Dynamic finite element simulation of wheel–rail contact response for the curved track case
Abstract
The wheel–rail interaction will be intensified on account of the complexity of the wheel–rail contact geometry on a curved track. It also may become more complicated and/or have significant difference as the train speed increases, since the dynamic effects cannot be ignored then. In this study, based on explicit Finite Element (FE) software LS-DYNA 971, a Three-Dimensional (3D) elastic-plastic FE model was built to simulate the dynamic wheel–rail contact behaviour of curve negotiating, where the superelevation and roll angle as well as the strain rate effect were considered. The evolution of contact patch and pressure, wheel–rail contact force, the stress/strain state and the acceleration of the axle were employed to examine the wheel–rail transient dynamic response. Furthermore, the influences of axle load, curve radius and strain rate effect were also discussed. It is found that the maximum vertical contact force, contact pressure, stress and strain on the curved track increase with the decreasing curve radius, and they increase with the increasing axle load except for lateral contact force. The wheel–rail dynamic responses on the curved track are significantly enhanced compared to the straight track. Moreover, the strain rate effect can enhance von-Mises stress and contact pressure, suppress the plastic deformation of the rail and wheel, but it has little effect on the vertical and lateral contact forces and stable acceleration of axle. The Rate-Sensitive Factors (RSF) of the wheel and rail on the curved track are weaker than those on the straight track. These findings will be very helpful to study the competitive relationship between the rolling contact fatigue and wear, as well as the crack initiation and propagation problem.
Keyword : wheel–rail interaction, curved track, dynamic response, strain-rate effect, finite element analysis
How to Cite
Zhou, X., Jing, L., & Ma, X. (2022). Dynamic finite element simulation of wheel–rail contact response for the curved track case. Transport, 37(5), 357–372. https://doi.org/10.3846/transport.2022.18292
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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BS EN 13104:2009+A1:2010. Railway Applications. Wheelsets and Bogies. Powered Axles. Design Method.
Dailydka, S.; Lingaitis, L. P.; Myamlin, S.; Prichodko, V. 2008. Modelling the interaction between railway wheel and rail, Transport 23(3): 236–239. https://doi.org/10.3846/1648-4142.2008.23.236-239
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Han, L.; Jing, L.; Zhao, L. 2018. Finite element analysis of the wheel–rail impact behavior induced by a wheel flat for high-speed trains: The influence of strain rate, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232(4): 990–1004. https://doi.org/10.1177/0954409717704790
Hertz, H. 1882. Ueber die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik 92: 156–171. https://doi.org/10.1515/9783112342404-004 (in German).
Jing, L.; Han, L. 2017. Further study on the wheel–rail impact response induced by a single wheel flat: the coupling effect of strain rate and thermal stress, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 55(12): 1946–1972. https://doi.org/10.1080/00423114.2017.1340651
Jing, L.; Han, L.; Zhao, L.; Zhang, Y. 2016. The dynamic tensile behavior of railway wheel steel at high strain rates, Journal of Materials Engineering and Performance 25(11): 4959–4966. https://doi.org/10.1007/s11665-016-2359-y
Jing, L.; Su, X.; Zhao, L. 2017. The dynamic compressive behavior and constitutive modeling of D1 railway wheel steel over a wide range of strain rates and temperatures, Results in Physics 7: 1452–1461. https://doi.org/10.1016/j.rinp.2017.04.015
Jing, L.; Liu, Z.; Liu, K. 2022a. A mathematically-based study of the random wheel-rail contact irregularity by wheel out-of-roundness, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 60(1): 335–370. https://doi.org/10.1080/00423114.2020.1815809
Jing, L.; Su, X.; Feng, C.; Zhou, L. 2022b. Strain-rate dependent tensile behavior of railway wheel/rail steels with equivalent fatigue damage: experiment and constitutive modeling, Engineering Fracture Mechanics 275: 108839. https://doi.org/10.1016/j.engfracmech.2022.108839
Kaewunruen, S.; Ngamkhanong, C.; Liu, X. 2019. Spectro-temporal responses of curved railway tracks with variable radii of arc curves, International Journal of Structural Stability and Dynamics 19(4): 1950044. https://doi.org/10.1142/S0219455419500445
Kalker, J. J. 1967. On the Rolling Contact of Two Elastic Bodies in the Presence of Dry Friction. PHD thesis, Delft University of Technology, Netherlands. 170 p. Available from Internet: https://repository.tudelft.nl/islandora/object/uuid%3Aaa44829b-c75c-4abd-9a03-fec17e121132
Kalker, J. J. 1973. Simplified theory of rolling contact, Delft Progress Report Series C 1(1): 1–10.
