铁道科学与工程学报2025，Vol.22Issue(1)：113-124,12.DOI:10.19713/j.cnki.43-1423/u.T20240515
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
摘要
Abstract
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 1 500 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 corrugation with a wavelength of 30 to 100 mm,the wave depth should be controlled to be below 0.05 mm.For rail corrugation with a wavelength of 100 to 300 mm,the wave depth should be controlled to be below 0.1 mm.The numerical algorithm presented in this paper is capable of efficiently and accurately simulating the dynamic performance of the vehicle-track coupled system.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Key words
linear complementary theory/vehicle-track coupling/dynamic response/time finite element/wheel-rail resonance分类
交通工程引用本文复制引用
陆晨旭,陈迪来,李培刚,高雅..一种基于时间有限元的车辆-轨道系统求解方法[J].铁道科学与工程学报,2025,22(1):113-124,12.基金项目
上海市"一带一路"中老铁路工程国际联合实验室项目(21210750300) （21210750300）
上海市科学技术委员会启明星计划项目(22YF1447600) （22YF1447600）
