Hunting stability analysis of high-speed train bogie under the frame lateral vibration active control

In this paper, we study a multi-objective optimal design of three different frame vibration control configurations and compare their performances in improving the lateral stability of a high-speed train bogie. The existence of the time-delay in the control system and its impact on the bogie hunting stability are also investigated. The continuous time approximation method is used to approximate the time-delay system dynamics and then the root locus curves of the system before and after applying control are depicted. The analysis results show that the three control cases could improve the bogie hunting stability effectively. But the root locus of low- frequency hunting mode of bogie which determinates the system critical speed is different, thus affecting the system stability with the increasing of speed. Based on the stability analysis at different bogie dynamics parameters, the robustness of the control case (1) is the strongest. However, the case (2) is more suitable for the dynamic performance requirements of bogie. For the case (1), the time-delay over 10?ms may lead to instability of the control system which will affect the bogie hunting stability seriously. For the case (2) and (3), the increasing time-delay reduces the hunting stability gradually over the high-speed range. At a certain speed, such as 200?km/h, an appropriate time-delay is favourable to the bogie hunting stability. The mechanism is proposed according to the root locus analysis of time-delay system. At last, the nonlinear bifurcation characteristics of the bogie control system are studied by the numerical integration methods to verify the effects of these active control configurations and the delay on the bogie hunting stability.     

Stability enhancement of a high-speed train bogie using active mass inertial actuators

In this study, a method regarding frame lateral vibration control based on the state feedback of an additional oscillator is proposed, so as to improve the bogie hunting stability. The multi-objective optimisation method (MOOP), with two objective functions of the stability index and control effort, is solved by the NSGA-II algorithm to obtain the feedback gains. The frame lateral vibration control can effectively improve the bogie hunting stability according to the linear and non-linear analysis of a high-speed train bogie, in which a fault of the yaw damper and time delay in the control system are considered. The effect of the oscillator suspension parameters and time delay on the system stability and robustness are analysed. The results show that the damped vibration frequency of the oscillator should be equal to the bogie hunting frequency, but a harder oscillator suspension can be used to improve the hunting critical speed margin of the bogie control system. However, just as how the feeding the frame states back directly, a hard oscillator suspension will lead to instability in the control system at a certain time delay. Therefore, the improvement of bogie hunting stability and reduction of control system stability must be considered when optimising the oscillator parameters. For the 350?km/h train bogie covered in this study, the optimal mass, natural frequency and damping ratio of the additional oscillator are acquired.     

Carbody elastic vibrations of high-speed vehicles caused by bogie hunting instability

In particular locations of the high-speed track, the worn wheel profile matched up with the worn rail profile will lead to an extremely high-conicity wheel–rail contact. Consequently, the bogie hunting instability arises, which further results in the so-called carbody shaking phenomenon. In this paper, the carbody elastic vibrations of a high-speed vehicle in service are firstly introduced. Modal tests are conducted to identity the elastic modes of the carbody. The ride comfort and running safety indices for the tested vehicle are evaluated. The rigid–flexible coupling dynamic model for the high-speed passenger car is then developed by using the FE and MBS coupling approach. The rail profiles in those particular locations are measured and further integrated into the simulation model to reproduce the bogie hunting and carbody elastic vibrations. The effects of wheel and rail wear on the vehicle system response, e.g. wheelset bifurcation graph and carbody vibrations, are studied. Two improvement measures, including the wheel profile modification and rail grinding, are proposed to provide possible solutions. It is found that the wheel–rail contact conicity can be lowered by decreasing wheel flange thickness or grinding rail corner, which is expected to improve the bogie hunting stability under worn rail and worn wheel conditions. The carbody elastic vibrations caused by bogie hunting instability can be further restrained.     

Wear simulation for the centre plate arrangement of a freight car

The bodies of many railway freight cars in many countries of the world are coupled to the running gear by means of a body centre plate that makes a friction pair with a centre bowl. During motion, the bogie is rotated and moved with respect to the car body. This leads to wear on the contact surfaces. Lubrication is inexpedient in this case because the friction forces damp the vibrations (so-called bogie hunting) during motion. Usually, centre plates exhibit noticeable wear after two years of operation. Reducing wear requires knowing details of the wear process which, in turn, requires computer simulation of freight car motion for an operation period of 10–15 years. The purpose of this paper is to develop a universal method for wear simulation of friction pairs that could be used, in particular, for the centre plate of a freight car.     