Liu, P.-F.; Zhai, W.-M.; Wang, K.-Y.; Feng, Q.-B.; Chen, Z.-G. 2018a. Theoretical and experimental study on vertical dynamic characteristics of six-axle heavy-haul locomotive on curve, Transport 33(1): 291–301. https://doi.org/10.3846/16484142.2016.1180638
Liu, W. F.; Du, L.; Liu, W. N.; Thompson, D. J. 2018b. Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232(7): 1932–1950. https://doi.org/10.1177/0954409718754470
Ma, W.; Xu, Z.; Luo, S.; Song, R. 2015. Influence of wheel axle stiffness character to the wheel/rail dynamic contact on the straight track, Transport 30(1): 24–32. https://doi.org/10.3846/16484142.2013.819035
Ma, X.; Jing, L.; Han, L. 2018. A computational simulation study on the dynamic response of high-speed wheel–rail system in rolling contact, Advances in Mechanical Engineering 10(11): 1–11. https://doi.org/10.1177/1687814018809215
Matsumoto, A.; Sato, Y.; Nakata, M.; Tanimoto, M.; Qi, K. 1996. Wheel–rail contact mechanics at full scale on the test stand, Wear 191(1–2): 101–106. https://doi.org/10.1016/0043-1648(95)06710-8
Matsumoto, A.; Sato, Y.; Ohno, H.; Mizuma, T.; Suda, Y.; Tanimoto, M.; Oka, Y. 2006. Study on curving performance of railway bogies by using full-scale stand test, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 44: 862–873. https://doi.org/10.1080/00423110600907402
Mosayebi, S.-A.; Zakeri, J.-A.; Esmaeili, M. 2016. Some aspects of support stiffness effects on dynamic ballasted railway tracks, Periodica Polytechnica Civil Engineering 60(3): 427–436. https://doi.org/10.3311/PPci.7933
Mosayebi, S.-A.; Zakeri, J.-A.; Esmaeili, M. 2017. Vehicle/track dynamic interaction considering developed railway substructure models, Structural Engineering and Mechanics 61(6): 775–784. https://doi.org/10.12989/sem.2017.61.6.775
Newland, D. E. 1968. Steering characteristics of bogie, Railway Gazette 124: 745–750.
Rezvani, M. A.; Owhadi, A.; Niksai, F. 2009. The effect of worn profile on wear progress of rail vehicle steel wheels over curved tracks, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 47(3): 325–342. https://doi.org/10.1080/00423110802108957
Sladkowski, A.; Sitarz, M. 2005. Analysis of wheel–rail interaction using FE software, Wear 258(7–8): 1217–1223. https://doi.org/10.1016/j.wear.2004.03.032
Su, X.; Zhou, L.; Jing, L.; Wang, H. 2020. Experimental investigation and constitutive description of railway wheel/rail steels under medium-strain-rate tensile loading, Journal of Materials Engineering and Performance 29(3): 2015–2025. https://doi.org/10.1007/s11665-020-04720-1
TB 10621-2014. Code for Design of High speed Railway. Chinese Standard (in Chinese).
