基于改进的Newmark-β法重载列车车钩纵向力仿真研究

Simulation research on the longitudinal force of heavy haul train coupler based on the improved Newmark-β method

重载列车运行过程中过大的车钩纵向力一直是制约重载列车发展的瓶颈,空气制动不同步是产生列车纵向冲动的根源,导致车体挤压车钩形成车钩力。传统的经过制动特性试验采集车钩力的方法耗时耗力,为了经济地获取重载列车在不同线路上运行时车钩力的大小,将Newmark-β法应用于重载列车车钩纵向力的仿真分析中。由于列车纵向动力学方程是非常复杂的非线性方程,传统方法为了保证计算精度而采用大量迭代运算,耗时长效率低。基于增量思想改进Newmark-β法,通过引入预测解直接对非线性方程进行处理,然后对预测解进行校正,最终得到收敛的近似解。算例结果表明,改进算法在保证了计算精度的同时计算效率更高,更适用于长大编组重载列车车钩纵向力的仿真计算和分析。

In the process of heavy haul train operation, the excessive longitudinal force of coupler has always been the bottleneck restricting the development of heavy haul train. The asynchronous air braking is the root of the longitudinal impulse of train, which causes the car body to squeeze the coupler to form the coupler force. The traditional method of collecting coupler force through braking characteristic test is time-consuming and labor-consuming. Therefore, in order to obtain the coupler force of heavy haul train running on different lines economically, Newmark-β method was applied to the simulation analysis of coupler longitudinal force of heavy haul train. Because the train longitudinal dynamic equation was a very complex nonlinear equation, the traditional method used a lot of iterative operations to ensure the accuracy of calculation, which was time-consuming and inefficient. In this paper, the Newmark-β method was improved based on the idea of increment. The nonlinear equation was dealt with directly by introducing predictive solution. Then the predictive solution was corrected. Finally the convergence approximate solution was obtained. The example shows that the improved algorithm not only ensures the calculation accuracy, but also improves the calculation efficiency. It is more suitable for the simulation calculation and analysis of the coupler longitudinal force of the long and heavy train.