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.     

Locomotive dynamic performance under traction/braking conditions considering effect of gear transmissions

Traction or braking operations are usually applied to trains or locomotives for acceleration, speed adjustment, and stopping. During these operations, gear transmission equipment plays a very significant role in the delivery of traction or electrical braking power. Failures of the gear transmissions are likely to cause power loses and even threaten the operation safety of the train. Its dynamic performance is closely related to the normal operation and service safety of the entire train, especially under some emergency braking conditions. In this paper, a locomotive–track coupled vertical–longitudinal dynamics model is employed with considering the dynamic action from the gear transmissions. This dynamics model enables the detailed analysis and more practical simulation on the characteristics of power transmission path, namely motor–gear transmission–wheelset–longitudinal motion of locomotive, especially for traction or braking conditions. Multi-excitation sources, such as time-varying mesh stiffness and nonlinear wheel–rail contact excitations, are considered in this study. This dynamics model is then validated by comparing the simulated results with the experimental test results under braking conditions. The calculated results indicate that involvement of gear transmission could reveal the load reduction of the wheelset due to transmitted forces. Vibrations of the wheelset and the motor are dominated by variation of the gear dynamic mesh forces in the low speed range and by rail geometric irregularity in the higher speed range. Rail vertical geometric irregularity could also cause wheelset longitudinal vibrations, and do modulations to the gear dynamic mesh forces. Besides, the hauling weight has little effect on the locomotive vibrations and the dynamic mesh forces of the gear transmissions for both traction and braking conditions under the same running speed.     

Dynamics of railway wagons subjected to braking torques on defective tracks

It is well known that track defects cause profound effects to the dynamics of railway wagons; normally such problems are examined for cases of wagons running at a constant speed. Brake/traction torques affect the speed profile due to the wheel–rail contact characteristics but most of the wagon–track interaction models do not explicitly consider them in simulation. The authors have recently published a model for the dynamics of wagons subject to braking/traction torques on a perfect track by explicitly considering the pitch degree of freedom for wheelsets. The model is extended for cases of lateral and vertical track geometry defects and worn railhead and wheel profiles. This paper presents the results of the analyses carried out using the model extended to the dynamics of wagons containing less ideal wheel profiles running on tracks with geometry defects and worn rails.     

High-speed trains subject to abrupt braking

The dynamic response of high-speed train subject to braking is investigated using the moving element method. Possible sliding of wheels over the rails is accounted for. The train is modelled as a 15-DOF system comprising of a car body, two bogies and four wheels interconnected by spring-damping units. The rail is modelled as a Euler–Bernoulli beam resting on a two-parameter elastic damped foundation. The interaction between the moving train and track-foundation is accounted for through the normal and tangential wheel–rail contact forces. The effects of braking torque, wheel–rail contact condition, initial train speed and severity of railhead roughness on the dynamic response of the high-speed train are investigated. For a given initial train speed and track irregularity, the study revealed that there is an optimal braking torque that would result in the smallest braking distance with no occurrence of wheel sliding, representing a good compromise between train instability and safety.     

Longitudinal train dynamics: an overview

This paper discusses the evolution of longitudinal train dynamics (LTD) simulations, which covers numerical solvers, vehicle connection systems, air brake systems, wagon dumper systems and locomotives, resistance forces and gravitational components, vehicle in-train instabilities, and computing schemes. A number of potential research topics are suggested, such as modelling of friction, polymer, and transition characteristics for vehicle connection simulations, studies of wagon dumping operations, proper modelling of vehicle in-train instabilities, and computing schemes for LTD simulations. Evidence shows that LTD simulations have evolved with computing capabilities. Currently, advanced component models that directly describe the working principles of the operation of air brake systems, vehicle connection systems, and traction systems are available. Parallel computing is a good solution to combine and simulate all these advanced models. Parallel computing can also be used to conduct three-dimensional long train dynamics simulations.     

