Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system

A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness.The wheelset is systematized into a onedimensional(1D)diffusion process by using the stochastic average method,the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system,and the critical speed of stochastic bifurcation is obtained.The stationary probability density and joint probability density are derived theoretically.Based on the topological structure change of the probability density function,the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined.The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed,and the simulation results verify the correctness of the theoretical analysis.The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system,and the left boundary characteristic value cL=1 is the critical state of hunting stability.Besides,stochastic D-bifurcation and P-bifurcation will appear in the wheelset system,and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity.

A Nondestructive Instrumented Wheelset System for Contact Forces Measurements

A nondestructive continuous instrumented wheelset design is proposed based on strain gauges placing inside of the wheel web and wireless telemetry system. The signal feature analysis including frequency contents and high order harmonic ripples is also carried out. The strain gradient decoupling method for vertical and lateral force identification is proposed based on the strain distributions under respective loads. The method implements minimum crosstalk effects and insensitive to the varying contact points. The KMT telemetry system is adopted for wireless inductive powering and signal transferring. The drilling holes on the wheel and axles are avoidable to ensure the integrity and long-term using of the wheelset. Bridging and demodulating schemes for lateral and vertical force are designed respectively as they have dramatic differences at the dynamic signal features. High order harmonic ripple analysis and error estimation are gotten by independent waveforms. Based on the data form calibration test rig, it is indicated that the high order ripple amplitudes are below 10% of the demodulation amplitudes and fulfill designed requirements.

Bifurcation and Stability Analysis of Time-Delayed Wheelset System under White Noise Excitation

Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is established. The wheelset system is transformed into a onedimensional Ito stochastic differential equation using central manifold and stochastic averaging methods. The analysis of the system's stochastic stability is conducted through the maximum Lyapunov exponent and singular boundary theory. The combination of the stationary probability density method and numerical simulation is employed to discuss the types and conditions of stochastic P-bifurcation in the wheelset system. The results indicate that changes in speed and time delay induce stochastic P-bifurcations in the wheelset system, while changes in noise intensity do not lead to stochastic P-bifurcations. Both time delay and equivalent conicity affect the critical speed of the wheelset system, and the critical speed gradually increases with the decrease of time delay and equivalent conicity.

Research on the influence of flexible wheelset rotation effect on wheel rail contact force

Purpose-Under the high-speed operating conditions,the effects of wheelset elastic deformation on the wheel rail dynamic forces will become more notable compared to the low-speed condition.In order to meet different analysis requirements and selecting appropriate models to analyzing the wheel rail interaction,it is crucial to understand the influence of wheelset flexibility on the wheel-rail dynamics under different speeds and track excitations condition.Design/methodology/approach-The wheel rail contact points solving method and vehicle dynamics equations considering wheelset flexibility in the trajectory body coordinate system were investigated in this paper.As for the wheel-rail contact forces,which is a particular force element in vehicle multibody system,a method for calculating the Jacobian matrix of the wheel-rail contact force is proposed to better couple the wheel-rail contact force calculation with the vehicle dynamics response calculation.Based on the flexible wheelset modeling approach in this paper,two vehicle dynamic models considering the wheelset as both elastic and rigid bodies are established,two kinds of track excitations,namely normal measured track irregularities and short-wave irregularities are used,wheel-rail geometric contact characteristic and wheel-rail contact forces in both time and frequency domains are compared with the two models in order to study the influence of flexible wheelset rotation effect on wheel rail contact force.Findings-Under normal track irregularity excitations,the amplitudes of vertical,longitudinal and lateral forces computed by the flexible wheelset model are smaller than those of the rigid wheelset model,and the virtual penetration and equivalent contact patch are also slightly smaller.For the flexible wheelset model,the wheel rail longitudinal and lateral creepages will also decrease.The higher the vehicle speed,the larger the differences in wheel-rail forces computed by the flexible and rigid wheelset model.Under track short-wave irregularity excitations,the vertical force amplitude computed by the flexible wheelset is also smaller than that of the rigid wheelset.However,unlike the excitation case of measured track irregularity,under short-wave excitations,for the speed within the range of 200 to 350 km/h,the difference in the amplitude of the vertical force between the flexible and rigid wheelset models gradually decreases as the speed increase.This is partly due to the contribution of wheelset's elastic vibration under short-wave excitations.For low-frequency wheel-rail force analysis problems at speeds of 350 km/h and above,as well as high-frequency wheel-rail interaction analysis problems under various speed conditions,the flexible wheelset model will give results agrees better with the reality.Originality/value-This study provides reference for the modeling method of the flexible wheelset and the coupling method of wheel-rail contact force to the vehicle multibody dynamics system.Furthermore,by comparative research,the influence of wheelset flexibility and rotation on wheel-rail dynamic behavior are obtained,which is useful to the application scope of rigid and flexible wheelset models.

