The stability mechanism and its application to heavy-haul couplers with arc surface contact

To investigate the stability mechanism of a type of heavy-haul coupler with arc surface contact, the force states of coupler were analysed at different yaw angles according to the friction circle theory and the structural characteristics of this coupler were summarised. A multi-body dynamics model with four heavy-haul locomotives and three detailed couplers was established to simulate the process of emergency braking. In addition, the coupler yaw instability was tested in order to investigate the effect of relevant parameters on the coupler stability. The results show that this coupler exhibits the self-stabilisation and less lateral force at a small yaw angle. The yaw angle of force line is less than the actual coupler yaw angle which reduces the lateral force and the critical instability. An increase in the friction coefficient of the arc contact surfaces can improve the stability of couplers. The friction coefficient needs to be increased with the increase in the maximum coupler longitudinal compressive force. The stability of couplers is significantly enhanced by increasing the secondary suspension stiffness and reducing the clearance of the lateral stopper of the locomotives. When the maximum coupler compressive force reaches 2500 kN, the required friction coefficient reduces from 0.6 to 0.35, which notably lowers the derailment risk caused by the coupler. The critical instability angle of the coupler mainly depends on the arc contact friction coefficient. When the friction coefficient is 0.3, the critical instability angle was 4–4.5°. The simulation results are consistent with the locomotive line tests. These studies establish meaningful improvements for the stability of couplers and match the heavy-haul locomotive with its suspension parameters.     

The stability and mechanical characteristics of heavy haul couplers with restoring bumpstop

To investigate the stability and mechanical characteristics of a type of heavy haul coupler with restoring bumpstop, the geometry and force states of couplers were analysed at different yaw angles and the longitudinal forces. The structural characteristics of this coupler were summarised. To aid in the investigation, a multi-body dynamics model with four heavy haul locomotives and three detailed couplers was established to simulate the process of emergency braking. In addition, the coupler yaw instability and lateral forces were tested in order to investigate the effect of relevant parameters on the locomotive's wheelset lateral forces. The results show that only when the bumpstop force exceeds half of the coupler longitudinal compression force, can the follower be rotated and the yaw angle of the coupler increase. The bumpstop preload is the most important stabilising factor. The coupler lateral force is constant when the coupler longitudinal force is smaller than the critical values of 2000, 1400 and 1150 kN at coupler free angles of 7°, 8° and 9°, respectively, for operation on straight track. The coupler free angle and the locomotive's lateral clearance of the secondary stopper are important in decreasing the wheelset lateral forces of the locomotive. It is advised that a smaller locomotive's secondary lateral suspension stiffness, a free clearance of 35 mm and an elastic clearance of 15 mm from the secondary lateral stopper be selected. If the coupler's free angle is less than the self-stabilising angle which is 5.5° for operation on straight track, the coupler is stable no matter how great the longitudinal force is. The wheelset lateral forces are allowed at the coupler longitudinal force of 2500 kN when the free angle is 6°. These studies establish meaningful improvements for the stability of couplers and match the heavy haul locomotive with its suspension parameters.     

Improvements for the stability of heavy-haul couplers with arc surface contact

To investigate the stability mechanism of heavy-haul couplers with arc surface contact, the geometry and force analysis were conducted according to the friction circle theory. To improve the stability of the coupler, four improvements were proposed, which are increasing the secondary lateral stiffness of locomotives, adding a restoring bumpstop at the end of the coupler, increasing the arc surfaces radii and changing the clearance and stiffness of secondary lateral stopping block. A multi-body dynamics model with four heavy-haul locomotives and three detailed couplers were established to simulate the emergency braking. In addition, the coupler yaw instability was tested to investigate the effects of relevant parameters on the coupler stability. The results show that increasing the secondary lateral stiffness of locomotives, adding a bumpstop with a smaller bumpstop gap, increasing the arc surfaces radii, increasing the stiffness and decreasing the clearance of secondary lateral stopping block are conducive to improving the stability of the coupler with arc surface contact.     

