非惯性坐标在列车纵向力分析中的运用

Use of the Non-inertial Coordinates in the Analysis of Train Longitudinal Forces

考虑车体与钩缓系统位移而造成的钩缓系统各部件间几何非线性特点,本文提出一种新的非线性列车车钩缓冲系统模型。忽略钩缓系统各部件惯性,将系统坐标分成惯性坐标和非惯性坐标:惯性坐标描述有惯性力作用其上的车体运动,与惯性力无关的非惯性坐标描述钩缓系统各部件的运动。在不增加状态方程数量、系统惯性坐标数量和约束方程数量的前提下,建立一个较为详细的钩缓系统模型,以体现系统各部件的运动自由度。本模型可在车体任意三维运动时捕捉钩缓系统各部位的运动自由度,而既有的简化钩缓系统模型则未能体现这一点。该方法还可避免由于过小质量的引入而带来系统微分方程组的刚性问题。最后,本文给出一个简化的列车模型算例来展示所述方法的运用。

A new three-dimensional non-linear train car coupler model is established, which takes into account the geometric nonlinearity due to the coupler and car body displacements. The proposed non-linear coupler model allows for arbitrary three-dimensional motion of the car bodies and captures kinetic degrees of freedom that are not captured using existing simpler models. By assuming the inertia of the coupler components negligible compared to the inertia of the car body, the system coordinates are partitioned into two distinct sets; inertial and non-inertial coordinates. The inertial coordinates that describe the car motion have inertia forces associated with them. The non-inertial coupler coordinates, on the other hand, describe the coupler kinetics and have no inertia forces associated with them. While the developed more-detailed coupler model captures the coupler kinetic degrees of freedom, it does not lead to an increase in the number of state equations, number of the system inertial coordinates, and number of constraint equations. Furthermore, by using this approach, one avoids having a system of stiff differential equations that can arise because of the relatively small coupler mass. Numerical results of simple train models are presented in order to demonstrate the use of the formulation developed in this paper.