Train–track coupled dynamics analysis: system spatial variation on geometry, physics and mechanics

Abstract

This paper aims to clarify the influence of system spatial variability on train–track interaction from perspectives of stochastic analysis and statistics. Considering the spatial randomness of system properties in geometry, physics and mechanics, the primary work is therefore simulating the uncertainties realistically, representatively and efficiently. With regard to the track irregularity simulation, a model is newly developed to obtain random sample sets of track irregularities by transforming its power spectral density function into the equivalent track quality index for representation based on the discrete Parseval theorem, where the correlation between various types of track irregularities is accounted for. To statistically clarify the uncertainty of track properties in physics and mechanics in space, a model combining discrete element method and finite element method is developed to obtain the spatially varied track parametric characteristics, e.g. track stiffness and density, through which the highly expensive experiments in situ can be avoided. Finally a train–track stochastic analysis model is formulated by integrating the system uncertainties into the dynamics model. Numerical examples have validated the accuracy and efficiency of this model and illustrated the effects of system spatial variability on train–track vibrations comprehensively.

Keywords

Railway engineering / Stochastic dynamic analysis / Train–track interaction / Vehicle–track coupled dynamics / Track irregularities / Longitudinal inhomogeneity

References

[1] Garg VK Dukkipati RV. Dynamics of railway vehicle systems, 1984 Ontario Academic Press

[2] EN14363:2005 (2005) Railway applications-testing for the acceptance of running characteristics of railway vehicles-testing of running behavior and stationary tests. CEN, Brussels, Beligium

[3] Xu L Zhai W Gao J. A probabilistic model for track random irregularities in vehicle/track coupled dynamics. Appl Math Model, 2017 51 145-158

[4] Perrin G Soize C Duhamel D Fünfschilling C. Track irregularities stochastic modelling. Probab Eng Mech, 2013 34 123-130

[5] Náprstek J Frýba L. Stochastic modelling of track and its substructure. Veh Sys Dy, 1995 24 sup 1 297-310

[6] Fröhling RD Scheffel H Ebersöhn W. The vertical dynamic response of a rail vehicle caused by track stiffness variations along the track. Veh Syst Dyn, 1996 25 Suppl 175-187

[7] Oscarsson J Nielsen JCO. Dynamic train/track interaction with state-dependent track properties, technical report F215, 1999 Göteborg, Sweden Department of Solid Mechanics, Chalmers University of Technology

[8] Oscarsson J. Dynamic train–track-ballast interaction with unevenly distributed track properties. Veh Syst Dyn, 2002 37 1 385-396

[9] Nielsen JCO Oscarsson J. Simulation of dynamic train–track interaction with state-dependent track properties. J Sound Vib, 2004 275 3–5 515-532

[10] Andersen L Øren S Nielsen RK. Vibrations of a track caused by variation of the foundation stiffness. Probab Eng Mech, 2003 18 171-184

[11] Wu TX Thompson DJ. Influence of random sleeper spacing and ballast stiffness on the vibration behaviour of railway track. Acta Acust United Acust, 2000 86 2 313-321

[12] Dahlberg T. Railway track stiffness variations: consequences and countermeasures. Int J Civil Eng, 2010 8 1 1-12

[13] Sañudo R dell’Olio L Casado JA Carrascal IA Diego S. Track transitions in railways: a review. Constr Build Mater, 2016 112 140-157

[14] Nielsen JCO Abrahamsson TJS. Coupling of physical and modal components for analysis of moving non-linear dynamic systems on general beam structures. Int J Numer Meth Eng, 1992 33 9 1843-1859

[15] Yang YB Chang CH Yau JD. An element for analysing vehicle-bridge systems considering vehicle’s pitching effect. Int J Numer Method Eng, 1999 46 1031-1047

[16] Zhai W Han Z Chen Z Ling L Zhu S. train–track-bridge dynamic interaction: a state-of-the-art review. Veh Syst Dyn, 2019 57 7 984-1027

[17] Chen XM Deng X Xu L. A three-dimensional dynamic model for railway vehicle-track interactions. J Comput Nonlinear Dyn, 2018 13 071006

[18] Zhai W. Vehicle-track coupled dynamics theory and applications, 2020 Singapore Springer

[19] Zhai W Wang K Cai C. Fundamentals of vehicle-track coupled dynamics. Veh Syst Dyn, 2009 47 11 1349-1376

[20] Arvidsson T Andersson A Karoumi R. Train running safety on non-ballasted bridges. Int J Rail Transp, 2019 7 1 1-22

[21] Zhao X Li Z. The solution of frictional wheel–rail rolling contact with a 3D transient finite element model: Validation and error analysis. Wear, 2011 271 444-452

[22] Vermeulen PJ Johnson KL. Contact of non-spherical bodies transmitting tangential forces. J Appl Mech, 1964 31 338-340

[23] Sladkowski A Sitarz M. Analysis of wheel–rail interaction using FE Software. Wear, 2005 258 1217-1223

[24] Xu L Zhai W. A three-dimensional dynamic model for train–track interactions. Appl Math Model, 2019 76 443-465

[25] Xu L Yu ZW Shi C. A matrix coupled model for vehicle-slab track-subgrade interactions at 3-D space. Soil Dyn Earthq Eng, 2020 128 105894

[26] Kalker JJ. Survey of wheel–rail rolling contact theory. Veh Syst Dyn, 1979 5 317-358

[27] Vermeulen PJ Johnson KL. Contact of nonspherical elastic bodies transmitting tangential forces. J Appl Mech, 1964 86 338-340

[28] Wen DZ Zhuo RH Ding DJ Zheng H Cheng J Li ZH. Generation of correlated pseudorandom variables in Monte Carlo simulation. Acta Phys Sin, 2012 61 22 220204(in Chinese)

[29] Golub GH Van Loan CF. Matrix computations, 1996 3 Baltimore Johns Hopkins

[30] Press W Flannery B Teukolsky S . Numerical recipes in C: the art of scientific computing, 1992 2 New York Cambridge University Press

[31] Cundall PA Strack ODL. A discrete numerical model for granular assemblies. Geotechnique, 1979 29 1 47-65

[32] Hunt GA (2000) EUROBALT optimises ballasted track, Railway Gazette International: 813–816

[33] Itasca Consulting Group, Inc. (2004) Particle flow code in 2 dimensions, version 3.1, user’s mannual

[34] Zhang X Zhao C Zhai W. Dynamic behavior analysis of high-speed railway ballast under moving vehicle loads using discrete element method. Int J Geomech, 2016 17 7 04016157

[35] Oscarsson J Dahlberg T. Dynamic train track ballast interaction computer models and full scale experiments. Veh Syst Dyn, 1998 29 73-84

[36] Oscarsson J. Dynamic train–track interaction: variability attributable to scatter in the track properties. Veh Syst Dyn, 2002 37 1 59-79

[37] Ma C. Research on evaluation index optimization method of high-speed railway ballasted bed. Railw Stand Des, 2016 60 5 20-24

Funding

the National Natural Science Foundation of China (CN)(11790283)

National Natural Science Foundation of China(51735012)