Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.     

Non-steady state modelling of wheel-rail contact problem for the dynamic simulation of railway vehicles

This paper deals with the solution of the non-steady state wheel-rail contact problem. Firstly, the existing models are analysed and it is concluded that none of them have the computational efficiency and/or accuracy characteristics required to be used in a railway simulation programme. Following this, a new solution is proposed to the problem that allows obtaining sufficiently accurate results with a relatively low computational cost. During the development of the proposed method it has been assumed that only one type of creepage is variable with respect to the time. Further work is necessary to extend it to more general cases.     

Non-steady state modelling of wheel-rail contact problem for the dynamic simulation of railway vehicles

Abstract

This paper deals with the solution of the non-steady state wheel-rail contact problem. Firstly, the existing models are analysed and it is concluded that none of them have the computational efficiency and/or accuracy characteristics required to be used in a railway simulation programme. Following this, a new solution is proposed to the problem that allows obtaining sufficiently accurate results with a relatively low computational cost. During the development of the proposed method it has been assumed that only one type of creepage is variable with respect to the time. Further work is necessary to extend it to more general cases.     

A two-dimensional tire model on uneven roads for vehicle dynamic simulation1

This study proposes a comprehensive analytical tire model for handling and ride comfort in low frequency ranges. A contact algorithm that is developed in this study provides a two-dimensional contact pressure distribution on even and uneven road surfaces with reasonable computational cost. Shear stresses and strains during cornering and braking are estimated by direct measurement of tread deformations. The model is validated against experimental force and moment data for general handling simulations. Cleat tests are also conducted and validated under different forward velocity and vertical load conditions for a tire vibration study.     

A novel method to model wheel–rail normal contact in vehicle dynamics simulation

An approximate analytical method is proposed for calculating the contact patch and pressure distribution in the wheel–rail interface. The deformation of the surfaces in contact is approximated using the separation between them. This makes it possible to estimate the contact patch analytically. The contact pressure distribution in the rolling direction is assumed to be elliptic with its maximum calculated by applying Hertz' solution locally. The results are identical to Hertz's for elliptic cases. In non-elliptic cases good agreement is achieved in comparison to the more accurate but computationally expensive Kalker's variational method (CONTACT code). Compared to simplified non-elliptic contact methods based on virtual penetration, the calculated contact patch and pressure distribution are markedly improved. The computational cost of the proposed method is significantly lower than the more detailed methods, making it worthwhile to be applied to rolling contact in rail vehicle dynamics simulation. Such fast and accurate estimation of contact patch and pressure paves the way for on-line modelling of damage phenomena in dynamics simulation packages.     

Cu基金属陶瓷摩擦材料的成本优化研究

为降低金属陶瓷摩擦材料的制造成本，介绍了Cu基金属陶瓷摩擦材料成本优化方案，并研究了优化方案对Cu基金属陶瓷摩擦材料性能的影响。研究结果表明，Fe可替代Cu用以降低成本，但Fe的含量不应超过20％；可选用低纯度的天然鳞片状石墨作为润滑组元以降低成本，但其纯度不应低于90％；通过合理选择烧结工艺参数，在保证钢背与金属陶瓷摩擦材料的结合强度不低于金属陶瓷摩擦材料自身的抗剪强度的前提下，可以用“平板”状钢背代替“碗状”钢背来降低成本。     

New methodology for fast prediction of wheel wear evolution

In railway applications wear prediction in the wheel–rail interface is a fundamental matter in order to study problems such as wheel lifespan and the evolution of vehicle dynamic characteristic with time. However, one of the principal drawbacks of the existing methodologies for calculating the wear evolution is the computational cost. This paper proposes a new wear prediction methodology with a reduced computational cost. This methodology is based on two main steps: the first one is the substitution of the calculations over the whole network by the calculation of the contact conditions in certain characteristic point from whose result the wheel wear evolution can be inferred. The second one is the substitution of the dynamic calculation (time integration calculations) by the quasi-static calculation (the solution of the quasi-static situation of a vehicle at a certain point which is the same that neglecting the acceleration terms in the dynamic equations). These simplifications allow a significant reduction of computational cost to be obtained while maintaining an acceptable level of accuracy (error order of 5–10%). Several case studies are analysed along the paper with the objective of assessing the proposed methodology. The results obtained in the case studies allow concluding that the proposed methodology is valid for an arbitrary vehicle running through an arbitrary track layout.     

