横向有限条与无砟轨道板段单元的车轨系统竖向振动分析法

Analysis Method of Vertical Vibration of Train and Ballastless Track System with the Lateral Finite Strip and Slab Segment Element

研究高速列车-板式轨道时变系统竖向振动。高速列车(以1动+4拖为例)中的动车及拖车均离散为具有二系悬挂的多刚体系统。针对无砟轨道(以板式轨道为例)的结构特点,提出横向有限条与无砟轨道板段单元分析模型。考虑轮轨竖向位移衔接条件,基于弹性系统动力学总势能不变值原理及形成系统矩阵的"对号入座"法则,建立了此系统竖向振动矩阵方程,采用Wilson-θ法求解。比较了钢轨与轨道板竖向位移的静、动态响应,结果接近。得出200 km/h车速下此系统竖向振动响应时程曲线,计算波形及量值均符合物理概念。分析车速及轨道高低不平顺对此系统竖向振动响应的影响,此系统竖向振动响应随车速及轨道高低不平顺的增大而增大。计算结果表明,本文提出的模型正确、可行。

The vertical vibration of the high-speed train and ballastless track time-dependent system is studied. Both the locomotive and car of the high-speed train such as the China-Star is modeled as a multi-body system with two suspensions. According to the structural characteristic of the ballastless track such as the slab track, a new model of the lateral finite strip and slab segment element is put forward. Based on the principle of total potential energy with the stationary value in elastic system dynamics and the rule of ＂Set-in-right-position＂ for formulating system matrixes, the vertical vibration equation set of the high-speed train and ballastless track time-dependent system is established by considering the vertical connecting condition between the wheel and rail. The equation set is solved by the Wilson-θ method. The comparison between the vertical static and dynamic displacements of the rail and slab is made, which demonstrates they are consistent. The time history curves of the vertical vibration of the system when the train runs at the speed of 200 km/h are obtained. Both the calculated waveforms and values are in accord with the physic concept. The effect of the speed and track vertical profile irregularity on the vertical vibration responses of the system is analyzed, and the vertical vibration responses of the system increase with the increase of the speed and track profile irregularity. All the calculated results demonstrate the correctness and feasibility of the new model.