Non-Linear Dynamics of Railway Vehicles

The theoretical development of the lateral dynamics of railway vehicles has made rapid strides in recent years and many of the instabilities arising from the geometry of the wheel-rail interface and the forces acting in the contact area are now understood. In addition methods of analysis of curving and dynamic response to track irregularities have been developed and validated by experiment. This paper reviews the present status of equations of motion, limit cycle solutions for hunting oscillations and the relationship of stability to behaviour in curves.     

Effect of System Nonlinearities on Locomotive Bogie Hunting Stability

This paper presents the effect of system parameters on hunting of a rail vehicle with nonlinear yaw dampers and wheel-rail interface. This study is intended to complement earlier studies by True et al. where they investigated the effect of nonlinearities stemming from creep-creep force saturation and wheel/rail contact forces. The rail vehicle is represented by a two-axle truck (bogie) that includes the dynamics of the wheelsets and the truck frame. The numerical simulation results show that yaw damping can have a mixed effect on the hunting critical speed. In some ranges, increasing damping can actually lower the critical speed, unlike the results commonly obtained from a linear model. Flange contact nonlinearities can also have a significant effect on the hunting behavior. Large lateral stiffness of the rail can increase lateral force to vertical force (L/V) ratio during hunting. Increasing the gauge clearance, however, can have an opposite effect. The effect of a variety of other parameters, such as the primary suspension yaw and lateral stiffness, primary suspension lateral damping, wheelset mass, and truck frame mass, are summarized in a table.     

Numerical Simulation and Experimental Verification of the German Roller Rig for Rail Vehicles*

SUMMARY

A numerical simulation model of the roller test stand located at Munich and loaded by a bogie is discussed including its technical structure, the governing physical equations of motion and the structure of the simulation program.

Both, the set up of the mathematical and numerical models time and the computation time of simulation runs have been considerably reduced (by a factor of 20) using formula manipulation programs.

Simulation results concerning the

• starting behaviour of a bogie,

• stationary limit cycle behaviour of bogies with ideal and wear profile and

• influence of gauge changes and spring/damper modifications on limit cycle behaviour of a bogie are presented, some of which are compared with experimental results gained from test facility measurements. The simulation results are in good agreement with the experimental results and provide an experimental verification of the roller rig simulation model presented.

     

Actuator optimal placement studies of high-speed power bogie for active hunting stability

ABSTRACT

We put forward three actuator placements of the high-speed train power bogie to improve the train hunting stability. The active control forces act on the frame, between the frame and the motor, and on the motor by the inertial or retractable actuator, respectively, based on the feedback states of vibration velocity of the front and rear end beams. The feedback gains and the motor suspension parameters in different cases are optimised with the two objectives of system stability margin and control effort. The required actuator outputs of the three cases are compared based on the theoretical analysis with a 8 DOF bogie model. The results show that the three control cases can effectively improve the hunting stability, especially at high speed. The active control of motor lateral movement is helpful to increase the dynamic vibration absorbing function of the motor flexible suspension, and the control output is obviously smaller than the other two control cases. In addition, the influence of system delay on stability was analysed and we could use or avoid the effects of delay on the stability.     

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values.

It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.     

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

SUMMARY

The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values.

It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.     

Dynamics of Automated Guideway Transit Vehicle with Single-axle Bogies

Summary The steering type of a mechanical guidance system has been used for Automated Guideway Transit (AGT) system in Japan. Recently, the single-axle bogie system has developed for AGT vehicle and applied to Yurikamome 7200 type vehicle. This paper describes dynamic characteristics of AGT vehicle with single-axle bogies. Introducing a nonlinear, 15 degree-of-freedom dynamic model, a computer simulation study on the lateral motion of the AGT vehicle with single-axle bogies are carried out. In order to show the dynamic characteristics of the single-axle bogie clearly, it is compared to that of the AGT vehicle with conventional steering system. The simulation study with actual vehicle parameters shows that single-axle bogie has suitable characteristics for AGT system. The multi-body dynamics modeler, DADS, is used to build the dynamic model of AGT vehicle with single-axle bogies and this is used to demonstrate the vehicle motion in actual guideway. Obtained results are compared to that of the field test. It is shown that the vehicle dynamic response can be obtained in realistic situation by using multibody dynamics code, that is useful for designing both vehicle and guideway.     

