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.

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.

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.

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.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge(WVB) system,there are various interactions among wind,vehicle and bridge.The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors,such as mean wind,fluctuating wind,buffeting,rail irregularities,light rail vehicle vibration and bridge stiffness.A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example.Firstly,a finite element model is built for the long cable-stayed bridge.The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements.Vehicles are modeled as mass-spring-damper systems.Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method.Then,aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests.Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method.Finally,dynamic responses of the WVB system are analyzed in a series of cases.The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent.The transverse forces of wheel axles mainly depend on the track irregularity.The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness.And the accelerations of the bridge are enlarged after adding the fluctuating wind.

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.

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.

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.

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.

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.

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.

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.

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.

9号道岔区铺设减振垫浮置板的行车安全性及舒适性研究

地铁道岔区在基本轨、尖轨处以及道岔钢轨接头处存在大量钢轨不连续地段,轮轨相互作用强烈,轨道系统振动明显,减振垫浮置板轨道作为一种高等减振措施已应用于地铁线路道岔区。为探究减振垫浮置板应用于9号道岔的适用性,并作为减振地段与普通无砟轨道的过渡段的可行性,以某地铁高架9号道岔为研究对象,建立桥上道岔三维有限元模型,仿真分析地铁B型车在120 km/h直向过岔和30 km/h侧向过岔的情况下,列车的行车安全性、舒适性以及轨下结构形变。对比在9号单开道岔区域设置的2种刚度过渡方式的优劣及其减振效果,较为系统地论证了在9号道岔区域铺设减振垫浮置板的可行性。研究结果表明:1)列车通过铺设减振垫浮置板的9号道岔区域时,浮置板位移极值出现在转辙区域和心轨区域,最大位移出现在尖轨位置,可增大尖轨处单板橡胶垫支承刚度,以保证轨道结构变形均匀;2)列车逆向侧向通过设置过渡段的减振垫浮置板道岔区时,2级过渡方式的车体最大垂向加速度、最大横向加速度、最大脱轨系数、最大轮重减载率、轨道刚度变化率以及减振效果等指标均优于1级过渡方式;3)在道岔区铺设减振垫浮置板,列车直向和侧向通过时的行车安全性和舒适性均能满足相关评价指标,且2级过渡方式更优。研究结果可为后续道岔区减振设计研究提供一定的理论参考。

基于结构振动响应的长型浮置板轨道隔振器失效检测方法

目前钢弹簧浮置板轨道的隔振器失效判别主要依赖于人工巡检或视觉成像系统,但此类方法效率低、检测滞后且成本高昂。本文提出了一种自动化的检测方法,该方法利用残差学习思想和卷积神经网络基本理论构建数据分类器,并通过列车动荷载作用下的结构动力响应对现役某常见的长型浮置板轨道进行隔振器失效的检测识别。首先,基于车-轨垂向耦合动力学建立考虑隔振器不同服役状态的地铁车辆-浮置板轨道垂向耦合动力学仿真分析模型,进而生成多种运营工况下的数据集,用于网络的训练和性能测试;其次,进一步研究了传感器布置方式对网络检测性能的影响,以决定适宜的传感器布置方案;最后,在实际地铁线路中开展试验,对所提出的方法进行了验证。结果表明:通过对传感器布置位置进行优化,深度残差网络模型的检测准确性显著提升;合理设置传感器的数量也可以提高本文方法的检测性能;此外,通过适当选取传感器布置方案,本文提出的基于深度残差网络的隔振器失效检测方法在仿真数据中实现了98.99%的准确度,并在试验数据中实现了96.33%的准确度。该方法具有较高的可行性和应用潜力,可为地铁浮置板隔振器智能运维提供参考,并有望在未来用于隔振器失效的自动化检测。

