Research On Calculation Method Of Complex Curve Of Railway Lines

The curve is an indispensable part of the railway line and has always been the focus of research by domestic and foreign experts and scholars.The design of complex curve is very important in the section with relatively complicated engineering conditions.It can better adapt to changes in the terrain,and meet the requirements of the curve in the specification,the safety requirements during train operation and the passenger comfort requirements.Therefore,it is very necessary to study the calculation method of the railway line complex curve.Through the analysis and calculation of the complex curve,the railway line can be better connected in the curve section.The article starts with the complex curve in practical engineering problems.Compiled by the domestic and foreign existing research situation analysis and on-site engineering data,a special kind of situation in the calculation of complex curve connection is concluded,it is called double-curve and the same-direction complex curve.In the study of the basic mathematical model of the same-direction complex curve,the problems that need attention in the calculation of complex curve connection are mastered.After that,the curve is fitted with the least square method to obtain the relevant information.Finally,based on the theoretical and practical connections,a mathematical calculation model of double-curve and the same-direction complex curve is established,and the details of all complex curves are classified.After the establishment of the mathematical calculation model,this paper analyzes the characteristics of the basic easement curves used for the connection transition of the complex curves.Starting from the role of the basic relaxation curve and the determination of the length of the relaxation curve,the pattern of the basic relaxation curve and the curve elements are analyzed in depth,and the multiple relationship between the length of the transition curve and the radius of the connected curve is obtained.It is found that the basic transition curve has the critical control condition of the abrupt change point when the length of the transition curve is longer.The theoretical basis for the transition of complex curves is proposed.After analyzing the setting criteria of the basic transition curve and the change of curvature,it is proposed that the tangent coincidence principle is a necessary condition for the successful connection transition of the complex curve.Through the theoretical analysis of complex curve connection,the calculation method of complex curve is emphasized.Firstly,according to the classification of the connection of the complex curve,the detailed descriptions of the calculation of the two basic cases of the same-direction complex curve and the double-curve and the same-direction complex curve are given.The complement curve method is proposed to solve the problems.Finally,thederivation method for the calculation formula of the coordinate equation in the calculation of the complex curve is given.From the determination of boundary conditions to the establishment of differential equations of curvature and then to the application of integral methods,the computational figures are analyzed and summarized,the overall calculation process is more complete.Finally,this paper applies the theoretical knowledge of the analysis to practical engineering problems.Taking the complex-curve connection of the small-radius group section of the Longhai Line as an example,detailed decomposition calculations are performed,and the lengthy calculation process is completed with FORTAN programming,it makes calculation more concise.Through verification and checking,the study of the calculation method of the complex curve is finally completed.During the verification process,the correctness of the aforementioned theoretical analysis and its effectiveness and feasibility in solving practical engineering problems are also confirmed,which has certain practical significance.