Dynamics of Automated Guideway Transit Vehicle with Single-axle Bogies

Summary The steering type of a mechanical guidance system has been used for Automated Guideway Transit (AGT) system in Japan. Recently, the single-axle bogie system has developed for AGT vehicle and applied to Yurikamome 7200 type vehicle. This paper describes dynamic characteristics of AGT vehicle with single-axle bogies. Introducing a nonlinear, 15 degree-of-freedom dynamic model, a computer simulation study on the lateral motion of the AGT vehicle with single-axle bogies are carried out. In order to show the dynamic characteristics of the single-axle bogie clearly, it is compared to that of the AGT vehicle with conventional steering system. The simulation study with actual vehicle parameters shows that single-axle bogie has suitable characteristics for AGT system. The multi-body dynamics modeler, DADS, is used to build the dynamic model of AGT vehicle with single-axle bogies and this is used to demonstrate the vehicle motion in actual guideway. Obtained results are compared to that of the field test. It is shown that the vehicle dynamic response can be obtained in realistic situation by using multibody dynamics code, that is useful for designing both vehicle and guideway.     

Fatigue life prediction based on the rainflow cycle counting method for the end beam of a freight car bogie

This paper presents a system for treating of the actual measured data for load histories. The approach consists of two steps: stress analysis and fatigue damage prediction. Finite element analysis is conducted for the component in question to obtain detailed stress-strain responses. A significant number of failures occurred in a brake end beam which led to economic losses and disruption of service. The cracks appeared to be fatigue cracks caused by the dynamic load produced in the loaded bogie frame. Strain gauge data were analyzed, and fatigue cycles were calculated from this data. Rainflow cycle counting was used to estimate cumulative damage of the end beam under in-service loading conditions. The fatigue life calculated with the rainflow cycle counting method, the P-S-N curve, and the modified Miner’s rule agreed well with actual fatigue life within an error range of 2.7%~31%.     

钢管混凝土拱空间极限承载力高精度分析

采用考虑材料非线性的钢管混凝土拱空间极限承载力计算方法对1个X型双肋拱与1个平行双肋拱进行了空间极限承载力计算。在该方法中，对钢管混凝土拱结构采用纤维单元模型，该模型假定钢管与混凝土完全粘接，钢管对核心混凝土的套箍作用体现在以一维形式表达的核心混凝土的应力-应变关系曲线之中，针对材料非线性分析中单元内各点刚度参差不齐的特点，采用单元内设小元的方法(相当于子结构)，编制了非线性有限元程序，在该程序中，计算模型完全是基于小元层次进行的，比如单元刚度矩阵由小元刚度矩阵凝聚而成，单元节点的残余力由小元节点的残余力构成，故只需改变单元内小元个数这1个参数就可实现对结构的重新划分且极大地降低了非线性方程组的阶数，非常方便且实用。在程序计算结果得到模型试验结果验证的基础上，还对不同的横撑根数对结构空间极限承载力的影响进行了分析。     

Pareto optimisation of railway bogie suspension damping to enhance safety and comfort

This paper presents the optimisation of damping characteristics in bogie suspensions using a multi-objective optimisation methodology. The damping is investigated and optimised in terms of the resulting performances of a railway vehicle with respect to safety, comfort and wear considerations. A complete multi-body system model describing the railway vehicle dynamics is implemented in commercial software Gensys and used in the optimisation. In complementary optimisation analyses, a reduced and linearised model describing the bogie system dynamics is also utilised. Pareto fronts with respect to safety, comfort and wear objectives are obtained, showing the trade-off behaviour between the objectives. Such trade-off curves are of importance, especially in the design of damping functional components. The results demonstrate that the developed methodology can successfully be used for multi-objective investigations of a railway vehicle within models of different levels of complexity. By introducing optimised passive damping elements in the bogie suspensions, both safety and comfort are improved. In particular, it is noted that the use of optimised passive damping elements can allow for higher train speeds. Finally, adaptive strategies for switching damping parameters with respect to different ride conditions are outlined and discussed.     

基于材料非线性的沥青路面结构当量力学分析方法

针对目前沥青路面结构分析中存在的线弹性层状体系假设无法描述材料非线性特性以及结构层模量取值不合理等问题,为了寻找更加符合路面结构非线性服役行为的沥青路面结构分析方法,将材料非线性与层状体系相结合,研究3种典型路面材料模量依赖模型,建立材料模量与结构模量跨越的联系机制,提出了一种基于材料非线性的沥青路面结构分析当量计算方法,并通过足尺环道实测应变结果对方法的可靠性进行了验证。研究结果表明：基于材料非线性的沥青路面结构分析当量计算方法,其计算结果与足尺环道实测结果之间具有良好的相关性,方法可靠、合理,可以作为沥青路面非线性分析的一种计算手段;基于材料非线性原理构建的沥青混合料、半刚性材料和路基土的模量依赖模型,可以用于表征路面结构计算中的材料非线性特性;采用Mises等效应力可作为室内单一应力状态和现场复杂应力状态的联系机制,以协调室内试验模式和现场实际受力状态;当路面结构形式、荷载与环境条件确定时,路面结构的力学响应具有唯一性。所提出的当量计算方法一方面获得了一种确定路面材料回弹模量取值的有效技术途径,另一方面改进了沥青路面结构力学分析的合理性和可靠性,在非线性沥青路面分析理论和计算方法等方面具有一定的学术意义和应用价值。     