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.

Research on the strain gauge mounting scheme of track wheel force measurement system based on high-speed wheel/rail relationship test rig

Purpose-This paper aims to analyze the stress and strain distribution on the track wheel web surface and study the optimal strain gauge location for force measurement system of the track wheel.Design/methodology/approach-Finite element method was employed to analyze the stress and strain distribution on the track wheel web surface under varying wheel-rail forces.Locations with minimal coupling interference between vertical and lateral forces were identified as suitable for strain gauge installation.Findings-The results show that due to the track wheel web’s unique curved shape and wheel-rail force loading mechanism,both tensile and compressive states exit on the surface of the web.When vertical force is applied,Mises stress and strain are relatively high near the inner radius of 710 mm and the outer radius of 1110mmof the web.Under lateral force,high Mises stress and strain are observed near the radius of 670mmon the inner and outer sides of the web.As the wheel-rail force application point shifts laterally toward the outer side,the Mises stress and strain near the inner radius of 710 mm of the web gradually decrease under vertical force while gradually increasing near the outer radius of 1110 mm of the web.Under lateral force,the Mises stress and strain on the surface of the web remain relatively unchanged regardless of the wheel-rail force application point.Based on the analysis of stress and strain on the surface of the web under different wheel-rail forces,the inner radius of 870 mm is recommended as the optimal mounting location of strain gauges for measuring vertical force,while the inner radius of 1143 mm is suitable for measuring lateral force.Originality/value-The research findings provide valuable insights for determining optimal strain gauge locations and designing an effective track wheel force measurement system.

Effects of wheelset vibration on initiation and evolution of rail short-pitch corrugation

The initiation and evolution of short-pitch corrugation in Beijing metro line 4 was studied from the viewpoint of wheelset vibration.A three-dimensional elastic model was set up.Numerical simulations were undertaken with this model to analyze the corrugation by the wheelset vertical vibration and torsional vibration.Based on numerical results,the relation between rail corrugation and wheelset vibration,and the relation between the position of electromotor and wheelset vibration were indicated.It is found that avoiding the wheelset-rail resonance is one method of controlling the rail short-pitch corrugation and solving the vibration and noise problem in metro lines.

Analysis of steering performance of differential coupling wheelset

In order to improve the curving performance of the conventional wheelset in sharp curves and resolve the steering ability problem of the independently rotating wheel in large radius curves and tangent lines, a differential cou- pling wheelset （DCW） was developed in this work. The DCW was composed of two independently rotating wheels （IRWs） coupled by a clutch-type limited slip differential. The differential contains a static pre-stress clutch, which could lock both sides of IRWs of the DCW to ensure a good steering performance in curves with large radius and tangent track. In contrast, the clutch could unlock the two IRWs of the DCW in a sharp curve to endue it with the characteristic of an IRW, so that the vehicles can go through the tight curve smoothly. To study the dynamic performance of the DCW, a multi-body dynamic model of single bogie with DCWs was established. The self-centering capability, hunting stability, and self-steering performance on a curved track were analyzed and then compared with those of the conventional wheelset and IRW. Finally, the effect of coupling parameters of the DCW on the dynamic performance was investigated.

Effect of wheelset flexibility on wheel–rail contact behavior and a specific coupling of wheel–rail contact to flexible wheelset

The fexibility of a train＇s wheelset can have a large effect on vehicle–track dynamic responses in the medium to high frequency range.To investigate the effects of wheelset bending and axial deformation of the wheel web,a specifi coupling of wheel–rail contact with a fexible wheelset is presented and integrated into a conventional vehicle–track dynamic system model.Both conventional and the proposed dynamic system models are used to carry out numerical analyses on the effects of wheelset bending and axial deformation of the wheel web on wheel–rail rolling contact behaviors.Excitations with various irregularities and speeds were considered.The irregularities included measured track irregularity and harmonic irregularities with two different wavelengths.The speeds ranged from 200 to400km/h.The results show that the proposed model can characterize the effects of fexible wheelset deformation on the wheel–rail rolling contact behavior very well.

