Dynamics of a mass variable drum winding a heavy rope

• Autorzy: Buśkiewicz J.

Identyfikatory

DOI

10.24423/aom.3860

• Języki publikacji: EN

Abstrakty

EN

The paper focuses on a winch drum winding a heavy rope to present the variety of issues related to the dynamics of systems with rotating parts of time-varying mass. The dynamic motion equations for such systems are frequently either incorrect or derived under the assumption of mass constancy. When the mass variability is taken into account, simpler cases are discussed. The considerations on the angular momentum theorem enables formulating a new two time parameters form of the rotational motion equation for the system with time varying mass. Four cases are considered and different approaches of motion equations derivation are applied. The assumptions and solution methods of the analyzed systems as well as ambiguities and possible contradictions that may arise as a result of the trial of the problem formulation on the grounds of rigid body mechanics are discussed. The numerical simulations are presented.

Słowa kluczowe

EN

angular momentum; two time parameters method; time-variable mass; dynamic equations; drum

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2021
• Tom: Vol. 73, nr 5-6
• Strony: 557--582
• Opis fizyczny: Bibliogr. 39 poz., rys., wykr.

Twórcy

autor

Buśkiewicz J.

• Institute of Applied Mechanics, Faculty of Mechanical Engineering, Poznan University of Technology, Poland

