交叉迭代算法求解车辆-轨道非线性耦合方程的收敛性讨论  

Convergence Condition of Cross Iterative Algorithm for VehicleTrack Nonlinear Coupling Equations

作　　者：吴神花 雷晓燕[1] 

机构地区：[1]华东交通大学铁路环境振动与噪声教育部工程研究中心,江西南昌330013

出　　处：《华东交通大学学报》2015年第3期23-31,共9页Journal of East China Jiaotong University

基　　金：国家自然科学基金项目(U1134107)

摘　　要：运用有限元法建立车辆-轨道非线性耦合系统动力分析模型,该模型将车辆-轨道系统以轮轨接触为界限分成车辆,轨道两个子系统并通过轮轨接触力的平衡和位移协调条件耦合在一起。通过交叉迭代算法分别求解车辆,轨道系统的运动方程,此时每一步都需要判断使之满足轮轨几何相容条件和相互作用力平衡条件,这样对时间步长的选取要求较高,但是如果时间步长超过某一限值,易于导致迭代失败。引入了修正因子对轮轨接触力进行修正,这不仅可以放宽对时间步长的选取,还能加速收敛,提高计算效率。为验证算法的正确性,不仅进行了算例验证,还给出了引入修正因子的交叉迭代算法求解车辆-轨道非线性耦合系统动力学方程的算例,算例中考虑了不同的时间步长和不同的修正因子对交叉迭代算法收敛速度的影响。计算结果表明引入修正因子的交叉迭代算法具有程序编制简单、收敛速度快、用时少、精度高的优点。A model for dynamic analysis of vehicle-track nonlinear coupling system was established by finite element method. The whole system was divided into two subsystems, i.e., the vehicle subsystem considered as second- ary spring vehicle model and the track subsystem regarded as three discrete elastic beams model. Cowling of the two systems was achieved by equilibrium conditions for wheel-rail nonlinear contact forces and geometrical com- patibility conditions. A cross-iterative algorithm was presented to solve the dynamics equations of vehicle-track nonlinear coupling system, but every step must be judged to satisfy equilibrium conditions for wheel-rail nonlinear c^ntact forces and geometrical compatibility conditions, leading to the selection of a higher time step that if the time step exceeded a certain value it would be easy to cause failure of the iteration. In view of this situation, a relaxation technique was introduced to correct the wheel-rail contact force, which not only could broaden the selection of the time step but also could accelerate the iterative convergence rate. By contrast with the example of refer- ence, the correctness of the algorithm was verified. Examples of cross-iterative algorithm of the relaxation tech- nique were given, in which the influence of different time steps and relaxation techniques were considered. Results demonstrated that the cross-iterative algorithm had the advantages of simple programming, fast convergence rate, less computation time and high accuracy.

关 键 词：修正因子 时间步长 交叉迭代算法 车辆-轨道非线性耦合 

分 类 号：U213.212[交通运输工程—道路与铁道工程]