分布式驱动电动汽车回馈制动失效的液压补偿控制

分布式驱动电动汽车各驱动轮转速和转矩可以单独精确控制,便于实现整车动力学控制和制动能量回馈,从而提升车辆的主动安全性和行驶经济性。但车辆在回馈制动过程中,一旦1台电机突发故障,其他电机产生的制动力矩将对整车形成附加横摆力矩,从而造成车辆失稳,此时虽可通过截断异侧对应电机制动力矩输出来保证行驶方向,但会使车辆制动力大幅衰减或丧失,同样不利于行车安全。为了解决此问题,提出并验证一种基于电动助力液压制动系统的制动压力补偿控制方法,力图有效保证整车制动安全性。以轮毂电机驱动汽车为例,首先建立了整车动力学模型以及轮毂电机模型,通过仿真验证了回馈制动失效的整车失稳特性以及电机转矩截断控制的不足;然后,建立了电动助力液压制动系统模型,并通过原理样机的台架试验验证了模型的准确性;接着,基于滑模控制算法设计了制动压力补偿控制器,并在单侧电机再生制动失效后的转矩截断控制基础上完成了液压制动补偿控制效果仿真验证;最后,通过实车试验证明了所提控制方法的有效性和实用性。研究结果表明：在分布式驱动电动汽车单侧电机再生制动失效工况下,通过异侧电机转矩截断控制和制动系统的液压主动补偿,能够使车辆快速恢复稳定行驶并满足制动强度需求。     

电子控制牵引力调节装置

丰田公司凌志ＬＳ４００型１９８０所型轿车装用电子控制牵引力调节有完全调节发动机的扭矩和后驱动轮的制和，并根据路面情况给出一个最佳的驱动力，它主要由制动主继电器，前轮速度传感器，牵引力调节系统执行器等１８个零部件组成，对各零部件的结构和功用进行了详细地介绍。     

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.     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

一种叶轮式MRF汽车制动器结构设计与性能仿真

设计了一种汽车轮内叶轮式磁流变液制动器,推导出该制动器的制动力矩计算方法,并在Matlab/Simulink环境下建立仿真模型,分析了制动器结构参数对制动力矩的影响。结果表明,叶轮式磁流变液制动器工作模式为剪切与流动的混合模式,其制动力矩与磁感应强度呈现对数变化规律,与工作间隙呈现负指数变化规律;叶片的径向尺寸、叶片数量和叶片厚度对制动力矩都有较大影响。所设计的汽车磁流变液制动器能够满足一般小型汽车的制动力矩需求。     

Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent Riccati equation technique

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.     

A new flatness-based control of lateral vehicle dynamics

This paper presents a new concept for vehicle dynamics control (VDC). The control of the longitudinal vehicle dynamics is not discussed, since we are assuming that it is much slower and weakly coupled to the lateral and yawing dynamics. The actuators are considered to be the traction and the braking torques of the individual wheels and only the standard sensors of the common VDC system are used. A modular interface to the subordinate wheel control system is provided by choosing the yaw torque as a fictitious control input. The VDC system is designed by means of a two degrees-of-freedom control scheme. It comprises a flatness-based feedforward part and a stabilising feedback part. The reference trajectory generation is introduced for the flat output which is given by the lateral velocity of the vehicle. Thus an advantageous kind of body side-slip angle control is provided with the standard VDC system hardware. Extensive simulation studies show excellent performance of the designed control concept.     

Dynamic model for the wheel–rail contact friction

Accurately estimating the coefficient of friction (CoF) is essential in modelling railroad dynamics, reducing maintenance costs, and increasing safety in rail operations. The typical assumption of a constant CoF is widely used in theoretical studies; however, it has been noticed that the CoF is not constant, but rather depends on various dynamic parameters and instantaneous conditions. In this paper, we present a newly developed three-dimensional nonlinear CoF model for the dry rail condition and test the CoF variation using this model with estimated dynamic parameters. The wheel–rail is modelled as a mass–spring–damper system to simulate the basic wheel–rail dynamics. Although relatively simple, this model is considered sufficient for the purpose of this study. Simulations are performed at a train speed of 20 m/s using rail roughness as an excitation source. The model captures the CoF extremes and illustrates its nonlinear behaviour and instantaneous dependence on several structural and dynamic parameters.     