• https://orcid.org/000-0002-8110-1473

Bibliografia

• 1. K. Chodnikiewicz, L. Moszczyński, Problems on Foundations of Electric Drives with Solutions (in Polish: Zbiór zadań z podstaw napędu elektrycznego z rozwiązaniami), Warsaw University of Technology (OWPW), Warsaw, 2014.
• 2. Y. Kharchenko, S. Sobkowski, Mathematical modelling of transients in drives of building elevating devices (in Polish: Modelowanie matematyczne procesów rozruchu układów napędowych podnośników budowlanych, Diagnostyka), Diagnostics, 35, 37–42, 2005.
• 3. Y. Kharchenko, Analysis of dynamic processes in drive systems on the basis of continuous-discreete nonlinear systems (in Polish: Analiza procesów dynamicznych w układach napędowych na bazie modeli nieliniowych ciągło-dyskretnych, Zeszyty Naukowe Politechniki Rzeszowskiej 59, Mechanika), Mechanics, 18, 267–270, 1989.
• 4. I. Birkeland, T.K. Than, O. Birkeland, T. Rolvag, Simulation of dynamic behaviour of a FPSO crane, 5th North Sea Offshore Crane Conference, Aberdeen, Scotland2000.
• 5. A. Rouvinen, T. Lehtinen, P. Korkealaakso, Container gantry crane simulator for operator training, Proceedings of the Institution of Mechanical Engineers, Part K: Journalof Multi-body Dynamics, 219, 4, 325–336, 2005.
• 6. A. Arena, A. Casalotti, W. Lacarbonara, M.P. Cartmell, Dynamics of container cranes: three- deling, full-scale experiments, and identification, International Journal of Mechanical Sciences, 93, 8–21, 2015.
• 7. F. Ju, Y.S. Choo, Dynamic analysis of tower cranes, Journal of Engineering Mechanics,131, 1, 88–96, 2005.
• 8. Y. Yang, P. Betsch, W. Zhang, Numerical integration for the inverse dynamics of a large class of cranes, Multibody System Dynamics, 48, 1–40, 2020, https://doi.org/10.1007/s11044-019-09691-3.
• 9. T. Mushiri, M. Jirivengwa, C. Mbohwa, Design of a hoisting system for a small scale mine, Procedia Manufacturing, 8, 738–45, 2017.
• 10. W.D. Zhu, N.A. Zheng, Exact response of a translating string with arbitrarily varying length under general excitation, Journal of Applied Mechanics, 75, 0310031–03100314,2008.
• 11. W.D. Zhu, Y. Chen, Forced response of translating media with variable length and tension: application to high-speed elevators, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 219, 35–53, 2005.
• 12. W. He, SS. Ge, D.Q. Huang, Modeling and vibration control for a nonlinear moving string with output constraint, IEEE/ASME Transactions on Mechatronics, 20, 1886–1897,2015.
• 13. S.H. Sandilo, W.T. van Horssen, On variable length induced vibrations of a vertical string, Journal of Sound and Vibration, 333, 2432–2449, 2014.
• 14. S.H. Sandilo, W.T. van Horssen, On a cascade of autoresonances in an elevator cable system, Nonlinear Dynamics, 80, 1613–1630, 2015.
• 15. K. Wu, W.D. Zhu, Parametric instability in a stationary string with a periodically varying length, Proceedings of the 26th Conference on Mechanical Vibration and Noise, Buffalo, New York, 17–20, 2014.
• 16. P. Zhang, C.M. Zhu, L.J. Zhang, Analysis of forced coupled longitudinal-transversevibration of flexible hoisting systems with varying length, Engineering Mechanics, 25, 202–207, 2008.
• 17. A. Kumaniecka, J. Niziol, Dynamic stability of a rope with slow variability of the parameters, Journal of Sound and Vibration, 178, 211–226, 1994.
• 18. J. Wang, Y.J. Pi, Y.M. Hu, X.S. Gong, Modeling and dynamic behavior analysis ofa coupled multi-cable double drum winding hoister with flexible guides, Mechanism and Machine Theory, 108, 191–208, 2017.
• 19. E. Imanishi, T. Nanjo, T. Kobayashi, Dynamic simulation of wire rope with contact, Journal of Mechanical Science and Technology, 23, 4, 1083–1088, 2009.
• 20. L. Cveticanin, Vibrations of a textile machine rotor, Journal of Sound and Vibration, 97, 2, 181–187, 1984.
• 21. L. Cveticanin, The oscillations of a textile machine rotor on which the textile is wound up, Mechanism and Machine Theory, 26, 3, 253–260, 1991.
• 22. L. Cveticanin, Stability of a clamped-free rotor with variable mass for the case of radial rubbing, Journal of Sound and Vibrations, 129, 3, 489–499, 1989.
• 23. L. Cveticanin, A. Dregelyi, R. Horvath, M. Zukovic, Dynamics of mass variablerotor and its application in modeling tuning operation, Acta Mechanica, 232, 1605–1620,2021. https://doi.org/10.1007/s00707-020-02918-x.
• 24. A.K. Abramyan, S.A. Vakulenko, Oscillations of a beam with a time-varying mass,Nonlinear Dynamics, 63, 135–147, 2011, https://doi.org/10.1007/s11071-010-9791-6.
• 25. A.K. Abramian, W.T. van Horssen, S.A. Vakulenko, On oscillations of a beamwith a small rigidity and a time-varying mass, Nonlinear Dynamics, 78, 449–459, 2014,https://doi.org/10.1007/s11071-014-1451-9.
• 26. H. Irschik, H.J. Holl, Mechanics of variable-mass systems – Part 1: Balance of massand linear momentum, Transactions of the ASME, Applied Mechanics Reviews, 57, 145–160, 2004.
• 27. R.M. Makharoblidze, I.M. Lagvilava, B.B. Basilashvili, R.M. Khazhomia, Dynamics calculation with variable mass of mountain self-propelled chassis, Annals of Agrarian Science, 14, 2016, doi: 10.1016/j.aasci.2016.10.006.
• 28. R. Starosta, G. Sypniewska-Kamińska, J. Awrejcewicz, Vibration of the oscillator exchanging mass with surroundings, Vibrations in Physical Systems, 27, 2016.
• 29. H. Rodrigues, N. Panza, D. Portes Jr, A. Soares, A model of oscillator with variablemass, Revista Mexicana de Física, 60, 31–38, 2014.
• 30. C.H. Lamarque, A. Ture Savadkoohi, Z. Dimitrijevic, Dynamics of a linear systemwith time-dependent mass and a coupled light mass with non-smooth potential, Meccanica,49, 135–145, 2014, doi: 10.1007/s11012-013-9778-8.
• 31. L. Cveticanin, I. Kovacic, On the dynamics of bodies with continual mass variation,Transactions of the ASME, Journal of Applied Mechanics, 74, 810–815, 2007.
• 32. L. Cveticanin, Dj. Djukic, Motion of body with discontinual mass variation, Nonlinear Dynamics, 52, 3, 249–261, 2008.
• 33. L. Cveticanin, Dynamics of Bodies with Time-variable Mass, Springer, Berlin, ISBN 9783319220567, 2015.
• 34. J. Awrejcewicz, Classical Mechanics Dynamics, Springer, Berlin, 2012.
• 35. H. Irschik, A. Humer, A rational treatment of the relations of balance for mechanical systems with a time-variable mass and other non-classical supplies, [in:]H. Irschik, A.K. Belyaev [eds.] Dynamics of Mechanical Systems with Variable Mass,CISM International Centre for Mechanical Sciences, Springer, Vienna, 557, 2014, https://doi.org/10.1007/978-3-7091-1809-2_1.
• 36. F.O. Eke, Dynamics of variable mass systems, Technical Report NASA/CR-1998-208246,NAS 1.26:208246, https://ntrs.nasa.gov/search.jsp?R=19980210404.
• 37. F.O. Eke, T.C. Mao, On the dynamics of variable mass systems, International Journal of Mechanical Engineering Education, 30, 2, 123–137, 2002, https://doi.org/10.7227IJMEE.30.2.4.
• 38. A. Nanjangud, O.K. Fidelis Angular momentum of free variable mass systems is partially conserved, Aerospace Science and Technology, 79, 1–4, 2018.
• 39. R.A. El-Nabulsi, Free variable mass nonlocal systems, jerks, and snaps, and their implications in rotating fluids in rockets, Acta Mechanica, 232, 89–109, 2021, https://doi.org/10.1007/s00707-020-02843-z.