An alternative characterization of bit-sticking phenomena in a multi-degree-of-freedom controlled drillstring

A piecewise-smooth model of three degrees of freedom, which exhibits friction-induced stick-slip oscillations, is considered. This model corresponds to a simplified torsional lumped-parameter model of an oilwell drillstring. An alternative method to characterize the stick-slip motion and other bit-sticking problems in such a drilling system is proposed. This method is based on the study of the relationships between the different types of system equilibria and the existing sliding motion when the bit velocity is zero. It is shown that such a sliding motion plays a key role in the presence of nondesired bit oscillations and transitions. Furthermore, a proportional-integral-type controller is designed in order to drive the rotary velocities to a desired value. The ranges of the controller and the system parameters which lead to a closed-loop system without bit-sticking phenomena are identified.