Geodesic
Bending vibrations of a heavy horizontal composite rotating shaft limited by a cylindrical baffle
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 79 (2022), pp. 135-151

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Drilling of wells, especially inclined and horizontal ones, is accompanied by the intense interaction of drilling tools with the borehole walls. Inborehole impacts negatively affect the drill pipe connections, electrical connections, strength characteristics of downhole motor structural elements, etc. The impact interaction of a drilling tool with a well is experimentally studied using a test bench, where the drilling tool sample is fixed in the middle of a heavy composite shaft arranged in cylindrical roller bearings. The rotating shaft is involved in the impact interaction with a cylindrical baffle due to bending vibrations. In this paper, a beam model of the described shaft is used to study the effect of the rotation speed, gravity forces, damping, and unbalance on the shaft motion. The research is carried out numerically using the ANSYS engineering software package. It is shown that the gravity forces shift the line of centers of gravity in shaft sections, relative to which it rotates. Damping, which is proportional to the speed, provides the shaft centering. The imbalance of the shaft causes bending vibrations. The possible modes of the shaft motion and the conditions for unstable motion are revealed. The mode of the shaft motion within a cylindrical baffle that ensures a steady periodic impact interaction is determined. This interaction induces elastic waves of the acceleration, transverse force and moments in the shaft.
Keywords: heavy rotating shaft, bending vibrations, impact interaction, acceleration waves, test bench, forward and backward whirl. 
@article{VTGU_2022_79_a11,
     author = {V. M. Pestrenin and I. V. Pestrenina and O. M. Perelman and A. S. Fadeykin and N. D. Derkach},
     title = {Bending vibrations of a heavy horizontal composite rotating shaft limited by a cylindrical baffle},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {135--151},
     publisher = {mathdoc},
     number = {79},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_79_a11/}
}
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%A O. M. Perelman
%A A. S. Fadeykin
%A N. D. Derkach
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V. M. Pestrenin; I. V. Pestrenina; O. M. Perelman; A. S. Fadeykin; N. D. Derkach. Bending vibrations of a heavy horizontal composite rotating shaft limited by a cylindrical baffle. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 79 (2022), pp. 135-151. http://geodesic.mathdoc.fr/item/VTGU_2022_79_a11/