Real-time catenary models for the hardware-in-the-loop simulation of the pantograph–catenary interaction

Hardware-in-the-loop (HIL) simulation is a promising technique to study the pantograph–catenary interaction problems by realising the interaction of a physical pantograph with a mathematical model of the overhead equipment (catenary). However, the computing power presently available on real-time CPUs only allows to run simplified models of the overhead equipment. Therefore, it is important to define catenary models that are suitable for real-time simulation and at the same time capable of accurately representing the dynamic behaviour of the catenary. In this paper, the use of a catenary model based on modal superposition is considered, and the effect of changing the number of modelled spans and the number of modal components allocated to the contact and messenger wires is investigated in view of finding the best model compatible with real-time simulation. Comparisons between HIL simulation results and line measurements are presented, to quantify the accuracy of the hybrid simulation method developed.     

Determining damping characteristics of railway-overhead-wire system for finite-element analysis

In order to investigate the damping characteristics of railway-overhead-wire systems, we propose herein an approach based on the continuous wavelet transform (CWT) and two existing formulas concerning Rayleigh damping coefficients (RDCs). In the proposed process, the displacement histories of a real catenary are first obtained by using a set of noncontact photogrammetric devices, following which an exclusive catenary damping ratio related to the first dominant modal component in the catenary response is identified through a complex Morlet CWT. Thereafter, iterative finite-element analysis is conducted to find the optimal RDCs, which involves using two related formulas and the similarity between the catenary displacements obtained by simulation and experimentation. The results of our study demonstrate that this combined approach is constructive, especially for structures with closely spaced modes, such as catenaries. For the case studied herein, the catenary modal damping ratio at 1.19?Hz is approximately 1%, and the mass and stiffness proportional Rayleigh damping coefficients are approximately 0.02845 and 0.00274, respectively.     

Probabilistic assessment of roadway departure risk in a curve

Roadway departure while cornering constitutes a major part of car accidents and casualties in France. Even though drastic policy about overspeeding contributes to reduce accidents, there obviously exist other factors. This article presents the construction of a probabilistic strategy for the roadway departure risk assessment. A specific vehicle dynamic model is developed in which some parameters are modelled by random variables. These parameters are deduced from a sensitivity analysis to ensure an efficient representation of the inherent uncertainties of the system. Then, structural reliability methods are employed to assess the roadway departure risk in function of the initial conditions measured at the entrance of the curve. This study is conducted within the French national road safety project SARI that aims to implement a warning systems alerting the driver in case of dangerous situation.     

基于桥梁系数的非线性静力分析方法评估

以桥梁系数作为参照标准,分别采用真实地震波反应谱和设计反应谱作为地震需求,对比分析了4种非线性静力方法(承载力反应谱法、N2法、改进的模态Pushover分析法和自适应承载力反应谱法)对钢筋混凝土连续桥梁结构的计算准确性。研究表明:随着地震强度的增大,4种非线性静力分析方法得到的计算结果逐渐接近于非线性动力分析的计算结果;对于采用真实地震波的情况,N2法给出了最接近动力分析的结果,而对于采用设计反应谱的情况,4种非线性静力分析方法得到的结果之间差别非常小。     

Single wheel hub motor failures and their impact on vehicle and driver behaviour

This research work studies the impact of single wheel hub motor failures on the dynamic behaviour of electric vehicles and the corresponding driver reactions. An experimental study in a moving-base driving simulator is conducted to analyse the influence of single wheel hub motor failures for motorway speeds. Driver reaction times are derived from the measured data and discussed in their experimental context. The failure is rated objectively on the dynamic behaviour of the vehicle and compared to the subjective evaluation. Findings indicate that critical traffic situations impairing traffic safety can occur for motorway speeds. Clear counteractions by the drivers had to be taken.     

