铁路缓和曲线代数式方程的通用设计方法

A General Method for Designing Railway Transition Curve Algebraic Equations

根据铁路缓和曲线的特点,介绍了利用缓和曲线边界条件确定其代数方程式的一种通用方法:首先给出缓和曲线要满足的边界条件,根据边界条件列出曲率待定方程;然后利用曲率边界条件确定出缓和曲线曲率方程;最后通过对曲率方程进行二次积分就可得到缓和曲线的方程。采用这种方法分别对各种类型的缓和曲线举出实例,详细说明了该方法的应用,证明了该方法正确、简单,是一种适用于推导缓和曲线方程的通用方法,可为铁路缓和曲线线型设计提供参考。

According to the characteristics of railway transition curve, a general and new method for desig- ning its algebraic equations is presented： firstly, according to the given boundary conditions of transition curve the equation of curvature with unknown coefficients is formulated. Secondly, the unknown coefficients in the cur- vature equation are determined by the boundary conditions of curvature and then the curvature equation is ob- tained. At last, the equation of transition curve in Cartesian coordinates can be obtained by double integration of curvature equation. By taking transition curves, which meet different boundary conditions, as examples, the ap- plicatibn of the proposed method is illustrated in detail. The proposed method is proved to be correct and simple. It is a general method that can be applied for determination of transition curve algebraic equations, and offers a new design method for railway transition curve.