The Propagation of Waves in a Semi-Infinite Chain of Material Points and Springs Representing a Long Train

SUMMARY

The dynamical behaviour of the longitudinal motion of a long train on which tractive or braking forces apply, often is investigated by representing the train by a model consisting of a continuous bar in which longitudinal vibrations can occur. In the present publication a model consisting of a chain of material points and springs is proposed. It can be investigated by means of difference equation methods and of Laplace transformations. In certain respects the discrepancies of the results with those obtained for a continuous model, are considerable and it may be concluded that a more complete investigation of the discrete model is necessary.     

一种新型混合动力汽车驱动系统的设计

在丰田公司Prius混合动力汽车的驱动结构及其控制策略基础上，提出了一种新型多模式混合动力汽车驱动系统的实现方案。该方案采用了行星轮系和4组齿轮副的传动机构，实现了驱动机构在7种工作模式下的连续传动。     

盾构隧道结构纵向优化设计方法研究

目前的纵向设计方法均假定盾构隧道结构纵向刚度不变。在此基础上进行的盾构隧道纵向结构设计,无法达到结构纵向的变形受力协调,也无法实现结构纵向优化设计。在传统的纵向等效连续化模型的基础上,提出纵向刚度非均匀等效连续模型。模型最大的优点是可以实现盾构隧道纵向刚度分配的非均匀性,从而为纵向设计优化以及隧道结构纵向变形和受力协调的实现打下基础。在该等效纵向模型的基础上,建立2种优化设计模型,其一是以变形为目标、受力为约束的优化模型,其二是以受力为目标、变形为约束的优化模型。利用2种模型对盾构隧道穿过软弱夹层等工况进行分析,验证了模型的正确性。另外,利用优化的结果可以得到较为合理的隧道结构纵向刚度分布方式,以及纵向受力和变形协调的刚度取值范围,从而最终实现变形和受力协调。     

Wave Propagation in a Finite Cascade of Masses and Springs Representing a Train

The response of a train, modelled with a cascade of bodies and springs, due to a step force at the locomotive is investigated. In this model the mass of the locomotive and the last wagon may differ from that of the other wagons. An analytic solution is given for a finite and for a semi-infinite cascade and a comparison to the solution of a continuous model is made.     

Modelling,simulation and applications of longitudinal train dynamics

ABSTRACT

Significant developments in longitudinal train simulation and an overview of the approaches to train models and modelling vehicle force inputs are firstly presented. The most important modelling task, that of the wagon connection, consisting of energy absorption devices such as draft gears and buffers, draw gear stiffness, coupler slack and structural stiffness is then presented. Detailed attention is given to the modelling approaches for friction wedge damped and polymer draft gears. A significant issue in longitudinal train dynamics is the modelling and calculation of the input forces – the co-dimensional problem. The need to push traction performances higher has led to research and improvement in the accuracy of traction modelling which is discussed. A co-simulation method that combines longitudinal train simulation, locomotive traction control and locomotive vehicle dynamics is presented. The modelling of other forces, braking propulsion resistance, curve drag and grade forces are also discussed. As extensions to conventional longitudinal train dynamics, lateral forces and coupler impacts are examined in regards to interaction with wagon lateral and vertical dynamics. Various applications of longitudinal train dynamics are then presented. As an alternative to the tradition single wagon mass approach to longitudinal train dynamics, an example incorporating fully detailed wagon dynamics is presented for a crash analysis problem. Further applications of starting traction, air braking, distributed power, energy analysis and tippler operation are also presented.     

Effects of rail thermal stress on the dynamic response of vehicle and track

A new method is proposed to obtain the dynamic responses of the vehicle–track coupling system under the conditions of rail thermal stress changes in high-speed railways. Exact models are established with different rail longitudinal forces, in which multibody dynamic models are used for vehicles and the direct stiffness method for structures. In order to provide a general, simple and flexible formulation to express longitudinal stress distribution, the accurate model of long slab track consists of many small units with parameters which can be initialised separately. The exact analytical equation of track frequency and modal function was obtained by the transition matrix method, which can be used in calculating the dynamic response of wheel–rail coupling model. The proposed model is verified through comparisons with other classical solutions. Under the influence of train velocities and track irregularities, the specific vibration performances that frequency shifted and amplitude peak enhanced with thermal force are demonstrated through examples. The results show that the response analyses of vehicle and track have great application potentiality for fast estimation of the rail longitudinal stress.     