Method for obtaining the wheel–rail contact location and its application to the normal problem calculation through ‘CONTACT’

This work presents a robust methodology for calculating inter-penetration areas between railway wheel and rail surfaces, the profiles of which are defined by a series of points. The method allows general three-dimensional displacements of the wheelset to be considered, and its characteristics make it especially suitable for dynamic simulations where the wheel–rail contact is assumed to be flexible. The technique is based on the discretisation of the geometries of the surfaces in contact, considering the wheel as a set of truncated cones and the rail as points. By means of this approach, it is possible to reduce the problem to the calculation of the intersections between cones and lines, the solution for which has a closed-form expression. The method has been used in conjunction with the CONTACT algorithm in order to solve the static normal contact problem when the lateral displacement of the wheelset, its yaw angle and the vertical force applied in the wheelset centroid are prescribed. The results consist of smooth functions when the dependent coordinates are represented as a function of the independent ones, lacking the jump discontinuities that are present when a rigid contact model is adopted. Example results are shown and assessed for the normal contact problem for different lateral and yaw positions of the wheelset on the track.     

上海地区大型桥梁基础桩型选择

根据上海软土地基地质条件和城市环境特点 ,通过收集本地区颇具特色的大型桥梁工程资料及笔者基础工程实践的回顾 ,认为桩型选择应考虑基础沉降变位控制与上部结构特性相协调 ,工程的城市环境是选择桩型的重要条件 ,选择桩型要满足工程建设要求。对大型水中墩钢管桩基础造价可能与钻孔灌注桩相近 ,甚至还要低。 PHC管桩是本市近年来具有较强发展潜力的桩型。     

Carpooling problem: A new mathematical model,branch-and-bound,and heuristic beam search algorithm

Carpooling is an environmentally friendly transportation system. It can efficaciously help resolve a variety of societal concerns of the urban areas, ranging from traffic congestion to environmental pollution. In this paper, we propose a new mathematical model to solve the carpooling problem. The model simultaneously minimizes the costs of travel times, the vehicle use, and the vehicle delays. An exact solution method based on Branch-and-Bound (B&B) algorithm is proposed to efficiently obtain the optimal solution of the problem. In order to find the near-optimal solutions for large-scale problems, a heuristic beam search algorithm is introduced, which is based on the partial relaxation of some fathoming criteria applied in our proposed B&B. The computational experiments are conducted, based upon the transportation network of Isfahan city, Iran. The results demonstrate the great capability of the proposed exact solution method in terms of both computational solving time required and the number of the evaluated nodes, in comparison with CPLEX software package. The findings of this research can be applied to solve the carpooling problem compatible to the real-life situations.     

公共卫生事件暴发初期的医疗物资调度优化

在公共卫生事件暴发初期，为了合理高效地分配医疗物资，兼顾医疗物资运输成本和运输延误，以新型冠状病毒感染的肺炎为例，研究了公共卫生事件暴发初期受影响较大地区的医疗物资调度问题。基于疫情期间医疗物资供给不足的实际情况，结合各个医疗点对医疗物资的不同需求，采用最优化理论与方法建立考虑物资延迟损失和物流成本的双目标医疗物资优化调度分配模型。同时，采用外逼近法对模型进行求解，通过算例分析验证模型的有效性和算法的高效性。结果表明：由所构建的兼顾延迟损失与物流成本的双目标模型及采用的算法，能够得到不同条件下的医疗物资分配方案，所构建的双目标优化模型可以更好地兼顾医疗物资分配过程中的延迟损失和物流成本，并根据疫情走势及医疗物资供给实际情况提供更为合理的调度方案。     

Adhesion estimation at the wheel–rail interface using advanced model-based filtering

The railway industry in the UK is currently expanding the use of condition monitoring of railway vehicles. These systems can be used to improve maintenance procedures or could potentially be used to monitor current vehicle running conditions without the use of cost prohibitive sensors. This paper looks at a novel method for the online detection of areas of low adhesion in the wheel/rail contact that cause significant disruption to the running of a network, particularly in the autumn season. The proposed method uses a Kalman–Bucy filter to estimate the creep forces in the wheel–rail contact area; post-processing is then applied to provide information indicative of the actual adhesion level. The algorithm uses data that, in practice, would be available from a set of modest cost inertial sensors mounted on the vehicle bogie and wheel-sets. The efficacy of the approach is demonstrated using simulation data from a nonlinear dynamic model of the vehicle and its track interface.     

Non-steady state modelling of wheel–rail contact problem

Among all the algorithms to solve the wheel–rail contact problem, Kalker's FastSim has become the most useful computation tool since it combines a low computational cost and enough precision for most of the typical railway dynamics problems. However, some types of dynamic problems require the use of a non-steady state analysis. Alonso and Giménez developed a non-stationary method based on FastSim, which provides both, sufficiently accurate results and a low computational cost. However, it presents some limitations; the method is developed for one time-dependent creepage and its accuracy for varying normal forces has not been checked. This article presents the required changes in order to deal with both problems and compares its results with those given by Kalker's Variational Method for rolling contact.     

