Vertical Vibration Analysis of Vehicle/Imperfect Track Systems

Summary This paper studies the vertical vibration of a vehicle traveling on an imperfect track system. The car body and sleepers are modeled as Timoshenko beams with finite length, and the rail is assumed as an infinite Timoshenko beam with discrete supports. Imperfection of the track system comes from a sleeper lost partial support by the ballast. Since deflection of the rail is limited within a certain interval where the vehicle is passing over, the infinite domain problem can be transformed into a finite domain problem with moving boundary. In this work, the equations of motion of the car body, rail and sleepers are discretized first by the finite element method. The discretized equations of motion for the vehicle and track systems are then assembled, respectively. Finally, the Newmark method is applied to obtain the response of the vehicle and track systems at each time step. The effect of the vehicle speed on the response of the vehicle and track systems is investigated.     

Experimental and numerical investigation of the effect of rail corrugation on the behaviour of rail fastenings

This paper presents the results of a detailed investigation of the effects of rail corrugation on the dynamic behaviour of metro rail fastenings, obtained from extensive experiments conducted on site and from simulations of train–track dynamics. The results of tests conducted with a metro train operating on corrugated tracks are presented and discussed first. A three-dimensional (3D) model of the metro train and a slab track was developed using multi-body dynamics modelling and the finite element method to simulate the effect of rail corrugation on the dynamic behaviour of rail fastenings. In the model, the metro train is modelled as a multi-rigid body system, and the slab track is modelled as a discrete elastic support system consisting of two Timoshenko beams for the rails, a 3D solid finite element (FE) model for the slabs, periodic discrete viscoelastic elements for the rail fastenings that connect the rails to the slabs, and uniformly viscoelastic elements for the subgrade beneath the slabs. The proposed train–track model was used to investigate the effects of rail corrugation on the dynamic behaviour of the metro track system and fastenings. An FE model for the rail fastenings was also developed and was used to calculate the stresses in the clips, some of which rupture under the excitation of rail corrugation. The results of the field experiments and dynamics simulations provide an insight into the root causes of the fracture of the clips, and several remedies are suggested for mitigating strong vibrations and failure of metro rail fastening systems.     

Simulation of vertical dynamic vehicle–track interaction using a two-dimensional slab track model

The vertical dynamic interaction between a railway vehicle and a slab track is simulated in the time domain using an extended state-space vector approach in combination with a complex-valued modal superposition technique for the linear, time-invariant and two-dimensional track model. Wheel–rail contact forces, bending moments in the concrete panel and load distributions on the supporting foundation are evaluated. Two generic slab track models including one or two layers of concrete slabs are presented. The upper layer containing the discrete slab panels is described by decoupled beams of finite length, while the lower layer is a continuous beam. Both the rail and concrete layers are modelled using Rayleigh–Timoshenko beam theory. Rail receptances for the two slab track models are compared with the receptance of a traditional ballasted track. The described procedure is demonstrated by two application examples involving: (i) the periodic response due to the rail seat passing frequency as influenced by the vehicle speed and a foundation stiffness gradient and (ii) the transient response due to a local rail irregularity (dipped welded joint).     

弹性长枕式无砟轨道枕长与支撑长度比例分析

根据弹性长枕的结构特点及受力特性,运用有限单元法建立弹性长枕无砟轨道垂向受力有限元计算模型。通过分析不同长度弹性轨枕在不同支撑长度下的轨下及枕中弯矩情况,确定了弹性长枕式无砟轨道枕长与支撑长度的合理比例约为04。     

On the effect of unsupported sleepers on the dynamic behaviour of a railway track

The effect of unsupported sleepers on the dynamic behaviour of a railway track is studied based on vehicle–track dynamic interaction theory, using a model of the track as a Timoshenko beam supported on a periodic elastic foundation. Considering the vehicle's running speed and the number of unsupported sleepers, the track dynamic characteristics are investigated and verified in the time and frequency domains by experiments on a 1:5 scale model wheel–rail test rig. The results show that when hanging sleepers are present, leading to a discontinuous and irregular track support, additional wheel–rail interaction forces are generated. These forces increase as further sleepers become unsupported and as the vehicle's running speed increases. The adjacent supports experience increased dynamic forces which will lead to further deterioration of track quality and the formation of long wavelength track irregularities, which worsen the vehicles’ running stability and riding comfort. Stationary transfer functions measurements of the dynamic behaviour of the track are also presented to support the findings.     

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.     

Variable Cross-Section Rectangular Beam and Sensitivity Analysis for Lightweight Design of Bus Frame

Timoshenko beam element of variable cross-section rectangular tube is developed and applied in the lightweight design of bus frame in this paper. Firstly, the finite element formulations of variable cross-section beam (VCB) are derived under the loadsteps of axial deformation, torsional deformation and bending deformation. Secondly, bending deformation experiment and its detailed shell finite element model (FEM) simulation of variable cross-section rectangular tube were conducted; and the proposed VCB, detailed shell FEM and experimental results can be highly consistent. Thirdly, VCBs are used to substitute for parts of the uniform ones in a bus frame. An innovatively lightweight bus frame is obtained and all the performance responses are improved simultaneously. Finally, rollover analysis further shows the advantage of variable cross-section bus frame in crashworthiness design.     

