Assessment of a semi-Hertzian method for determination of wheel-rail contact patch

Wheel-rail contact calculations are essential for simulating railway vehicle dynamic behavior. Currently, these simulations usually use the Hertz contact theory to calculate normal forces and Kalker's 'FASTSIM' program to evaluate tangential stresses. Since 1996, new methods called semi-Hertzian have appeared: 5, 7 (STRIPES). These methods attempt to estimate the non-elliptical contact patches with a discrete extension of the Hertz theory. As a continuation of 2, a validation of the STRIPES method for normal problem computing on three test cases is proposed in this article. The test cases do not fulfill the hypothesis required for the Hertz theory. Then, the Kalker's FASTSIM algorithm is adapted to STRIPES patch calculus to perform tangential forces computation. This adaptation is assessed using Kalker's CONTACT algorithm.     

Methodology and verification of calculations for contact stresses in a wheel–rail system

The distribution of contact stresses in the wheel–rail system is a decisive factor for the wear of elements and the safety of rail transport. Analytical calculations of stresses based on the Hertz theory can only be applied to elastic deformation of materials. High dynamic loads leading to plastic deformation (not considered in the Hertz theory) are a predominant cause of problems in the contact vicinity. These problems can be successfully resolved by applying the finite-elements method. Two- and three-dimensional test models were generated to estimate an error in numerical calculations in the MSC.MARC program. We compared the results of numerical calculations with analytical calculations. Based on the obtained results we defined the effect of parameters describing the finite-elements mesh on the calculation error for contact stresses, and adjusted mesh parameters appropriately to achieve as low as possible error in numerical calculations. We also defined the effect of material characteristics on the value of contact stresses on the wheel–rail interface.     

Influence of polygonal wear of railway wheels on the wheel set axle stress

The coupled vehicle/track dynamic model with the flexible wheel set was developed to investigate the effects of polygonal wear on the dynamic stresses of the wheel set axle. In the model, the railway vehicle was modelled by the rigid multibody dynamics. The wheel set was established by the finite element method to analyse the high-frequency oscillation and dynamic stress of wheel set axle induced by the polygonal wear based on the modal stress recovery method. The slab track model was taken into account in which the rail was described by the Timoshenko beam and the three-dimensional solid finite element was employed to establish the concrete slab. Furthermore, the modal superposition method was adopted to calculate the dynamic response of the track. The wheel/rail normal forces and the tangent forces were, respectively, determined by the Hertz nonlinear contact theory and the Shen–Hedrick–Elkins model. Using the coupled vehicle/track dynamic model, the dynamic stresses of wheel set axle with consideration of the ideal polygonal wear and measured polygonal wear were investigated. The results show that the amplitude of wheel/rail normal forces and the dynamic stress of wheel set axle increase as the vehicle speeds rise. Moreover, the impact loads induced by the polygonal wear could excite the resonance of wheel set axle. In the resonance region, the amplitude of the dynamic stress for the wheel set axle would increase considerably comparing with the normal conditions.     

基于接触理论与数值分析下复合墙体抵抗冲击力研究

在建筑复合隔墙墙体正常使用的过程中通常会受到外界物体的偶然碰撞,相互碰撞后所产生的冲击力会使墙体发生局部变形或产生应力集中现象从而影响墙体的整体稳定性、耐久性和使用性能.由于目前建筑复合隔墙墙体在抗冲击方面缺乏结构层面的计算方法,因此,为研究复合墙体在低速碰撞下抗冲击问题并分析该类型墙体在受到碰撞所产生的冲击力对其性能...     

A fast-simplified wheel–rail contact model consistent with perfect plastic materials