Coupler rotation behaviour and its effect on heavy haul trains

When a locomotive coupler rotates at an angle, the lateral component of the coupler force has an adverse effect on the locomotive's safety, particularly in heavy haul trains. In this paper, a model of a head-mid configuration, a 20,000-t heavy haul train is developed to analyse the rotation behaviour of the locomotive's coupler system and its effect on the dynamic behaviour of such a train's middle locomotive when operating on tangent and curved tracks. The train model includes detailed coupler and draft gear with which to consider the hysteretic characteristics of the rubber draft gear model, the friction characteristics of the coupler knuckles, and the alignment-control characteristics of the coupler shoulder. The results indicate that the coupler's rotation behaviour differs between the tangent and curved tracks, significantly affecting the locomotive's running performance under the braking condition. A larger coupler rotation angle generates a larger lateral component, which increases the wheelset's lateral force and the derailment coefficient. Decreasing the maximum coupler free angle can improve the locomotive's operational performance and safety. Based on these results, the recommended maximum coupler free angle is 4°.     

Dynamic performances of an innovative coupler used in heavy haul trains

An innovative structure for a heavy haul coupler with an arc surface contact and restoring bumpstop is proposed. This coupler has a small lateral force at a small yaw angle and a limitable yaw angle to ensure an allowable coupler lateral force under intense compressive force. The main structural characteristic of the combined contact coupler is a lateral movable follower with an appropriate friction coefficient of 0.06–0.08 and a slide block with a single freedom of longitudinal movement. In order to verify and simulate the performances, a multi-body dynamics model with four heavy haul locomotives and three detailed couplers was established to simulate the process of emergency braking. In addition, the coupler yaw instability and wheel set lateral forces were tested in order to investigate the effect of relevant parameters on the coupler performances. The combined contact coupler is suitable for heavy haul train for a good dynamic performance.     

基于横摆力矩的汽车稳定性控制策略

为提高车辆的横向稳定性,获得良好的操纵性能,利用ADAMS/car和MATLAB/simulink建立了以横摆角速度和质心侧偏角为控制变量的多级PID仿真模型,分别采用了单个车轮制动和单侧车轮制动产生附加横摆力矩的方式.通过蛇形试验验证了ESP控制器的有效性和对比了2种制动方式的控制效果.仿真试验表明：采用该ESP控制器可以很好地保持车辆的稳定性,采用单侧车轮制动产生附加横摆力矩的方式具有更快的控制速度和更好的控制效果.     

Simulation analysis on the coupler behaviour and its influence on the braking safety of locomotive

In order to simulate the runtime behaviour of coupler and buffer systems accurately, the dynamic model was improved by adopting the polygonal contact model. And the reliability of the friction phenomenon in flat-pin coupler’s tail and the connecting constraint between coupler heads were verified. Then the detailed model which fully considered the dynamic characteristics of middle locomotive and its adjacent wagons was incorporated into the simplified longitudinal dynamic model of combined heavy-haul train. The dynamic response of coupler and its influence on the running safety of locomotive under flat straight line emergency braking condition and long steep grade cycle braking condition were simulated respectively. According to the simulation results, the following suggestions were proposed: flat-pin coupler is more suitable for heavy-haul locomotive, but the inspection work on the friction surface of coupler tail needs to be strengthened; and the vertical anti-off stopping device should be added to avoid the occurrence of decoupling accidents.     

Vehicle dynamic stability improvements through gain-scheduled steering and braking control

This paper is concerned with the synthesis of a robust gain-scheduled ?_∞ MIMO vehicle dynamic stability controller (VDSC) involving both steering and rear braking actuators. This VDSC aims at improving automotive vehicle yaw stability and lateral performances. The aim of this work is to provide a methodology to synthesise such a controller while taking into account the braking actuator limitations and use the steering actuator only if it is necessary. These objectives are treated in an original way by the synthesis of a parameter-dependent controller built in the LPV framework and by the solution of an LMI problem. The proposed solution is coupled with a local ABS strategy to guarantee slip stability and make the solution complete. Nonlinear time and frequency domain simulations on a complex full vehicle model (which has been validated on a real car), subject to critical driving situations, show the efficiency and robustness of the proposed solution.     

