Abstract: Stick-slip vibrations in drill string systems appear to generate effects that increase continuously over time. To address this issue, we studied the characteristics of self-excited oscillations that occur during stick-slip vibrations. By constructing a mechanical model for stick-slip vibrations in drill string systems, we have derived state equations to describe a drill in its sticking and slipping stages and obtained the oscillatory response of the drill during its slipping stage. Based on the characteristics of stick-slip vibrations in drill string systems, we then studied the phase trajectory of the relative rotary motion of a drill in varying initial conditions. The results indicate that a perturbation in the initial phase point of the drill will result in motions that trend toward a stable form of stick-slip vibration. This manifests as a phase trajectory that converges to a stable limit cycle. We also analyzed the reasons underlying the generation of stick-slip vibrations, and found that drill string systems undergoing stickslip vibrations always display a decrease in friction torque during the transition between sticking and slipping states, which is equivalent to the application of an external load in the direction of rotation of the drill. In other words, the negative damping effect that is present during the critical state transition of a drill changes the vibrations of the drill string into self-excited oscillations.

Key words: drill string, stick-slip vibrations, self-excited oscillations, limit cycle, friction torque