A model for vehicle–track random interactions on effects of crosswinds and track irregularities

A stochastic mathematical model is developed to evaluate the dynamic behaviours and statistical responses of vehicle–track systems when random system excitations including crosswinds and track irregularities are imposed. In this model, the railway vehicle is regarded as a multi-rigid-body system, the track system is modelled by finite element theory. These two systems are spatially coupled by the nonlinear wheel–rail contact forces and unsteady aerodynamic forces. The high efficiency and accuracy of this stochastic model are validated by comparing to the robust Monte-Carlo method. Numerical studies show that crosswinds have a great influence on the dynamic performance of vehicle–track systems, especially on transverse vibrations. When the railway vehicle initially runs into the wind field, it will experience a severe vibration stage, and then stepping into a relatively steady state where the fluctuating winds and track irregularities will play deterministic roles in the deviations of system responses. Moreover, it is found that track irregularities should be properly considered in the safety assessment of the vehicle even in strong crosswinds.     

Sensitivity of train stochastic dynamics to long-term evolution of track irregularities

The influence of the track geometry on the dynamic response of the train is of great concern for the railway companies, because they have to guarantee the safety of the train passengers in ensuring the stability of the train. In this paper, the long-term evolution of the dynamic response of the train on a stretch of the railway track is studied with respect to the long-term evolution of the track geometry. The characterisation of the long-term evolution of the train response allows the railway companies to start off maintenance operations of the track at the best moment. The study is performed using measurements of the track geometry, which are carried out very regularly by a measuring train. A stochastic model of the studied stretch of track is created in order to take into account the measurement uncertainties in the track geometry. The dynamic response of the train is simulated with a multibody software. A noise is added in output of the simulation to consider the uncertainties in the computational model of the train dynamics. Indicators on the dynamic response of the train are defined, allowing to visualize the long-term evolution of the stability and the comfort of the train, when the track geometry deteriorates.     

Effect of vehicle vibration environment of high-speed train on dynamic performance of axle box bearing

In this study, we developed a comprehensive three-dimensional vehicle–track coupled dynamics model considering the traction drive system and axle box bearing. In this model, dynamic interactions between the axle box bearing and other components, such as the wheelset and bogie frame, are considered based on a detailed analysis of the structural properties and working mechanism of the axle box bearing. A few complicated dynamic excitations, such as the time-varying mesh stiffness of gears, time-varying stiffness of bearing, bearing gaps and track irregularities, are considered. Then, the dynamic responses of the vehicle–track system are demonstrated via numerical simulations based on the established dynamics model. The results indicate that the traction drive system and track irregularities can significantly influence the dynamic interactions of the axle box bearing. The necessity of considering the excitation caused by gear meshing and track irregularities when assessing the dynamic performance of the axle box bearing is demonstrated.     

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).     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part I: system integration and modelling

In this paper, it is aimed to investigate semi-active suspension systems using magnetorheological (MR) fluid dampers for improving the ride quality of railway vehicles. A 17-degree-of-freedom (DOF) model of a full-scale railway vehicle integrated with the semi-active controlled MR fluid dampers in its secondary suspension system is proposed to cope with the lateral, yaw, and roll motions of the car body, trucks, and wheelsets. The governing equations combining the dynamics of the railway vehicle integrated with MR dampers in the suspension system and the dynamics of the rail track irregularities are developed and a linear quadratic Gaussian (LQG) control law using the acceleration feedback is adopted, in which the state variables are estimated from the measurable accelerations with a Kalman estimator. In order to evaluate the performances of the semi-active suspension systems based on MR dampers for railway vehicles, the random and periodical track irregularities are modelled with a uniform state-space formulation according to the testing data and incorporated into the governing equation of the railway vehicle integrated with the semi-active suspension system. Utilising the governing equations and the semi-active controller developed in this paper, the simulation and analysis are presented in Part II of this paper.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part II: simulation and analysis