Telliskivi, T.; Olofsson, U. 2001. Contact mechanics analysis of measured wheel–rail profiles using the finite element method, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 215(2): 65–72. https://doi.org/10.1243/0954409011531404
Vo, K. D.; Tieu, A. K.; Zhu, H. T.; Kosasih, P. B. 2014. A 3D dynamic model to investigate wheel–rail contact under high and low adhesion, International Journal of Mechanical Sciences 85: 63–75. https://doi.org/10.1016/j.ijmecsci.2014.05.007
Vo, K. D.; Zhu, H. T.; Tieu, A. K.; Kosasih, P. B. 2015. FE method to predict damage formation on curved track for various worn status of wheel/rail profiles, Wear 322–323: 61–75. https://doi.org/10.1016/j.wear.2014.10.015
Wang, K.; Huang, C.; Zhai, W.; Liu, P.; Wang, S. 2014. Progress on wheel-rail dynamic performance of railway curve negotiation, Journal of Traffic and Transportation Engineering 1(3): 209–220. https://doi.org/10.1016/S2095-7564(15)30104-5
Wang, W. J.; Guo, J.; Liu, Q. Y.; Zhu, M. H.; Zhou, Z. R. 2009. Study on relationship between oblique fatigue crack and rail wear in curve track and prevention, Wear 267(1–4): 540–544. https://doi.org/10.1016/j.wear.2008.12.100
Yang, Z.; Li, Z.; Dollevoet, R. 2016. Modelling of non-steady-state transition from single-point to two-point rolling contact, Tribology International 101: 152–163. https://doi.org/10.1016/j.triboint.2016.04.023
Zakeri, J. A.; Tajalli, M. R. 2018. Comparison of linear and nonlinear behavior of track elements in contact-impact models, Periodica Polytechnica Civil Engineering 62(4): 963–970. https://doi.org/10.3311/PPci.12058
Zboiński, K. 1998. Dynamical investigation of railway vehicles on a curved track, European Journal of Mechanics – A/Solids 17(6): 1001–1020. https://doi.org/10.1016/S0997-7538(98)90506-X
Zhai, W.; Wang, K.; Cai, C. 2009. Fundamentals of vehicle–track coupled dynamics, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 47(11): 1349–1376. https://doi.org/10.1080/00423110802621561
Zhao, X.; Li, Z. 2011. The solution of frictional wheel–rail rolling contact with a 3D transient finite element model: validation and error analysis, Wear 271(1–2): 444–452. https://doi.org/10.1016/j.wear.2010.10.007
Zhou, X.; Wang, J.; Jing, L. 2022. Coupling effects of strain rate and fatigue damage on wheel-rail rolling contact behaviour: a dynamic finite element simulation, International Journal of Rail Transportation 1–22. https://doi.org/10.1080/23248378.2022.2083711
BS EN 13104:2009+A1:2010. Railway Applications. Wheelsets and Bogies. Powered Axles. Design Method.
Dailydka, S.; Lingaitis, L. P.; Myamlin, S.; Prichodko, V. 2008. Modelling the interaction between railway wheel and rail, Transport 23(3): 236–239. https://doi.org/10.3846/1648-4142.2008.23.236-239
Elkins, J. A.; Gostling, R. J. 1977. A general quasi-static curving theory for railway vehicles, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 6(2–3): 100–106. https://doi.org/10.1080/00423117708968515
Han, L.; Jing, L.; Zhao, L. 2018. Finite element analysis of the wheel–rail impact behavior induced by a wheel flat for high-speed trains: The influence of strain rate, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232(4): 990–1004. https://doi.org/10.1177/0954409717704790
Hertz, H. 1882. Ueber die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik 92: 156–171. https://doi.org/10.1515/9783112342404-004 (in German).
