改进迭代过程的车轨耦合振动数值解法及应用

NUMERICAL APPROACH FOR VEHICLE-TRACK COUPLING VIBRATION BASED ON IMPROVED ITERATIVE PROCESS AND ITS APPLICATION

针对列车-轨道耦合振动迭代求解过程,结合Newmark-β积分格式,提出一种基于有限元法与非线性接触理论的改进迭代过程数值解法。考虑分别建立车辆系统和轨道系统振动方程,在耦合和解耦迭代过程中,构造松弛因子函数和收敛准则函数,简化轮轨界面协调适应条件,利用轮轨相互作用力在两子系统之间的快速迭代实现动态耦合关系的高效求解。此算法增强了对迭代收敛精度、迭代过程稳定性的控制,同时也减小了程序设计的难度。应用此算法分别对竖错和路基沉降两类典型线路缺陷引起的车轨振动响应进行了算例对比和分析,计算结果表明,改进解法在迭代速度和迭代稳定性上具有优势,可广泛应用于高速铁路车辆运行和轨道结构动力学问题的分析中。

Combined with Newmark-fl integration scheme, an improved algorithm for iterative process, based on the finite element method and nonlinear contact theory, is presented and applied to analyze the dynamic response of a vehicle-track coupling system. For vehicle and track systems, vibration equations are established respectively. In the process of coupling and decoupling iteration, a relaxation factor function and a convergence criterion function are constructed, and the compatibility conditions at the wheel/rail interface are simplified. The wheel/rail interaction force is used to complete iterations in a rapid succession between two systems to realize the efficient solution for the coupling relationship. This algorithm improves the convergence precision of iteration and the stability of the iterative process. At the same time it reduces the difficulty of program design. The vibration responses of a coupling system caused by two kinds of line defects, the stepped irregularity and differential settlement of subgrade, are calculated using the proposed algorithm. The results show that the algorithm has advantages in iterative speed and iterative stability, and it can be widely used in vehicle-track coupled vibration analysis.