On one way to build up a computer model of the multibody system dynamics

Authors

  • Ivan I. Kosenko Moscow Aviation Institute (National Research University), 4, Volokolamskoe Shosse, Moscow, 125993, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2022.112

Abstract

A technology of an object-oriented modeling is under consideration. This technology is applied to the cases of the multibody systems virtual prototypes dynamics creating. General approach for creating the models is described. The approach is based on the multiport representation for the mechanical system to be simulated. The object-oriented paradigm turned out to be an efficient tool for constructing complicated models especially for the cases of large or very large dimencions. Several examples of the machines dynamical models from different topics were implemented.

Keywords:

object-oriened modeling, dynamics of a vehicle, rolling disc on the horizontal plane dynamics, dynamics of the wheelset, joint constraint, servoconstraints, skateboard, non-holonomic constraints, contact models, dynamical verification

Downloads

Download data is not yet available.
 

References

Литература

1. Kosenko I. I., Gerasimov K.V. Physically-oriented modeling and simulation of the omni vehicle dynamics. Proceedings of the 3rd Joint International Conference on Multibody System Dynamics and the 7th Asian Conference on Multibody Dynamics, June 30 - July 3, 2014, BEXCO, Busan, Korea (2014).

2. Косенко И.И. Графовые представления моделей динамики систем тел. Математическое моделирование 21 (9), 80–88 (2009).

3. Wittenburg J. Dynamics of multibody systems. Berlin, Springer-Verlag (2008).

4. Шилен В., Эберхард П. Прикладная динамика. Численное моделирование механических систем в машиностроении. Москва, Ижевск, НИЦ "Регулярная и хаотическая динамика", Институт компьютерных исследований (2018).

5. Кирпичников С.Н., Новоселов В.С. Математические аспекты кинематики твердого тела. Ленинград, Изд-во Ленингр. ун-та (1986).

6. Modelica - A unified object-oriented language for physical systems modeling. Tutorial. Modelica Association (2000).

7. Stramigioli S., Blankenstein G., Duindam V., Bruyninckx H., Melchiorri C. Power port concepts in robotics. The geometrical-physical approach. Tutorial at 2003 IEEE International conference on robotics and automation. IEEE (2003).

8. Cellier F. E. Continuous system modeling. New York, Springer-Verlag (1991).

9. Lewis A.D., Ostrowski J. P., Murray R.M., Burdick J.W. Nonholonomic mechanics and locomotion: The snakeboard example. Proceedings of the IEEE international conference on robotics and automation, San Diego, May 1994, IEEE, 2391–2400 (1994).

10. Борисов А.В., Мамаев И.С., Килин А.А. Динамика катящегося диска. В сб.: Неголономные динамические системы. Интегрируемость, хаос, странные аттракторы. Москва, Ижевск, Институт компьютерных исследований, 99–117 (2002).

11. Kosenko I. I., Kuleshov A. S. Modelica Implementation of the Skateboard Dynamics. Proceedings of the 6th International Modelica Conference, University of Applied Sciences Bielefeld, Bielefeld, Germany, March 3–4, 2008, 727–734 (2008).

12. Vil’ke V.G., Kosenko I. I., Aleksandrov E.B. On computer implementation of the Hertz elastic contact model and its simplifications. Regular and Chaotic Dynamics 14 (6), 693–714 (2009). https://doi.org/10.1134/S1560354709060070

13. Контенсу П. Связь между трением скольжения и трением верчения и ее учет в теории волчка. В кн.: Проблемы гироскопии, пер. с франц., 60–77. Москва, Мир (1967).

14. Erismann Th. Theorie und Anwendungen des echten Kugelgetriebes. Z. angew. Math. Phys. 5, 355–388 (1954).

15. Журавлев В.Ф. О модели сухого трения в задаче качения твердых тел. Прикладная математика и механика 62 (5), 762–767 (1998).

16. Leine R. I., Glocker Ch. A set-valued force law for spatial Coulomb - Contensou friction. European Journal of Mechanics - A/Solids 22 (2), 193–216 (2003). https://doi.org/10.1016/S0997- 7538(03)00025-1

17. Modelica Libraries. Доступно на: https://modelica.org/libraries.html (дата обращения: 20.12.2021).

18. Pelchen C., Schweiger C., Otter M. Modeling and simulating the efficiency of gearboxes and of planetary gearboxes. Proceedings of the 2nd International Modelica Conference, Deutsches Zentrum f¨ur Luft- und Raumfahrt e. V. (DLR), Oberpfaffenhofen, Germany, March 18–19, 2002, 257–266 (2002).

19. Kosenko I., Gerasimov K. Object-oriented approach to the construction of an omni vehicle dynamical model. Journal of Mechanical Science and Technology 29 (7), 2593–2599 (2015). https://doi.org/10.1007/s12206-015-0503-5

20. Лестев М.А., Тихонов А.А. Нелинейные явления в динамике микромеханических гироскопов. Вестник Cанкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия, вып. 1, 83–88 (2009).

