Bit-Bounce and Stick-Slip in Drill-String Dynamics

A recently proposed two degrees-of-freedom model for axial and torsional vibrations of drill string elsewhere is here revisited. The model involves state-dependent time delay, with discontinuous cutting and friction force nonlinearities. The original model is, here, enhanced by introducing axial and torsional damping, and axial stiffness. Stability analysis, which is relatively recent for systems with state-dependent delays, is conducted on the enhanced model. For representative parameter values, it is concluded from the analysis that the original model (with no damping) had no stable operating regime, while the enhanced model possesses some practically relevant stable operating regime. The steady drilling state corresponding to the enhanced model is, however, still unstable for a major portion of the operating regime leading to stick-slip and bit-bounce situations.