粒料层当量模量求解新方法——以粒料基层沥青路面为例

为了给沥青路面合理设计提供参考,围绕粒料的非线性特性对粒料层当量模量展开研究。基于Uzan三参数模型编制材料子程序,并引入Cary&Zapata模型对粒料回弹模量进行湿度调整;利用有限元方法开展不同温湿度组合下的沥青路面非线性结构计算;自主开发迭代反演算法,提出基于关键结构响应(沥青层底最大拉应变等效)的粒料层当量模量求解新方法,并结合当前基于路表弯沉的结构层反算模量进行比较分析。结果表明：(1)由于粒料的非线性,路表弯沉等效并不意味着内部关键结构响应等效,采用基于路表弯沉的线弹性模量反算体系对具有明显非线性的粒料层模量进行求解,存在不合理性;(2)自主开发的基于关键结构响应等效的粒料层当量模量求解方法快速稳定,沥青面层底部最大拉应变的相对误差可控制在1%之内;(3)以层状弹性体系为理论基础的沥青路面设计方法忽略了粒料层的非线性,造成荷载传力路径与真实情况存在偏差,使得实际弯沉(非线性)大于计算弯沉(线弹性),从理论上论证了中国当前“柔性基层沥青路面弯沉验收难以通过”的现实困境;(4)基于关键结构响应的当量模量与当前基于路表弯沉的反算模量之间存在良好的相关性,提出了二者的转换模...     

Fatigue Life Prediction of a Railway Bogie under Dynamic Loads through Simulation

For dynamically loaded lightweight structures fatigue strength is an important design criteria. In this paper a new method to predict fatigue lifetime is shown. This is based on the combination of frequency domain and time domain calculations, which allows lifetime prediction with reduced computational effort. The method is implemented to work in a concurrent engineering software environment together with a computer aided design (CAD), a finite-element-method (FEM) and a multibody system (MBS) program. The benefits of the new approach are demonstrated by application to the bogie of a freight locomotive. The dynamic loads acting on the bogie are computed by multibody simulation. The bogie frame is considered as an elastic body of the MBS and the highly nonlinear wheel rail contact is modeled quasi-elastically. For the ride on a straight track the equations of motion can be linearized and the covariance matrix of the loads is calculated. The ride through a ramp is simulated by using the nonlinear differential equations. FEM yields the stresses in the most stressed locations of the bogie depending on the loads calculated by multibody simulation. Based on these stresses the fatigue life prediction is carried out in the MBS post-processing program FATIGUE.     

Multiobjective optimisation of bogie suspension to boost speed on curves

To improve safety and maximum admissible speed on different operational scenarios, multiobjective optimisation of bogie suspension components of a one-car railway vehicle model is considered. The vehicle model has 50 degrees of freedom and is developed in multibody dynamics software SIMPACK. Track shift force, running stability, and risk of derailment are selected as safety objective functions. The improved maximum admissible speeds of the vehicle on curves are determined based on the track plane accelerations up to 1.5?m/s². To attenuate the number of design parameters for optimisation and improve the computational efficiency, a global sensitivity analysis is accomplished using the multiplicative dimensional reduction method (M-DRM). A multistep optimisation routine based on genetic algorithm (GA) and MATLAB/SIMPACK co-simulation is executed at three levels. The bogie conventional secondary and primary suspension components are chosen as the design parameters in the first two steps, respectively. In the last step semi-active suspension is in focus. The input electrical current to magnetorheological yaw dampers is optimised to guarantee an appropriate safety level. Semi-active controllers are also applied and the respective effects on bogie dynamics are explored. The safety Pareto optimised results are compared with those associated with in-service values. The global sensitivity analysis and multistep approach significantly reduced the number of design parameters and improved the computational efficiency of the optimisation. Furthermore, using the optimised values of design parameters give the possibility to run the vehicle up to 13% faster on curves while a satisfactory safety level is guaranteed. The results obtained can be used in Pareto optimisation and active bogie suspension design problems.     

一种新型小型单轨游览车牵引悬挂装置

随着跨座式单轨火车的发展,部分小型单轨高架游览车车厢较小,车厢重量较轻,采用的单节车厢设置一个转向架的结构,现有的单轨车牵引悬挂系统不适用于此类结构,故本文基于该状况,设计开发一种新型小型单轨游览车牵引悬挂装置。