An approximate analysis of dry-friction-induced stick-slip vibrations by a smoothing procedure.

*(English)*Zbl 0966.70013The authors consider the dynamics of oil exploration drill strings. In engineering practice, dry friction often generates undesirable effects such as self-sustained stick-slip vibrations which produce noise and shorten the lifespan of mechanisms. To study the behaviour of torsional stick-slip vibrations of oil exploration drill strings, the discontinuous forces are approximated by smooth forces. The authors use 1-DOF and 2-DOF block-and-belt models, and analyse both stable and unstable periodic solutions. Simultaneously, the authors introduce a nonlinear 2-DOF model where the drill pipe is modelled by linear torsional spring, the drill collars are assumed to be rigid and are modelled by an equivalent mass with the corresponding moment of inertia and linear damping, and the drill bit is subjected to Coulomb’s friction force.

Reviewer: Yuri N.Sankin (Ul’yanovsk)

##### MSC:

70K40 | Forced motions for nonlinear problems in mechanics |

70K05 | Phase plane analysis, limit cycles for nonlinear problems in mechanics |

70-08 | Computational methods for problems pertaining to mechanics of particles and systems |