| Drillstring undergoes several modes of vibrations simultaneously. These vibrations can be classified into three main groups based on their directions: axial, transverse and torsional vibrations. Coupling between these vibrations is possible and it yields uncertainty in vibration analysis and monitoring. Stick-slip in drillstrings is a specific type of torsional vibrations. Stick-slip involves periodic fluctuations in bit rotational speed, ranging from almost zero velocity to a stage of high rotational speed, often more than twice the surface speed.; In this study, a dynamic model of the drillstring is formulated using consistent mass finite element approach. The developed model accounts for the coupling between axial and bending vibrations, the dynamic coupling between bending and torsional vibrations as well as the effect of rotary inertia, gyroscopic moment and gravitational axial stiffening. Stick-slip is modeled using proper downhole boundary conditions, which admit the excitation of stick-slip oscillations. The effects of stick-slip are investigated by studying the associated dynamic responses of the drillstring. |
