不确定车轨耦合系统辛随机振动分析

建立了轨道不平顺作用下具有不确定参数车轨耦合系统随机振动评估方法. 车辆系统采用物理坐标下多刚体系统模型,并应用高斯随机变量模拟车体、转向架和轮对一系、二系连接系统中动力学参数具有的不确定性. 采用无穷周期结构进行弹性轨道模拟,在哈密顿状态空间下建立了典型轨道子结构的状态运动方程,通过轮轨耦合关系建立了混合 物理坐标及辛模态坐标车轨耦合系统运动方程. 应用Hermite正交多项式展开得到了耦合系统动力响应相对于不确定性参数的控制方程. 由于利用轨道周期特性建模,所获得的控制方程有效地降低了方程维度. 轮轨接触处轨道不平顺载荷模拟为完全相干多分量平稳随机过程,推广和发展虚拟激励法建立了耦合系统随机振动受不确定动力学 参数影响的量化评估方法. 通过Monte Carlo数值模拟,验证了该方法在不确定参数变异很大时也能够保持较好的精度,具有一定的工程实用性.     

基于对称性的三维车辆轨道耦合系统随机振动虚拟激励方法

基于结构的对称性提出了用于三维车辆轨道耦合系统高效随机动力响应分析的虚拟激励方法.车辆采用刚体动力学模型,轨道结构利用三维轨道广义单元建模,车辆与轨道通过线性轮轨关系耦合.采用虚拟激励法将高低、方向和水平三类轨道不平顺转化为一系列筒谐的虚拟不平顺;考虑车辆及轨道结构的对称性,分别推导了耦合系统的对称和反对称凝聚矩阵,提出了用于车辆轨道耦合系统动力响应计算的自由度凝聚方法,将耦合系统的自由度缩减至原来的一半以下,并在此基础上实现了耦合系统随机振动的高效分析.数值算例将本文方法与传统有限元方法进行对比,验证了本文方法的正确性和有效性.     

车辆-轨道系统垂向随机振动的辛方法分析

将轨道视为无限长的周期结构,建立车辆轨道垂向耦合模型. 使用虚拟激励法将随机的轨道不平顺激励转化为确定性的简谐激励,再用辛数学方法求解轨道结构的频率响应特性和耦合系统的响应功率谱. 整个计算模型只有26个自由度,求解过程快速而精确.数值算例中,将该方法与常规有限元方法进行了比较,验证了方法的高效性和正确性,讨论了车辆速度对系统随机响应的影响.      

跳车冲击力作用下车桥耦合动力学数值分析

考虑到传统的Hertz弹簧模型进行车桥耦合动力学分析存在诸多问题,本文基于简单的车桥耦合模型,导出了车桥耦合与非耦合动力学方程。考虑轨道周期和随机不平顺情况,车辆在不平顺轨道曲线上运行时,当离心力大于车辆自重时,自动确定车辆的起跳时间和起跳高度。起跳后的车辆在重力作用下,将重新回到梁上,同时对梁有一冲击作用力。文章假设了此冲击力的作用规律,并由有限元模拟确定冲击力系数。通过自编程序,对单轴行车简支梁进行了数值计算。数值分析结果表明,考虑跳车冲击力的动力模型能够更加精准地反应车桥耦合振动特征,且本模型首次给出了跳车高度。考虑轨道具有相同幅值的周期不平顺和随机不平顺时,轨道随机不平顺将导致桥梁,尤其是车辆的响应更大,舒适性更差或结构更危险,在车桥耦合动力学分析中应重点关注。     

轨下支承失效对直线轨道动态响应的影响

建立了基于Timoshenko梁模型的车辆/轨道耦合动力学模型,分析轨下支承失效对直线轨道动态响应的影响. 钢轨被视为连续弹性离散点支承上的无限长Timoshenko梁,通过假设轨道系统刚度沿纵向分布发生突变来模拟轨下支承失效状态. 推导了考虑钢轨横向、垂向和扭转运动的轮轨滚动接触蠕滑率计算公式. 利用Hertz法向接触理论和沈氏蠕滑理论计算轮轨法向力及轮轨滚动接触蠕滑力. 采用移动轨下支承模型的车辆/轨道耦合系统激振模式,考虑轨枕离散支承对系统动力响应的影响. 通过新型显式积分法求解车辆/轨道耦合动力学系统运动方程,由数值分析计算得到不同轨下支承失效状态下直线轨道的动态响应. 结果表明,轨下支承失效对直线轨道变形及加速度有显著的影响,随着失效轨下支承个数的增加,轮轨相互作用力和轨道部件的位移、加速度将会急剧增大,将加速失效区段线路状况的恶化.      