In this paper, the semi-active suspension system for railway vehicles based on the controlled (MR) fluid dampers is investigated, and compared with the passive on and passive off suspension systems. The lateral, yaw, and roll accelerations of the car body, trucks, and wheelsets of a full-scale railway vehicle integrated with four MR dampers in the secondary suspension systems, which are in the closed and open loops respectively, are simulated under the random and periodical track irregularities using the established governing equations of the railway vehicle and the modelled track irregularities in Part I of this paper. The simulation results indicate that (1) the semi-active controlled MR damper-based suspension system for railway vehicles is effective and beneficial as compared with the passive on and passive off modes, and (2) while the car body accelerations of the railway vehicle integrated with semi-active controlled MR dampers can be significantly reduced relative to the passive on and passive off ones, the accelerations of the trucks and wheelsets could be increased to some extent. However, the increase in the accelerations of the trucks and wheelsets is insignificant.     

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.     

Extended study of railway vehicle lateral stability in a curved track

This article presents results of the studies aimed at more accurate stability analysis of railway vehicles in a curved track. More accurate analysis means extended study of the stability as compared with the method used by the authors so far. New measures undertaken by the authors in order to achieve the goal are explained. Besides, differences between results obtained with the earlier and extended approaches are presented and discussed. Results that are expected on the basis of the theory are confronted with practical capabilities to generate them through simulations at the same time. The issues of interest are precise determination of nonlinear critical velocity, determination of linear system critical velocity, determination of unstable periodic and unstable stationary solutions, existence of multiple solutions and correct determination of velocity at which unbounded growth of the solutions (lateral dynamics coordinates) happens during calculations resulting in their stop.     

A structural articulation method for assessing railway bridges subject to dynamic impact loading from track irregularities

This paper discusses the importance of track irregularities in railway bridge design, and presents a new technique for calculating the dynamic impact load induced by such irregularities: the structural articulation method. The properties of the combined bridge-suspension system are coupled through global mass, stiffness, and damping matrices. Under the proposed method, the true suspension system over a particular point on the bridge girder at time t is divided into equivalent suspension systems attributed to adjacent finite-element nodes of the bridge. The time-dependent effects of a moving mass are thereby included in the equation of motion.     

多条件约束下的汽车微观动态滚动轨迹规划

针对高度复杂未知运动环境下最优车辆轨迹的生成问题,在考虑道路形状、路面附着 系数、道路宽度、障碍物及车辆外型尺寸、驾驶风格等因素的基础上,文章提出一种基于多条件约束的汽车微观动态滚动轨迹规划方法。以距离最短为优化目标,对基于多项式的曲线,进行躲避障碍物和免于碰撞道路边界的轨迹规划;以预瞄距离、最大侧向加速度限制值定义不同风格驾驶员作为寻优约束,分析不同驾驶员对行驶轨迹的决策。考虑到真实驾驶员的规 划习惯,根据车辆当前位置及预瞄区间,更新规划范围,滚动寻优,确定轨迹。文章最后利 用 Simulink 仿真平台进行仿真实验,验证了该方法的有效性。     

车辆动力学控制的模拟

本文用模拟方法研究了车辆动力学控制系统。采用闭环的横摆角速度及车辆侧偏角控制，用它们之间的相平面分析确定控制策略。这一控制集成了基于滑移率控制的ＡＢＳ系统，实施简单，鲁棒性强，模拟结果显示该系统能有效地改善车辆的动力学性能。     

Influence of uneven rail irregularities on the dynamic response of the railway track using a three-dimensional model of the vehicle–track system

A mathematical model of the vehicle–track interaction is developed to investigate the coupled behaviour of vehicle–track system, in the presence of uneven irregularities at left/right rails. The railway vehicle is simplified as a 3D multi-rigid-body model, and the track is treated as the two parallel beams on a layered discrete support system. Besides the car-body, the bogies and the wheel sets, the sleepers are assumed to have roll degree of freedom, in order to simulate the in-plane rotation of the components. The wheel–rail interface is treated using a nonlinear Hertzian contact model, coupling the mathematical equations of the vehicle–track systems. The dynamic interaction of the entire system is numerically studied in time domain, employing Newmark's integration method. The track irregularity spectra of both the left/right rails are taken into account, as the inputs of dynamic excitations. The dynamic responses of the track system induced by such irregularities are obtained, particularly in terms of the vertical (bounce) and roll displacements. The numerical model of the present research is validated using several benchmark models reported in the literature, for both the smooth and unsmooth track conditions. Four sample profiles of the measured rail irregularities are considered as the case studies of excitation sources, examining their influences on the dynamic behaviour of the coupled system. The results of numerical simulations demonstrate that the motion of track system is significantly influenced by the presence of uneven irregularities in left/right rails. Dynamic response of the sleepers in the roll direction becomes more sensitive to the rail irregularities, as the unevenness severity of the parallel profiles (quantitative difference between left and right rail spectra) is increased. The severe geometric deformation of the track in the bounce–pitch–roll directions is mainly related to such profile unevenness (cross-level) in left/right rails.     