FPGA Implementation of Extended Kalman Filter for Parameters Estimation of Railway Wheelset

It is necessary to know the status of adhesion conditions between wheel and rail for efficient accelerating and decelerating of railroad vehicle.The proper estimation of adhesion conditions and their real-time implementation is considered a challenge for scholars.In this paper,the development of simulation model of extended Kalman filter(EKF)in MATLAB/Simulink is presented to estimate various railway wheelset parameters in different contact conditions of track.Due to concurrent in nature,the Xilinx®System-on-Chip Zynq Field Programmable Gate Array(FPGA)device is chosen to check the onboard estimation ofwheel-rail interaction parameters by using the National Instruments(NI)myRIO®development board.The NImyRIO®development board is flexible to deal with nonlinearities,uncertain changes,and fastchanging dynamics in real-time occurring in wheel-rail contact conditions during vehicle operation.The simulated dataset of the railway nonlinear wheelsetmodel is tested on FPGA-based EKF with different track conditions and with accelerating and decelerating operations of the vehicle.The proposed model-based estimation of railway wheelset parameters is synthesized on FPGA and its simulation is carried out for functional verification on FPGA.The obtained simulation results are aligned with the simulation results obtained through MATLAB.To the best of our knowledge,this is the first time study that presents the implementation of a model-based estimation of railway wheelset parameters on FPGA and its functional verification.The functional behavior of the FPGA-based estimator shows that these results are the addition of current knowledge in the field of the railway.

Influence of dynamic unbalance of wheelsets on the dynamic performance of high-speed cars

With further increasing in running speed of newer high-speed EMUs（electric multiple units）,higher demand for wheelset dynamic balance is required.In order to study the influence of the dynamic unbalance of wheelset on the stability,ride quality,and curving performance for a high-speed car,a detailed dynamic model of a high-speed EMU car is established using the software SIMPACK.The analysis results indicate that the dynamic unbalance of the wheelset significantly influences the dynamic performance of the high-speed car.The increase in dynamic unbalance of the wheelset will decrease the hunting critical speed,worsen the vertical ride quality,and increase the wheelset lateral force,derailment coefficient,and wheel unloading ratio.Therefore,in order to improve the stability,ride quality,and running safety of high-speed car,the values of dynamic unbalance of wheelset should be strictly controlled in manufacturing,and periodically monitored in operation.

Influence of unsupported sleepers on the dynamic stability of ballasted bed based on wheelset impact tests

The unsupported sleeper can change the load characteristics of ballast particles and thus affect the dynamic stability of a ballasted bed.In this work,a laboratory test was constructed on a ballasted track containing unsupported sleepers.The ballasted track was excited by a wheelset,and the influence of unsupported sleepers on the dynamic stability of a ballasted bed was studied.The results show that the main frequency of the sleeper vibration appeared at 670 Hz,and the first-order rigid vibration mode at the frequency of 101 Hz had a significant effect on the condition without the unsupported sleeper.When the sleepers were continuously unsupported,the vibration damping effect of ballasted bed within the frequency range of 0–450 Hz was better than that at higher frequencies.Within the frequency range of 70–250 Hz,the vibration damping effect of the ballasted bed with unsupported sleepers was better than that without the unsupported sleeper.Owing to the excitation from the wheelset impact,the lateral resistance of the ballasted bed with unsupported sleepers whose hanging heights were 30,60,and 90 mm increased by 37.43%,12.25%,and 18.23%,respectively,while the lateral resistance of the ballasted bed without the unsupported sleeper remained basically unchanged.The unsupported sleeper could increase the difference in the quality of the ballasted bed between two adjacent sleepers.In addition,test results show that the hanging height of the unsupported sleeper had little effect on the lateral resistance of a ballasted bed without external excitation,but had an obvious effect on the rate of change of the lateral resistance of a ballasted bed and the acceleration amplitude of the sleeper vibration under the wheelset impact.

