Optimization of the Lateral Stability of Rail Vehicles

Summary The lateral stability of a rail vehicle is optimized using a combination of multibody dynamics, sequential quadratic programming, and a genetic algorithm. Several steps are taken to validate this integrated approach and to show its effectiveness. First, a hand-derived solution to a 17 degree of freedom linear rail vehicle model is compared to the simulation results from the A'GEM multibody dynamics software. Second, the calculation of the ‘critical speed’ (above which a rail vehicle response becomes unstable) using sequential quadratic programming is validated for a specific example. In the process, the existence of sharply-discontinuous ‘cliffs’ in the plots of critical speed versus suspension stiffnesses are identified. These cliffs, which are due to switching of the least-damped mode in the system, greatly hinder the application of gradient-based optimization methods. Two methods that do not require gradient information, a genetic algorithm and the Nelder-Mead's Simplex algorithm, are used to optimize the critical speed. The two algorithms and their results are compared. In recognition of the cliff phenomenon, the definition of critical speed is generalized to make it a more practical measure of lateral stability.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A’GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A'GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models

In this paper, a vehicle's lateral dynamic model is developed based on the pure and the combined-slip LuGre tyre models. Conventional vehicle's lateral dynamic methods derive handling models utilising linear tyres and pure-slip assumptions. The current article proposes a general lateral dynamic model, which takes the linear and nonlinear behaviours of the tyre into account using the pure and combined-slip assumptions separately. The developed methodology also incorporates various normal loads at each corner and provides a proper tyre–vehicle platform for control and estimation applications. Steady-state and transient LuGre models are also used in the model development and their responses are compared in different driving scenarios. Considering the fact that the vehicle dynamics is time-varying, the stability of the suggested time-varying model is investigated using an affine quadratic stability approach, and a novel approach to define the critical longitudinal speed is suggested and compared with that of conventional lateral stability methods. Simulations have been conducted and the results are used to validate the proposed method.     

行星齿轮结构的混合动力汽车的系统效率

首先分析了一种行星齿轮结构的混合动力电动汽车的纵向动力学方程，并且研究了不同情况下的汽车系统效率，得到了系统效率优化的目标函数和约束条件，随后利用序列二次规划算法对混合动力电动汽车系统效率进行了优化计算，从而确定了每种工况下的最佳蓄电池功率和最佳减速比。     

Region of attraction analysis for nonlinear vehicle lateral dynamics using sum-of-squares programming

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates.     

基于前车轨迹预测的高速智能车运动规划

针对现有运动规划算法大多只考虑障碍车当前状态,本文中提出一种基于前车运动轨迹预测的高速车辆运动规划算法。首先,融合考虑驾驶意图与基于车辆运动模型的方法对前车轨迹进行预测;然后,采用贝塞尔曲线(Bezier)规划主车运动轨迹,结合避撞过程中与前车碰撞风险概率,高速避撞车辆速度变化特点以及车辆运动稳定性等因素建立目标函数,并考虑车辆动力学与运动学约束,使用序列二次规划(SQP)方法对Bezier曲线的控制点和主车运动目标点位置进行优化求解,得到最优避撞运动轨迹;最后,以前车直行和换道两种工况为例,对主车的避撞运动轨迹进行规划,分析不同工况下主车避撞过程中的运动状态变化以及与前车碰撞风险概率变化。结果表明,所提出的运动规划算法能够保证车辆的避撞安全性与运动稳定性。     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

General Purpose Vehicle System Dynamics Software Based on Multibody Formalisms

SUMMARY

This paper pursues two objectives: Firstly, to review the state-of-the-art of general purpose vehicle system dynamics software and secondly, to describe two representatives, the program MEDYNA and the program NEWEUL. The general modeling requirements for vehicle dynamics software, the multibody system approach and a comparative discussion of multibody software are given. The two programs NEWEUL and MEDYNA are described with respect to modeling options, computational methods, software engineering as well as their interfaces to other software. The applicability of these programs is demonstrated on two selected examples, one from road vehicle problems and the other from wheel/rail dynamics. It is concluded that general purpose software based on multibody formalisms will play the same role for mechanical systems, especially vehicle systems, as finite element methods play for elastic structures.     

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.     

Influence of wheel–rail contact modelling on vehicle dynamic simulation

This paper presents a comparison of four models of rolling contact used for online contact force evaluation in rail vehicle dynamics. Until now only a few wheel–rail contact models have been used for online simulation in multibody software (MBS). Many more models exist and their behaviour has been studied offline, but a comparative study of the mutual influence between the calculation of the creep forces and the simulated vehicle dynamics seems to be missing. Such a comparison would help researchers with the assessment of accuracy and calculation time. The contact methods investigated in this paper are FASTSIM, Linder, Kik–Piotrowski and Stripes. They are compared through a coupling between an MBS for the vehicle simulation and Matlab for the contact models. This way the influence of the creep force calculation on the vehicle simulation is investigated. More specifically this study focuses on the influence of the contact model on the simulation of the hunting motion and on the curving behaviour.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.     

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.     

Crash analysis and dynamical behaviour of light road and rail vehicles

The main goal of crashworthiness is to ensure that vehicles are safer for occupants, cargo and other road or rail users. The crash analysis of vehicles involves structural impact and occupant biomechanics. The traditional approaches to crashworthiness not only do not take into account the full vehicle dynamics, but also uncouple the structural impact and the occupant biomechanics in the crash study. The most common strategy is to obtain an acceleration pulse from a vehicle structural impact analysis or experimental test, very often without taking into account the effect of suspensions in its dynamics, and afterwards feed this pulse into a rigid occupant compartment that contains models of passengers. Multibody dynamics is the most common methodology to build and analyse vehicle models for occupant biomechanics, vehicle dynamics and, with ever increasing popularity, structural crash analysis. In this work, the aspects of multibody modelling relevant to road and rail vehicles and to occupant biomechanical modelling are revised. Afterwards, it is shown how multibody models of vehicles and occupants are used in crash analysis. The more traditional aspects of vehicle dynamics are then introduced in the vehicle models in order to appraise their importance in the treatment of certain types of impact scenarios for which the crash outcome is sensitive to the relative orientation and alignment between vehicles. Through applications to the crashworthiness of road and of rail vehicles, selected problems are discussed and the need for coupled models of vehicle structures, suspension subsystems and occupants is emphasized.     

