The buckling of a drill string in a curvilinear borehole with axial line imperfections

The problem of the elastic buckling of drill strings in the channels of deep curved boreholes with geometric axial line imperfections is formulated. Imperfections in the form of localized helices are considered. The relation between the forces resisting the motion of the string and the amplitudes, pitches and sites of localization of the imperfections is analysed. The distributed forces of contact and friction interaction between the drill string and the borehole surface are found and the effects of seizure of the drill string are established. It is shown that the resistive forces and their moments increase as the amplitudes of the imperfections increase, and as their pitches and the displacement of the zones where they are relocated from the lower most distorted parts to the upper least distorted parts, decrease.