Rotary drilling dynamics with an asymmetric distribution of cutters on the drill-bit

This work investigates the global dynamics of the bottom hole assembly with non-uniformly distributed cutters on drill-bit which improves stability of steady drilling. In this work, the drill string with a bottom hole assembly is considered as a lumped parameter model in the axial and torsional directions to accommodate axial and torsional vibrations, respectively. The regenerative effect due to the variation in the depth of cut is considered the only source of instability in the system. The engagement of individual cutters with the cut surface is modeled by formulating separate cut surface profile between two simultaneous cutters which is essential in capturing the true global dynamics of the system. Linear stability analysis through eigenvalue analysis reveals the system’s improved stability compared to the system equipped with uniformly distributed cutters. An optimal distribution of cutters on the drill-bit for different number of cutters leading to the most stable steady drilling is obtained. This optimal distribution has been found to be robust with respect to changes in the rock strength as well as drill-rig parameters. A detailed nonlinear numerical analysis of the system with the optimal distribution reveals the existence of subcritical and supercritical Hopf bifurcation at different lobes of stability boundaries. Further analysis unveils various complex phenomenon, such as the co-existence of the steady solutions with the chaotic solution, partial bit-bounce, complete bit-bounce, and stick–slip vibrations.