Оптимізація розміщення точок умовної реперної мережі для кривих ділянок залізниць

Abstract

UA: Контроль геодезичних параметрів дуже важливий для безпеки руху на залізниці. Такий контроль необхідно проводити регулярно через відхилення осі колії внаслідок руху поїздів. Метою статті є розроблення математичного обґрунтування розміщення залізничних реперів для створення «власної» умовної реперної мережі залізниці. Ці постійні репери є основними точками як для етапу будівництва, так і етапу експлуатації. Описано метод і отримано координати кривої від будь-якої точки умовної реперної мережі залізниці.

EN: Railway facilities are responsible and complex structures related to the safety of passenger traffic and cargo transportation. To ensure the reliability of all systems, the railway track needs continual control of its geometric parameters. Railways require high accuracy of survey and monitoring both at the construction stage and at the operation stage. Such control can be carried out using control points of the geodetic benchmark network. These control points must be located near the railway track to provide it in the design position and in proper working condition. That is why the development of "own" railways benchmark network is topical. The purpose of this article is to create a mathematical basis for calculating the locations of own repers near the railway. These benchmarks will be control points that will be used by trackoperation stations, track machine stations, engineering and geodetic departments, track-surveying stations, services and departments, as well as project and construction organizations during research, design, operation, repair, reconstruction, or new construction. This will keep the track in good condition and be used for leveling the track during repair work. The paper considers the calculation method for the placement of control points of the conditional benchmark network on the curved section of the railway. The novelty is the usage of the mean-value theorem of integral calculus to calculate the coordinates of the curve independently of the national geodetic network. The creation of "own" conditional benchmark network allows railways to perform the pegging of lines and curves regardless of the presence or remoteness of control points of the local or state geodetic network. After choosing a conditional benchmark, the coordinates of the railway curve, which is divided into 5 parts, were calculated. It is shown that the number of points does not affect the accuracy of determining the coordinates. Thus, fewer rappers can be dispensed, and the speed of the pegging will increase. The polar coordinates for the two polar distances from the conventional benchmark have been determined. It is established that the use of the mean-value theorem of the integral calculus to find the coordinates of a point gives more accurate data, since this method does not involve replacing the arc with a chord. The described method of determining polar coordinates from any point of one's own network of conditional benchmarks is of practical importance. After deviating the axis of the track from the movement of trains, maintenance workers can put it back without additional calculation.