装载机避障轨迹规划及模型预测轨迹跟踪

轮式装载机在工作区域行驶时，避障过程频繁，以往的避障轨迹规划未考虑整车转向半径约束和车速变化，也较少考虑整车在动力学模型条件下的轨迹跟踪性能。针对上述情况，以自动驾驶轮式装载机为对象，基于最优快速随机扩展树算法（RRT^*），考虑车身膨胀圆个数，生成全局最优避障路径，以整车最小稳定转向半径为约束，利用CC-Steer算法对避障路径进行平滑处理，采用路径-速度分解算法规划满足整车在加速、匀速和减速状态下的避障行驶轨迹。基于整车动力学模型，考虑行驶过程中的横向位置偏差和航向角偏差，并将整车动力传动系统视为1阶惯性环节，构建装载机动力学状态空间方程。以加速度和铰接角为控制输入，以车速、横向位置偏差和航向角偏差为控制输出，建立整车动力学预测模型，以加速度、铰接角和车速为约束条件，将目标函数转换为二次规划问题，建立满足装载机在工作区域避障的模型预测轨迹跟踪控制系统。以规划的非匀速行驶避障轨迹为目标，利用构建的模型预测轨迹跟踪系统，进行自动驾驶轮式装载机的轨迹跟踪仿真。研究结果表明：所提方法能够很好地控制自动驾驶轮式装载机从初始位姿驶向目标位姿，实现整车在工作区域的避障过程，且在避障过程中满足整车的约束要求，保证整车在轨迹跟踪过程中的安全稳定性能。     

Switch Panel wear loading – a parametric study regarding governing train operational factors

The acting forces and resulting material degradation at the running surfaces of wheels and rail are determined by vehicle, track, interface and operational characteristics. To effectively manage the experienced wear, plastic deformation and crack development at wheels and rail, the interaction between vehicle and track demands a system approach both in maintenance and in design. This requires insight into the impact of train operational parameters on rail- and wheel degradation, in particular at switches and crossings due to the complex dynamic behaviour of a railway vehicle at a turnout. A parametric study was carried out by means of vehicle-track simulations within the VAMPIRE® multibody simulation software, performing a sensitivity analysis regarding operational factors and their impact on expected switch panel wear loading. Additionally, theoretical concepts were cross-checked with operational practices by means of a case study in response to a dramatic change in lateral rail wear development at specific switches in Dutch track. Data from train operation, track maintenance and track inspection were analysed, providing further insight into the operational dependencies. From the simulations performed in this study, it was found that switch rail lateral wear loading at the diverging route of a 1:9 type turnout is significantly influenced by the level of wheel–rail friction and to a lesser extent by the direction of travel (facing or trailing). The influence of other investigated parameters, being vehicle speed, traction, gauge widening and track layout is found to be small. Findings from the case study further confirm the simulation outcome. This research clearly demonstrates the contribution flange lubrication can have in preventing abnormal lateral wear at locations where the wheel–rail interface is heavily loaded.     

基于非线性模型预测控制的车辆纵向队列协调控制

本文中针对基于分层控制结构的车辆队列上、下层控制缺少联系的问题,提出了车辆队列跟驰与个体车辆动力学稳定性协调控制的思路,其基本思想是在保证队列中个体车辆安全稳定行驶的同时,尽可能实现队列跟驰控制的目标。基于非线性模型预测控制(nonlinear model predictive control,NMPC)方法设计了车辆队列协调控制方案,设计了包括跟驰间距误差、跟驰速度误差以及车速与车轮圆周速度差3个子目标的优化目标函数,将队列跟驰与车辆动力学稳定性的协调控制转化为约束优化控制问题;基于序列二次规划(sequential quadratic programming,SQP)方法进行求解,得到车辆前、后轴的制动/驱动力矩来实现上层决策输出的期望跟驰加速度。基于由3车辆组成的非线性队列模型对控制方案进行了仿真分析,结果表明,所提出的基于NMPC的车辆队列协调控制策略可以在大范围操纵工况下,在保证车辆安全稳定行驶的基础上实现队列的跟驰控制。     

Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated.

Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only.

This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity.

The influence of some geometrical factors typical of the wheel-rail contact, such as side clearance and linearized conicity, will also be discussed. The approach is based on the application of statistical methods to dynamic linear systems.     

FSAC赛车轨迹跟踪协同控制策略研究

针对中国大学生方程式赛车（FSAC）在比赛中横向-纵向协同控制的轨迹跟踪精度和稳定性问题,根据现代控制理论和经典控制理论提出一种以纵向速度为结合点的线性二次控制器（LQR）和比例-积分-微分算法（PID）的横纵向协同控制策略,并根据赛车相对参考轨迹的位置设计了一种协同控制器。建立二自由度车辆动力学模型,基于该模型设计了横向LQR位置跟踪控制器和纵向PID速度跟踪控制器。所设计的控制策略在CarSim和Simulink搭建的循迹工况联合仿真场景下进行仿真验证,仿真结果为纵向位置偏差小于0.07 m,横向位置偏差小于0.03 m。对控制算法进行实车验证,结果表明,该策略有效提高了赛车的轨迹跟踪精度和行驶稳定性。