On the implementation of an auxiliary pantograph for speed increase on existing lines

The contact between pantograph and catenary at high speeds suffers from high dynamic contact force variation due to stiffness variations and wave propagation. To increase operational speed on an existing catenary system, especially for soft catenary systems, technical upgrading is usually necessary. Therefore, it is desirable to explore a more practical and cost-saving method to increase the operational speed. Based on a 3D pantograph–catenary finite element model, a parametric study on two-pantograph operation with short spacing distances at high speeds shows that, although the performance of the leading pantograph gets deteriorated, the trailing pantograph feels an improvement if pantographs are spaced at a proper distance. Then, two main positive effects, which can cause the improvement, are addressed. Based on a discussion on wear mechanisms, this paper suggests to use the leading pantograph as an auxiliary pantograph, which does not conduct any electric current, to minimise additional wear caused by the leading pantograph. To help implementation and achieve further improvement under this working condition, this paper investigates cases with optimised uplift force on the leading pantograph and with system parameter deviations. The results show that the two positive effects still remain even with some system parameter deviations. About 30% of speed increase should be possibly achieved still sustaining a good dynamic performance with help of the optimised uplift force.     

以位移为基础的钢筋混凝土连续梁桥抗震设计方法

利用等效线性化方法将钢筋混凝土(RC)连续梁桥结构简化为多自由度线弹性体系,采用振型反应谱的概念研究了结构在横向地震作用下考虑多阶模态效应的直接基于位移的抗震设计方法。探讨了连续梁桥的上部结构(主梁)及桥墩(台)刚度的变化对结构横向振动模态质量与模态周期的影响,给出了多阶模态设计方法的具体设计过程。对对称与非对称连续梁桥采用相同的设计步骤进行基于位移的抗震设计,并对设计算例用非线性时程分析验证了设计结果的合理性。     

发动机附件台架疲劳试验工况的探索

通过对发动机附件及其支架的振动信号进行总值和阶次分析,结合基于阶次分析的计算位移,确定振动信号的主要频率成分及最大振动和最大位移产生时的发动机运行工况,并结合疲劳损伤理论,确定了考核发动机附件及其支架可靠性的各个转速和持续时间,为相应耐久工况的制定提供参考依据。     

Analysis of the nonlinear dynamics of a 2–axle freight wagon in curves

This paper deals with the study of the nonlinear dynamic behaviour of 2-axle freight wagons in curves, considering the case of one single wagon (neglecting inter-car coupling forces) and of multiple wagons interacting through the buffers and the couplers. A multi-body model of a single wagon and of a three-car assembly is introduced, paying particular attention to the nonlinear and nonsmooth modelling of the suspensions and of the inter-car coupling elements. Using this model, a numerical analysis of the steady-state solution reached after the negotiation of curve transition is presented and bifurcations are identified for some particular values of the curve radius. For the single car case, it is shown that depending on the curve radius and the vehicle speed the carbody may experience severe periodic oscillations at speeds lying in the operating range of the vehicle. For the car-assembly case, it is shown that the coupling forces exchanged by the wagons significantly affect their dynamics in a curve, reducing the amplitude of vibration.     

Nonlinear dynamic behaviour of a railway wheelset

Nonlinear dynamic systems are well known to contain certain characteristic additional phenomena compared with linear systems. One example is the fact that nonlinear systems can have multiple stable solutions for one set of parameters. In that case, which one of the multiple stable solutions will be realised will depend on the initial conditions. From the domains of initial conditions which are domains of attraction, probabilities of occurrence of the stable solutions can be calculated. The described dynamical behaviour is studied in the present paper using two examples. To introduce the basic phenomena, the well-known academic Duffing oscillator with harmonic excitation is considered. Domains of attraction are shown for the two stable solutions and the probability of occurrence of the two solutions in the case of equally distributed initial conditions is calculated. The main example to be considered in this paper is the railway wheelset, which is known to show (depending on the nonlinearities in the model) a subcritical Hopf bifurcation depending on the vehicle speed. In that case a range of speeds exists, where a stable trivial solution and a stable limit cycle solution coexist in addition to an unstable limit cycle solution. Again domains of attraction of the two stable solutions are calculated and their dependence on the vehicle speed is shown. The probabilities of occurrence of the two stable solutions are calculated, where special interest is given to the probability of occurrence of the undesired limit cycle solution.     

