Computer simulation of the interaction between a wheel and a corrugated rail

The paper discusses the problems of modelling and simulation of the wheel/rail contact in the case when geometrical irregularities of the rail are taken into account. The iterative method for determining the geometrical relationship between the profile of a rigid rail and the trajectory of the centre of a rigid wheel is presented. The computer code that implements this method is a part of the computer model of the wheel/rail system. The model allows the case when the wheel loses contact with the rail and afterwards hits the rail. Simulation analysis is focused on the question as to whether the wheel bouncing off and on the rail may occur under normal operation conditions. The other question is how this bouncing influences the pressure forces between the wheel and the rail, and how it influences the stress distribution within the contact zone.     

基于有限元法的轮轨蠕滑特性研究

轮轨滚动接触蠕滑率／力理论是轮轨相互作用一系列问题研究的基础．现有的几种计算蠕滑力的理论模型均建立在Hertz接触条件和半空间假设的基础上，已经无法完成对复杂的接触问题的进一步研究．使用有限元参数二次规划法来求解轮轨的三维弹性／弹塑性接触问题，得出了在不同的轴重、牵引力矩、摩擦系数、踏面形状、横向力条件下的轮轨接触力．提出用轮轨接触的轮周位移计算蠕滑率的新方法，并对在各种参数下所得到的蠕滑率进行了分析比较．     

Railway Train-Track Dynamics for Wheelflats with Improved Contact Models

A variety of methods have been proposed to calculate the dynamic response caused by a railway vehicle affected by a wheelflat. Most of the sophisticated procedures evaluate the elastic properties of the wheel-rail contact by means of the Hertz model. However, the hypotheses that must be satisfied in order to apply the Hertzian contact model are not fulfilled when the wheel-rail contact occurs in the area of wheel affected by the flat. This gives rise to deviations in the results of the dynamic model compared to the real situation. With the objective of analysing the influence of the elastic wheel-rail contact model, a procedure was developed to determine the dynamic response caused by a geometric irregularity (in rail or wheel) by means of Hertzian and non-Hertzian contact models. Results of the wheelflat impact simulations given by both types of contact model have been compared in this work.     

曲率半径对车轮滚动接触疲劳性能的影响

滚动接触疲劳和磨损是铁路轮轨损伤的主要问题.本文中应用赫兹接触理论,在JD-1型轮轨模拟试验机上,通过改变试验冲角,研究了干态工况下曲率半径对车轮钢滚动接触疲劳性能的影响,并用光学显微镜和扫描电子显微镜观察车轮试样剖面与磨痕表面交界处的疲劳裂纹,分析不同曲率半径条件下车轮的滚动接触疲劳机理.结果表明:由于加工硬化的作用试验后所有试样的硬度均有提高;随着曲率半径的减小,车轮钢的磨损量增大,塑性流变层增厚且不均匀,车轮试样疲劳裂纹扩展加剧;裂纹在交变应力作用下容易继续向下扩展,从而形成严重的疲劳破坏.     

轮轨滚动摩擦温升分析

利用有限元法,考虑轮轨间非稳态热传导、与环境的热对流以及热辐射的影响,建立了轮轨滚动接触热耦合计算模型来模拟轮轨滚滑摩擦温升;在模拟轮轨纯滑动条件下,计算分析了由磨损引起的滑动接触斑的尺寸增大对轮轨温度场的影响;在模拟轮轨接触斑部分滑动工况时,针对不同蠕滑率、摩擦系数以及轴重对轮轨温度场的影响进行了相应的计算分析.结果表明:接触斑材料的磨损速度只影响磨损过程中的温度场分布,其稳态温度场分布基本一致;热载荷随着纵向载荷、蠕滑率以及摩擦系数的增大而增大,进而影响轮轨滚动接触热疲劳.     

自然环境条件下轮轨接触黏着特性研究进展

轮轨黏着是铁路运输中的关键基础性科学问题之一,而轮轨接触界面良好的黏着状态是列车安全和高品质运行的根本保障. 轮轨系统作为1个开放的系统,受到各种自然环境因素的影响,如湿度、温度、水、风沙甚至铁氧化物,而所有的这些环境因素都会影响轮轨接触界面的黏着状态和损伤行为. 本文中综述了水、湿度、温度和风沙等自然环境因素对轮轨黏着特性影响规律的研究进展,分析了自然环境因素下轮轨界面铁氧化物特征,重点探讨了自然环境因素对铁氧化物形成的影响及其对轮轨接触黏着特性的影响规律和作用机理,并提出了轮轨黏着的未来研究方向.      

