Analysis of the nonlinear dynamic behavior of longitudinal systems in heavy-haul trains

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Abstract

The payload, coupler slack, and buffer device performance in heavy-haul trains substantially affect their longitudinal dynamic systems under operational conditions. These factors result in the bifurcation of the system, consequently leading to chaos. To study this phenomenon in depth, a two-degrees-of-freedom longitudinal dynamics model of the train is established. The system is analyzed using the fourth-order Runge–Kutta (R-K₄) numerical integration method, incorporating bifurcation diagrams, phase planes, Poincaré mapping, and time-domain analysis to elucidate the trajectory of the system as it transitions into a chaotic state of motion via period-doubling bifurcations and quasi-periodic motions. A comprehensive analysis of the complex nonlinear dynamics of the train’s longitudinal system can establish a theoretical foundation for forecasting and regulating the chaotic motion of the train system.

Keywords

heavy-haul trains / coupler buffer device / periodic motion / bifurcation / chaos

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References

[1] O. P. Yadav, N. S. Vyas, Influence of slack of automatic AAR couplers on longitudinal dynamics and jerk behavior of rail vehicles, Veh. Syst. Dyn., 61 (2023), 2317-2337. https://doi.org/10.1080/00423114.2022.2107546

[2] C. Feng, Cause analysis and prevention of a series of faults in the lower action coupler-lift rod seat of railway freight cars (in Chinese), J. Technol. Wind, 19 (2021), 187-189. https://doi.org/10.19392/j.cnki.1671-7341.202119084

[3] S. Zhao, Failure analysis and solutions of coupler buffer device of railway freight car (in Chinese), Harbin Railway Technol., 04 (2020), 7-8+32.

[4] J. Wang, C. Gong, Analysis and treatment of common faults of coupler buffer device for railway freight cars (in Chinese), J. Technol. Wind, 20 (2019), 174-175. https://doi.org/10.19392/j.cnki.1671-7341.201920149

[5] J. Xu, T. Zhu, M. Yin, C. Wang, S. Xiao, G. Yang, et al., An analytical method for coupler strength of heavy-haul trucks (in Chinese), Mach. Build. Autom., 51 (2022), 29-33. https://doi.org/10.19344/j.cnki.issn1671-5276.2022.02.009

[6] P. Li, T. Zhu, C. Wang, S. Xiao, Nonlinear finite element simulation analysis of coupler strength of heavy haul trucks (in Chinese), Mach. Build. Autom., 50 (2021), 90-94. https://doi.org/10.19344/j.cnki.issn1671-5276.2021.03.023

[7] T. Qin, X. Ren, F. Hu, Y. Liu, N. Ao, Q. Kan, et al., Residual life prediction of coupler yoke of heavy haul railway freight car based on measured load spectrum (in Chinese), Chin. J. Theor. Appl. Mech., 54 (2022), 1830-1838.

[8] X. Tian, T. Zhu, C. Wang, M. Yin, J. Xu, S. Shou, et al., Research on fatigue life of coupler knuckle of railway heavy haul freight car based on equivalent crack method (in Chinese), J. Mech. Strength, 44 (2022), 696-704. https://doi.org/10.16579/j.issn.1001.9669.2022.03.026

[9] M. Yin, Research on Data-Driven Prediction Method of Full Life and Residual Life of Freight Car Couplers (in Chinese) , Master thesis, Southwest Jiaotong University, 2021. https://doi.org/10.27414/d.cnki.gxnju.2021.002143

[10] H. Yang, J. Yuan, Y. Fu, Z. Li, Dynamic characteristics of heavy haul train QKX100 and MT-2 buffer (in Chinese), J. Beijing Univ. Technol., 46 (2020), 1018-1026.

[11] X. Zhao, Research on Dynamic Model of HM-1 Buffer Based on Impact Test (in Chinese) , Master thesis, Dalian Jiaotong University, 2018.

[12] X. Wang, Research on the Modeling of MT-2 Buffer with Compression Speed Characteristics (in Chinese) , Master thesis, Dalian Jiaotong University, 2023.

[13] W. Wei, Y. Hu, Q. Wu, X. Zhao, J. Zhang, Y. Zhang, An air brake model for longitudinal train dynamics studies, Veh. Syst. Dyn., 55 (2017), 517-533. https://doi.org/10.1080/00423114.2016.1254261

[14] O. P. Yadav, N. S. Vyas, The influence of AAR coupler features on estimation of in-train forces, Railway Eng. Sci., 31 (2023), 233-251. https://doi.org/10.1007/S40534-022-00297-8

[15] T. Zhu, J. Zhang, Q. Wu, R. Lv, X. Wang, S. Xiao, et al., Review of the influence of coupler buffer device on the collision safety of rail train (in Chinese), J. Traffic Transp. Eng., 21 (2021), 233-249. https://doi.org/10.19818/j.cnki.1671-1637.2021.01.011

[16] C. Yang, Q. Li, X. Wang, Application of generalized multi-step explicit integration algorithm for nonlinear rail vehicle dynamics (in Chinese), J. Dyn. Control, 18 (2020), 51-55.

