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, su pplemented with results for the linearized method. The stability criterion is firmly based on the form of the boundary condition linked to the rock de struction process. This rock/bit interaction function can be deduced using studies on rock mechanics, based on yield design formalism. Assuming a quas i-static axial evolution, numerical simulations illustrate the instability of the stationary solution: the bit motion can converge on a limit cycle, o ften 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 as sumption. The instability of the stationary solution is confirmed by the li nearized method for the undamped system with the postulated boundary condit ions. Even for small damping values the same result is achieved. Even thoug h a limit cycle appears in the axial plane (small amplitude), stick-slip ca n be described adequately by considering a quasi-static axial evolution. (C ) 2000 Academic Press.