The simulation of in-plane tyre modal behaviour: a broad modal range comparison between analytical and discretised modelling approaches

In-plane tyre modal behaviour determines the response of tyres to ride excitations and braking/traction manoeuvres. In many studies, the interest is limited to relatively low frequencies and a detailed investigation into the ability of models to accurately simulate higher-order responses is unnecessary. In cases where an in-plane model is to be used for the generation of the contact deformation and stresses, or where modal reduction methods are implemented, a detailed knowledge of the modal response is desirable. The present work forms a study on the ability of a number of frequently used modelling approaches to generate realistic modal data throughout a wide frequency range. The analytical ring on elastic foundation model is used as a benchmark throughout the paper. Its predictions are compared with those of two discretised models, namely a truss- and a beam-based model. The sensitivity of the ring’s response to a number of physical parameters is discussed. The results are used to inform the comparison between the analytical ring and the discretised models, providing explanations for any discrepancies observed. The limited applicability of the truss model is pointed out, while the accuracy of the beam-based model is enhanced by a circumferential inextensible string element. Both the ring and the enhanced beam models are further improved with the addition of a nonlinear string-based sidewall that accounts for the change in sidewall stiffness with inflation pressure. The findings may offer a reference when setting up in-plane models, including the stage of planning modal tests for parameter identification.     

Stochastic Monte Carlo simulations of the pantograph–catenary dynamic interaction to allow for uncertainties introduced during catenary installation

The simulation of the pantograph–catenary dynamic interaction is at present mainly based on deterministic approaches. However, any errors made during the catenary stringing process are sources of variability that can affect the dynamic performance of the system. In this paper, we analyse the influence of dropper length, dropper spacing and support height errors on the current collection quality by applying a classic Monte Carlo method to obtain the probability density functions of several output quantities. The effects of installation errors are also studied for a range of train speeds. Finally, the pre-sag that, on average, produces the best behaviour of the system is identified, allowing for the uncertainty in the catenary installation. The results obtained show the convenience to consider variability in pantograph–catenary dynamic simulations.     

某型复杂变速器壳体的模态研究

首先分析了工作模态法的优点及其所用的随机子空间法理论;然后应用工作模态法对某型变速器复杂壳体的模态进行实验辨识,得到了壳体各阶的模态频率和振型。并利用有限元软件MSC.Patran和MSC.Nastran对壳体模态进行数值计算,通过实验模态和数值计算模态的对比,发现在低频段实验结果与数值计算结果较吻合,说明采用工作模态法能较精确地识别出壳体的低阶模态。     

Suspension parameter estimation in the frequency domain using a matrix inversion approach

The dynamic lumped parameter models used to optimise the ride and handling of a vehicle require base values of the suspension parameters. These parameters are generally experimentally identified. The accuracy of identified parameters can depend on the measurement noise and the validity of the model used. The existing publications on suspension parameter identification are generally based on the time domain and use a limited degree of freedom. Further, the data used are either from a simulated ‘experiment’ or from a laboratory test on an idealised quarter or a half-car model. In this paper, a method is developed in the frequency domain which effectively accounts for the measurement noise. Additional dynamic constraining equations are incorporated and the proposed formulation results in a matrix inversion approach. The nonlinearities in damping are estimated, however, using a time-domain approach. Full-scale 4-post rig test data of a vehicle are used. The variations in the results are discussed using the modal resonant behaviour. Further, a method is implemented to show how the results can be improved when the matrix inverted is ill-conditioned. The case study shows a good agreement between the estimates based on the proposed frequency-domain approach and measurable physical parameters.     

