DYNAMICS OF A CONVEX BIT ROLLING OVER CURVILINEAR WELL BOTTOM

摘要

The problem of the dynamical bending of a drill string rotating in a deep borehole with self-excitation of whirling oscillations of the bit on the well bottom is stated. A mathematical model describing the rolling of a spherical bit over an ellipsoidal bottom is developed. The whirling modes of the bit in fixed and rotating frames of reference are plotted. It is shown that the calculated trajectories of the bit can be spirals that unwind (unstable mode) or wind (stable mode). They are characterized by high accelerations and, therefore, are dangerous for the system.