Abstract

In this study, a new approach is proposed for the characterization and quantification of the spiral transitions in railroad vehicle system algorithms. Definitions of the super-elevation and balance speed are provided in order to have a better understanding of their variations within the space curve of the spiral segment. In order to develop this understanding, three different curves which have fundamentally different geometries are considered; a super-elevated constant-curvature curve with zero twist and zero vertical elevation, a vertically-elevated helix curve with a constant curvature and twist and zero super-elevation, and a spiral curve with non-zero varying-curvature, twist, super-elevation, and vertical elevation. The curve equations are developed in terms of Euler angles used by the rail industry to describe the track geometry in the computer simulations. Because the geometry of the spiral space curve can be completely defined in terms of two Euler angles only, the horizontal-curvature and the vertical-development angles; a third Euler angle referred to as the Frenet bank angle is written in terms of these two angles using an algebraic equation. The fact that, for given curvature and elevation angles, the Frenet bank angle cannot be treated as an independent geometric parameter is used to obtain accurate quantification of the spiral-intersection discontinuities. The severity of the twist and elevation discontinuities at the spiral intersections with the tangent and curve segments demonstrates the need for the adjustments used in practice by the rail engineers to achieve a higher degree of smoothness. In order to properly define the direction of the centrifugal force, a distinction is made between the super-elevation of a surface and the bank angle of a curve on the surface.

摘要

在这项研究中，提出了一种新的方法来表征和量化铁路车辆系统算法中的螺旋过渡。提供超高和平衡速度的定义是为了更好地理解它们在螺旋段空间曲线内的变化。为了加深这种理解，我们考虑了三种不同的曲线，它们具有根本不同的几何形状；具有零扭曲和零垂直高程的超高等曲率曲线，具有恒定曲率和扭曲和零超高的垂直高程螺旋曲线，以及螺旋曲线具有非零变化曲率、扭曲、超高和垂直高程。曲线方程是根据铁路工业用来描述计算机模拟中的轨道几何形状的欧拉角来开​​发的。因为螺旋空间曲线的几何可以完全用两个欧拉角来定义，水平曲率和垂直发展角；第三个欧拉角，称为Frenet bank 角用代数方程用这两个角度写成。事实上，对于给定的曲率和仰角，Frenet 坡度角不能被视为独立的几何参数，用于获得螺旋交叉不连续性的准确量化。与切线段和曲线段的螺旋相交处的扭曲和高程不连续性的严重性表明，铁路工程师需要在实践中进行调整，以实现更高程度的平滑度。为了正确定义离心力的方向，对曲面的超高和曲面上曲线的坡度角进行了区分。