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Nonlinear dynamic responses of locomotive excited by rail corrugation and gear time-varying mesh stiffness

    Zaigang Chen Affiliation
    ; Jie Zhang Affiliation
    ; Kaiyun Wang Affiliation
    ; Pengfei Liu Affiliation

Abstract

Rail corrugation is usually generated in modern railway transportations, such as high-speed railway, urban railway, and heavy-haul railway. It is one of the major excitations to the wheel–rail dynamic interaction, which will cause extra vibration and noise, failures, or even risk of derailment to the vehicle and its components. A dynamics model of a heavy-haul locomotive considering the traction power from the electric motor to the wheelset through gear transmission is employed to investigate the nonlinear dynamic responses of the locomotive. This dynamics model couples the motions of the vehicle, the track, and the gear transmission together. In this dynamics model, excitations from the rail corrugation, the nonlinear wheel–rail contact, the time-varying mesh stiffness, and the nonlinear gear backlash are considered. Then, numerical simulations are performed to reveal the dynamic responses of the locomotive. The calculated results indicate that different nonlinear phenomenon can be observed under the excitation of the rail corrugation with different amplitude and wavelength. The high frequency vibrations excited by the time-varying mesh stiffness are usually modulated by the low frequency vibrations caused by the rail corrugation. However, this is likely to vanish under the chaotic conditions with some corrugation wavelength. The vibration level of the vehicle and the gear transmission increases generally with the corrugation amplitude. However, some corrugation lengths have been found to be more responsible for the vibration of the dynamics system, which should be concerned greatly during the locomotive operation. Meanwhile, involvement of gear transmission systems will cause different dynamic responses between the wheelsets under rail corrugation and gear mesh excitations.


First published online 17 January 2023

Keyword : nonlinearity, rail corrugation, mesh stiffness, gear backlash, dynamic response, railway vehicle

How to Cite
Chen, Z., Zhang, J., Wang, K., & Liu, P. (2022). Nonlinear dynamic responses of locomotive excited by rail corrugation and gear time-varying mesh stiffness. Transport, 37(6), 383–397. https://doi.org/10.3846/transport.2022.17065
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Dec 31, 2022
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References

Andersson, C.; Johansson, A. 2004. Prediction of rail corrugation generated by three-dimensional wheel–rail interaction, Wear 257(3–4): 423–434. https://doi.org/10.1016/j.wear.2004.01.006

Chaari, F.; Fakhfakh, T.; Haddar, M. 2009. Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness, European Journal of Mechanics – A/Solids 28(3): 461–468. https://doi.org/10.1016/j.euromechsol.2008.07.007

Chen, Z.; Shao, Y. 2011. Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth, Engineering Failure Analysis 18(8): 2149–2164. https://doi.org/10.1016/j.engfailanal.2011.07.006

Chen, Z.; Shao, Y. 2013. Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack, Mechanism and Machine Theory 62: 63–74. https://doi.org/10.1016/j.mechmachtheory.2012.10.012

Chen, Z. G.; Shao, Y. M.; Lim, T. C. 2012. Non-linear dynamic simulation of gear response under the idling condition, International Journal of Automotive Technology 13(4): 541–552. https://doi.org/10.1007/s12239-012-0052-1

Chen, Z.; Zhai, W.; Shao, Y.; Wang, K.; Sun, G. 2016. Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack, Engineering Failure Analysis 66: 502–514. https://doi.org/10.1016/j.engfailanal.2016.05.006

Chen, Z.; Zhai, W.; Wang, K. 2017a. A locomotive–track coupled vertical dynamics model with gear transmissions, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobilitys 55(2): 244–267. https://doi.org/10.1080/00423114.2016.1254260

Chen, Z.; Zhai, W.; Wang, K. 2017b. Dynamic investigation of a locomotive with effect of gear transmissions under tractive conditions, Journal of Sound and Vibration 408: 220–233. https://doi.org/10.1016/j.jsv.2017.07.017

Chen, Z.; Zhang, J.; Zhai, W.; Wang, Y.; Liu, J. 2017c. Improved analytical methods for calculation of gear tooth fillet-foundation stiffness with tooth root crack, Engineering Failure Analysis 82: 72–81. https://doi.org/10.1016/j.engfailanal.2017.08.028

Correa, N.; Oyarzabal, O.; Vadillo, E. G.; Santamaria, J.; Gomez J. 2011. Rail corrugation development in high speed lines, Wear 271(9–10): 2438–2447. https://doi.org/10.1016/j.wear.2010.12.028

Grassie, S. L. 2009. Rail corrugation: characteristics, causes, and treatments, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 223(6): 581–596. https://doi.org/10.1243/09544097JRRT264

Grassie, S. L.; Kalousek, J. 1993. Rail corrugation: characteristics, causes and treatments, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 207(1): 57–68. https://doi.org/10.1243/PIME_PROC_1993_207_227_02

