铁路列车-轨道-基础结构动力相互作用统一分析Part Ⅰ:动力学模型构造与求解

Unified analysis model for railway train-track-substructure dynamic interaction Part I:the dynamics model construction and its solution

铁路列车、轨道及基础结构是铁路工程系统的基本研究对象,在动力学层面对三者间相互作用进行统一描述与分析,是开展铁路工程系统动力学研究的前提。视列车、轨道和基础结构为整体系统,以车辆-轨道耦合动力学理论为方法核心,以弹性总势能不变值原理及形成矩阵的“对号入座”法则为建模思路,将三大子系统耦合为动力学统一矩阵方程,建立铁路列车-轨道-基础结构动力相互作用统一分析模型。该模型引入轮轨空间动态耦合方法描述轮轨系统横向饱和蠕滑作用,垂向弹性接触采用Hertz非线性接触理论,且将车轮和钢轨均作弹性梁处理,实现轮轨柔性系统非线性时变耦合;轨道及基础结构采用不同有限单元类型模拟和组装,直接通过单元节点坐标控制单元位置并推算尺寸,实现轨道-基础结构层间多尺度单元的点、面耦合;引入循环计算方法,解决列车在长距离轨道-基础结构上的时变动力学计算问题;为了实现列车-轨道-基础结构系统的高效振动分析,将整体系统分为上部列车-轨道系统和下部基础结构系统,采用多步长-混合积分模式高效求解。研究结果表明:该统一模型能较好地反映轮轨高频振动特性,且能开展多基础结构形式下的列车-轨道-基础结构耦合动力学分析,具有工程可靠性和适用性。

Railway train,track and substructure are the basic research objects of railway engineering systems.The unified description and analysis of the interaction between the three objects at the dynamics level is the main content and precondition of railway engineering dynamics research.By considering the train,track,and substructures as an integrated system,the coupled vehicle-track dynamics theory was taken as the core of the method,and the principle of total potential energy with a stationary value and the“set-in-right-position”rule for matrix formation were taken as the modeling methodology.The three sub-systems were coupled into a dynamic unified matrix equation,and a unified analysis model for the railway train-track-substructure dynamic interaction was established subsequently.In this model,the lateral wheel-rail creep adopted the wheel-rail space dynamic coupling model,and the wheel-rail vertical elastic contact adopted the Hertz nonlinear contact theory.The wheel and rail were treated as elastic beams,and their nonlinear time-dependent coupling was achieved.The track and substructures were simulated and assembled with different types of finite elements,and the position of the element was directly controlled by the element nodal coordinates with the sizes calculated.The point and surface coupling of the multi-scale finite elements between the track and the substructural layers were realized.The cyclic calculation method was used to solve time-varying dynamics problem of the train on the long-distance track-substructure systems.To realize the high-efficiency vibration analysis of the train-track-substructure system,the entire system was divided into the upper train-track system and the lower substructure system.The multi-timestep hybrid integration mode was used to solve the problem.The results show that the unified model can properly reflect the high-frequency vibration characteristics of the wheel and rail and thus can achieve the coupled dynamics analysis of the train-track-substructure system subject to multi-substructural forms.The research findings have engineering reliability and applicability.