A method is described which is an extension of rolling contact models with respect to plasticity. This new method, which is an extension of the STRIPES semi-Hertzian (SH) model, has been implemented in a multi-body-system (MBS) package and does not result in a longer execution time than the STRIPES SH model [J.B. Ayasse and H. Chollet, Determination of the wheel–rail contact patch in semi-Hertzian conditions, Veh. Syst. Dyn. 43(3) (2005), pp. 161–172]. High speed of computation is obtained by some hypotheses about the plastic law, the shape of stresses, the locus of the maximum stress and the slip. Plasticity does not change the vehicle behaviour but there is a need for an extension of rolling contact models with respect to plasticity as far as fatigue analysis of rail is concerned: rolling contact fatigue may be addressed via the finite element method (FEM) including material non-linearities, where loads are the contact stresses provided by the post-processing of MBS results [K. Dang Van, M.H. Maitournam, Z. Moumni, and F. Roger, A comprehensive approach for modeling fatigue and fracture of rails, Eng. Fract. Mech. 76 (2009), pp. 2626–2636]. In STRIPES, like in other MBS models, contact stresses may exceed the plastic yield criterion, leading to wrong results in the subsequent FEM analysis. With the proposed method, contact stresses are kept consistent with a perfect plastic law, avoiding these problems. The method is benchmarked versus non-linear FEM in Hertzian geometries. As a consequence of taking plasticity into account, contact patch area is bigger than the elastic one. In accordance with FEM results, a different ellipse aspect ratio than the one predicted by Hertz theory was also found and finally pressure does not exceed the threshold prescribed by the plastic law. The method also provides more exact results with non-Hertzian geometries. The new approach is finally compared with non-linear FEM in a tangent case with a unidirectional load and a complete slip: when plasticity is taken into account, and for large adhesion values, friction forces have an influence on the size of the contact patch. The proposed approach enables also to assess extensively the level of plasticity along a track through an indicator associated with a given yield stress.     

Determination of the wheel rail contact patch in semi-Hertzian conditions

This paper deals with the subject of the semi-Hertzian contact, which is a way to represent the wheel rail contact in railways or roller bearing applications. The method is based on the interpenetration of the two underformed bodies' profiles. The first step deals with the problem of the shape ratio; it is proposed to compensate the two main curvatures to obtain the good ratio in Hertzian conditions. Then, Hertz and Kalker's equations are used to establish the stresses at the level of a strip. These stresses expressions are used directly in a contact model discretized in strips and tabulated as a function of the lateral displacement between the wheel and the rail. The validation is made by comparison to the previous multi-Hertzian model of the VOCOLIN software. A first test shows identical results in Hertzian conditions; a second one shows only a small difference in semi-Hertzian conditions like S1002/UIC60 1:40.     

Determination of the wheel rail contact patch in semi-Hertzian conditions

This paper deals with the subject of the semi-Hertzian contact, which is a way to represent the wheel rail contact in railways or roller bearing applications. The method is based on the interpenetration of the two underformed bodies' profiles. The first step deals with the problem of the shape ratio; it is proposed to compensate the two main curvatures to obtain the good ratio in Hertzian conditions. Then, Hertz and Kalker's equations are used to establish the stresses at the level of a strip. These stresses expressions are used directly in a contact model discretized in strips and tabulated as a function of the lateral displacement between the wheel and the rail. The validation is made by comparison to the previous multi-Hertzian model of the VOCOLIN software. A first test shows identical results in Hertzian conditions; a second one shows only a small difference in semi-Hertzian conditions like S1002/UIC60 1:40.     

Simulations of roughness growth on rails - results from a 2D non-Hertzian, non-steady contact model

A new model for simulating rail roughness growth on tangent track is presented in this paper. The model consists of three relatively independent components: (1) a time-domain vehicle/track interaction model; (2) a 2D non-Hertzian and non-steady wheel/rail contact model; and (3) a wear model. Wheel/rail contact forces for a given initial roughness obtained from the vehicle/track interaction model are used by the contact model to calculate the contact patch size, normal pressure and tangential stresses with material removal assumed to be linearly proportional to the friction work in the contact patch. The roughness profile is updated and fed back into vehicle/track interaction model. The 2D contact model is initially compared with a 3D model for various wavelength of initial sinusoidal roughness. Long term roughness growth is then simulated with the 2D contact model. Simulation shows that all initial sinusoidal roughness of wavelengths between 20-100 mm are levelled out. The wavelength-fixing mechanism, that has previously been used to explain the cause of corrugation, is not found in the present investigations.     