Real-time implementation of a traction control algorithm on a scaled roller rig

Traction control is a very important aspect in railway vehicle dynamics. Its optimisation allows improvement of the performance of a locomotive by working close to the limit of adhesion. On the other hand, in case the adhesion limit is surpassed, the wheels are subjected to heavy wear and there is also a big risk that vibrations in the traction occur. Similar considerations can be made in the case of braking. The development and optimisation of a traction/braking control algorithm is a complex activity, because it is usually performed on a real vehicle on the track, where many uncertainties are present due to environmental conditions and vehicle characteristics. This work shows the use of a scaled roller rig to develop and optimise a traction control algorithm on a single wheelset. Measurements performed on the wheelset are used to estimate the optimal adhesion forces by means of a wheel/rail contact algorithm executed in real time. This allows application of the optimal adhesion force.     

电传动矿用自卸车轮边电机驱动系统动态特性研究

矿区环境复杂,电传动矿用汽车的轮边电机传动系统对整车动力性、制动性及平顺性有极大影响,为了综合路面激励和电机自身激励综合分析驱动系统动态特性,采用数值仿真软件建立轮边电机传动系统模型,分析其在启动加速、平稳运行及制动时的动态特性,为了验证模型的准确性进行了实车实验。结果表明该轮边电机传动系统的输出转矩发生考虑波动转矩后会较大影响整车加速和制动性能,常见车速的加速和减速性能会减弱5%,稳定行驶阶段差别不大。刚柔耦合模型能更准确地描述驱动系统及整车动力特性,对整车的设计有指导意义。     

Advanced emergency braking under split friction conditions and the influence of a destabilising steering wheel torque

The steering system in most heavy trucks is such that it causes a destabilising steering wheel torque when braking on split friction, that is, different friction levels on the two sides of the vehicle. Moreover, advanced emergency braking systems are now mandatory in most heavy trucks, making vehicle-induced split friction braking possible. This imposes higher demands on understanding how the destabilising steering wheel torque affects the driver, which is the focus here. Firstly, an experiment has been carried out involving 24 subjects all driving a truck where automatic split friction braking was emulated. Secondly, an existing driver–vehicle model has been adapted and implemented to improve understanding of the observed outcome. A common conclusion drawn, after analysing results, is that the destabilising steering wheel torque only has a small effect on the motion of the vehicle. The underlying reason is a relatively slow ramp up of the disturbance in comparison to the observed cognitive delay amongst subjects; also the magnitude is low and initially suppressed by passive driver properties.     

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.     

列车制动过程仿真计算系统研究与开发

在列车牵引计算理论方法的基础上,设计了基于等时间步长法的列车制动过程仿真算法,开发了列车制动过程仿真系统。系统根据给定列车管减压量可计算相应的制动距离,也可根据设定的停车目标位置反推出所需要的列车管减压量。系统还能够计算制动距离、时间、列车管减压量等技术指标,显示列车制动过程的速度一距离曲线。应用系统定量研究了线路条件、编组条件、停车位置对列车制动过程的影响。     

基于BP神经网络的列车制动控制仿真研究

针对列车制动过程存在的复杂性、非线性、时变性、不确定性等因素,通过分析影响建立BP神经网络模型的主要因素,建立了用于列车制动控制的BP神经网络模型。以货物列车为仿真对象,在Matlab环境中进行了仿真研究。仿真结果表明,该方法控制安全性好、停车误差小,基于BP神经网络的智能算法运用于列车制动控制是可行的。