基于大样本浮动车数据的武汉市车辆行驶速度获取与分析

采用基于浮动车行进方向与道路方向约束的道路匹配算法,将浮动车数据准确地匹配到城市道路上;在此基础上分析了大样本浮动车平均瞬时速度与路段平均行驶速度的关系,提出了用大样本浮动车的平均瞬时速度快速评估道路行驶速度.最后利用武汉市约1万辆出租车的GPS数据,对武汉市道路车辆行驶速度情况进行了计算和分析.     

Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem

ABSTRACT

In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached.     

考虑多目标的城市停车换乘选址优化模型及算法

停车换乘选址问题是城市交通网络设计研究的重点领域,已有研究的优化目标多集中在系统总费用方面,而对交通可持续发展方面考虑不足。为此,提出综合考虑多方面目标的停车换乘设施选址优化模型及其求解算法。首先,基于超网络理论,提出多方式城市交通系统的超网络模型并定义O-D (Origin-destination)间的超路径、有效超路径及子路径,结合出行者出行过程及交通网络拥挤特征,给出超路径费用的数学表达;其次,基于多方式交通网络随机均衡配流结果,构建交通总阻抗、污染物排放量以及交通系统公平性等系统优化指标的计算模型,并建立用以描述停车换乘设施选址问题的多目标优化模型;进而,以多目标系统优化模型为上层问题,以超网络下满足Logit分配的多方式交通网络配流模型为下层问题,构建描述城市多方式交通系统停车换乘设施选址问题的双层规划模型,并基于模型特征,结合“记录-搜索”思想设计非支配排序遗传算法进行求解;最后,基于Sioux Falls网络设计算例。研究结果表明：算法能够在有限的步骤内搜索到90%以上的Pareto最优解;平均而言,停车换乘措施使得交通总阻抗减小了0.31%,污染物排放量减少了7.32%...     

CANDY statement of methods

This paper presents a detailed overview of CANDY, a catenary–pantograph dynamic interaction software. Authors describe the main key points of the formulation, focusing on its time-integration scheme, the pantograph and contact models as well as the solution of the initial equilibrium problem. Nonetheless one of the most important features of CANDY is its moving finite element mesh, which enables accurate results without excessive computational cost. The validation of the model against the European Standard EN 50318 and some conclusions and comments about the results of the benchmark are also included.     

An alternative to FASTSIM for tangential solution of the wheel–rail contact

In most rail vehicle dynamics simulation packages, tangential solution of the wheel–rail contact is gained by means of Kalker's FASTSIM algorithm. While 5–25% error is expected for creep force estimation, the errors of shear stress distribution, needed for wheel–rail damage analysis, may rise above 30% due to the parabolic traction bound. Therefore, a novel algorithm named FaStrip is proposed as an alternative to FASTSIM. It is based on the strip theory which extends the two-dimensional rolling contact solution to three-dimensional contacts. To form FaStrip, the original strip theory is amended to obtain accurate estimations for any contact ellipse size and it is combined by a numerical algorithm to handle spin. The comparison between the two algorithms shows that using FaStrip improves the accuracy of the estimated shear stress distribution and the creep force estimation in all studied cases. In combined lateral creepage and spin cases, for instance, the error in force estimation reduces from 18% to less than 2%. The estimation of the slip velocities in the slip zone, needed for wear analysis, is also studied. Since FaStrip is as fast as FASTSIM, it can be an alternative for tangential solution of the wheel–rail contact in simulation packages.     

五种方法测定拉索索力的特点与适用性分析

拉索索力测定的方法很多。为更好地测定拉索索力,结合之前各种研究成果,就目前常用的五种拉索索力测定方法,分析了各自特点和适用性,提出应根据各实际课题的目的、精度要求、成本和结构形式来选用拉索索力测定方法的建议,并将五种方法的适用性划分成“好”、“较好”、“较差”、“差”4个等级。     

Eigensystem of Tangential Contact in Tyre Models

Summary In this paper, a simplified model of tangential contact between tyre and rigid surface is investigated. By linearization the eigensystem of the contact equations is obtained and parameter variations are carried out. It is shown, that some vehicle model parameters have great influence on the eigensystem of tangential contact and can determine the highest eigenfrequency of the system vehicle and tyre. Root loci are used to investigate the influence of parameters like vehicle velocity and gridwidth of the discretization. Based on the eigensystem, stability areas of numerical methods in solving the partial differential equations of tangential contact are calculated. Numerical solutions using stiff and nonstiff integrators are compared with respect to the stability areas, computational effort and accuracy. The results are discussed with a view to further development.