References

1. Kosenko I. I., Gerasimov K.V. Physically-oriented modeling and simulation of the omni vehicle dynamics. Proceedings of the 3rd Joint International Conference on Multibody System Dynamics and the 7th Asian Conference on Multibody Dynamics, June 30 - July 3, 2014, BEXCO, Busan, Korea (2014).

2. Kosenko I. I. Graph representations of the multibody systems dynamics models. Matematicheskoe modelirovanie 21 (9), 80–88 (2009). (In Russian)

3. Wittenburg J. Dynamics of multibody systems. Berlin, Springer-Verlag (2008).

4. Shilen W., Eberhard P. Applied dynamics. Numerical modeling of mechanical systems in mechanical engineering. Moscow, Izhevsk, NIC Regulyarnaya i khaoticheskaya dinamika Publ., Institut kompyuternykh issledovanij Publ. (2018). (In Russian)

5. Kirpichnikov S.N., Novoselov V. S. Mathematical aspects of rigid body kinematics. Leningrad, Leningrad Univ. Press (1986). (In Russian)

6. Modelica A unified object-oriented language for physical systems modeling. Tutorial. Modelica Association (2000).

7. Stramigioli S., Blankenstein G., Duindam V., Bruyninckx H., Melchiorri C. Power port concepts in robotics. The geometrical-physical approach. Tutorial at 2003 IEEE International conference on robotics and automation. IEEE (2003).

8. Cellier F. E. Continuous system modeling. New York, Springer-Verlag (1991).

9. Lewis A.D., Ostrowski J. P., Murray R.M., Burdick J.W. Nonholonomic mechanics and locomotion: The snakeboard example. Proceedings of the IEEE international conference on robotics and automation, San Diego, May 1994, IEEE, 2391–2400 (1994).

10. Borisov A.V., Mamaev I. S., Kilin A.A. Rolling disc dynamics. In: Nonholonomic dynamical systems. Integrability, chaos, strange attractors. Moscow, Izhevsk, Institut komputernykh isslelovaniy Publ., 99–117 (2002). (In Russian)

11. Kosenko I. I., Kuleshov A. S. Modelica Implementation of the Skateboard Dynamics. Proceedings of the 6th International Modelica Conference, University of Applied Sciences Bielefeld, Bielefeld, Germany, March 3–4, 2008, 727–734 (2008).

12. Vil’ke V.G., Kosenko I. I., Aleksandrov E.B. On computer implementation of the Hertz elastic contact model and its simplifications. Regular and Chaotic Dynamics 14 (6), 693–714 (2009). https://doi.org/10.1134/S1560354709060070

13. Contensou P. Couplage entre frottement de pivotement et frottement de pivotement dans la th´eorie de latoupie. In: Kreiselprobleme Gyrodynamics: IUTAM Symp. Celerina. Berlin, Springer, 201– 216 (1963). [Rus. ed.: Kontensu P. Svjaz’ mezhdu treniem skol’zhenija i treniem verchenija i ee uchet v teorii volchka. In: Problemy giroskopii. Мoscow, Mir Publ., 60–77 (1967)].

14. Erismann Th. Theorie und Anwendungen des echten Kugelgetriebes. Z. angew. Math. Phys. 5, 355–388 (1954).

15. Zhuravlev V. F. The model of dry friction in the problem of the rolling of rigid bodies. Prikladnaya matematika i mekhanika 62 (5), 762–767 (1998). (In Russian)

16. Leine R. I., Glocker Ch. A set-valued force law for spatial Coulomb - Contensou friction. European Journal of Mechanics - A/Solids 22 (2), 193–216 (2003). https://doi.org/10.1016/S0997- 7538(03)00025-1

17. Modelica Libraries. Available at: https://modelica.org/libraries.html (accessed: December 20, 2021).

18. Pelchen C., Schweiger C., Otter M. Modeling and simulating the efficiency of gearboxes and of planetary gearboxes. Proceedings of the 2nd International Modelica Conference, Deutsches Zentrum f¨ur Luft- und Raumfahrt e. V. (DLR), Oberpfaffenhofen, Germany, March 18–19, 2002, 257–266 (2002).

19. Kosenko I., Gerasimov K. Object-oriented approach to the construction of an omni vehicle dynamical model. Journal of Mechanical Science and Technology 29 (7), 2593–2599 (2015). https://doi.org/10.1007/s12206-015-0503-5

20. Lestev M.A., Tikhonov A.A. Nonlinear phenomena in the dynamics of micromechanical gyroscopes. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, iss. 1, 83–88 (2009). (In Russian) [Eng. transl.: Vestnik St Petersburg University, Mathematics 42 (1), 53–57 (2009). https://doi.org/10.3103/S1063454109010087].

Published

2022-04-11

How to Cite

Kosenko, I. I. (2022). On one way to build up a computer model of the multibody system dynamics. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(1), 126–134. https://doi.org/10.21638/spbu01.2022.112

Issue

Section

Mechanics