State-Dependent Delay and Drill-String Dynamics

In this work, stability analysis carried out with a reduced-order model of a drill string is presented. This model, which is nonlinear in nature and contains a state-dependent delay, is used to study coupled axial and torsion dynamics of the system. The axial penetration rate and drill spin speed are used as control parameters, and the analysis reveals that the consideration of the state-dependent delay is critical for capturing the influence of the axial penetration rate. As a part of the analysis, the linearized system associated with state-dependent delay is constructed and the D-subdivision method is utilized. The results are presented in the form of stability charts in the plane of spin speed and cutting coefficient and in the plane of spin speed and penetration rate. These results confirm the earlier findings obtained through numerical means with full and reduced-order models.