An efficient approach to the analysis of rail surface irregularities accounting for dynamic train–track interaction and inelastic deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.     

整车多体动力学模型的建立、验证及仿真分析

利用多体动力学方法建立了某轿车的整车非线性多体动力学模型,模型中考虑了前后悬架、转向系统的详细几何结构参数,以及连接处的橡胶衬套、阻尼器的非线性特性,轮胎采用M agic Formu la模型。对所建模型进行了多种试验验证,并分析了该样车的操纵稳定性等相关特性,仿真结果表明所建整车多体模型有较高的精度。     

车辆控制系统集成开发系统

本文介绍了一种新型的集成开发系统,该系统将模拟计算、实时硬件仿真和实车试验巧妙地放置在同一台微机内,利用微机软、硬件功能、实现了从模拟到样机全过程的高效开发,采用ＶｉｓｕａｌＢａｓｉｃ语言实现了模块化编程,程序在不同的模拟试验条件下具有可重用性,最后给出了一个车辆防抱死系统模拟试验的实便,验证了该系统的实用性与高效性。     

Nonlinear single track model analysis using Volterra series approach

In this paper, an original approach based on the Volterra series theory is applied in order to analyse a nonlinear single track model, which is considered to describe the vehicle dynamics behaviour in the nonlinear domain. This model is based on a polynomial approximation up to the third order of the Pacejka formula that describes the full tyre behaviour. The analysis of the model is carried out using a truncated form of the Volterra series; this allows the extraction of an analytical formulation of the nonlinear response characteristics. The analysis is focused on the extraction of the first order frequency response function expression and the understeer angle curve vs lateral acceleration, which characterises the vehicle typology and stability. The resulting equations and illustrations in both the cases are presented.     

Probabilistic assessment of railway vehicle-curved track systems considering track random irregularities

The randomness of track irregularities directly leads to the random vibration of the vehicle–track systems. To assess the dynamic performance of a railway system in more comprehensive and practical ways, a framework for probabilistic assessment of vehicle-curved track systems is developed by effectively integrating a vehicle–track coupled model (VTCM), a track irregularity probabilistic model (TIPM) with a probability density evolution method (PDEM). In VTCM, the railway vehicle and the curved track are coupled by the nonlinear wheel–rail interaction forces, and through TIPM, the ergodic properties of random track irregularities on amplitudes, wavelengths and probabilities can be properly considered in the dynamic calculations. Lastly, PDEM, a newly developed method for solving probabilistic transmissions between stochastic excitations and deterministic dynamic responses, is introduced to this probabilistic assessment model. Numerical examples validate the correctness and practicability of the proposed models. In this paper, the results of probabilistic assessment are presented to illustrate the dynamic behaviours of a high-speed railway vehicle subject to curved tracks with various radii, and to demonstrate the importance of considering the actual status of wheel–rail contacts and curve negotiation effects in vehicle-curved track interactions.     

考虑路面不平度的汽车稳定性控制的研究

考虑路面不平度对汽车稳定性的影响，建立了一个含路面不平度激励的14自由度的汽车动力学模型。在主动悬架技术的基础上，运用直接的反馈控制制定了提高汽车操纵稳定性的控制策略。利用该模型进行了汽车稳定性的仿真研究。与没有稳定性控制系统的仿真结果相比，该控制器的应用能够较好地改善汽车的稳定性。