The Research Conversion Model Between Spatial Coordinate And Mileage In Railway Central Line

The conversion between spatial coordinate and mileage in railway central line exists in the entire process of railway construction, which is an important part of the construction of railway. The traditional coordinate positive and negative computation of railway central line is based on construction plane mileage indexing, in which the calculation model is complex, un-universal and uneven accuracy. The railway coordinate system is not uniform, reveals a great limitation, especially in the high-speed railway project "Integration of Three Networks" measurement technology system. After railway opened to traffic, track spatial mileage is easy to accurately measure compared with construction horizontal mileage, and is easy to search track disease, but cannot be directly used for coordinate calculation of central line. Its application scope is greatly restricted. Therefore, it is very necessary to study on the existing coordinate conversion model of railway central line and its conversion accuracy, to establish a general mathematical model for coordinate positive and negative computation of railway central line. At the same time, track spatial mileage is introduced into central line coordinate conversion model, to establish rigorous conversion model for track spatial mileage and construction horizontal mileage.In order to be able to quickly and accurately obtain the design value of three dimensional coordinates (X, Y, H) of central line, and determine the relative relation between the side pile and the central line, this paper first systematically exposits the calculation methods of comprehensive elements for symmetry and asymmetrical easement curve, quantitatively analyzes easement curve coordinates series expansion truncation errors and numerical integral model approximation error. Both methods, normal vertical distance reaching method and the tangent vertical distance method, are put forward for calculating corresponding centerline mileage and offset of the side pile. The conversion of coordinate and mileage between any center pile and side pile may be achieved with broken chain processing. Then, the approximate calculation model errors of traditional vertical curve elevation is quantitatively analyzed, and their on the smoothness effect is qualitatively analyzed. A more precision model of calculating vertical curve elevation is established. Finally, the earth curvature effect on track spatial mileage is qualitatively and quantitatively analyzed. A rigorous conversion model between track spatial mileage and construction horizontal mileage is established. The accuracy of established model is validated by an example in some dedicated passenger line (DK19+406~DK56+435).The experimental results show that the easement curve coordinate series expansion at least take the first two in order to meet the coordinate millimeter positioning accuracy requirement. The numerical integration method can be suitable for establishing the general unified conversion model between coordinate and mileage for railway central line, and5node Gauss-Legendre formulas can meet the accuracy requirement of coordinate calculation for any combination of railway alignment. The method of normal vertical distance reaching with constraints can avoid the manual intervention and multi-value problem in iterative solution. The mileage of center pile and side pile may be automatically computed by program based on their coordinate. Track spatial mileage may be used as index for calculating the central line coordinate, and finding track diseases, which can effectively improve the efficiency of railway operation and maintenance. These conclusions would have some practical reference value on railway digital construction and maintenance management.