Wheel-rail contact models for vehicle system dynamics including multi-point contact

Advanced modelling of rail vehicle dynamics requires realistic solutions of contact problems for wheels and rails that are able to describe contact singularities, encountered for wheels and rails. The basic singularities demonstrate themselves as double and multiple contact patches. The solutions of the contact problems have to be known practically in each step of the numerical integration of the differential equations of the model. The existing fast, approximate methods of solution to achieve this goal have been outlined. One way to do this is to replace a multi-point contact by a set of ellipses. The other methods are based on so-called virtual penetration. They allow calculating the non-elliptical, multiple contact patches and creep forces online, during integration of the model. This allows nearly real-time simulations. The methods are valid and applicable for so-called quasi-Hertzian cases, when the contact conditions do not deviate much from the assumptions of the Hertz theory. It is believed that it is worthwhile to use them in other cases too.     

载重子午轮胎与路面相互作用的分析

根据全钢载重子午线轮胎12.00R20的实际结构,考虑轮胎的几何非线性、材料非线性、接触非线性以及大变形等力学特性,应用有限元的方法建立轮胎的三维模型,橡胶材料采用Yeoh模型,橡胶-帘线复合材料采用加强筋模型,并通过轮胎径向刚度的测试验证了模型的有效性.在数值模拟中分析了轮胎在一定充气压力时,在不同垂直载荷和牵引速度的作用下,与地面在接触区域的变形情况、应力分布、摩擦应力分布等滚动接触规律.结果表明,轮胎与地面接触应力分布存在明显的非均匀性,轮胎的接地面积和地面总反力随着滚动速度的升高而增大.     

Prediction of Tyre-Road Friction with an Inverted-Boat Shaped Pressure Distribution

In this paper, a predictive model is formulated to describe the frictional forces between the tyre and road. The model is based on an inverted-boat normal pressure distribution. The determination of the input parameters is simplified by the suggested stationary point approach for calculation of the frictional coefficients, which are analytically obtained. The verification of the established model shows that the predicted values are in a good agreement with measured data. A sensitivity study of the shape factors demonstrates that it is necessary to take the unsymmetric normal pressure distribution proposed in this paper into consideration to accurately predict frictional forces.     

Modification of the semi-Hertz wheel–rail contact method based on recalculating the virtual penetration value

ABSTRACT

Wheel–rail contact calculation is of vital importance in vehicle system dynamics. In the existing methods of wheel–rail contact calculation, the finite element method and Kalker’s CONTACT program, which are based on the complementary energy principle, are the two methods with accuracy recognised. However, because of its very slow calculation speed, it cannot meet the requirement of online calculation, so a variety of fast non-elliptic algorithms have been proposed. The semi-Hertz method, which is recognised for its great contributions to the fast wheel–rail contact calculation, is based on the concept of virtual penetration. The calculation of virtual penetration is crucial to evaluate the shape and normal pressure distribution of the contact patch. In practice, the virtual penetration is related to the curvature of the whole contact patch; however, the range of the contact patch is determined by the value of penetration. Such an interaction leads the calculation into a dead loop. In the semi-Hertz method, the penetration is calculated by the Hertz parameters of the initial contact point. Thus, the practical range of the method is limited. In this paper, a fast-iterative method for solving virtual penetration is proposed, and a reliable value of virtual penetration can be obtained under any lateral wheel–rail relative curvature variation with good stability and speed. The normal and tangential solutions are analysed with different methods in this paper.     

Investigation of the effects of sleeper-passing impacts on the high-speed train

The sleeper-passing impact has always been considered negligible in normal conditions, while the experimental data obtained from a High-speed train in a cold weather expressed significant sleeper-passing impacts on the axle box, bogie frame and car body. Therefore, in this study, a vertical coupled vehicle/track dynamic model was developed to investigate the sleeper-passing impacts and its effects on the dynamic performance of the high-speed train. In the model, the dynamic model of vehicle is established with 10 degrees of freedom. The track model is formulated with two rails supported on the discrete supports through the finite element method. The contact forces between the wheel and rail are estimated using the non-linear Hertz contact theory. The parametric studies are conducted to analyse effects of both the vehicle speeds and the discrete support stiffness on the sleeper-passing impacts. The results show that the sleeper-passing impacts become extremely significant with the increased support stiffness of track, especially when the frequencies of sleeper-passing impacts approach to the resonance frequencies of wheel/track system. The damping of primary suspension can effectively lower the magnitude of impacts in the resonance speed ranges, but has little effect on other speed ranges. Finally, a more comprehensively coupled vehicle/track dynamic model integrating with a flexible wheel set is developed to discuss the sleeper-passing-induced flexible vibration of wheel set.     