An integrated draft gear model with the consideration of wagon body structural characteristics

With the increase of railway wagon axle load and the growth of marshalling quantity, the problem caused by impact and vibration of vehicles is increasingly serious, which leads to the damage of vehicle structures and the components. In order to improve the reliability of longitudinal connection model for vehicle impact tests, a new railway wagon longitudinal connection model was developed to simulate and analyse vehicle impact tests. The new model is based on characteristics of longitudinal force transmission for vehicles and parts. In this model, carbodies and bogies were simplified to a particle system that can vibrate in the longitudinal direction, which corresponded to a stiffness-damping vibration system. The model consists of three sub-models, that is, coupler and draft gear sub-model, centre plate sub-model and carbody structure sub-model. Compared with conventional draft gear models, the new model was proposed with geometrical and mechanical relations of friction draft gears considered and with behaviours of sticking, sliding and impact between centre plate and centre bowl added. Besides, virtual springs between discrete carbodies were built to describe the structural deformation of carbody. A computation program for longitudinal dynamics based on vehicle impact tests was accomplished to simulate. Comparisons and analyses regarding the train dynamics outputs and vehicle impact tests were conducted. Simulation results indicate that the new wagon longitudinal connection model can provide a practical application environment for wagons, and the outputs of vehicle impact tests agree with those of field tests. The new model can also be used to study on longitudinal vibrations of different vehicles, of carbody and bogie, and of carbody itself.     

Dynamic analysis of a pantograph-catenary system using absolute nodal coordinates

The dynamic interaction between the catenary and the pantographs of high-speed trains is a very important factor that affects the stable electric power supply. In order to design a reliable current collection system, a multibody simulation model can provide an efficient and economical method to analyze the dynamic behavior of the catenary and pantograph. In this article, a dynamic analysis method for a pantograph-catenary system for a high-speed train is presented, employing absolute nodal coordinates and rigid body reference coordinates. The highly flexible catenary is modeled using a nonlinear continuous beam element, which is based on an absolute nodal coordinate formulation. The pantograph is modeled as a rigid multibody system. The analysis results are compared with experimental data obtained from a running high-speed train. In addition, using a derived system equation of motion, the calculation method for the dynamic stress in the catenary conductor is presented. This study may have significance in providing an example that a structural and multibody dynamics model can be unified into one numerical system.     

Effect of wind speed variation on the dynamics of a high-speed train

The severe shaking due to wind speed variation in high-speed trains has a negative impact on driving safety and riding comfort. It is difficult to solve this problem by directly applying civil engineering technology because of the actual conditions. Therefore, set up a reasonable train operation plan considering the wind speed variation under strong winds is very important. In this study, a multi-body simulation model of a CRH2 high-speed rail vehicle is constructed, and the overturning coefficient is set as the safety limit, we established a crosswind model on the basis of measured wind speed curves and investigated the effect of the rate of wind speed changes, the duration of maximum wind speed and the variation of wind speed in different amplitude on the dynamics of the high-speed train. Considering the most critical wind speed variation conditions, the characteristic wind curve is obtained, which can be used as a reference to set up a reasonable train operation scheme considering the wind speed variation.     

Modelling and analysis of the crush zone of a typical Australian passenger train

In this paper, a three-dimensional nonlinear rigid body model has been developed for the investigation of the crashworthiness of a passenger train using the multibody dynamics approach. This model refers to a typical design of passenger cars and train constructs commonly used in Australia. The high-energy and low-energy crush zones of the cars and the train constructs are assumed and the data are explicitly provided in the paper. The crash scenario is limited to the train colliding on to a fixed barrier symmetrically. The simulations of a single car show that this initial design is only applicable for the crash speed of 35 km/h or lower. For higher speeds (e.g. 140 km/h), the crush lengths or crush forces or both the crush zone elements will have to be enlarged. It is generally better to increase the crush length than the crush force in order to retain the low levels of the longitudinal deceleration of the passenger cars.     