Useful zero friction simulations for assessing MBS codes Pascal’s formula giving wheelsets frequency for zero wheel-rail friction

Present study provides a simple analytical formula,the“Klingel-like formula”or“Pascal’s Formula”that can be used as a reference to test some results of existing railway codes and specifically those using rigid contact.It develops properly the 3D Newton-Euler equations governing the 6 degrees of freedom(DoF)of unsuspended loaded wheelsets in case of zero wheel-rail friction and constant conicity.Thus,by solving numerically these equations,we got pendulum like harmonic oscillations of which the calculated angular frequency is used for assessing the accuracy of the proposed formula so that it can in turn be used as a fast practical target for testing multi-body system(MBS)railway codes.Due to the harmonic property of these pendulum-like oscillations,the squareω2 of their angular frequency can be made in the form of a ratio K/M where K depends on the wheelset geometry and load and M on its inertia.Information on K and M are useful to understand wheelsets behavior.The analytical formula is derived from the first order writing of full trigonometric Newton-Euler equations by setting zero elastic wheel-rail penetration and by assuming small displacements.Full trigonometric equations are numerically solved to assess that the formula providesω2 inside a 1%accuracy for usual wheelsets dimensions.By decreasing the conicity down to 1×10^(−4) rad,the relative formula accuracy is under 3×10^(−5).In order to test the formula reliability for rigid contact formulations,the stiffness of elastic contacts can be increased up to practical rigidity(Hertz stiffness×1000).

应用于轮对主动径向控制的数字阀控液压系统研究

针对主动径向液压伺服控制系统发热量过高的问题,文章提出了一种基于脉冲编码调制技术的轮对主动径向数字阀液压控制系统方案,以高速开关阀脉冲编码调制控制代替伺服阀控制,从根源上解决热量产生的主要环节。文章介绍了脉冲编码调制数字阀控制原理,推导了脉冲编码调制数字阀控液压系统数学模型,提出了包含位置控制和压力控制的速度前馈项的闭环控制器设计方法;在完成系统的位置轨迹跟踪控制性能仿真后,搭建脉冲编码调制数字阀控液压系统试验台,开展了车辆通过曲线半径250 m线路时关于轮对的期望位置轨迹跟踪性能试验和故障工况试验。试验结果表明,系统不仅具有较好的位置轨迹跟踪控制精度,而且有较好的容错性能,为解决主动径向液压伺服控制技术应用于车辆时系统出现发热的问题提出了解决方案。

基于信息交互的牵引系统控制策略研究

采用独立轮对的有轨电车可最大程度降低低地板车辆的地板高度,无需高站台设计且方便乘客上下车,发展前景十分广阔。但是独立轮对理论上不存在纵向蠕滑力,曲线导向能力下降,因此对列车牵引制动过程中的出力及控制策略提出更高要求,针对独立轮对有轨电车的特点,本文介绍了一种牵引变流器的设计方案及控制策略,从主电路设计、工作原理、硬件结构等方面进行阐述,基于双功率模块的信息交互,从顶层给出牵引力的优化施加目标,基于分段同步调制及矢量控制策略,实现列车牵引力输出的优化控制。最后,通过现场牵引制动试验及极端恶劣线路空转滑行试验验证了所提设计方案的有效性,对独立轮对牵引系统及类似应用场合的牵引系统硬件设计及控制策略具有一定的指导意义。

Optimal allocation method of electric/air braking force of high-speed train considering axle load transfer

Reasonable distribution of braking force is a factor for a smooth,safe,and comfortable braking of trains.A dynamic optimal allocation strategy of electric-air braking force is proposed in this paper to solve the problem of the lack of consideration of adhesion difference of train wheelsets in the existing high-speed train electric-air braking force optimal allocation strategies.In this method,the braking strategy gives priority to the use of electric braking force.The force model of a single train in the braking process is analyzed to calculate the change of adhesion between the wheel and rail of each wheelset after axle load transfer,and then the adhesion of the train is estimated in real time.Next,with the goal of maximizing the total adhesion utilization ratio of trailer/motor vehicles,a linear programming distribution function is constructed.The proportional coefficient of adhesion utilization ratio of each train and the application upper limit of braking force in the function is updated according to the change time point of wheelset adhesion.Finally,the braking force is dynamically allocated.The simulation results of Matlab/Simulink show that the proposed algorithm not only uses the different adhesion limits of each trailer to reduce the total amount of braking force undertaken by the motor vehicle,but also considers the adhesion difference of each wheelset.The strategy can effectively reduce the risk and time of motor vehicles during the braking process and improve the stability of the train braking.

