibrations.Using the state-of-the-art three-dimensional coupled periodic finite element-boundary element(FE-BE) method,the dynamic track-tunnel-soil interaction model for metro line 15 was used to predict vibrations in the free field at a train speed of 80 km/h.Three types of tracks(direct fixation fasteners,floating slab track and floating ladder track) on the Beijing metro network were considered in the model. For each track,the acceleration response in the free field was obtained.The numerical results show that the influence of vibrations from underground trains on sensitive equipment depends on the track types.At frequencies above 10 Hz,the floating slab track with a natural frequency of 7 Hz can be effective to attenuate the vibrations.

Influence of structure and material on the vibration modal characteristics of novel combined flexible road wheel

Aiming at the independent development of tracked vehicles,it is urgent to improve its mobility,passability and ride comfort,a new type of flexible road wheel with a“wheel-hinge-hub”combined structure is proposed in this study.The vibration model characteristics of the flexible road wheel were studied by the combination of numerical simulation and experiments.The superelasticity of rubber is obtained through uniaxial tensile experiment of the material and a detail three-dimensional nolinear finite element model of the flexible road wheel is established through finite element software ABAQUS.The free vibration equation of the flexible road wheel is solved by Lanczos vector direct superposition method,and its predicted modes and natural frequencies are compared with experimental results,which verifies the accuracy and reliability of the established finite element model.On this basis,the effects of various key structural or material factors on the natural frequencies of the flexible road wheel are studied using orthogonal experimental design method.Besides,the vibration modal characteristics of the flexible road wheel are also compared with those of the rigid road wheel.The research results provide a theoretical basis for the vibration and noise reduction of flexible road wheel.

Impact coefficient and reliability of mid-span continuous beam bridge under action of extra heavy vehicle with low speed

To analyze the dynamic response and reliability of a continuous beam bridge under the action of an extra heavy vehicle, a vehicle–bridge coupled vibration model was established based on the virtual work principle and vehicle–bridge displacement compatibility equation, which can accurately simulate the dynamic characteristics of the vehicle and bridge. Results show that deck roughness has an important function in the effect of the vehicle on the bridge. When an extra heavy vehicle passes through the continuous beam bridge at a low speed of 5 km/h, the impact coefficient reaches a high value, which should not be disregarded in bridge safety assessments. Considering that no specific law exists between the impact coefficient and vehicle speed, vehicle speed should not be unduly limited and deck roughness repairing should be paid considerable attention. Deck roughness has a significant influence on the reliability index, which decreases as deck roughness increases. For the continuous beam bridge in this work, the reliability index of each control section is greater than the minimum reliability index. No reinforcement measures are required for over-sized transport.

Seismic response analysis of road vehicle-bridge system for continuous rigid frame bridges with high piers

The objective of this study is to investigate the effects of earthquakes on road vehicle-bridge coupling vibration systems. A two-axle highway freight vehicle is treated as a 13 degree-of-freedom system composed of several rigid bodies, which are connected by a series of springs and dampers. The framework of the earthquake-vehicle-bridge dynamic analysis system is then established using an earthquake as the extemal excitation. The equivalent lateral contact force serves as the judgment criteria for sideslip accidents according to reliability theory. The entire process of the vehicle crossing the bridge is considered for a very high pier continuous rigid frame bridge. The response characteristics of the vehicle and the bridge are discussed in terms of various parameters such as earthquake ground motion, PGA value of the earthquake, incident angle, pier height, vehicle speed and mass. It is found that seismic excitation is the most influential factor in the responses of the vehicle-bridge system and that the safety of vehicles crossing the bridge is seriously impacted by the dual excitations of earthquake and bridge vibration.

Modeling and simulation of railway vehicle vertical dynamic behavior by considering the effect of passenger-carbody coupling vibration

In order to reflect the vertical random vibration characteristics of railway vehicles more truly and effectively,this paper regards the human body as a single-degree-of-freedom system attached to the bottom of the carriage,and establishes a vertical dynamic model of railway vehicles by considering the influence of the coupling vibration effect between the passenger and the car body.The correctness of the model is verified by the real vehicle test.Then,the influence of the passengers on the vertical vibration characteristics of railway vehicles is analyzed,and the influence of the railway vehicle vibration on the vertical vibration characteristics of passengers is discussed in this paper.The research made in this paper can provide an effective model reference for the analysis of the vertical random vibration characteristics of railway vehicles and passengers,and for the optimization design of the suspension system parameters.

Dynamic Characteristics of Metro Vehicle under Thermal Deformation of Long-Span Cable-Stayed Bridge

In order to study the influence of thermal deformation of long-span cable- stayed bridge (LSCSB) on the dynamic characteristics of metro vehicle on the bridge, based on the theory of vehicle-track coupled dynamics, the rigid-flexible coupled dynamic model of metro vehicle-track-LSCSB system is established by using finite element method and multi-rigid-body dynamics. Adopting this model, the deformation of LSCSB subject to temperature is analyzed, then the comprehensive effect of track random irregularity and rail deformation caused by temperature load is considered to study the dynamic characteristics of metro vehicle running through the bridge, and finally the influences of temperature increment and running speed on concerned dynamic indices of vehicle are studied. The results show that the LSCSB deforms obviously subject to temperature load, and the overall performance is that the cooling is arched, and the heating is bent, and the shape variable changes almost linearly with the temperature load. According to the parameters studied in this paper, the rail deformation caused by temperature load increases the wheel-rail vertical force, derailment coefficient and wheel load reduction rate by 1.5%, 3.1% and 5% respectively. The vertical acceleration of the vehicle body decreases by 2.4% under the cooling condition, while increases by 3.7% under the heating condition. The dynamic response of the bridge changes under temperature load. The maximum vertical and horizontal displacement in the middle of the main beam span are 6.24 mm and 2.19 mm respectively, and the maximum vertical and horizontal acceleration are 1.29 cm/s2 and 2.54cm/s2 respectively. The derailment coefficient and vertical acceleration of vehicle body are more affected by temperature load, and the wheel load reduction rate and wheel-rail vertical force are more affected by speed. The conclusion of this paper provides a reference for subsequent scholars to study the influence of thermal deformation on the dynamic response of vehicles on LSCSB.