Simulation of longitudinal dynamics of a freight train operating through a car dumper

A heavy haul train and car dumper model was created to analyse train longitudinal dynamics during dumping. Influence of such factors as performance curve of draft gears, total free slack in couplers, operating mode of train positioner and braking of last two cars of train on the in-train forces was considered.     

Energy and wear optimisation of train longitudinal dynamics and of traction and braking systems

Traction and braking systems deeply affect longitudinal train dynamics, especially when an extensive blending phase among different pneumatic, electric and magnetic devices is required. The energy and wear optimisation of longitudinal vehicle dynamics has a crucial economic impact and involves several engineering problems such as wear of braking friction components, energy efficiency, thermal load on components, level of safety under degraded or adhesion conditions (often constrained by the current regulation in force on signalling or other safety-related subsystem). In fact, the application of energy storage systems can lead to an efficiency improvement of at least 10% while, as regards the wear reduction, the improvement due to distributed traction systems and to optimised traction devices can be quantified in about 50%. In this work, an innovative integrated procedure is proposed by the authors to optimise longitudinal train dynamics and traction and braking manoeuvres in terms of both energy and wear. The new approach has been applied to existing test cases and validated with experimental data provided by Breda and, for some components and their homologation process, the results of experimental activities derive from cooperation performed with relevant industrial partners such as Trenitalia and Italcertifer. In particular, simulation results are referred to the simulation tests performed on a high-speed train (Ansaldo Breda Emu V250) and on a tram (Ansaldo Breda Sirio Tram). The proposed approach is based on a modular simulation platform in which the sub-models corresponding to different subsystems can be easily customised, depending on the considered application, on the availability of technical data and on the homologation process of different components.     

高速铁路斜交刚构连续梁桥车桥耦合振动分析

分别采用板单元、四片式、两片式和单片式梁单元模型来计算高速铁路斜交刚构连续梁桥的空间自振频率，通过比较和分析，推荐采用四片式梁单元进行车桥耦合振动分析。计算结果表明斜交刚构连续梁桥具有足够的刚度和良好的整体性，可以满足高速列车行车时的安全性和舒适性要求。     

Second-order sliding mode controller with model reference adaptation for automatic train operation

In this paper, a new approach to model reference based adaptive second-order sliding mode control together with adaptive state feedback is presented to control the longitudinal dynamic motion of a high speed train for automatic train operation with the objective of minimal jerk travel by the passengers. The nonlinear dynamic model for the longitudinal motion of the train comprises of a locomotive and coach subsystems is constructed using multiple point-mass model by considering the forces acting on the vehicle. An adaptation scheme using Lyapunov criterion is derived to tune the controller gains by considering a linear, stable reference model that ensures the stability of the system in closed loop. The effectiveness of the controller tracking performance is tested under uncertain passenger load, coupler-draft gear parameters, propulsion resistance coefficients variations and environmental disturbances due to side wind and wet rail conditions. The results demonstrate improved tracking performance of the proposed control scheme with a least jerk under maximum parameter uncertainties when compared to constant gain second-order sliding mode control.     

基于社会力模型的地铁站乘客上下车行为影响因素分析

在上下班高峰期,缩短乘客的上下车时间,更多乘客将会被送达目的地,从而可以提高现有地铁系统的载客能力.现有的国内外研究乘客上下车行为的文献,大多以全部乘客下车为前提进行研究,这与现实生活中只有部分乘客下车的现象不符.因此在社会力模型的基础上加入规定未下车乘客行为的等待模型,在等待模型中,未下车乘客倾向于停留在初始位置.模拟了部分乘客下车行为,并研究了乘客初始位置分布、上下车乘客比例、门的宽度等因素对部分上下车乘客所需上下车时间的影响.结果表明,车门宽度增加23.08%,最多可节约39.7%的上车时间和39.62%的下车时间;随着上下车人数比例不断上升,平均上车时间不断下降,平均下车时间不断上升;通过改变下车乘客初始分布位置,可以将乘客下车时间缩短至原来的72.16%.      