列车车轮滚动接触疲劳裂纹评价研究

列车车轮踏面表层金属滚动接触疲劳是影响列车运行安全性和舒适性的核心科学问题. 借助金相显微镜、扫描电镜、透射电镜和显微硬度计，通过开展列车车轮材料的标准滚动接触疲劳试验，将标准接触疲劳样品的损伤行为与实际服役车轮的损伤行为对比分析，研究了列车车轮的滚动接触疲劳裂纹评价方法. 结果表明:车轮表层金属接触疲劳开裂是表层金属累积塑性变形损伤的结果；标准滚动接触疲劳样品剥离坑的深度恰好等于硬化层的深度，实际服役车轮剥离坑的深度小于硬化层的深度；将车轮表面的滚动接触疲劳裂纹命名为“三角形指向性裂纹”；初步建立了车轮表面滚动接触疲劳损伤程度的定量评价方法.      

机车车轮踏面与钢轨接触的仿真计算及试验研究

应用轮轨型面测量仪测量实际运用中的磨耗后机车车轮，基于标准与磨耗后机车车轮型面，建立轮轨接触三维有限元模型，计算分析不同横移量下的接触斑和等效应力. 搭建轮轨接触试验台，使用取自现场的车轮与钢轨试块进行试验，分析不同横移量下轮轨接触状态. 针对磨耗前后车轮与标准钢轨接触的有限元计算与试验进行对比分析. 结果表明:横移量对轮轨接触状态有着显著的影响，横移量过大会加速机车车轮的磨耗；与标准型面相比，磨耗后车轮型面与标准钢轨接触时的接触斑面积较大，最大等效应力较小；通过轮轨接触试验台所得接触斑形状和大小与仿真计算所得结果一致性较好，证明了有限元仿真计算的可靠性.      

轮轨滚动接触力学的发展

轮轨滚动接触力学主要研究轮轨滚动接触过程中的作用行为。由于其研究的复杂性,目前在该领域的研究已基本形成既独立又关联的六个分支,它们分别是轮轨滚动接触蠕滑率/力理论、轮轨粘着、接触表面波浪形磨损、轮轨滚动疲劳、脱轨和轮轨噪音。本文综述了这几个方面研究的发展历史和现状。由于轮轨滚动接触作用的研究又是以轮轨滚动接触蠕滑率/力理论为基础的,故本文着重评述目前常用于车辆/轨道动力学和轮轨关系研究中几个经典滚动接触理论模型的优缺点。根据实际工程中轮轨作用存在的严重问题,并提出轮轨滚动接触理论及其试验在今后的研究方向和所要考虑的有关重要因素。      

On the Computer Formulations of the Wheel/Rail Contact Problem

In this investigation, four nonlinear dynamic formulations that can be used in the analysis of the wheel/rail contact are presented, compared and their performance is evaluated. Two of these formulations employ nonlinear algebraic kinematic constraint equations to describe the contact between the wheel and the rail (constraint approach), while in the other two formulations the contact force is modeled using a compliant force element (elastic approach). The goal of the four formulations is to provide accurate nonlinear modeling of the contact between the wheel and the rail, which is crucial to the success of any computational algorithm used in the dynamic analysis of railroad vehicle systems. In the formulations based on the elastic approach, the wheel has six degrees of freedom with respect to the rail, and the normal contact forces are defined as function of the penetration using Hertzs contact theory or using assumed stiffness and damping coefficients. The first elastic method is based on a search for the contact locations using discrete nodal points. As previously presented in the literature, this method can lead to impulsive forces due to the abrupt change in the location of the contact point from one time step to the next. This difficulty is avoided in the second elastic approach in which the contact points are determined by solving a set of algebraic equations. In the formulations based on the constraint approach, on the other hand, the case of a non-conformal contact is assumed, and nonlinear kinematic contact constraint equations are used to impose the contact conditions at the position, velocity and acceleration levels. This approach leads to a model, in which the wheel has five degrees of freedom with respect to the rail. In the constraint approach, the wheel penetration and lift are not permitted, and the normal contact forces are calculated using the technique of Lagrange multipliers and the augmented form of the system dynamic equations. Two equivalent constraint formulations that employ two different solution procedures are discussed in this investigation. The first method leads to a larger system of equations by augmenting all the contact constraint equations to the dynamic equations of motion, while in the second method an embedding procedure is used to obtain a reduced system of equations from which the surface parameter accelerations are systematically eliminated. Numerical results are presented in order to examine the performance of various methods discussed in this study.     

