The parametric oscillations of rotating rods under action of the axial beat load
DOI:
https://doi.org/10.32347/2410-2547.2020.104.309-320Keywords:
numerical differentiation, complex bend forms, spline, geometric nonlinearity, axial loads, hammer drillsAbstract
The paper presents the results of investigation of the axial beat loads’ influence on the transverse rotating rods’ oscillations and their stability. The perforator's long drills are considered as objects of investigation.
The analysis of different author’s papers that are studded the dynamics of oscillations of shafts and rotating rods is carried out. The relevance of the research topic is substantiated. The model of the considered dynamic system is described and equations of oscillations in space are given.
The technique for investigation is presented. This technique is based on search for new bend forms of rotating rod by solving the equations of oscillations with using the Hubbolt time integration method and the polynomial functions (splines) that are described the current bend form. In it, the spline functions are found by current bend form approximation where each of the found functions is responsible to certain point of rod elastic line and describes the position of nearby points.
Described technique was realized in a computer program with graphic user interface that is developed by author. Program allows to monitor for dynamics of the oscillatory motion of the modeled system in real-time by calculating and drawing the current band forms of the rotating rod during the oscillation.
Diagrams with regions of stable and instable motion of the rods, that were found by different parameters and boundary conditions are shown. The analysis of the results is obtained and the conclusion about possibility of operating the equipment in certain frequency ranges is done. The space oscillating process of rotating rods is considered with account of the gyroscopic loads and geometric nonlinearity.
References
Ahlberg J., Nilson E., Walsh J. Teoriya splaynov i ee primenenie (Spline theory and its application). M.: Mur, 1972, 319 pp.
Bakhvalov N.S., Judkov N.P., Kobelkov G.M. Chislennye metody (Numerical methods). M.: BINOM, Laboratoriya znaniy, 2015, 639 pp.
Bolotin V.V. Dinamicheskaya ustoychivost uprugih system (The dynamic stability of elastic systems). M.: Izdatelstvo tekhniko-teoreticheskoj literatury, 1956, 600 pp.
Gulyayev V. I. Bifurkatsionnoye vypuchivaniye vertikalnykh kolonn sverkhgdubokogo bureniya (Bifurcational buckling of vertical super-deep drilling columns) / V.I. Gulyayev, V.V. Gaydaychuk, I.V. Gorbunovich // Promyslove budivnytstvo ta inzhenerni sporudy. –2009. – No. 2. – S. 10–15.
Gulyayev V. I. Kompyuternoye modelirovaniye dinamiki konstruktsiy ustanovok glubokogo bureniya (Computer modeling of dynamics of deep drilling rigs’ constructions) / V. I. Gulyayev, V.V. Gaydaychuk, S.N. Xudolij // Zbirnyk naukovykh pratsʹ Ukrayinsʹkoho naukovo-doslidnoho ta proektnoho instytutu stalevykh konstruktsiy imeni V. M. Shymanovskoho. – 2009. - Vip. 4. – S. 208–216.
Zavyalov YU.S., Kvasov B.I., Miroshnichenko V.L. Metody splajn-funkcij (Spline functions methods). M.: «Nauka», 1980, 352 pp.
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 kompyuternoye 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.
Tondl A. Dinamika rotorov turbogeneratorov (The rotor dynamics of turbines). L., Energiya, 1971, 297 pp.
Maurice Petyt. Introduction to Finite Element Vibration Analysis. Cambridge University Press, 1990. – 558 p.
Songyong Liu. Coupling vibration analysis of auger drilling system / Songyong Liu, Xinxia Cui, Xiaohui Liu // Journal of vibroengineering. – 2013. Vol. 15. – P.1442–1453.
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.
Downloads
Published
Issue
Section
License
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
