Stick-slip oscillations of drag bits by considering damping of drilling mud and active damping system

Abstract

This paper studies self-excited stick-slip oscillations of a rotary drillstring with a drag bit. In previous researches coupling between torsional and axial vibration was studied for a system with two degrees of freedom and without considering the effects of rotary table, damping of drilling mud and active damping system. In this research, for the first time a complete model is considered. This model is a discrete model with two degrees of torsional freedom and one degree of axial freedom. Both frictional contact and cutting process at bit-rock interface have been considered by bit-rock interaction law. There is a coupling between torsional mode and the axial mode through this law. In this paper, the effects of damping, active damping ratios and bit-rock interaction number have been studied on stick-slip motion. The equations of motion have been solved by numerical method. The technique of solution is Euler-forward finite difference technique. This research shows that by increasing the damping of drilling mud, bit parameter and by appropriate selection of active damping ratios, stick-slip oscillation of bit can be avoided and oscillation of rotary table be damped.