A new coordinate system for Longitudinal Train Dynamics simulations

Qing Wu


This paper presents a new coordinate system for whole-trip Longitudinal Train Dynamics (LTD) simulations. The new coordinate system integrate the concepts of both inertial and non-inertial coordinate systems which are called the global coordinate system and the local coordinate system respectively in this paper. The global coordinate system is used to describe vehicle positions, velocities, and accelerations on the track. The local coordinate system is a movable coordinate system attached on the train; it is designed to determine draft gear deflections only. The purpose of the new coordinate system is to decrease the truncation errors for whole-trip LTD simulations that have very long simulated train trips, for example 600 km. Results in this paper have demonstrated the effectiveness of the new non-inertial coordinate system. Simulation results provide the confidence to study very long train trips. The new coordinate system can maintain the computational precision and reduce the computational time by 8.6%.

Full Text:



‎[1]‎ Cantone L. TrainDy: The new Union Internationale ‎Des Chemins de Fer software for freight train ‎interoperability. J Rail Rapid Transit. 2011; 225(1): ‎‎57-70. ‎

‎[2]‎ Klauser PE. Advances in the simulation of long train ‎longitudinal dynamics. Vehicle System Dynamics. ‎‎1988; 17(s1):210-214. ‎

‎[3]‎ Wu Q, Luo S, Qu T, Yang X. Comparisons of draft ‎gear damping mechanisms. Vehicle System Dynamics ‎‎2017; 55(4): 501-516. ‎

‎[4]‎ Shabana AA, Ding L, Aboubakr AK. Use of the ‎non-inertial coordinates in the analysis of train ‎longitudinal forces. J Comput Nonlinear Dyn. 2011; ‎‎7(1): 011001/1–10.‎

‎[5]‎ Andersen DR, Booth GF, Vithani AR, et al. Train ‎Energy and Dynamics Simulator (TEDS)-A state-of-‎the-art longitudinal train dynamics simulator. Paper ‎presented at: the ASME 2012 Rail Transportation ‎Division Fall Technical Conference (RTDF2012), ‎October 16-17, 2012, Omaha NE. ‎

‎[6]‎ Wu Q, Cole C, Luo S, Spiryagin M. A review of dy-‎namics modelling of friction draft gear. Vehicle ‎System Dynamics. 2014; 52(6):733-758. ‎

‎[7]‎ Oprea RA, Cruceanu C, Spiroiu MA. Alternative ‎friction models for braking train dynamics, Vehicle ‎System Dynamics. 2013; 51(3):460–480.‎

‎[8]‎ Barbosa RS. Longitudinal train dynamics [Masters ‎Thesis]. Sao Paulo, (Brazil): State University of ‎Campinas; 1993. Portuguese.‎

‎[9]‎ Zobory I, Bekefi E. On real-time simulation of the ‎longitudinal dynamics of trains on a specified railway ‎line. Periodica Polytechnica Ser Transp Eng. 1995; ‎‎23(1):3–18.‎

‎[10]‎ Wu Q, Spiryagin M, Cole C. Longitudinal train dy-‎namics: an overview. Vehicle System Dynamics 2016; ‎‎54(12): 1688-1714. ‎

‎[11]‎ Myamlin SV, Naumenko NE, Nikitchenko AA. [The ‎construction of a mathematical model of friction ‎polymer absorbing device]. J Dnipropetrovsk National ‎University of Railway Transport named after ‎Academician V Lazaryan. 2008; (4):25–33. Russian.‎

‎[12]‎ Cole C, Spiryagin M, Bosomworth C. Examining ‎longitudinal train dynamics in ore car tipplers. Vehicle ‎System Dynamics. 2017; 55(4): 534-551. ‎

‎[13]‎ Wu Q, Cole C, Spiryagin M. Parallel computing ena-‎bles whole-trip train dynamics optimization. Journal of ‎Computational and Nonlinear Dynamics, 2016; 11(4): ‎‎044503– 044503-4. ‎

‎[14]‎ Chang C, Guo G, Wang J, Ma Y. Study on longitudi-‎nal force simulation of heavy-haul train. Vehicle ‎System Dynamics 2017; 55(4): 571-582.‎

‎[15]‎ Wei W, Hu Y, Wu Q, et al. An air brake model for ‎longitudinal train dynamics studies. Vehicle System ‎Dynamics. 2017; 55(4): 517-533. ‎

‎[16]‎ Wu Q, YangX, ColeC, etal. Modelling polymer draft ‎gear. Vehicle System Dynamics. 2016; 54(9): 1208–‎‎1225.‎

‎[17]‎ Cheli F, Di Gialleonardo E, Melzi S. Freight trains ‎dynamics: effect of payload and braking power ‎distribution on coupling forces. 2017; 55(4): 464-479. ‎

‎[18]‎ Bosso N, Zampieri N. Long train simulation using a ‎multibody code. 2017; 55(4): 552-570. ‎

‎[19]‎ Evans J, Berg M. Challenges in simulation of rail ve-‎hicle dynamics, Vehicle System Dynamics, 2009; ‎‎47(8): 1023-1048.‎

‎[20]‎ Kerr K, Blair JR. Simulation of the longitudinal dy-‎namics of a train. Paper presented at: Dynamics of ‎Multibody Systems Symposium, 1977, August 29- ‎September 3, Munich, Germany. ‎

‎[21]‎ Cole C. Longitudinal train dynamics. In: Iwnicki S, ‎editor. Handbook of Railway Vehicle Dynamics. ‎Chapter 9. London: Taylor & Francis; 2006, p.239-278. ‎

‎[22]‎ Witt T, Muller L. Methods for the validation of algo-‎rithms for the simulation of longitudinal dynamics. ‎VehSystDyn. 1999; 33(S): 386-393. ‎

‎[23]‎ Cole C, Spiryagin M, Wu Q, Sun Y. Modelling, ‎simulation and applications of longitudinal train ‎dynamics. VehSystDyn. 2017; ‎http://dx.doi.org/10.1080/00423114.2017.1330484‎

‎[24]‎ Garg VK, Dukkipati RV. Dynamics of railway ‎vehicle systems. Academic Press, 1984, New York, NY.‎

‎[25]‎ Wu Q, Cole C, Spiryagin M, McSweeney. Parallel ‎multiobjective optimisations of draft gear designs. ‎Proceedings of the Institution of Mechanical ‎Engineers, Part F: Journal of Rail and Rapid Transit, ‎‎2017, DOI: 10.1177/0954409717690981‎

‎[26]‎ Spiryagin M, Wu Q, Wolfs P, et al. Comparison of ‎locomotive energy storage systems for heavy-haul ‎operation. International Journal of Rail ‎Transportation, 2017, DOI: ‎‎10.1080/23248378.2017.1325719. ‎

‎[27]‎ Spiryagin M, Wu Q, Cole C. International ‎benchmarking of longitudinal train dynamics ‎simulators: benchmarking questions. Vehicle System ‎Dynamics. 2017; 55(4): 450-463.‎


  • There are currently no refbacks.