[17] Z. Zhang, G. Li, G. Chu, H. Zu, D. Kennedy, Compressed stability analysis of the coupler and buffer system of heavy-haul locomotives, Veh. Syst. Dyn., 53 (2015), 833-855. https://doi.org/10.1080/00423114.2015.1023318

[18] J. Liu, Research on the Influence of Buffer Modeling on Train Longitudinal Dynamics Simulation (in Chinese) , Master thesis, Southwest Jiaotong University, 2019. https://doi.org/10.27414/d.cnki.gxnju.2019.001564

[19] L. Yang, S. Luo, M. Fu, W. Zeng, Numerical simulation of impedance characteristics of friction buffer in service (in Chinese), J. China Railway Soc., 46 (2024), 57-65.

[20] E. D. Ward, R. G. Leonard, Automatic parameter identification applied to a railroad car dynamic draft gear model, J. Dyn. Syst. Meas. Control, 96 (1974), 460-465. https://doi.org/10.1115/1.3426846

[21] Z. Zhang, K. Lv, G. Chu, H. Qi, F. Wang, Research on dynamic simulation method and dynamic performance of 102 type coupler and draft gear for heavy haul locomotive (in Chinese), J. Vibr. Shock, 43 (2024), 12-21+ 59. https://doi.org/10.13465/j.cnki.jvs.2024.02.002

[22] Q. Wu, S. Luo, Z. Xu, W. Ma, Coupler jackknifing and derailments of locomotives on tangent track, Veh. Syst. Dyn., 51 (2013), 1784-1800. https://doi.org/10.1080/00423114.2013.830184

[23] J. Duan, W. Zhou, D. Li, C. Grebogi, Birth of strange nonchaotic attractors in a piecewise linear oscillator, Chaos, 32 (2022), 103106. https://doi.org/10.1063/5.0096959

[24] Z. Wei, Y. Li, T. Kapitaniak, W. Zhang, Analysis of chaos and capsizing of a class of nonlinear ship rolling systems under excitation of random waves, Chaos, 34 (2024), 043106. https://doi.org/10.1063/5.0187362

[25] K. Popp, P. Stelter, Stick-slip vibrations and chaos, Philos. Trans. R. Soc. London, Ser. A, 332 (1990), 89-105. https://doi.org/10.1098/rsta.1990.0102

[26] X. Lv, K. Zhang, X. Zhu, G. Luo, Two-parameter non-smooth bifurcation of a two-degree-of-freedom vibro-impact system, J. Vib. Eng., 36 (2023), 107-115. https://doi.org/10.16385/j.cnki.issn.1004-4523.2023.01.012

[27] O. P. Yadav, S. R. Balaga, N. S. Vyas, Forced vibrations of a spring-dashpot mechanism with dry friction and backlash, Int. J. Non-Linear Mech., 124 (2020), 103500. https://doi.org/10.1016/j.ijnonlinmec.2020.103500

[28] O. P. Yadav, N. S. Vyas, Stick-slips and jerks in an SDOF system with dry friction and clearance, Int. J. Non-Linear Mech., 137 (2021), 103790. https://doi.org/10.1016/j.ijnonlinmec.2021.103790

[29] P. Korondi, J. Halas, K. Samu, A. Bojtos, P. Tamás, Robot Applications , BME MOGI, 2014.

[30] Q. Wu, M. Spiryagin, C. Cole, Advanced dynamic modelling for friction draft gears, Veh. Syst. Dyn., 53 (2015), 475-492. https://doi.org/10.1080/00423114.2014.1002504

[31] T. Hsu, D. A. Peters, A simple dynamic model for simulating draft-gear behavior in rail-car impacts, J. Eng. Ind., 100 (1978), 492-496. https://doi.org/10.1115/1.3439467

[32] C. Cole, M. Spiryagin, Q. Wu, C. Bosomworth, Practical modelling and simulation of polymer draft gear connections, in First International Conference on Rail Transportation 2017, American Society of Civil Engineers, (2018), 413-423. https://doi.org/10.1061/9780784481257.041

[33] Z. Fu, Research on the Dynamic Model of MT-2 Buffer Based on Impact Test (in Chinese) , Master thesis, Dalian Jiaotong University, 2018.

[34] Y. Chu, Y. Chang, J. Zhang, Numerical Calculation Method (in Chinese) , Science Press, 2016.

[35] G. Luo, J. Xie, Periodic Motion and Bifurcation of Vibro-Impact System (in Chinese) , Science Press, 2004.

[36] B. Liu, J. Peng, Nonlinear Dynamics (in Chinese) , Higher Education Press, 2004.