Motion of a wheel on snow

A model of a snow layer represented by a continuous set of columns whose deformations are described by the nonlinear model of an ideal elastoplastic continuous medium with viscous properties is proposed. Under the action of a rigid wheel on snow, the field of shear stresses is specified by the law of dry friction. Prom the equations of motion describing the plane-parallel motion of the wheel, there are determined a zone of contact of the wheel with snow, the steady motions of the wheel, and a mode of slipping the wheel. The numerical results are given in tables and figures. These results are obtained by solving the nonlinear equations of motion containing definite integrals with variable integration limits.     

接触状态对叶根轮槽应力分布影响的研究

汽轮机叶片叶根、轮槽连接区域常因加工误差及磨损等原因导致接触状态的改变,从而改变整个区域应力分布并大大降低汽轮机的使用寿命。本文运用数字光弹性技术实验测试了长叶片叶根、轮槽在不同接触状态下的应力分布情况,同时结合有限元进行了仿真计算。结果表明,叶根、轮槽对称接触时,全部齿同时接触的应力集中系数最小且分布较均匀;而当部分接触齿产生间隙时,接触状态发生显著变化,应力集中系数明显增大;尤其是当左右齿非对称接触时,最大应力集中系数明显增大且应力分布不均匀。本文研究可为叶根、轮槽的优化设计、加工以及叶片的装配、维护提供实验依据。     

Improvement of a power tiller cage wheel for use in swampy peat soils

This study was aimed at investigating traction performance of a cage wheel for use in swampy peat soils in Indonesia. The tests were conducted in a soil bin filled with peat soil taken from the swampy areas. A set up was developed to measure tractive performance of a single cage wheel. Deep sinkage and high wheel slip were identified as the major problems of using the existing cage wheel design in swampy peat soils. The results revealed that increasing the lug angle from 15 to 35° and the length of lug improved the tractive performance of the cage wheel significantly, while increasing the number of lugs from 14 to 18 and width of lug did not improve the tractive performance significantly. A cage wheel with lug size 325×80 mm, 35° lug angle, 14 lugs (26° lug spacing), with 2 circumferential flat rings installed on the inner side of the lugs, out performed the other settings for use with power tillers in swampy peat soils.     

接触应力对轮轨材料滚动摩擦磨损性能影响

利用MMS-2A型微机控制摩擦磨损试验机研究了接触应力对轮轨材料的滚动摩擦磨损性能影响.结果表明：随接触应力的增加,滚动摩擦系数呈增加趋势,车轮和钢轨试样磨损加剧;相同接触应力水平下,车轮试样磨损量大于钢轨试样,表面损伤严重;随接触应力的增加,车轮试样表面从犁沟且轻微剥落向严重剥落损伤转变,钢轨试样表面损伤主要表现为犁沟效应并伴随有剥落现象,但相比车轮试样的剥离损伤要轻微.     

Interaction between a moving two-mass oscillator and an infinite homogeneous structure: Green’s functions method

This paper deals with the interaction between a vehicle and a slab track using the model of moving wheel for both frequency and time-domain. The vehicle is reduced to a moving two-mass oscillator and the slab track is considered as an infinite structure consisting of elastically supported double Euler–Bernoulli beams. In order to perform the time-domain analysis, a semi-analytical method based on the outstanding properties of the time-domain Green’s functions of the slab track has been developed. The method allows the computing of the non-linear wheel/rail contact (the contact loss and the non-linear contact stiffness). The vehicle/track interaction due to the polygonal wheel and the corrugated rail has been investigated and the running velocity and non-linear wheel/rail contact influences have been pointed out.     

