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A Mathematical Model of the Dynamic Behavior of a Transportation System with Pendulum Shock Absorbers

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Strength of Materials Aims and scope

A new mathematical model is proposed that describes the process of damping longitudinal transport effects, which is based on the use of special shock-absorbing pendulum-type turnstiles. The purpose of the work is to assess the level of effectiveness of shock absorbers to reduce longitudinal dynamic effects on heavy and oversized cargo during its transportation by rail. An extreme variant of dynamic loading of a transport system equipped with the proposed damping system was studied by mathematical modeling methods. Differential equations of motion of the transport system are formulated and integrated by numerical methods. As a result of numerical experiments, the main regulatory characteristics of pendulum shock absorbers, which affect the quality of their functioning, have been established. A quantitative assessment of the effectiveness of the use of such shock-absorbing devices is given. It is shown that when using pendulum shock absorbers, the level of dynamic effects on transported goods can be reduced by four times compared to the existing traditional method of railway transportation. It is noted that the influence of the length of pendulum suspensions on various elements of the vibration protection system is multidirectional: with a decrease in the length of pendulum suspensions, the maximum modules of acceleration of support cars decrease somewhat, and the maximum module of acceleration of the load increases noticeably. In the boundary case, when the length of pendulum suspensions tends to zero, all three indicated acceleration modules tend to the same single value. The numerical analysis of the dynamic behavior of the vibration protection system once again confirmed the following general result of previous theoretical and experimental studies: in order to significantly reduce the maximum level of longitudinal transport effects on the load, its fastening relative to the cars should be carried out in a “movable-adjustable” way.

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References

  1. Technical Conditions of Accommodation and Fastening of Cargo, Annex 3 to the Agreement on International Goods Transport by Rail (IGTR) [in Russian], Organization of Cooperation between Railways (OCRW), Devolta, Kyiv (2011).

  2. Technical Conditions for Loading and Securing Cargo, Annex 3 to the Agreement on International Goods Transport by Rail (IGTR) [in Russian], Organization of Cooperation between Railways (OCRW), Devolta, Kyiv (2018).

  3. Loading Guidelines Code of Practice for the Loading and Securing of Goods on Railway Wagons, International Union Railways, Paris (2019).

  4. V. I. Pastushenko and V. P. Legeza, “Theoretical investigations of transport loads on a building structure when fastening it to a wagon with the application of wedge damper”, in: Building Structures [in Russian], Issue 36, Budivelnyk, Kiev (1983), pp. 102–105.

  5. A. D. Malov, O. I. Mikhailov, G. M. Shteinfer, et al., Cargo Placement and Fastening in Wagons [in Russian], Transport, Moscow (1980).

  6. A. V. Shatunov, The Load of a Double Platform Coupling at the Resource-Saving Way of Transportation of Long-Length Cargo [in Russian], Author’s Abstract of the Candidate Degree Thesis (Tech. Sci.), Dnepropetrovsk Institute of Railway Engineers, Dnepropetrovsk (1992).

  7. L. A. Manashkin, B. S. Ratner, A. V. Yurchenko, et al., “Research with computer loads acting on wagons and depreciated loads during coupling collision and start-up of freight trains”, in: Problems of Mechanics of Land Transport [in Russian], Issue 199/25, Dnepropetrovsk (1978), pp. 87–93.

  8. S. M. Vasil’ev, “Comparative analysis of dynamic characteristics of turnstile-securing devices of roller, slide, and wedge types”, Nauka Pogr. Transport., No. 23, 16–19 (2008).

  9. S. M. Vasil’ev, A. D. Zheleznyakov, and L. P. Tselkovikova, “Modeling of wagon collisions under dry friction in cargo supports”, Nauka Progr. Transport., No. 4 (64), 116–124 (2016).

  10. V. I. Sen’ko, A. D. Zheleznyakov, and S. M. Vasil’ev, “Rolling stock and fastening devices for the transportation of long goods”, Vestn. BGUT, Nauka Transport, No. 1 (8), 4–6 (2004).

  11. V. P. Legeza, “Application of the theory of roller shock absorbers to the vibroprotection of transport structures”, Strength Mater., 38, No. 2, 214–219 (2006), https://doi.org/10.1007/s11223-006-0034-5.

