Mathematical Modelling of Tank Wagon Vibrations Considering Partially Filling of the Tank with Liquid Cargo
https://doi.org/10.30932/1992-3252-2021-19-2-4
Abstract
Mathematical modelling of processes of motion makes it possible to assess the dynamic characteristics of a wagon at the stage of its design. However, it is necessary to consider the type of cargo transported, the movement of which affects the values of these features.
The paper considers a mathematical model of an eight-axle railway tank wagon developed using the Lagrange’s equation of the second kind. The considered mathematical model suggests an approach based on the consideration of the influence of the energy of a liquid cargo in a steady state of motion. This influence was considered by evaluating the kinetic and potential energies of vibrations of the transported liquid cargo.
Differential equations of vibration compiled for the model under consideration represent the liquid cargo as a solid. The approach for considering the effect of liquid cargo during vibrations of a tank wagon assumes that the total volume of the displaced liquid approximately corresponds to the volume of the layer of the fluid determined by displacement of bouncing, or in the case of galloping, with an angular displacement of one end section of the tank wagon, the second section rises by the same value, in other words, we observe the system of communicating vessels. Based on these assumptions, energy additions are obtained that consider movement of a liquid cargo under steady-state modes of motion.
According to the proposed approach, preliminary calculations were performed, and the results obtained were assessed. The results obtained showed satisfactory convergence with the calculations carried out using other approaches to modelling of the processes of movement of railway tank wagons.
About the Authors
P. S. Grigoriev
Russian University of Transport
Russian Federation
Russian Federation
Ph.D. (Eng), Associate Professor at the Department of Electric Trains and Locomotives,
Moscow
S. N. Korzhin
Russian University of Transport
Russian Federation
Russian Federation
Ph. D. (Eng), Associate Professor at the Department of Wagons and Wagon Operations,
Moscow
Sh. R. Ibodulloev
National University of Uzbekistan named after Mirzo Ulugbek
Uzbekistan
Uzbekistan
Ph.D. student at the Department of Mechanics and Mathematical Modelling,
Tashkent
Phu Thuan Tran
Society of Vietnamese Citizens in the Russian Federation
Viet Nam
Viet Nam
D.Sc. (Eng), First Deputy Chairman,
Ho Chi Minh City
References
1. Bogomaz, G. I. Dynamics of railway tank wagons [Dinamika zheleznodorozhnykh vagonov-tsistern]. Kiev, Naukova Dumka publ., 2004, 223 p. [Electronic resource]: https://www.studmed.ru/bogomaz-g-i-dinamikazheleznodorozhnyh-vagonov-cistern_741466e810b.html. Last accessed 19.02.2021.
2. Cherkashin, Yu. M. Dynamics of a bulk train [Dinamika nalivnogo poezda]. Proceedings of TsNII MPS, Moscow, Transport publ., 1975, Iss. 543, 136 p.
3. Sergeev, K. A., Grigoriev, P. S., Kozlov, M. P., Suvorova, K. E. Stress-strain state of the cylindrical shell of the tank during oscillations on periodic irregularities of the track [Napryazhenno-deformirovannoe sostoyanie tsilindricheskoi obolochki kotla tsisterny pri kolebaniyakh na periodicheskoi nerovnosti puti]. Nauka i tekhnika transporta, 2020, pp. 66−70. [Electronic resource]: https://www.elibrary.ru/item.asp?id=42854183. Last accessed 19.02.2021
4. Vershinsky, S. V., Danilov, V. N., Khusidov, V. D. Dynamics of the wagon: Textbook for higher educational institutions of railway transport [Dinamika vagona: Uchebnik dlya vuzov zh-d transporta]. Ed. by S. V. Vershinsky. 3rd ed., rev. and enl. Moscow, Transport publ., 1991, 360 p.
5. Iwnicki, S. D., Stichel, S., Orlova, A., Hecht, M. Dynamics of railway freight vehicles. Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, 2015, Vol. 53, Iss. 7, pp. 995−1033. DOI: https://doi.org/10.1080/00423114.2015.1037773.
