Modeling and numerical research of the self-excitation phenomenon of the drill bit whirlings vibrations


  • O. V. Vashchilina Taras Shevchenko National University of Kyiv
  • I. V. Lebedyeva Taras Shevchenko National University of Kyiv
  • O. I. Bilobrytska National Transport University, Kyiv



In the paper an initial stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of nonholonomic kinematic models of mechanic interaction between the contacting uneven bodies. It is assumed that the drill bit is an absolutely rigid spherical body, the well bottom surface is spherical too. It is supposed that the system coaxiality is disturbed through small initial curvature of the drill string, defects of the bit and bore-well geometry or the debalance of the system mass. Linearized equations of the drill bit movement are derived, the frequencies of periodic motions are calculated, and their types are constructed for different geometric parameters of the spherical bits. It is shown that, depending on the system properties, the drill bit motion can to transit to the state of stationary spinning relative to an immovable center of velocities or acquire the regimes of forward and backward whirlings.

Key words: Deep drilling, drill bits, nonholonomic dynamics, forward and backward whirls n.

Pages of the article in the issue: 28-33

Language of the article: Ukrainian


BORISOV, A. V., MAMAJEV, I. S. & KILIN A.A. (2005) Izbrannyye zadachi negolo-nomnoy mekhaniki. Moskva-Izhevsk: Institut komp'yuternykh issledovaniy.

VASILYEVA, A.V. & BUTUZOV, A.V. (1978) Singulyarno vozmushchennyye uravneniya v kriticheskikh sluchayakh. Moskva: MGU.

GULYAYEV, V. I., GLAZUNOV, S. N., GLUSHAKOVA, O. V. et al (2017) Modelirovaniye neshtatnykh situatsiy pri burenii glubokikh skvazhin. Kiev: Yuston publishing.

CHEN, S.L., BLACKWOOD, K. & LAMINE, E. (2002) Field investigation of the effects of stickslip, lateral, and whirl vibrations on roller-cone bit performance. SPE: Drilling & Completion.

GLAZUNOV, S. M., VASHCHILINA, O. V. & LEBEDYEVA, I. V. (2016) Frequency analysis of periodic regimes of drill bit rollings on uneven bottom of a deep bore-hole. Visnyk Kyyivs’koho natsional’noho universytetu imeni Tarasa Shevchenka, Seriya: fizykomatematychni nauky. 1, pp. 41 – 44.

NEIMARK, Yu. I. & FUFAEV, N. A. (1972) Dynamics of nonholonomic systems. Providence, RI: American mathematical society.


How to Cite

Vashchilina, O. V., Lebedyeva, I. V., & Bilobrytska, O. I. (2019). Modeling and numerical research of the self-excitation phenomenon of the drill bit whirlings vibrations. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 28–33.



Differential equations, mathematical physics and mechanics