Rock destruction effect on the stability of a drilling structure

The motion of a drilling structure is studied in torsion. The stability of the stationary solution is determined by the direct method of Liapounov, supplemented with results for the linearized method. The stability criterion is firmly based on the form of the boundary condition linked to the rock destruction process. This rock/bit interaction function can be deduced using studies on rock mechanics, based on yield design formalism. Assuming a quasi-static axial evolution, numerical simulations illustrate the instability of the stationary solution: the bit motion can converge on a limit cycle, often called stick-slip. The beam therefore evolves as a complex cone-shaped limit surface. A simple two-degrees-of-freedom system is now considered in both axial and torsional directions, to quantify the quasi-static axial assumption. The instability of the stationary solution is confirmed by the linearized method for the undamped system with the postulated boundary conditions. Even for small damping values the same result is achieved. Even though a limit cycle appears in the axial plane (small amplitude), stick-slip can be described adequately by considering a quasi-static axial evolution. (C) 2000 Academic Press.