Jing, L.; Han, L. 2017. Further study on the wheel–rail impact response induced by a single wheel flat: the coupling effect of strain rate and thermal stress, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 55(12): 1946–1972. https://doi.org/10.1080/00423114.2017.1340651
Jing, L.; Han, L.; Zhao, L.; Zhang, Y. 2016. The dynamic tensile behavior of railway wheel steel at high strain rates, Journal of Materials Engineering and Performance 25(11): 4959–4966. https://doi.org/10.1007/s11665-016-2359-y
Jing, L.; Su, X.; Zhao, L. 2017. The dynamic compressive behavior and constitutive modeling of D1 railway wheel steel over a wide range of strain rates and temperatures, Results in Physics 7: 1452–1461. https://doi.org/10.1016/j.rinp.2017.04.015
Jing, L.; Liu, Z.; Liu, K. 2022a. A mathematically-based study of the random wheel-rail contact irregularity by wheel out-of-roundness, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 60(1): 335–370. https://doi.org/10.1080/00423114.2020.1815809
Jing, L.; Su, X.; Feng, C.; Zhou, L. 2022b. Strain-rate dependent tensile behavior of railway wheel/rail steels with equivalent fatigue damage: experiment and constitutive modeling, Engineering Fracture Mechanics 275: 108839. https://doi.org/10.1016/j.engfracmech.2022.108839
Kaewunruen, S.; Ngamkhanong, C.; Liu, X. 2019. Spectro-temporal responses of curved railway tracks with variable radii of arc curves, International Journal of Structural Stability and Dynamics 19(4): 1950044. https://doi.org/10.1142/S0219455419500445
Kalker, J. J. 1967. On the Rolling Contact of Two Elastic Bodies in the Presence of Dry Friction. PHD thesis, Delft University of Technology, Netherlands. 170 p. Available from Internet: https://repository.tudelft.nl/islandora/object/uuid%3Aaa44829b-c75c-4abd-9a03-fec17e121132
Kalker, J. J. 1973. Simplified theory of rolling contact, Delft Progress Report Series C 1(1): 1–10.
Liu, P.-F.; Zhai, W.-M.; Wang, K.-Y.; Feng, Q.-B.; Chen, Z.-G. 2018a. Theoretical and experimental study on vertical dynamic characteristics of six-axle heavy-haul locomotive on curve, Transport 33(1): 291–301. https://doi.org/10.3846/16484142.2016.1180638
Liu, W. F.; Du, L.; Liu, W. N.; Thompson, D. J. 2018b. Dynamic response of a curved railway track subjected to harmonic loads based on the periodic structure theory, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232(7): 1932–1950. https://doi.org/10.1177/0954409718754470
Ma, W.; Xu, Z.; Luo, S.; Song, R. 2015. Influence of wheel axle stiffness character to the wheel/rail dynamic contact on the straight track, Transport 30(1): 24–32. https://doi.org/10.3846/16484142.2013.819035
Ma, X.; Jing, L.; Han, L. 2018. A computational simulation study on the dynamic response of high-speed wheel–rail system in rolling contact, Advances in Mechanical Engineering 10(11): 1–11. https://doi.org/10.1177/1687814018809215
Matsumoto, A.; Sato, Y.; Nakata, M.; Tanimoto, M.; Qi, K. 1996. Wheel–rail contact mechanics at full scale on the test stand, Wear 191(1–2): 101–106. https://doi.org/10.1016/0043-1648(95)06710-8
Matsumoto, A.; Sato, Y.; Ohno, H.; Mizuma, T.; Suda, Y.; Tanimoto, M.; Oka, Y. 2006. Study on curving performance of railway bogies by using full-scale stand test, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 44: 862–873. https://doi.org/10.1080/00423110600907402
Mosayebi, S.-A.; Zakeri, J.-A.; Esmaeili, M. 2016. Some aspects of support stiffness effects on dynamic ballasted railway tracks, Periodica Polytechnica Civil Engineering 60(3): 427–436. https://doi.org/10.3311/PPci.7933
Mosayebi, S.-A.; Zakeri, J.-A.; Esmaeili, M. 2017. Vehicle/track dynamic interaction considering developed railway substructure models, Structural Engineering and Mechanics 61(6): 775–784. https://doi.org/10.12989/sem.2017.61.6.775
Newland, D. E. 1968. Steering characteristics of bogie, Railway Gazette 124: 745–750.