车辆-轨道系统动力极值预测及可靠度计算

为从车辆-轨道系统的动力极值预测及其可靠度计算角度分析车辆系统行车安全、衡量系统可靠程度,基于车辆-轨道耦合动力学及概率理论,提出一种车轨系统动力极值预测及可靠度评估方法。首先,基于轨道不平顺概率模型,采用轨道不平顺累计概率谱确定具有不同激振能量的随机不平顺序列;依据离散Parseval定理,建立轨道不平顺时域序列和功率谱间的对应关系;将轨道不平顺概率模型与车辆-轨道耦合动力学模型相结合,从随机动力计算中提取车辆-轨道的动力极值及可靠度信息;随后利用车辆-轨道耦合动力模型及二维插值算子,根据谱线能量关系实现动力极值预测;此外,基于此系统激励输入与响应输出间的概率等效性,导出了动力极值的可靠度计算式。以实测的轨道不平顺和车体加速度数据及4种类型不平顺在不同累计概率下的谱组合计算得出的轮轨横向力和钢轨垂向位移的计算结果为样本,与预测结果进行对比。研究结果表明:计算时程的分布趋势基本与实测时程一致,动力极值预测结果与实际的动力计算结果较为接近。由于轨道不平顺随机性的存在使得车辆-轨道系统的动力响应存在随机离散及方差特征,但通过轨道不平顺的幅频及能量特性预测车辆-轨道系统的动力极值的方法是较为可行的。

基于等效刚度阻尼系统的中低速磁浮列车与大跨度桥梁耦合振动响应分析

针对中低速磁浮列车与大跨度连续梁桥的耦合动力响应问题,本文基于等效刚度阻尼系统建立多编组磁浮列车模型;基于国内在建磁浮专线连续梁桥(35m+55m+35m),采用ANSYS中实体单元建立全桥模型.并将两个独立系统在SIMPACK进行车桥耦合,设定车重参数分别为空载、定员和超载,且列车按单线和双线工况运行,计算耦合系统的动力响应.结果表明,本文建立的列车模型受到轨道激励时,磁浮间隙在额定范围内浮动,即等效刚度阻尼系统有良好的控制效果;车辆磁浮间隙的变化量、车体竖向加速度与车重成反比,而磁浮力与车重成正比;在计算工况下,桥梁主跨及边跨的竖向位移均满足设计要求的限值,双线列车超载运行桥梁跨中最大位移仅为4.503mm.说明连续梁桥具有较大的刚度,能满足磁浮车辆安全运行的要求;对比列车单双线运行,主跨跨中的竖向位移最大值后者达到前者两倍,而边跨位移的最大值后者仅比前者增大70%,表明双线列车对开运行对桥梁的动力响应存在增大效应.相关研究成果对磁浮线路建设有一定参考意义.

CRTSⅢ型板和双块式无砟轨道振动噪声特性研究

【目的】探究高速铁路CRTSⅢ型板和双块式无砟轨道的结构振动与噪声特性。【方法】以有限元、多体动力学与边界元相结合的方法为基础,通过建立高速列车-无砟轨道-箱梁耦合动力学模型和边界元模型,研究列车高速通过时的列车-轨道-箱梁耦合系统的结构动力响应,以及噪声辐射特性。【结果】结果表明,列车通过桥上CRTSⅢ型板与双块式轨道结构段时,列车的最大轮重减载率分别为0.0536与0.1657,下部箱梁挠度分别为1/9673与1/8457。与双块式无砟轨道相比,CRTSⅢ型板的轨道板及底座位移响应更小,并且轨道-箱梁系统的竖向振动衰减更快,减振性能更优。另外,比较两种轨道结构条件下的高架箱梁结构噪声,CRTSⅢ型板段的箱梁噪声总声压级更小。但是,桥下远场点噪声峰值差异较小,峰值频率接近,均为31.5Hz左右;而桥下峰值频率差异较大,Ⅲ型板的峰值频率为63Hz,双块式则为20Hz。【结论】CRTSⅢ型板式无砟轨道更适合在高速铁路桥梁段使用。