随机不平顺激励下磁浮车辆轨道梁动力响应

建立了高速常导磁浮交通车辆轨道梁空间耦合模型，探讨了合理的磁浮线路功率谱形 式，利用分离迭代的数值积分方法求解了大规模非线性耦合动力方程. 利用计算结果分析了 随机不平顺对系统动力学指标影响规律，并采用功率谱密度曲线进行了谱分析，得到了高速 磁浮交通车梁耦合系统随机振动的基本规律.     

单轨火箭橇靴-轨冲击响应传递特性研究

单轨火箭橇靴-轨的冲击响应是影响其运动过程中系统稳定性的主要问题。本文以单轨火箭橇为研究对象,采用有限元结构动力学仿真分析方法建立了非线性火箭橇-轨道耦合动力学模型;对比分析了理想平直轨和不平顺轨两种轨道模型条件下滑靴、卡环、发动机的振动量变化,并进行了火箭橇的试验验证和数据对比。结果表明:不平顺轨道对火箭橇靴-轨冲击响应振动加速度均方根值的影响大于理想平直轨道,滑靴处二者最大偏差为3～5倍,且随机振动特性显著;最大速度时刻的靴-轨冲击预测结果与实测值在侧向和竖向振动趋势上具有很好的一致性。研究结果为火箭橇结构优化设计及稳定性分析提供了理论依据和技术保障。     

基于虚拟激励法的车-轨-桥耦合系统的随机振动响应分析

轨道随机不平顺作为引起车辆-轨道-桥梁耦合系统振动的最重要的激励源,对列车过桥平稳性有着至关重要的影响．建立车辆-轨道-桥梁耦合垂向振动模型,采用虚拟激励法,计算随机不平顺激励下车辆运行的平稳性以及轨道和桥梁结构的振动特性,避免了繁复的时频转换和复杂的数值积分．数值分析了不同速度下列车过桥的平稳性和列车对不平顺波长的敏感范围．经过分析得到,列车运行速度越大,过桥平稳性指标越大,即舒适性越差;而且影响列车平稳性的不平顺波长越长,其影响范围越大．     

三维车桥耦合系统的非平稳随机振动分析

推导了线性时变系统非平稳随机响应的多维虚拟激励法,研究了三维车桥耦合系统受轨道激励而产生的非平稳随机振动。桥梁模型采用空间Euler梁单元,轨道激励假设为均匀调制多点异相位非平稳随机激励。采用多维虚拟激励法把轨道不平度转化为一系列简谐不平度的叠加,通过简单分解精细积分格式进行迭代计算,最终得到系统随机响应的时变功率谱及均方根。数值算例中,用时间历程法验证了本文方法的正确性,并且分析了方向、高低、水平三类轨道激励同时作用下三维车桥耦合系统的非平稳随机振动特性。     

含三次耦合项的两自由度Duffing系统的共振及混沌行为

研究了一类含三次耦合项的两自由度Duffing系统的动力学行为。首先应用多尺度方法近似求解系统的一阶稳态响应。通过讨论系统的主共振和1∶1内共振,分析了三次耦合项对系统响应的影响。随后研究系统随外加周期力强度变化的分岔过程,发现除了常见的倍周期分岔通向混沌外,还存在一种直接由周期运动进入混沌的突发路径。结合对系统的最大Lyapunov指数,相轨图及Poincar啨映射的分析验证了上述结论。     

A novel method to estimate derailment probability due to track geometric irregularities using reliability techniques and advanced simulation methods

Track irregularities have a dramatic impact on the response and vibration of a railway vehicle and on the interaction between wheel and rail. The random nature of the track structure and constituent materials and the effects of other factors such as maintenance conditions and transit traffic give rise to the random nature of track irregularities. This research provides a method to estimate the derailment probability of a railway vehicle where track irregularities are assumed to be random, and the interaction of the track and the moving train is considered using advanced dynamic analysis. For this purpose, the limit state function of derailment was estimated using the response surface method and advanced simulation. The probability of derailment was then estimated using a Level 3 reliability method.     

Stochastic sensitivity analysis of coupled acoustic-structural systems under non-stationary random excitations

This paper presents a new sensitivity analysis method for coupled acoustic–structural systems subjected to non-stationary random excitations. The integral of the response power spectrum density (PSD) of the coupled system is taken as the objective function. The thickness of each structural element is used as a design variable. A time-domain algorithm integrating the pseudo excitation method (PEM), direct differentiation method (DDM) and high precision direct (HPD) integration method is proposed for the sensitivity analysis of the objective function with respect to design variables. Firstly, the PEM is adopted to transform the sensitivity analysis under non-stationary random excitations into the sensitivity analysis under pseudo transient excitations. Then, the sensitivity analysis equation of the coupled system under pseudo transient excitations is derived based on the DDM. Moreover, the HPD integration method is used to efficiently solve the sensitivity analysis equation under pseudo transient excitations in a reduced-order modal space. Numerical examples are presented to demonstrate the validity of the proposed method.     

