Określanie geometrii tras szynowych z wykorzystaniem aproksymacyjnych funkcji sklejanych

Opracowanie skupia się na metodach rozpoznawania geometrii odcinków trasy kolejowej, przeprowadzanego na potrzeby regulacji torów. Wymieniono metody klasyczne z opisem ich ograniczeń, zaproponowano również nowy algorytm, bazujący na skalowalnym wykresie krzywizn, tworzonym w oparciu o aproksymacyjne funkcje sklejane opisujące oś toru. Analizowany nowy typ wykresu różni się od stosowanego powszechnie wykresu krzywizn tym, że pozwala na zredukowanie wrażliwości na błędy pomiarowe i deformacje geometrii toru. Ułatwia także klasyfikowanie poszcze-gólnych odcinków krzywoliniowych tworzących regulowany tor.

The study focuses on methods of recognition of the geometry of the railway sections, carried out for the adjustment of railway tracks. It is proposed a new algorithm, based on scalable curvature graph, created based on the approximating spline functions describing the axis of the track. The article presents the classical method of identifying the geometry, using angle graphs, cant graphs, curvature graphs, and the arrows of the arc graph (Fig. 1, 2, 3), discussing their characteristic features. Emphasis was put on the curvature graph, which allows accurate readings. However this graph is sensitive to measuring errors and deformations of track geometry, making it difficult to perform readings. In addition, although greater in comparison with other methods of precision, with his help differentiate segments of the small differences in curvature (segmental arcs) can raise doubts. To reduce these limitations proposed new way of creating a scalable curvature graph (chapter 3), which is determined to track described by the approximating spline functions with a given damping ratio distortion. In order to present the possibility of the method, constructed with the help of it curvature graphs for two independent sections of the track, comparing them to the classical curvature graphs (chapter 4). Towards them, the new method allows to reduce the sensitivity of the measurement errors and deformations of track geometry (Figures 8 and 9), facilitating the readings. It also increases the precision of the demarcation of segments of the small differences in curvature (Figures 10 and 11).