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

Abstract

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.