Traction performance of a pushed/pulled drive wheel

A comprehensive method for prediction of off-road driven wheel performance is presented, assuming a parabolic wheel–soil contact surface. The traction performance of a driven wheel is predicted for both driving and braking modes. Simulations show significant non-symmetry of the traction performance of the driving and braking wheels. The braking force is significantly greater than the traction force reached in the driving mode. In order to apply the suggested model for prediction of the traction performance of a 4WD vehicle, the load transfer effect was considered. Simulated traction performances of front and rear driven wheels differ significantly, due to the load transfer. In the driving mode, the rear driven wheel develops a net traction force greater than that of the front wheel. On the other hand, in the braking mode the front driven wheel develops a braking force significantly greater than that of the rear driven wheel due to a pushed/pulled force affected by the load transfer. The suggested model was successfully verified by the data reported in literature and by full-scale field experiments with a special wheel-testing device. The developed approach may improve the prediction of off-road multi-drive vehicle traction performance.     

A piecewise bearing capacity method of unstructured terrain considering characteristics of soil mechanic and wheel geometry

Bearing capacity of the unstructured terrain considering the effects of the wheel geometry and soil mechanic properties is analyzed in this paper. Two-dimensional pressure-sinkage simulations are conducted to evaluate the degrees of similarity between the flat plate and wheel in terms of their ultimate bearing characteristics of Terzaghi theory. The results show that these degrees of similarity are mainly reflected in the soil in-depth direction and the corresponding failure behaviors. Based on the approximation of the ultimate bearing capacity between the wheel and flat plate, a piecewise bearing capacity evaluation method with the effects of the soil mechanic properties and three-dimensional wheel geometry is proposed. The pressure-sinkage values of the proposed model show a satisfactory agreement with the experimental ones. The proposed model performs better than the semi-empirical models, as it considers more soil bearing features and needs less fitting parameters to assess the unstructured terrain.     

高速列车车轮踏面剥离引起的轮轨冲击力学响应有限元模拟

车轮踏面剥离是轨道车辆车轮非圆化损伤的常见形式之一。轮轨滚动接触过程中,车轮踏面剥离会循环冲击钢轨,诱发异常大的轮轨动态相互作用,严重影响高速列车运行平稳性和安全性。基于三维轮轨滚动接触有限元模型,模拟了高速列车车轮踏面剥离引起的轮轨冲击力学响应,分析了轮轨冲击过程中的轮轨接触力/压力、接触斑及黏/滑特性、钢轨表面节点速度分布和应力/应变状态等响应特征,讨论了列车速度、剥离长度和剥离深度等关键参数对轮轨冲击响应的影响。结果发现,车轮踏面剥离引起的轮轨动态垂向接触力随列车速度的提高呈现出先增大后减小的变化趋势,并在列车速度为300 km/h出现最大值,约为轮轨准静态垂向接触力的1.35倍;随着剥离长度的增大,轮轨动态接触力、轮/轨von Mises应力和等效塑性应变均显著增大;随着剥离深度的增大,仅车轮von Mises应力和等效塑性应变显著增大。     

不同轮轨接触模型在车桥耦合振动中的比较

以工程实例为研究对象,建立了整车-整桥系统耦合振动数值分析模型。考虑车轮的跳轨和挤密情况,建立了单边弹簧-阻尼系统弹性轮轨接触模型。采用基于多体系统动力学和有限元法结合的联合仿真技术,计算了两种轮轨接触时动车组列车以不同车速通过大跨度连续桥梁的耦合振动响应。数值计算结果表明:两种轮轨接触模型的桥梁动力响应比较接近;列车的横向轮轨力、轮重减载率和脱轨系数相差较大,当速度为350km/h时,横向轮轨力增大了46.5%,轮重减载率增大了130.8%,脱轨系数增大了24.66%;用单边-弹簧阻尼系统弹性轮轨接触模型更符合实际。     

Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch

This paper focuses on the study of a frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid flat punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. An analytical closed-form solution is obtained for the normal contact stress, electric displacement and magnetic induction distributions. The main objective of this paper is to study the effect of the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat stamp profile.