Andrusenko O. Non-linear elastic deforming of drill strings in cavities of deep curvilinear bore-holes with geometric imperfections

In the dissertation, the improved mathematical model of non-linear elastic deforming of drill strings in the channels of curvilinear bore-holes is created. On the basis of usage of a specially chosen movable reference frame, the simplified constitutive equations are elaborated. They differ by absence of singularities connected with transformation of the radii of curvature and twist into infinity. The computer analysis of influence of the bore-hole axis line geometry imperfections on the forces resisting to drill string motion during performing lifting-lowering operations is performed. The questions of the forces minimization through the choice of optimal ratio between the velocities of axial and rotary motions are considered. The cases when the geometric imperfections have the shapes of localized harmonics with variable amplitudes, localized 3D-spirals and localized smoothed breaks are analyzed. The computer simulation of the elastic process of the drill string post-critical deforming in a cylindrical cavity is performed. It is shown that the drill string buckling proceeds in the shape of 3D spiral with variable pitch.