Rezvani, M. A.; Owhadi, A.; Niksai, F. 2009. The effect of worn profile on wear progress of rail vehicle steel wheels over curved tracks, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 47(3): 325–342. https://doi.org/10.1080/00423110802108957
Sladkowski, A.; Sitarz, M. 2005. Analysis of wheel–rail interaction using FE software, Wear 258(7–8): 1217–1223. https://doi.org/10.1016/j.wear.2004.03.032
Su, X.; Zhou, L.; Jing, L.; Wang, H. 2020. Experimental investigation and constitutive description of railway wheel/rail steels under medium-strain-rate tensile loading, Journal of Materials Engineering and Performance 29(3): 2015–2025. https://doi.org/10.1007/s11665-020-04720-1
TB 10621-2014. Code for Design of High speed Railway. Chinese Standard (in Chinese).
Telliskivi, T.; Olofsson, U. 2001. Contact mechanics analysis of measured wheel–rail profiles using the finite element method, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 215(2): 65–72. https://doi.org/10.1243/0954409011531404
Vo, K. D.; Tieu, A. K.; Zhu, H. T.; Kosasih, P. B. 2014. A 3D dynamic model to investigate wheel–rail contact under high and low adhesion, International Journal of Mechanical Sciences 85: 63–75. https://doi.org/10.1016/j.ijmecsci.2014.05.007
Vo, K. D.; Zhu, H. T.; Tieu, A. K.; Kosasih, P. B. 2015. FE method to predict damage formation on curved track for various worn status of wheel/rail profiles, Wear 322–323: 61–75. https://doi.org/10.1016/j.wear.2014.10.015
Wang, K.; Huang, C.; Zhai, W.; Liu, P.; Wang, S. 2014. Progress on wheel-rail dynamic performance of railway curve negotiation, Journal of Traffic and Transportation Engineering 1(3): 209–220. https://doi.org/10.1016/S2095-7564(15)30104-5
Wang, W. J.; Guo, J.; Liu, Q. Y.; Zhu, M. H.; Zhou, Z. R. 2009. Study on relationship between oblique fatigue crack and rail wear in curve track and prevention, Wear 267(1–4): 540–544. https://doi.org/10.1016/j.wear.2008.12.100
Yang, Z.; Li, Z.; Dollevoet, R. 2016. Modelling of non-steady-state transition from single-point to two-point rolling contact, Tribology International 101: 152–163. https://doi.org/10.1016/j.triboint.2016.04.023
Zakeri, J. A.; Tajalli, M. R. 2018. Comparison of linear and nonlinear behavior of track elements in contact-impact models, Periodica Polytechnica Civil Engineering 62(4): 963–970. https://doi.org/10.3311/PPci.12058
Zboiński, K. 1998. Dynamical investigation of railway vehicles on a curved track, European Journal of Mechanics – A/Solids 17(6): 1001–1020. https://doi.org/10.1016/S0997-7538(98)90506-X
Zhai, W.; Wang, K.; Cai, C. 2009. Fundamentals of vehicle–track coupled dynamics, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 47(11): 1349–1376. https://doi.org/10.1080/00423110802621561
Zhao, X.; Li, Z. 2011. The solution of frictional wheel–rail rolling contact with a 3D transient finite element model: validation and error analysis, Wear 271(1–2): 444–452. https://doi.org/10.1016/j.wear.2010.10.007
Zhou, X.; Wang, J.; Jing, L. 2022. Coupling effects of strain rate and fatigue damage on wheel-rail rolling contact behaviour: a dynamic finite element simulation, International Journal of Rail Transportation 1–22. https://doi.org/10.1080/23248378.2022.2083711