Active front wheel steering model and controller for integrated dynamics control systems

We report a model and controller for an active front-wheel steering (AFS) system. Two integrated dynamics control (IDC) systems are designed to investigate the performance of the AFS system when integrated with braking and steering systems. An 8-degrees-of-freedom vehicle model was employed to test the controllers. The controllers were inspected and compared under different driving and road conditions, with and without braking input, and with and without steering input. The results show that the AFS system performs kinematic steering assistance function and kinematic stabilisation function very well. Three controllers allowed the yaw rate to accurately follow a reference yaw rate, improving the lateral stability. The two IDC systems improved the lateral stability and vehicle control and were effective in reducing the sideslip angle.     

Vehicle stability control system for enhancing steerabilty,lateral stability,and roll stability

The Vehicle stability control system is an active safety system designed to prevent accidents from occurring and to stabilize dynamic maneuvers of a vehicle by generating an artificial yaw moment using differential brakes. In this paper, in order to enhance vehicle steerability, lateral stability, and roll stability, each reference yaw rate is designed and combined into a target yaw rate depending on the driving situation. A yaw rate controller is designed to track the target yaw rate based on sliding mode control theory. To generate the total yaw moment required from the proposed yaw rate controller, each brake pressure is properly distributed with effective control wheel decision. Estimators are developed to identify the roll angle and body sideslip angle of a vehicle based on the simplified roll dynamics model and parameter adaptation approach. The performance of the proposed vehicle stability control system and estimation algorithms is verified with simulation results and experimental results.     

Design of a rollover index-based vehicle stability control scheme

This paper presents a rollover index (RI)-based vehicle stability control (VSC) scheme. A rollover index, which indicates an impending rollover, is developed by a roll dynamics phase plane analysis. A model-based roll estimator is designed to estimate the roll angle and roll rate of the vehicle body with lateral acceleration, yaw rate, steering angle and vehicle velocity measurements. The rollover index is computed using an estimated roll angle, estimated roll rate, measured lateral acceleration and time-to-wheel lift. A differential braking control law is designed using a direct yaw control method. The VSC threshold is determined from the rollover index. The effectiveness of the RI, the performance of the estimator and the control scheme are investigated via simulations using a validated vehicle simulator. It is shown that the proposed RI can be a good measure of the danger of rollover and the proposed RI-based VSC scheme can reduce the risk of a rollover.     

Effects of model response on model following type of combined lateral force and yaw moment control performance for active vehicle handling safety

This paper presents a comparison study of the effect of model response on the performance of the model following type combined lateral force and yaw moment control. The combined controls aim to maximize stability limit as well as vehicle responsiveness. In order to realize this aim, two types of model responses are proposed to introduce the required lateral force and yaw moment control. The model responses (a) is the side-slip angle and yaw rate vehicle response of the two degree of freedom vehicle motion (bicycle model). The model responses (b) is an intentional modification from the model responses (a) to the side slip angle converging to zero and first order yaw rate. Three different cases of combining lateral force and yaw moment control have been investigated using the two types of model responses. The effect of model responses is proved by computer simulations of the vehicle response to a single sine wave steering input with braking for the combined control methods proposed. It is found that the influence of the model response has a significant effect on the combined control performance.     

对开路面弯道制动ABS控制策略研究

在对开路面弯道制动工况下分析了轮胎受力情况,提出一种基于转角预测前馈、路径偏移量反馈的车辆最佳滑移率动态调节方法,在SIMPACK中建立汽车多体模型,在MATLAB/Simulink中搭建控制系统,并进行了虚拟在环试验。试验结果显示,与传统ABS相比,所提出的控制方法可以显著改善车辆的侧偏位移、横摆角速度以及制动时方向的稳定性,保证了制动效能,使车辆侧向稳定性得到显著提高。     

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.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

The effect of spring pads in the secondary suspension of railway vehicles on bogie yaw resistance

This paper deals with properties of bogie yaw resistance of an electric locomotive with secondary suspension consisting of flexi-coil springs supplemented with tilting spring pads. Transversal stiffness of a sample of a spring/pad assembly was measured on a dynamic test stand of the University of Pardubice (Czech Republic) and the results were applied into a multi-body model of the locomotive created in the simulation tool ‘SJKV’. On the basis of the simulation results, a detailed analysis of the bogie yaw resistance was performed in order to explain the effect in dynamic behaviour of the locomotive when the moment against bogie rotation (and therefore the distribution of guiding forces on individual wheels, as well) is influenced with the vehicle speed in a certain curve. Results of this analysis show that the application of suspension elements with strongly directionally dependent transversal stiffness into the secondary suspension can just lead to a dependency of the bogie yaw resistance on cant deficiency, i.e. on the vehicle speed in curve. This fact has wide consequences on the vehicle dynamics (especially on the guiding behaviour of the vehicle in curves) and it also points out that the current method of evaluation of the bogie yaw resistance according to relevant standards, which is related with assessment of the quasistatic safety of a railway vehicle against derailment, is not objective enough.     

