# RAILWAY TRACK REPRESENTATION IN MATHEMATICAL MODEL OF VEHICLES MOVEMENT

## Authors

• M. B. Kurhan Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Ukraine
• D. M. Kurhan Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Ukraine

## Keywords:

railway track, interaction of track and rolling stock, railway track model, track stiffness, track dissipation, dynamic track deflection, passenger traffic

## Abstract

Purpose. The tasks of modeling the interaction of track and rolling stock are basic ones for most areas of mo-dern scientific research of railway transport. The compilation of the model by the principle of Lagrange d'Alembert has found a very wide application for solving the problems of rolling stock dynamics. Representation of the railway track in the model of crew movement can be implemented in several ways, which, among other things, will differ in detail. The purpose of this work is to create a methodology for representing the railway track in mathematical mo-dels of interaction with rolling stock and obtaining practical results for different characteristics and design of the track and the level of maximum speed. Methodology. The problem consists of determining such characteristics of the path as the reduced mass, the stiffness coefficient, and the dissipation coefficient. As a tool for solving this problem it was used the model of the stress-strain behavior of the railway track based on the joint use of the elastic wave propagation equations to describe the geometry of the outline of the part of the system space that is involved in the interaction at a given time and the equations of dynamic equilibrium of its deformation. This makes it possible to take into account the dynamics of the deflection of the under-rail base, which is especially important for the conditions of passenger traffic, which can be carried out at high speed. Findings. Theoretically justified stiffness and dissipation coefficients of the railway track for calculating the dynamics of rolling stock in modern models based on systems of equations in accordance with the Lagrange d'Alembert principle are obtained. The established va-lues, in contrast to those given in other sources, have a reasonable dependence on the design of the path and the speed of movement. Originality. The approaches of railroad track representation in models of rolling stock described by systems of equations by the Lagrange-d'Alembert principle are expanded. A method for determining the characteristics of the railway track for such models is developed based on the results of variant calculations of the dynamic deflection of the rail from the passage of the wheel. Practical value. The values of the stiffness and dissipation coefficients of the railway track are obtained depending on the design and speed of motion for practical use in appropriate models of interaction between track and rolling stock.

## Author Biographies

### M. B. Kurhan, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan

Dep. «Roads Design and Construction», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel +38 (056) 373 15 48, e-mail kunibor@gmail.com

### D. M. Kurhan, Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan

Dep. «Track and Track Facilities», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipro, Ukraine, 49010, tel. +38 (056) 373 15 42, e-mail kurhan.d@gmail.com

## References

Vershinskiy, S. V., Danilov, V. N., & Chelnokov, I. I. (1972). Dinamika vagona. Moscow: Transport. (in Russian)

Danilenko, E. I. (2010). Zaliznychna koliia [Textbook] (Vol. 2). Kyiv: Inpres. (in Ukrainian)

Darenskiy, A. N., & Klimenko, A. V. (2012). Modelirovaniye vzaimodeystviya puti i podvizhnogo sostava pri diskretnom podrelsovom osnovanii v zone relsovykh stykov. Informacijno-kerujuchi systemy na zaliznychnomu transporti, 4 (101), 15-22. (in Russian)

Kurhan, M., Kurhan, D., & Khmelevska, N. (2017). Pidhotovka kolii dlia pidvyshchennia shvydkosti rukhu poizdiv. Ukrainska zaliznytsia, 9-10 (51-52), 14-21. (in Ukrainian)

Kurhan, M. B., & Kurhan, D. M. (2016). Teoretychni osnovy vprovadzhennia vysokoshvydkisnoho rukhu poizdiv v Ukraini [Monograph]. Dnipro: Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan. (in Ukrainian)

Connolly, D. P., & Forde, M. C. (2015). Use of Conventional Site Investigation Parameters to Calculate Critical Velocity of Trains from Rayleigh Waves. Transportation Research Record: Journal of the Transportation Research Board, 2476, 32-36. doi:10.3141/2476-05

Kouroussis, G., Vogiatzis, K. E., & Connolly, D. P. (2017). A combined numerical/experimental prediction method for urban railway vibration. Soil Dynamics and Earthquake Engineering, 97, 377-386. doi:10.1016/j.soildyn.2017.03.030

Kurhan, D. M. (2015). Features of perception of loading elements of the railway track at high speeds of the movement. Science and Transport Progress, 2 (56), 136-145. doi:10.15802/stp2015/42172

Meli, E., & Ridolfi, A. (2015). An innovative wheel–rail contact model for railway vehicles under degraded adhesion conditions. Multibody System Dynamics, 33 (3), 285-313. doi:10.1007/s11044-013-9405-4

Fisher, S., Eller, B., Kada, Z., & Németh, A. (2015). Railway Construction. Győr: Universitas-Győr Nonprofit Kft.

Fernández Ruiz, J., Costa, P. A., Calçada, R., Medina Rodríguez, L., & Colaço, A. (2016). Study of ground vibrations induced by railway traffic in a 3D FEM model formulated in the time domain: experimental validation. Structure and Infrastructure Engineering, 13 (5), 652-664. doi:10.1080/15732479.2016.1172649

2017-12-13

## How to Cite

Kurhan, M. B., & Kurhan, D. M. (2017). RAILWAY TRACK REPRESENTATION IN MATHEMATICAL MODEL OF VEHICLES MOVEMENT. Science and Transport Progress, (6(72), 40–48. https://doi.org/10.15802/stp2017/118380