Coupled torsional and bending vibrations of actively controlled drillstrings

The dynamics of actively controlled drillstrings is studied. The equations of motion are derived using a lumped parameter model in which the coupling between torsional and bending vibrations is considered. The model also includes the dynamics of the rotary drive system which contains the rotary table, the gearbox and an armature controlled DC motor. The interactions between the drillstring and the borehole which are considered, include the impacts of collars with the borehole wall as well as bit rotation-dependent weight and torque on bit (WOB and TOE). Simulation results obtained by numerically solving the equations of motion are in close qualitative agreement with field and laboratory observations regarding stick-slip oscillations. A linear quadratic regulator (LQR) controller is designed based on a linearized model and is shown to be effective in eliminating this type of oscillations. It is also shown that for some operational parameters the control action may excite large bending vibrations due to coupling with the torsional motion. (C) 2000 Academic Press.