Glazunov S. Quasi-static and dynamic frictional effects in deep bore-hole drilling

Owing to the joint application of civil engineering methods for flexible curvilinear elastic rods deforming together with methods of theoretical mechanics, differential geometry and calculation mathematics, new mathematic models and differential equations are constructed. They describe drill string dragging with rotation inside curvilinear bore-holes with three-dimensional axes prescribed in a discrete (tabular) form with the use of results of geophysical survey (bore-hole navigation). They permit one to calculate the forces of contact and friction resistance to the drill string displacement and prognosticate the dead lock states. With their use, the new techniques for design connection of the trajectory segments with differing curvatures are elaborated. It is proposed for this aim to apply the Cornu spiral arcs or cubic parabols. On the basis of the functions of nonlinear frictional interaction of the drill bit with the destroyed rock (cutting forces) available in the modern literature, new mathematic models of drill string torsional autovibrations in viscous mud medium are elaborated. Computer simulation of bifurcation transfers from states of simple rotation of the drill string to the states of its autovibrations are studied.