一种基于时间有限元的车辆-轨道系统求解方法  

Solution for vehicle-track system based on time finite element

作　　者：陆晨旭 陈迪来 李培刚 高雅 LU Chenxu;CHEN Diai;LI Peigang;GAO Ya(School of Railway Transportation,Shanghai Institute of Technology,Shanghai 201418,China;Infrastructure Inspection Research Institute,China Academy of Railway Sciences,Beijing 100081,China)

机构地区：[1]上海应用技术大学轨道交通学院,上海201418 [2]中国铁道科学研究院基础设施检测研究所,北京100081

出　　处：《铁道科学与工程学报》2025年第1期113-124,共12页Journal of Railway Science and Engineering

基　　金：上海市“一带一路”中老铁路工程国际联合实验室项目(21210750300);上海市科学技术委员会启明星计划项目(22YF1447600)。

摘　　要：为克服轮轨动力方程时变特性以及轮轨脱离情况带来的仿真效率低,稳定性差等问题,基于线性互补理论及时间有限元法,提出一种求解车轨系统方程的新方法。该方法首先将轮轨接触问题转化为一个标准的线性互补问题,并通过将二阶动力方程转化为一阶动量方程实现不连续轮轨力的求解;接着与传统的Herz-Newmark法对比,验证该方法的准确性和稳定性;最后应用该方法探究轮轨系统耦合振动特性,并给出时速350km高速铁路不同波长钢轨波磨控制限值。研究结果表明:动量方程可以消除接触力的快速变化,避免大步长条件下接触力不连续引起的稳定问题,临界稳定步长为1ms。方法具有较好的计算性能,求解过程轮轨系统为时不变体系,不用逐步更新动力矩阵,相同积分步长条件下,计算效率提高2倍左右。多轮约束作用会显著改变钢轨振动特性,使得车轨耦合模型振动模态更加丰富。0~1500Hz范围内,钢轨存在5种典型振动模态,分别对应P2共振振型、钢轨1阶局部弯曲、2阶局部弯曲、3阶局部弯曲及4阶局部弯曲振型。钢轨局部共振会造成特定频段轮轨力放大现象,波长30~100mm的钢轨波磨,波深应控制在0.05mm以下;波长100~300mm的钢轨波磨,波深应控制在0.1mm以下。本文数值算法能够实现对车轨动力系统高效、准确的仿真。To address the issues of low simulation efficiency and poor stability resulting from the time-varying characteristics of the wheel-rail dynamic equation and wheel-rail separation,a new method was proposed for solving the vehicle-track system.This method was based on the linear complementary theory and time finite element method.The proposed method transformed the wheel-rail contact problem into a standard linear complementarity problem,and achieved the solution of the discontinuous wheel-rail force by converting the second-order dynamic equation into the first-order momentum equation.Subsequently,the numerical accuracy and reliability of this method were verified in comparison with the conventional Herz-Newmark method.Finally,this method was applied to explore the coupled vibration characteristics of the wheel-rail system.The research results demonstrate that the momentum equation can eliminate rapid changes in contact force and avoid stability problems caused by contact force discontinuity under large step conditions.Furthermore,the critical stability step is found to be 1 ms.The computational performance of the method proposed in this paper is also evaluated and found to be satisfactory.It is unnecessary to gradually update the dynamic matrix during the solution process due to the time-invariant wheel-rail system.The calculation efficiency is increased by approximately twofold when the same integration step size is used.The impact of multi-wheel restraint will markedly alter the vibration characteristics of the rail,resulting in a greater diversity of vibration modes in the vehicle-track coupling model.In the frequency range of 0 to 1500 Hz,five typical vibration modes of the rail can be identified,which correspond to the P2 resonance vibration mode,the first-order local bending,the second-order local bending,the third-order local bending,and the fourth-order local bending mode of the rail.Local resonance of the rail will result in an amplification of wheel-rail force within a specific frequency band.For rail c

关 键 词：线性互补理论 车辆-轨道耦合 动力响应 时间有限元 轮轨耦合共振 

分 类 号：U213.1[交通运输工程—道路与铁道工程]