汽车爆胎特性建模与主动制动控制策略

为了提高汽车在突发爆胎事故时的稳定性,对爆胎汽车主动制动控制策略进行了研究。根据车轮爆胎时间与压力变化的关系,在UniTire模型基础上建立了爆胎模型;根据电子稳定性控制系统中横摆角速度及质心侧偏角对汽车稳定性影响的关系,基于二自由度汽车动力学模型,通过计算汽车横摆角速度及质心侧偏角实际值与理想值的偏差,并基于线性二次型调节器最优控制方法决策出最优附加横摆力矩,从而修正爆胎后汽车的运动状态。最后通过计算机仿真对所提策略的有效性进行了验证。结果表明：主动制动控制策略可以保证爆胎过程中汽车的行驶稳定性和安全性。     

Simulation of curving at low speed under high traction for passive steering hauling locomotives

The traction control in modern electric and diesel electric locomotives has allowed rail operators to utilise high traction adhesion levels without undue risk of damage from uncontrolled wheel spin. At the same time, some locomotive manufacturers have developed passive steering locomotive bogies to reduce wheel rail wear and further improve locomotive adhesion performance on curves. High locomotive traction loads in curving are known to cause the loss of steering performance in passive steering bogies. At present there are few publications on the curving performance of locomotive steering with linkage bogies. The most extreme traction curving cases of low speed and high adhesion for hauling locomotives have not been fully investigated, with effects of coupler forces and cant excess being generally ignored. This paper presents a simulation study for three axle bogie locomotives in pusher and pulling train positions on tight curves. The simulation study uses moderate and high traction adhesion levels of 16.6% and 37% for various rail friction conditions. Curving performance is assessed, showing forced steering bogies to have considerable advantages over self steering bogies. Likewise it is shown that self steering bogies are significantly better than yaw relaxation bogies at improving steering under traction. As the required traction adhesion approaches the rail friction coefficient, steering performance of all bogies degrades and yaw of the bogie frame relative to the track increases. Operation with excess cant and tensile coupler forces are both found to be detrimental to the wear performance of all locomotive bogies, increasing the bogie frame yaw angles. Bogie frame pitching is also found to have significant effect on steering, causing increased performance differences between bogie designs.     

A Qualitative Analysis of the Dynamics of Self-Steering Locomotive Trucks

The primary purpose of this study is to provide a qualitative analysis of the dynamics of the self-steering trucks that are commonly used for freight locomotives - namely, EMD's Radial Truck and GE's Steerable Truck - on improving curving performance and increasing adhesion in curves. Although there exists a number of anecdotal statements on the ability of steerable trucks to reduce curving forces and increase adhesion in curves, to the best of our knowledge, there exists no study that provides a qualitative or quantitative analysis of these features of steerable trucks. Two aspects of locomotive trucks are essential for their ability to deliver small curving forces and high adhesion in curves. First, the ability to allow the axles to yaw sufficiently relative to the truck frames, such that they can hold a small angle of attack with the rail. Second, providing sufficiently large longitudinal stiffness between the end axles and the axles and truck frame, to accommodate high adhesions. An equivalent stiffness analysis is used to show that the two steerable trucks that are considered for this study are far superior to conventional, three-axle, straight trucks in providing both a smaller angle of attack and a higher longitudinal stiffness for better curving and adhesion characteristics. The qualitative analysis of this study agrees with the experience the railroads have had with their self-steering trucks. The findings of this study indicate that self-steering trucks can result in lower lateral forces, accommodate tighter curves, and deliver higher adhesion in curves; without lowering the critical hunting speed of the locomotive. The results further show that the steering mechanism stiffness can have a large effect on the lateral, longitudinal, and yaw stiffness between the end axles; therefore, significantly lowering curving forces, and increasing adhesion and critical hunting speed of the truck.