Stability analysis of a state dependent delayed, coupled two DOF model of drill-stringvibration

Stick-slip and bit-bounce are dangerous dynamic phenomena encountered during rotary drilling of oil-wells, but their exact origins and interplay are far from obvious. In this paper, we consider a fully coupled two degrees-of-freedom model, which assumes a state-dependent time delay and a viscous damping for both the axial and torsional motions. Without making any asymptotic assumptions, we have conducted a detailed linear stability analysis of the resultant mathematical model, which is composed of two coupled delay differential equations. The main significance of our work lies in providing practically useful results, which are in the form of stability charts in the plane of drilling rates and rotary speeds.