Glovach L. Direct and inverse problems of mechanic bending of drill columns in curvilinear deep bore-holes

New urgent scientific problems on mechanical behavior of drill columns in their elastic bending in curvilinear channels of hyper-deep inclined and horizontal bore-holes are stated and solved with the aim to prognosticate and avert the emergency regimes of their functioning. Using the theory of curvilinear flexible rods, the mathematical model is elaborated and differential equations are formulated, which describe elastic deforming of drill columns in channels of curvilinear deep bore-holes. In the model, the stiffnesses in bending, inhomogeneous gravity forces as well as forces of contact and friction interaction of the drill columns with the bore-hole wall are taken into consideration. Direct and inverse problems are formulated for the constructed equations. The problems about determination of resistance forces and moments at axial motion and rotation of the drill columns in the bore-holes with circular, catenary, elliptic, parabolic and hyperbolic trajectories are solved. The problems about modeling of elastic bending and origin of critical states for drill strings in curvilinear bore-holes with spiral and cosinusoidal imperfections are stated. The diapasons of geometry and imperfection parameters corresponding to favorable and unfavorable regimes of functioning are found; their critical values corresponding to the drill columns sticking are calculated.