Ishikawa, Y.; Kawamura, A. 1997. Maximum adhesive force control in super high speed train, in Proceedings of Power Conversion Conference – PCC’97, 6 August 1997, Nagaoka, Japan, 2: 951–954. https://doi.org/10.1109/PCCON.1997.638382

Iwnicki, S. 2003. Simulation of wheel–rail contact forces, Fatigue & Fracture of Engineering Materials & Structures 26(10): 887–900. https://doi.org/10.1046/j.1460-2695.2003.00699.x

Kalker, J. J.; Piotrowski, J. 1989. Some new results in rolling contact, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 18(4): 223–242. https://doi.org/10.1080/00423118908968920

Li, S.; Li, Z.; Núñez, A.; Dollevoet, R. 2017. New insights into the short pitch corrugation enigma based on 3D-FE coupled dynamic vehicle-track modeling of frictional rolling contact, Applied Sciences 7(8): 807. https://doi.org/10.3390/app7080807

Liang, X.; Zuo, M. J.; Pandey, M. 2014. Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set, Mechanism and Machine Theory 76: 20–38. https://doi.org/10.1016/j.mechmachtheory.2014.02.001

Ling, L.; Li, W.; Shang, H.; Xiao, X.; Wen, Z.; Jin, X. 2014. Experimental and numerical investigation of the effect of rail corrugation on the behaviour of rail fastenings, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 52(9): 1211–1231. https://doi.org/10.1080/00423114.2014.934844

Ma, H.; Zeng, J.; Feng, R.; Pang, X.; Wang, Q.; Wen, B. 2015. Review on dynamics of cracked gear systems, Engineering Failure Analysis 55: 224–245. https://doi.org/10.1016/j.engfailanal.2015.06.004

Matsumoto, A.; Sato, Y.; Ono, H.; Tanimoto, M.; Oka, Y.; Miyauchi, E. 2002. Formation mechanism and countermeasures of rail corrugation on curved track, Wear 253(1–2): 178–184. https://doi.org/10.1016/S0043-1648(02)00097-2

Polach, O. 2005. Creep forces in simulations of traction vehicles running on adhesion limit, Wear 258(7–8): 992–1000. https://doi.org/10.1016/j.wear.2004.03.046

Sainsot, P.; Velex, P.; Duverger, O. 2004. Contribution of gear body to tooth deflections – a new bidimensional analytical formula, Journal of Mechanical Design 126(4): 748–752. https://doi.org/10.1115/1.1758252

Sato, Y.; Matsumoto, A.; Knothe, K. 2002. Review on rail corrugation studies, Wear 253(1–2): 130–139. https://doi.org/10.1016/S0043-1648(02)00092-3

Shabana, A. A.; Sany, J. R. 2001. A survey of rail vehicle track simulations and flexible multibody dynamics, Nonlinear Dynamics 26(2): 179–210. https://doi.org/10.1023/A:1012976302105

Shao, Y.; Chen, Z. 2013. Dynamic features of planetary gear set with tooth plastic inclination deformation due to tooth root crack, Nonlinear Dynamics 74(4): 1253–1266. https://doi.org/10.1007/s11071-013-1038-x

Tian, X. 2004. Dynamic Simulation for System Response of Gearbox Including Localized Gear Faults. MSc Thesis. University of Alberta, Edmonton, Alberta, Canada. 109 p. https://doi.org/10.7939/r3-05s3-by17

Wang, K.; Liu, P.; Zhai, W.; Huang, C.; Chen, Z.; Gao, J. 2015. Wheel/rail dynamic interaction due to excitation of rail corrugation in high-speed railway, Science China Technological Sciences 58(2): 226–235. https://doi.org/10.1007/s11431-014-5633-y

Weber, C. 1951. The Deformation of Loaded Gears and the Effect on their Load Carrying Capacity. Department of Scientific and Industrial Research, London, UK. 111 p.

Wu, S.; Zuo, M. J.; Parey, A. 2008. Simulation of spur gear dynamics and estimation of fault growth, Journal of Sound and Vibration 317(3–5): 608–624. https://doi.org/10.1016/j.jsv.2008.03.038

Yang, D. C. H.; Lin, J. Y. 1987. Hertzian damping, tooth friction and bending elasticity in gear impact dynamics, Journal of Mechanisms, Transmissions, and Automation in Design 109(2): 189–196. https://doi.org/10.1115/1.3267437

Zhai, W.-M. 1996. Two simple fast integration methods for large-scale dynamic problems in engineering, International Journal for Numerical Methods in Engineering 39(24): 4199–4214. https://doi.org/10.1002/(SICI)1097-0207(19961230)39:24<4199::AID-NME39>3.0.CO;2-Y

Zhai, W.; Sun, X. 1994. A detailed model for investigating vertical interaction between railway vehicle and track, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility 23(Suppl 1): 603–615. https://doi.org/10.1080/00423119308969544

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