轮胎在水平路面上的自由滚动接触分析

利用轮胎的模态参数直接对轮胎在水平路面上的滚动建立了便于解析计算的仿真模型。该模型可模拟轮胎稳态的滚动过程并可计算出不小同工况下的滚动特性、有效滚动半径、载荷与下沉量的关系以及印迹内变形和分布力。计算结果揭示了以往模型难以描述的微观现象,与以往文献的试验研究结果定性一致,充分显示了模型的合理性。     

富水隧道施工期及运营期衬砌结构力学特性研究

以米亚罗3号隧道为依托工程,首先通过现场实测应力监测数据,对米亚罗3号隧道施工期支护结构应力的演变规律进行了分析研究;然后进一步借助数值分析软件,对不同初始水头高度下,米亚罗3号隧道运营期间围岩和衬砌结构的力学特征进行了研究。应力监测结果表明:隧道上台阶开挖后,拱顶和拱肩处的围岩-初支接触压力、钢拱架应力和外水压力迅速增大,约在30~40d后趋于稳定;下台阶开挖后,拱腰处的接触压力、钢拱架应力和外水压力快速增长,约在30~50d后趋于稳定;随着下台阶的开挖,拱肩处的围岩-初支接触压力再度缓慢增长,而钢拱架应力则明显下降;二衬施作后,其内力快速增长,并在20d后趋于稳定。数值模拟结果表明:当初始水头高度增加时,运营期间米亚罗3号隧道的洞周位移、二衬内力和外水压力均成一定比例的增加;隧道变形主要为竖直和水平方向的挤压变形,最大位移发生在拱底;相对于无地下水的情况,地下水的存在会影响衬砌弯矩分布,导致弯矩最大截面从拱顶转移至拱脚;衬砌所受外水压力在拱底处最小,其余部位分布较为均匀;随着初始水头的增大,拱腰和拱脚背后围岩的塑性区范围会明显增加。     

Tire Modeling for Vertical Properties Including Enveloping Properties Using Experimental Modal Parameters

Summary Tire modal parameters reflect the natural properties of the tire. This paper models tire performance using experimental tire modal parameters to calculate the static vertical tire stiffness on both drum and flat road surfaces and the distribution of vertical and shear forces. The model was used to investigate tire enveloping properties. In addition to the radial and tangential displacements, the rotational angular displacement of the contact element is considered. This study examined the obstacle's effect on tire static vertical properties, the axle load responses under rectangle obstacles with a fixed axle height, and the effects of tire pressure on enveloping properties.     

轮胎模型刚度对前部偏置碰撞结果的影响

建立了整车碰撞模型中的轮胎模型后,通过调整模型参数,使模拟的轮胎刚度特性曲线近似于试验的轮胎刚度特性曲线,并应用于整车前部偏置碰撞模拟中,分析轮胎刚度对偏置碰撞结果的影响.结果表明,轮胎刚度对碰撞过程整车加速度、截面力、防火墙侵入量等均有一定的影响.     

差速器锥齿轮的接触分析

建立精确的差速器齿轮模型,根据齿轮啮合原理和赫兹公式,计算出单对轮齿啮合时可能出现最大应力的位置。运用有限元法,计算齿面的接触应力,通过与传统计算结果比较,表明了有限元法在差速器齿轮设计中适用性。     

攀枝花新密地大桥拱圈悬臂浇注施工监控

攀枝花新密地大桥为主跨182m的混凝土拱桥,采用悬臂浇筑法施工拱圈,为确保施工过程的安全性和成桥状态的准确性,需要在施工各阶段对线形、索力及应力等参数进行监控。以上游拱圈监控工作为背景,利用MIDAS Civil建立全桥空间分析模型,基于正装法计算出各拱段浇筑及张拉过程的理想结构参数,在误差允许范围内合理调整扣锚索的索力来调整悬臂结构的实际状态,再根据拱段实测参数修正监控计算模型,达到计算模型与实桥施工状态的统一。施工过程中对拱圈线形、扣索和锚索的索力、拱圈应力、临时塔位移等结构参数的监控结果表明,主拱圈各项参数控制良好,满足设计要求。