摘要
针对笛卡尔坐标系下轨道几何三点弦测系统存在的缺点,采用移动Frenet坐标系进行数学建模优化,重新建立了轨道几何描述的方程和三点弦测系统正矢计算模型;根据建立的频域方程和计算模型,方法一:已知任何一种车型的理论轨道DC、CB、DB弦长的情况下比较了通过线路公里标位置的移动计算出C点正矢;方法二:通过已知任何一种车型的理论轨道DC、CB、DB弦长的情况下解算出线路曲率进一步在计算出C点正矢;详细介绍了两种方法及其特点。研究结果表明:Frenet坐标系下,轨道几何描述方程简捷易用,三点弦测系统正矢计算模型直观清晰;在已知理论轨道几何情况下通过线路位置计算正矢的方法较为简便有效。
In response to the shortcomings of the three-point chord measurement system in Cartesian coordinate system,a mobile Frenet coordinate system was used for mathematical modeling optimization,and the equations for describing the orbit geometry and the orthovector calculation model of the three-point chord measurement system were re-established.According to the established frequency domain equation and calculation model,Method 1:Given the theoretical track DC,CB,and DB chord lengths of any vehicle model,the C-point positive vector is calculated by comparing the movement through the kilometer post position of the line;Method 2:By knowing the theoretical track DC,CB,and DB chord lengths of any vehicle model,calculate the curvature of the track and further calculate the positive vector at point C;Detailed introduction to two methods and their characteristics.The research results show that in the Frenet coordinate system,the orbit geometry description equation is simple and easy to use,and the calculation model of the three point chord measurement system's positive vector is visualized and clear.The method of calculating the positive vector based on the position of the track is relatively simple and effective when the theoretical orbit geometry is known.
作者
赵雪玉
马占川
Zhao Xueyu;Ma Zhanchuan(Institute of Electrical and Intelligent Research and Design,China Railway Construction High-tech Equipment Co.,Ltd.,Yunnan,Kunming 650215,China;Representative of Kunming Maintenance Machinery and Vehicle Supervision Project Department,Yunnan,Kunming 650215,China)
出处
《铁道技术标准(中英文)》
2025年第7期17-22,共6页
Railway Technical Standard(Chinese & English)
关键词
Frenet坐标系
三点弦测系统模型
轨道几何描述
轨道正矢算法
捣固车
frenet coordinates
3-point chord measurement system model
track geometry mathematical expression
algorithm of track versine values
tamping machine