桥上Rheda 2000无砟轨道轨下基础模态分析

采用有限元分析方法,建立桥上Rheda 2000无砟轨道轨下基础三维有限元模型,进行动力学的模态分析,获得了轨下结构前十阶自振频率和主振型,分析了不同桥梁弹性模量对自振频率的影响。结果表明,弹性模量越大,结构自振频率越大。     

汽车前纵梁碰撞性能影响因素的仿真研究

以某车型的前纵梁为研究对象,应用CATIA软件建立该车型前纵梁的三维几何模型。利用有限元理论与方法,建立该纵梁基于HyperMesh/LS-DYNA环境下的有限元模型,LS-DYNA求解器对该纵梁进行轴向碰撞性能的仿真分析。分别从梁的截面形状、诱导槽的位置、深度、形状、梁的厚度、加强板、蜂窝铝填充材料几个方面来研究其对薄壁直梁轴向碰撞性能的影响,为汽车前纵梁的设计与研发提供理论参考依据。     

Extended applications of track irregularity probabilistic model and vehicle–slab track coupled model on dynamics of railway systems

Track irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel–rail interactions. For depicting the dynamic behaviours of vehicle–track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle–track coupled model by properly considering the wheel–rail nonlinear contact mechanisms. In the present study, the vehicle–track coupled model is programmed by combining finite element method with wheel–rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.     

Sliding window method for vehicles moving on a long track

The rail is modelled as a simply supported beam in the vehicle–track coupled dynamics. The beam is formulated by a partial differential equation that is transformed into an ordinary differential equation by the method of mode superposition for numerical calculation. However, the size of the matrix that is formed by the mode-superposition method increases significantly with track length, which limits the calculation efficiency. Some methods have been developed to solve this calculation issue, but they diminish the merits of the vehicle–track coupled dynamics, which would systematically investigate the dynamics of a vehicle and a track from the entire vehicle–track system. A new method is developed to resolve this contradiction. First, a theory based on a sliding window is established to improve the computational stability with respect to the length and the window-movement ratio. Then, two methods, namely finite element method analysis and an analytical solution, are used to verify the accuracy of the new method, which is highly efficient when used in a vertical half-vehicle–track coupled model to calculate the vehicle response when the vehicle moves on a long track. The results of the vehicle response calculated with and without the sliding window show good consistency.     

A linear complementarity method for the solution of vertical vehicle–track interaction

A new method is proposed for the solution of the vertical vehicle–track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel–rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel–rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel–rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle–track interaction including a separation between wheel and rail.     

Influence of some vehicle and track parameters on the environmental vibrations induced by railway traffic

A study is performed on the influence of some typical railway vehicle and track parameters on the level of ground vibrations induced in the neighbourhood. The results are obtained from a previously validated simulation framework considering in a first step the vehicle/track subsystem and, in a second step, the response of the soil to the forces resulting from the first analysis. The vehicle is reduced to a simple vertical 3-dof model, corresponding to the superposition of the wheelset, the bogie and the car body. The rail is modelled as a succession of beam elements elastically supported by the sleepers, lying themselves on a flexible foundation representing the ballast and the subgrade. The connection between the wheels and the rails is realised through a non-linear Hertzian contact. The soil motion is obtained from a finite/infinite element model. The investigated vehicle parameters are its type (urban, high speed, freight, etc.) and its speed. For the track, the rail flexural stiffness, the railpad stiffness, the spacing between sleepers and the rail and sleeper masses are considered. In all cases, the parameter value range is defined from a bibliographic browsing. At the end, the paper proposes a table summarising the influence of each studied parameter on three indicators: the vehicle acceleration, the rail velocity and the soil velocity. It namely turns out that the vehicle has a serious influence on the vibration level and should be considered in prediction models.     

