基于Newmark格式的车辆-轨道耦合迭代过程的改进算法

Improved algorithm of iterative process for vehicle-track coupled system based on Newmark formulation

针对车辆-轨道耦合系统振动方程联立求解过程,考虑车辆和轨道2个子系统模型,提出一种将有限元法和非线性接触理论相结合的交叉迭代数值改进算法。该算法将子系统方程非荷载项矩阵进行修正和求逆的预处理,基于Newmark-β积分格式规则,构造具有较高收敛速度及精度的松弛因子函数和收敛准则函数,利用轮轨相互作用力在车辆系统与轨道系统之间的快速交叉迭代,改进并实现轮轨耦合关系的求解。研究结果表明:提出的算法正确、有效,极大地提高了动力学方程数值计算效率;时间步长对系统数值解的稳定性影响显著,松弛因子的合理选择,可起到加速系统迭代和增强迭代稳定性的作用;该算法在解决大型工程振动问题时更具高效求解的优越性。

Based on finite element method and nonlinear contact theory, an improved staggered iterative algorithm for the simultaneous solution process of vehicle-track system equations was presented. In the algorithm, the dynamic model was divided into vehicle subsystem and track subsystem. For the non-load matrices in two subsystems were carried out some necessary preprocesses such as correction and inversion. Based on rules of the Newmark-β integration scheme, the relaxation factor function and convergence criterion function were constructed with higher convergence speed and convergence precision respectively. To accomplish the solution of the wheel/rail coupled relationship, the fast staggered iteration of wheel/rail interaction force between vehicle subsystem and track subsystem was applied. The results show that the proposed algorithm is correct, effective and able to greatly enhance resolution efficiency of the kinetic equations compared with conventional integration mode. The time step has tremendous effect on the stability of numerical solution, and the reasonable choice of relaxation factor plays a crucial role in accelerating iteration and enhancing the stability of iterative solution. The proposed algorithm is more efficient in large engineering dynamic response.