Interaction of railway vehicles with track in cross-winds

This paper presents a framework for simulating railway vehicle and track interaction in cross-wind. Each 4-axle vehicle in a train is modeled by a 27-degree-of-freedom dynamic system. Two parallel rails of a track are modeled as two continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The vehicle subsystem and the track subsystem are coupled through contacts between wheels and rails based on contact theory. Vertical and lateral rail irregularities simulated using an inverse Fourier transform are also taken into consideration. The simulation of steady and unsteady aerodynamic forces on a moving railway vehicle in cross-wind is then discussed in the time domain. The Hilber–Hughes–Taylor α-method is employed to solve the nonlinear equations of motion of coupled vehicle and track systems in cross-wind. The proposed framework is finally applied to a railway vehicle running on a straight track substructure in cross-wind. The safety and comfort performance of the moving vehicle in cross-wind are discussed. The results demonstrate that the proposed framework and the associated computer program can be used to investigate interaction problems of railway vehicles with track in cross-wind.     

复杂机车振动环境下牵引电机轴承服役寿命评估

牵引电机是铁路机车的动力源, 其关键零部件(支承轴承等)的服役性能直接影响机车传动系统的稳定性和可靠性. 对于重载机车, 传统轴承服役寿命评估方法主要基于定载荷工况, 难以准确评估轨道不平顺等复杂外部激励作用下电机轴承的服役寿命. 因此, 本文根据车辆-轨道耦合动力学理论, 考虑轨道车辆运行过程中的轮轨相互作用和齿轮啮合作用, 建立了具有牵引动力传动系统的机车-轨道耦合动力学模型; 采用线性损伤累积准则和ISO 281标准计算方法, 评估了复杂机车振动环境下牵引电机轴承的服役寿命. 结果表明, 在轨道随机不平顺激励下, 机车轮轨垂向力、齿轮啮合力、牵引电机内部转子离心力、不平衡磁拉力等明显增大; 在复杂机车振动环境中, 电机轴承内部滚子-滚道相互作用加剧, 传动端与非传动端轴承的疲劳寿命缩短; 随着线路状态的不断恶化和机车运行速度的提高, 牵引电机轴承的预测寿命里程不断减小; 由于传动端轴承承受较大的外部动态载荷, 传动端轴承的服役寿命明显低于非传动端轴承. 本文提出的评估方法可为机车牵引电机轴承的设计、选型和寿命评估提供理论指导.      

桥梁表面不平顺对车-桥耦合振动系统动力效应的影响

利用模态分析法以及时变力学系统的求解方法,考虑桥面不平顺产生的随机激励,以简支梁桥为对象,计算了四自由度模型车辆-桥梁耦合系统的动力效应,讨论了不同等级桥面平整度情况下桥梁冲击系数、车辆垂直加速度、车轮对桥的作用力的变化规律。结果表明,随着不平整度系数逐渐增大,冲击系数逐渐增大;平整度较差等级的桥面,车辆垂直加速度较大,车轮对桥的作用力也较大。     

Track dynamic behavior at rail welds at high speed

As a vehicle passing through a track with different weld irregularities, the dynamic performance of track com- ponents is investigated in detail by using a coupled vehi- cle-track model. In the model, the vehicle is modeled as a multi-body system with 35 degrees of freedom, and a Timoshenko beam is used to model the rails which are dis- cretely supported by sleepers. In the track model, the sleepers are modeled as rigid bodies accounting for their vertical, lat- eral and rolling motions and assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the study of the coupled vehicle and track dynamics, the Hertizian contact theory and the theory proposed by Shen-Hedrick-Elkins are, respectively, used to calculate normal and creep forces between the wheel and the rails. In the calculation of the normal forces, the coefficient of the normal contact stiffness is determined by transient contact condition of the wheel and rail surface. In the calcu- lation of the creepages, the lateral, roll-over motions of the rail and the fact that the relative velocity between the wheel and rail in their common normal direction is equal to zero are simultaneously taken into account. The motion equations of the vehicle and track are solved by means of an explicit integration method, in which the rail weld irregularities are modeled as local track vertical deviations described by some ideal cosine functions. The effects of the train speed, the axle load, the wavelength and depth of the irregularities, and the weld center position in a sleeper span on the wheel-rail impact loading are analyzed. The numerical results obtained are greatly useful in the tolerance design of welded rail pro- file irregularity caused by hand-grinding after rail welding and track maintenances.