TY - JOUR
AU - Kudaibergenov, Askat K.
AU - Khajiyeva, L. A.
PY - 2018/08/27
Y2 - 2024/10/13
TI - On dynamic stability of drill strings in a supersonic gas flow
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 97
IS - 1
SE - Mechanics
DO - 10.26577/jmmcs-2018-1-488
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/488
SP - 101-110
AB - <p>In this work stability of the drill string nonlinear dynamics, complicated by the effect of an external<br>axial load, initial curvature of the drill string, geometric nonlinearity and the influence of a<br>supersonic gas flow as a circulating medium is studied. The drill string is modelled as a rotating<br>elastic isotropic rod with constant cross-section. Pressure of the gas flow used to clean the borehole<br>from drill cuttings and to transport them from the bottom to the surface is determined by the<br>nonlinear dependences of the piston theory in the third approximation. Utilization of the Galerkin<br>method allows to reduce the drill string mathematical model to an ordinary differential equation<br>for the generalized time function, containing an asymmetric nonlinear characteristic, which is further<br>eliminated by introducing the corresponding substitution. Considering a small perturbation<br>to the system and applying the harmonic balance method, characteristic determinants are constructed.<br>Equations describing boundaries of instability zones of basic resonance, which allow to<br>determine the range of dangerous frequency regimes and to increase safety of the drilling process,<br>are obtained.</p>
ER -