Simulation model for the study of overhead rail current collector systems dynamics, focused on the design of a new conductor rail

Overhead rigid conductor arrangements for current collection for railway traction have some advantages compared to other, more conventional, energy supply systems. They are simple, robust and easily maintained, not to mention their flexibility as to the required height for installation, which makes them particularly suitable for use in subway infrastructures. Nevertheless, due to the increasing speeds of new vehicles running on modern subway lines, a more efficient design is required for this kind of system.

In this paper, the authors present a dynamic analysis of overhead conductor rail systems focused on the design of a new conductor profile with a dynamic behaviour superior to that of the system currently in use. This means that either an increase in running speed can be attained, which at present does not exceed 110 km/h, or an increase in the distance between the rigid catenary supports with the ensuing saving in installation costs.

This study has been carried out using simulation techniques. The ANSYS programme has been used for the finite element modelling and the SIMPACK programme for the elastic multibody systems analysis.     

Analysis of the Dynamic Response of a Rolling String-Type Tire Model to Lateral Wheel-Plane Vibrations

A theory has been developed for the analysis and prediction of the dynamic frequency response of lateral force and moment acting upon a pneumatic tire when the wheel is moved laterally and swivelled about the vertical axis. The theory establishes the force and moment response of a tire model which consists of a stretched circular string with mass, elastically supported to the wheel-center-plane. The analysis is confined to small deviations from rectilinear motion such that it is permissible to assume that sliding does not occur in the contact area. In this manner, the equations are kept linear.

The theory which gives an exact analysis of the dynamic response of the model adopted shows satisfactory qualitative agreement with experiments. The change in the moment response due to tire inertia reduces the tendency to shimmy at higher frequencies and higher speeds. The lateral force response, however, changes in an unfavorable fashion which, for castered wheels, may result in a decrease of the effective damping about the king-pin at higher speeds and frequencies.     

基于发动机悬置动刚度分析的车内降噪研究

某微型客车在行驶过程中发动机高转速时驾驶室产生共鸣声,车身有严重的振动现象。NVH测试结果显示发动机右悬置支架Z向动刚度偏低。采用有限元分析方法对发动机右悬置进行动刚度分析,基于动力总成悬置系统刚度匹配原则和结构参数敏感性分析,并考虑装配及焊接工艺等因素,提出一个较为合理的改进方案。改进方案装车后NVH测试结果表明车内噪声明显降低,发动机转速为3 315 r/min时降了4.3 dB,3 671 r/min时降了10 dB,3 860r/min时降了4.5 dB,车身振动主观感觉亦有明显减弱。     

环境激励下桥梁结构模态识别与损伤检测的新方法

已有的环境激励下模态参数识别的方法对模态频率的识别精度相对较高,而对位移模态的识别则误差较大。本文提出一种利用移动质量块在不同位置时对桥梁的模态频率进行多次测量,用各次测得的频率值确定位移模态的新方法,使得位移模态识别的精度接近频率识别的精度,推导了频率与位移模态关系的理论公式,并给出利用以曲率形式表示的单元模态应变能对结构进行损伤标定的基本方法。最后,通过数值模拟对该方法的有效性进行说明。     

大客车车身结构动力学建模与随机响应分析

建立了某型全承载式车身结构大客车包括蒙皮和固定玻璃在内的完整的动力学有限元模型,合理地模拟了该车使用的空气弹簧悬架,通过与理论模型求解结果对比,验证了模型的正确性。运用结构动力学的频域求解方法,在模态分析、频率响应分析的基础上,进行了大客车整车结构的动应力随机响应分析。     

轿车白车身模态仿真计算与相关性分析

白车身模态分析是车身动态特性分析的基础。工程上常采用仿真计算和试验测试2种方法识别白车身模态参数。这2种方法相辅相成,互相促进,共同指导和改进设计。文章通过仿真建模计算了某车型白车身的模态频率,将计算结果和试验测试相比较,并采用相关性分析的方法验证了模型的可靠性,同时对比了不同焊点类型对于分析结果的影响。结果表明,建立的白车身仿真模型具有较高的精度,仿真计算所采用的模拟方法是合适的,为内部仿真建模指导规范的建立提供了参考。