6. Bespalko, S., Grigorev, P., Ibodulloev, Sh., Turajonov, K., Numonov, A. Mathematical model of oscillations of a railway tank car with partial fillingunder shunting collision. 2020 IOP Conf. Series: Materials Science and Engineering. 2020, Vol. 883, 012134. [Electronic resource]: https://iopscience.iop.org/article/10.1088/1757-899X/883/1/012134. Last accessed 19.02.2021.
7. Bespalko, S. V., Grigoriev, P. S., Ruzmatov, M. I., Ibodulloev, Sh. R. A study method for possible breakdown of boiler tank for dangerous goods in an emergency collision. E3S Web of Conferences, 2020, Vol. 224, Art. 01045. DOI: https://doi.org/10.1051/e3sconf/202022401045.
8. Ranganathan, R., Yang, Y. S. Impact of Liquid Shift on the Braking Characteristics of Partially Filled Tank Vehicles. Vehicle System Dynamics, 1996, Vol. 26, Iss. 3, pp. 223−240. DOI: 10.1080/00423119608969310.
9. Vysotsky, M. S., Pleskachevsky, Yu. M., Shimanovsky, A. O. Dynamics of automobile and railway tanks [Dinamika avtomobilnykh i zheleznodorozhnykh tsistern]. Minsk, Belavtotraktorostroenie, 2007, 320 p.
10. Shimanovsky, A. O., Pleskachevsky, Yu. M., Vysotsky, M. S. Prospects of research of dynamics of tanks for transportation of liquid cargo [Perspektivy issledovanii dinamiki tsistern dlya transportirovki zhidkikh gruzov]. Mekhanika mashin, mekhanizmov i materialov, 2007, No. 1, pp. 38−42.
11. Putyato, A. V., Shimanovsky, A. O. Modeling the loading of tank structure elements [Modelirovanie nagruzhennosti elementov konstruktsii tsistern]. Problems of railway transport mechanics: traffic safety, dynamics, strength of rolling stock, energy saving: Abstracts of reports of the 1 2th International Conference, 28–30.05.2008. Dnepropetrovsk, DNUZhT publ., 2008, p. 142.
12. Universal Mechanism: software, user manual, presentations. Website. [Electronic resource]: www.umlab.ru. Last accessed 19.02.2021.
13. Boronenko, Yu. P., Zhitkov, Yu. B. Features of the dynamics of a tank wagon with a liquid cargo [Osobennosti dinamiki vagona-tsisterny s zhidkim gruzom]. Izvestiya PGUPS, 2017, Iss. 4, pp. 597−604. [Electronic resource]: https://cyberleninka.ru/article/n/osobennostidinamiki-vagona-tsisterny-s-zhidkim-gruzom/pdf. Last accessed 19.02.2021.
14. Mantriota, G. Directional stability of articulated tank vehicles: A simplified model. Heavy Vehicle Systems, Int. J. of Vehicle Design, 2003, Vol. 10, Iss. ½, pp. 144–165. DOI: 10.1504/IJHVS.2003.002438.
15. Lavrenko, D. T. Mathematical model of spatial oscillations of tank cars [Matematicheskaya model prostranstvennykh kolebanii vagonov-tsistern]. Zbirnik prats DonIZT, 2008, Iss. 14, pp. 126−136. [Electronic resource]: https://cyberleninka.ru/article/n/matematicheskayamodel-prostranstvennyh-kolebaniy-vagonov-tsistern/pdf. Last accessed 19.02.2021.
16. Maxfield, B. Essential PTC Mathcad Prime 3.0: A Guide for New and Current Users. Elsevier Inc., 2014, 564 p. ISBN: 978-0-12-410410-5.
Review
For citations:
Grigoriev P.S., Korzhin S.N., Ibodulloev Sh.R., Tran P. Mathematical Modelling of Tank Wagon Vibrations Considering Partially Filling of the Tank with Liquid Cargo. World of Transport and Transportation. 2021;19(2):25-30. https://doi.org/10.30932/1992-3252-2021-19-2-4
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