    Article  CAS  Google Scholar 

  12. V. P. Legeza, “Kinematics and dynamics of a mechanical system on rollers that provide nonholonomic constraints”, J. Math. Sci., 72, No. 5, 3299–3305 (1994).

    Article  Google Scholar 

  13. V. Legeza, I. Dychka, R. Hadyniak, and L. Oleshchenko, “Mathematical model of the dynamics in a one nonholonomic vibration protection system”, Int. J. Intell. Syst. Appl. (IJISA), 10, No. 10, 20–26 (2018).

    Google Scholar 

  14. I. Vikovych, L. Krainyk, R. Zin’ko, et al., “Design of shock absorbers for transporting loads by bimetric transport vehicles”, Eastern-European J. Enterprise Technol., 2, No. 7, 85–94 (2021), https://doi.org/10.15587/1729-4061.2021.229447.

    Article  Google Scholar 

  15. B. N. Lavrenov, Methods of Placement and Fastening of Cargoes on Platform Couplings Using a New Pendulum-Type Turnstile [in Russian], Author’s Abstract of the Candidate Degree Thesis (Tech. Sci.), MIIT, Moscow (1989).

  16. Q. Wu, M. Spiryagin, and C. Cole, “Longitudinal train dynamics: an overview”, Vehicle Syst. Dyn., 54, No. 12, 1688–1714 (2016).

    Article  Google Scholar 

  17. N. Andersson, P. Andersson, R. Bylander, et al., Equipment for Rational Securing of Cargo on Railway Wagons, VINNOVA Report VR 2004:05, VINNOVA – Swedish Agency for Innovation Systems (2004).

  18. M. Ansari, E. Esmailzadeh, and D. Younesian, “Longitudinal dynamics of freight trains”, Int. J. Heavy Veh. Syst., 16, Nos. 1–2, 102–131 (2009).

    Article  Google Scholar 

  19. P. Belforte, F. Cheli, G. Diana, and S. Melzi, “Numerical and experimental approach for the evaluation of severe longitudinal dynamics of heavy freight trains”, Vehicle Syst. Dyn., 46, Suppl., 937–955 (2008).

  20. G. Diana, F. Cheli, P. Belforte, and S. Melzi, “Numerical and experimental investigation of heavy freight train dynamics”, in: Proc. of IMECE, Paper No: IMECE2007-42693, Washington (2007), pp. 439–448.

  21. C. Cole, “Improvements to wagon connection modelling for longitudinal train simulation”, in: Proc. of Conf. on Railway Engineering, Rockhampton (1998), pp. 187–194.

  22. C. Cole, “Longitudinal train dynamics”, in: S. Iwnicki (Ed.), Handbook of Railway Vehicle Dynamics, Taylor&Francis, London (2006), pp. 239–278.

  23. C. Cole, M. Spiryagin, Q. Wu, and Y. Q. Sun, “Modeling, simulation and applications of longitudinal train dynamics”, Vehicle Syst. Dyn., 55, No. 10, 1498–1571 (2017).

    Article  Google Scholar 

  24. D. Z. Wang, “Consideration on the overlength goods transportation”, Railway Freight Transport, 5, 31–33 (2002).

    Google Scholar 

  25. L. N. Nikol’skii and B. G. Keglin, Shock Absorbers of Rolling Stock [in Russian], Mashinostroenie, Moscow (1986).

  26. O. V. Sytnykov, Fundamentals of MathCad [in Ukrainian], KPI, Kyiv (2013), https://ahv.kpi.ua/wp-content/uploads/Osnovi_roboti_z_MathCad.pdf.

  27. DBN V1.2.-2:2006. System of Ensuring Reliability and Safety of Building Structures. Pressure and Influence. Design Standards [in Ukrainian] Kyiv (2006).

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    V. P. Legeza & O. M. Neshchadym

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  1. V. P. Legeza
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  2. O. M. Neshchadym
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Correspondence to V. P. Legeza.

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Translated from Problemy Mitsnosti, No. 3, pp. 59 – 70, May – June, 2022.

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Legeza, V.P., Neshchadym, O.M. A Mathematical Model of the Dynamic Behavior of a Transportation System with Pendulum Shock Absorbers. Strength Mater 54, 396–406 (2022). https://doi.org/10.1007/s11223-022-00415-1

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