Vertical random vibration analysis of vehicle–track coupled system using Green's function method

A vertical vehicle–track coupled dynamic model, consisting of a high-speed train on a continuously supported rail, is established in the frequency-domain. The solution is obtained efficiently by use of the Green's function method, which can determine the vibration response over a wide range of frequency without any limitations due to modal truncation. Moreover, real track irregularity spectra can be used conveniently as input. The effect of the flexibility of both track and car body on the entire vehicle–track coupled dynamic response is investigated. A multi-body model of a vehicle with either rigid or flexible car body is defined running on three kinds of track: a rigid rail, a track stiffness model and a Timoshenko beam model. The results show that neglecting the track flexibility leads to an overestimation of both the contact force and the whole vehicle vibration response. The car body flexibility affects the ride quality of the vehicle and the coupling through the track and can be significant in certain frequency ranges. Finally, the effect of railpad and ballast stiffness on the vehicle–track coupled vibration is analysed, indicating that the stiffness of the railpad has an influence on the system in a higher frequency range than the ballast.     

A study on a dynamic model of a vehicle simulator with 6 DOF for the Korean tilting train

This article presents a dynamic model of a railway vehicle for the development of a 6-DOF (degrees of freedom) tilting-train simulator. It will be used to verify the tilting-electronics and tilting-control algorithm that are to be applied to the Korean tilting train. It is composed of 6 electrically driven actuators, a track generation system, a graphic user interface, and a visualization system with a 1600-mm-diameter dome screen. Each system shares the data by means of Ethernet network in real time. In this study, a train model of 9-DOF with a force generation system to tilt the train body has been used. Dynamic analysis for the straight track running and curve negotiation of a railway vehicle can be performed in the model. A verification study for the application of the model to the simulator has been conducted on curving tracks with different radii.     

Establishment and verification of three-dimensional dynamic model for heavy-haul train–track coupled system

For the long heavy-haul train, the basic principles of the inter-vehicle interaction and train–track dynamic interaction are analysed firstly. Based on the theories of train longitudinal dynamics and vehicle–track coupled dynamics, a three-dimensional (3-D) dynamic model of the heavy-haul train–track coupled system is established through a modularised method. Specifically, this model includes the subsystems such as the train control, the vehicle, the wheel–rail relation and the line geometries. And for the calculation of the wheel–rail interaction force under the driving or braking conditions, the large creep phenomenon that may occur within the wheel–rail contact patch is considered. For the coupler and draft gear system, the coupler forces in three directions and the coupler lateral tilt angles in curves are calculated. Then, according to the characteristics of the long heavy-haul train, an efficient solving method is developed to improve the computational efficiency for such a large system. Some basic principles which should be followed in order to meet the requirement of calculation accuracy are determined. Finally, the 3-D train–track coupled model is verified by comparing the calculated results with the running test results. It is indicated that the proposed dynamic model could simulate the dynamic performance of the heavy-haul train well.     

大悬臂弧形腹板钢箱梁剪力滞效应和偏载效应分析

大悬臂弧形腹板钢箱梁的空间受力特征非常明显,在采用常规的单梁杆系模型进行箱梁纵向受力分析前,需要正确把握结构的受力特性。以萧山东人城口环境综合整治工程中主线高架的某三跨连续钢箱梁为例,利用ANSYS建立全桥的三维板壳模型,分析了钢箱梁在典型荷载作用下的剪力滞效应和偏载效应,得到了箱梁剪力滞系数沿纵、横桥向的分布规律和关键截面的活载偏载系数,为常规单梁模型的计算方法提供了可靠的简化参数。     

Stability and performance analysis of a full-train system with inerters

This paper discusses the use of inerters to improve the stability and performance of a full-train system. First, we construct a 28 degree-of-freedom train model in AutoSim, and obtain a linearised model for analysis in Matlab. Then, the benefits of inerters are investigated by the critical speed, settling time and passenger comfort. In addition, we apply a new mechatronic network for further performance improvement, and synthesise the optimal electrical circuit for experimental verification. From the results, inerters are shown to be effective in improving the stability and performance of train systems.