Аннотация
In this work stability of the drill string nonlinear dynamics, complicated by the effect of an external axial load, initial curvature of the drill string, geometric nonlinearity and the influence of a supersonic gas flow as a circulating medium is studied. The drill string is modelled as a rotating elastic isotropic rod with constant cross-section. Pressure of the gas flow used to clean the borehole from drill cuttings and to transport them from the bottom to the surface is determined by the nonlinear dependences of the piston theory in the third approximation. Utilization of the Galerkin method allows to reduce the drill string mathematical model to an ordinary differential equation for the generalized time function, containing an asymmetric nonlinear characteristic, which is further eliminated by introducing the corresponding substitution. Considering a small perturbation to the system and applying the harmonic balance method, characteristic determinants are constructed. Equations describing boundaries of instability zones of basic resonance, which allow to determine the range of dangerous frequency regimes and to increase safety of the drilling process, are obtained.