The stability of shafts under the action of periodic axial loads

Authors

DOI:

https://doi.org/10.32347/2410-2547.2021.107.257-264

Keywords:

geometric nonlinearity, inertia forces, axial forces, dynamic stability, numeric differentiation

Abstract

The paper presents the investigation results of the harmonic periodic axial loads’ influence on the stability of shaft. Such loads can be appeared during the running of the vessel passing the turbulence zones from the side of the propeller to the shafting. In shafting, the influence of oscillatory motion performed in adjacent part, which is transmitted through the coupling due to longitudinal movements, can be periodic, too. Therefore, the question of the stability of such shafts during rotation is relevant. In this way, the task of such drill-rod study stability has actuality. In this case, the various modes of vibration and stability loss are possible. In this regard, the study was done by developed software, in which a technique of computer simulation of the oscillating motion of considerable length rotating rods under the action of axial periodic loads is implemented. Such software gives the possibility to model the oscillatory motion of rotating rods and determine the parameters by witch the dynamic stability loss of the studying system can occur. Using this software the diagrams with regions of stable and unstable motion of the rotating shaft were drawn for various parameters of the considered system. The process of oscillation is considered in space with account of inertia forces and geometric nonlinearity of the rod. It is shown, that on certain rotational speeds and frequencies of vibro-impact load there are ranges of unstable motion where the run of equipment can inevitably lead to destruction. The obtained results are analyzed. The conclusion about the possibility of running the equipment in certain frequency ranges is made.

Author Biographies

Petro Lizunov, Kyiv National University of Construction and Architecture

Doctor of Technical Science, Professor, Head of the Department of Structural Mechanics

Hryhorii Ivanchenko, Kyiv National University of Construction and Architecture

Doctor of Technical Science, Professor, Dean of the Construction Faculty

Valentyn Nedin, Kyiv National University of Construction and Architecture

Candidate of Technical Science, Associate Professor of the Department of Structural Mechanics

References

Bazhenov V.A., Pohorelova O.S., Postnikova T.G. Khaos ta stsenariyi perekhodu do khaosu u vibroudarniy systemi (Chaos and scenarios of transition to chaos in the vibratory system). – Kyiv: Vyd-vo «Karavela», 2019. – 146 pp.

Bakhvalov N.S., Judkov N.P., Kobelkov G.M. Chislennye metody. M.: BINOM, Laboratoriya znaniy, 2015, 639 pp.

Belyaev A. Dynamics of rod under axial impact by a body / Alexander K. Belyaev, Chien-Ching Ma, Nikita F. Morozov, Petr E. Tovstik, Tatiana P. Tovstik, Anatoly O. Shurpatov // Vestnik SPbGU. Matematika. Mekhanika. Astronomiya. – 2017. V. 4 (62). –P. 506-515.

Belyaev A. Dinamicheskiy podkhod k zadache Ishlinskogo–Lavrent'yeva / A.K. Belyayev, D.N. Il'in, N.F. Morozov // Mekhanika tverdogo tela. – 2013. No. 5. – P. 28-33.

Belyaev A. Parametric resonances in the problem of longitudinal impact on a thin rod / Alexander K. Belyaev, Nikita F. Morozov, Petr E. Tovstik, Tatiana P. Tovstik // Vestnik SPbGU. Matematika. Mekhanika. Astronomiya. – 2016. V. 3 (61). – P. 77-94.

Bolotin V.V. Dinamicheskaya ustoychivost uprugikh system. M.: Izdatelstvo tekhniko-teoreticheskoj literatury, 1956, 600 pp.

Lizunov P.P., Nedin V.O. The gyroscopic forces influence on the oscillations of the rotating shafts // Strength of materials and theory of structures. – 2020. – Issue 105. P. 199–209.

Lizunov P., Nedin V. The parametric oscillations of rotating elastic rods under the action of the periodic axial forces // Management of Development of Complex Systems. – 2020, 44, 56–64.

Lizunov P.P., Nedin V.O. The stability of rotating rods under the action of vibro-impact load // Strength of materials and theory of structures. – 2021. – Issue 106. P. 113 – 121.

Morozov N.F. Static and Dynamics of a Rod at the Longitudinal Loading / N.F. Morozov, P.E. Tovstik, T.P. Tovstik // Vestnik YUUrGU. Seriya «Matematicheskoye modelirovaniye i programmirovaniye». – 2014. – Vol. 7, No. 1. – S. 76–89.

Morozov N.F. The rod dynamics under short longitudinal impact / N.F. Morozov, P.E. Tovstik // Vestnik SPbGU. – 2013. – Vup. 3. P.131–141.

Munitsyn A.I. Prostranstvennyye izgibnyye kolebaniya sterzhnya, vrashchayushchegosya vokrug svoyey osi (Space bending oscillations of a rod rotating around its axis) // Matematicheskoye i komp'yuternoye modelirovaniye mashin i sistem. – 2008. S. 64–67.

Murtazin I.R. Research of flexural vibrations of rotating shafts with distributed inertial, elastic and eccentricity properties / I.R. Murtazin, A.V. Lukin, I.A. Popov // Scientific and Technical Journal of Information Technologies, Mechanics and Optics. – 2019. – Vol. 19, no. 4, P. 756–766.

Nedin V.O. The parametric oscillations of rotating rods under action of the axial beat load // Strength of materials and theory of structures. – 2020. – Issue 104. P. 309 – 320.

Nedin V. Numerical differentiation of complex bend forms of long rotating rods // Management of Development of Complex Systems. – 2020, 43, 110 –115.

Maurice Petyt. Introduction to Finite Element Vibration Analysis. Cambridge University Press, 1990. – 558 p.

Yimin Wei. Influence of Axial Loads to Propagation Characteristics of the Elastic Wave in a Non‑Uniform Shaft / Yimin Wei, Zhiwei Zhao, Wenhua Chen and Qi Liu // Chinese Journal of Mechanical Engineering. – 2019 – No. 32:70. P.13.

Published

2021-10-29

Issue

Section

Статті