Effect of curved track support failure on vehicle derailment

In order to investigate the effect of curved track support failure on railway vehicle derailment, a coupled vehicle–track dynamic model is put forward. In the model, the vehicle and the structure under rails are, respectively, modelled as a multi-body system, and the rail is modelled with a Timoshenko beam rested on the discrete sleepers. The lateral, vertical, and torsional deformations of the beam are taken into account. The model also considers the effect of the discrete support by sleepers on the coupling dynamics of the vehicle and track. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the calculation of the coupled vehicle and track dynamics, the normal forces of the wheels/rails are calculated using the Hertzian contact theory and their creep forces are determined with the nonlinear creep theory by Shen et al [Z.Y. Shen, J.K. Hedrick, and J.A. Elkins, A comparison of alternative creep-force models for rail vehicle dynamic analysis, Proceedings of the 8th IAVSD Symposium, Cambridge, MA, 1984, pp. 591–605]. The motion equations of the vehicle/track are solved by means of an explicit integration method. The failure of the components of the curved track is simulated by changing the track stiffness and damping along the track. The cases where zero to six supports of the curved rails fail are considered. The transient derailment coefficients are calculated. They are, respectively, the ratio of the wheel/rail lateral force to the vertical force and the wheel load reduction. The contact points of the wheels/rails are in detail analysed and used to evaluate the risk of the vehicle derailment. Also, the present work investigates the effect of friction coefficient, axle load and vehicle speed on the derailments under the condition of track failure. The numerical results obtained indicate that the failure of track supports has a great influence on the whole vehicle running safety.     

槽型宽翼梁剪滞效应分析的有限段法

针对槽型宽翼梁剪滞效应分析已有方法通常忽略横向剪切变形的影响、计算工作量大、不便于工程应用的局限性,提出一种能准确分析变截面槽型宽翼梁剪滞、剪切双重效应的有限段法。基于最小势能原理,建立了槽型宽翼梁考虑剪滞效应和剪切变形双重影响的平衡控制微分方程及自然边界条件。在由方程得出均布荷载作用下的内力和位移初参数解的基础上,导出了槽型宽翼梁的有限段单元刚度矩阵和等效节点荷载列阵。应用有限段法,结合有机玻璃模型梁试验,分析了槽型宽翼梁竖向位移和应力的横向分布规律。数值算例表明,有限段法计算结果与有机玻璃模型试验实测结果以及ANSYS解符合良好;槽型宽翼梁的剪力滞效应明显;在槽型宽翼梁桥的设计与施工控制中,必须充分考虑剪力滞效应和剪切变形对结构应力和位移的影响。     

大瑞铁路梯形轨枕减振材料参数研究

根据梯形轨枕结构形式的特点和大瑞线"三高四活跃"的地质条件,初步确定了高黎贡山隧道内L形混凝土支座式无砟轨道的结构形式,运用有限单元法建立梯形轨枕垂向受力有限元计算模型。通过分析各工况轨枕下减振材料在不同支撑间距下对梯形轨枕和L形支座的弯矩、梯形轨枕和钢轨的竖向位移情况,确定了梯形轨枕减振材料合理支撑间距为1.25m。     

基于响应灵敏度的桥梁下部结构损伤识别方法研究

为实现桥梁下部结构横、竖向状态的同步识别,以多跨简支梁桥下部结构为研究对象,提出了基于响应灵敏度的桥梁下部结构损伤识别方法。首先,基于车桥耦合动力分析理论推导了桥梁下部结构响应灵敏度方程；其次,基于响应灵敏度模型修正算法和数值算例对所提方法的有效性和抗噪性进行了验证。结果表明：(1)当梁体、墩身、基底约束同时损伤时,所提算法可准确、有效地识别墩身单元刚度和基底约束刚度值；(2)所提算法具有较强的抗噪性,在5%噪声影响下仍能有效识别墩底弹性支承的损伤,并能准确定位损伤桥墩单元位置和识别损伤值。     

有限差分方法在锚索框格梁内力计算中的应用

为使锚索框格梁内力计算方法更通用,能适应不同类型框架形式,基于Winkler弹性地基模型,用有限差分法方法推导了单根有限长梁内力计算公式,以此为基础提出了框格梁内力整体求解的计算方法,即根据框格梁锚索作用位置力的平衡和变形协调条件求解锚索力在横梁和竖梁上的分配,并根据分配结果分别计算每根梁的内力.单根梁计算实例证明,有限差分法是一种较精确的数值计算方法.整体求解计算实例及现场试验结果表明:整体求解方法不受结构对称性及锚索力个数的限制,更适用于一般情况;计算结果与现场试验结果吻合较好,Winkler 弹性地基模型用于计算锚索框格梁内力是合适的;锚索位置弯矩计算结果偏于安全可进行适当修正,同时此处应增加构造措施保证局部承载能力.     

大悬臂预应力组合桥面板实用计算方法

为了解决不同位置荷载作用下组合桥面板的荷载横向分布计算问题,根据脊骨梁中波形钢腹板挑梁并排支撑的预应力大悬臂组合桥面板的受力特点及抗弯和抗扭刚度沿挑梁纵向的变化规律,采用基于换算截面法的修正刚接梁法,假设受载挑梁的荷载横向分布系数随荷载作用位置变化沿挑梁纵向按三次曲线分布。然后,根据"波形钢腹板不抵抗弯矩"的结论和拟平截面假定,推导出波形钢腹板组合挑梁的开裂弯矩和弹性极限弯矩计算公式。最后,通过试验和有限元分析来验证该公式的正确性。结果表明:该计算公式能够满足工程设计的精度要求。