Train wheel-rail force collaborative calibration based on GNN-LSTM

Accurate wheel-rail force data serves as the cornerstone for analyzing the wheel-rail relationship.However,achieving continuous and precise measurement of this force remains a significant challenge in the field.This article introduces a calibration algorithm for the wheel-rail force that leverages graph neural networks and long short-term memory networks.Initially,a comprehensive wheel-rail force detection system for trains was constructed,encompassing two key components:an instrumented wheelset and a ground wheel-rail force measuring system.Subsequently,utilizing this system,two distinct datasets were acquired from the track inspection vehicle:instrumented wheelset data and ground wheel-rail force data,a feedforward neural network was employed to calibrate the instrumented wheelset data,referencing the ground wheel-rail force data.Furthermore,ground wheel-rail force data for the locomotive was obtained for the corresponding road section.This data was then integrated with the calibrated instrumented wheelset data from the track inspection vehicle.Leveraging the GNN-LSTM network,the article establishes a mapping relationship model between the wheel-rail force of the track inspection vehicle and the locomotive wheel-rail force.This model facilitates continuous measurement of locomotive wheel-rail forces across three typical scenarios:straight sections,long and steep downhill sections,and small curve radius sections.

基于ARM的测力轮对标定试验台控制系统研究

针对现有测力轮对标定试验台控制系统的发展现状,设计一种基于ARM的测力轮对标定试验台控制系统。完成控制系统硬件电路的设计和软件功能的开发,实现液压加载控制、伺服电机控制等功能,并对相关功能进行测试。结果表明:基于ARM的测力轮对标定试验台控制系统功能完备、资源丰富、集成度和自动化程度高,轮对正转和反转的分度控制精度分别为0.42‰和0.46‰,施加2 t载荷下的左轮垂向力、右轮垂向力、左轮横向力和右轮横向力的加载控制精度分别为0.45‰、0.25‰、0.105%和0.160%,满足试验台标定功能需求。

铁路客车车轮失圆故障声振特性研究

应用单轴滚振试验对轮辋故障报警轮对进行振动及噪声测试,测试结果能很好地反映出非圆化对轮对振动噪声的直接影响,轮对几何不圆的主阶次会以基频及其倍频呈现于测试数据中;为充分研究报警轮对在车辆维度的动力学及声辐射特性,建立了车辆-轨道耦合动力学模型及轮对声学仿真模型,并以实测车轮表面粗糙度为输入激励,结合试验和计算结果可知,动力学模型能够反映轮辋故障;在频域对比中,实测和仿真结果中低频带的30 Hz、35 Hz、52 Hz和104 Hz均有波峰对应,即来自主阶次9阶、17阶和中心波长为500 mm的车轮径向缺陷特征频率均能反映在仿真模型上;研究了跟随速度变化的动力冲击和辐射声压幅值,结果指出当前故障轮对的噪声超限。

基于LabVIEW的高速列车变轨轮对性能试验测试系统研究

变轨距轮对技术是解决铁道车辆在轨距不同区间直通运行的一种行之有效的方法,根据某主机厂设计的新型变轨距轮对的变轨原理和技术参数,研制了变轨距轮对综合性能试验台,模拟变轨距轮对解锁/锁紧、变轨、跑合等功能。变轨距轮对的性能直接影响到变轨距转向架的性能,对列车的运行安全起到至关重要的作用。以变轨距轮对为研究对象,针对轮对在变轨过程中的运动状态及性能,进行了测试方法与试验研究。利用上位机软件LabVIEW进行编程控制,通过采集的数据进行分析处理,实时监测轮对运行的状态。试验结果表明,系统能够完成轮对的型式试验性能测试,并且可以有效地监控设备运行状态并能进行故障预警和处理。研究可为变轨距转向架和变轨列车的运行提供技术支持,具有一定的工程应用价值。