Global modelling of nonlinear spatiotemporal dynamics of a drill‐string with multiple regenerative effects

Abstract

We develop an integrated model with spatially distributed inertia to study the axial and torsional dynamics of a drill-string. This model involves nonlinearities that arise due to regenerative cutting and frictional effects in drill-bit/rock interaction, which couple the axial and torsional dynamics with each other. Moreover, the multiple regenerative effects arising from bit-bounce are also taken into account by modelling the evolution of the cutting surface profile. The developed dynamic model is tested by checking its convergence and prediction ability, showing that the model is robust. Then, the linear eigenvalue analysis for drilling stability is performed, and a special attention is devoted to the influence of spatial discretization resolution of the drill-string. Numerical bifurcation analysis reveals both subcritical and supercritical types of instability near the stability boundaries, which trigger various co-existing attractors and nonlinear drilling dynamics, such as stable limit-cycle motion, periodic stick-slip vibration and bit-bounce. Delving further into the unstable region outside the left stability boundary, we capture more complex dynamics including periodic-two and even chaotic chatters with bit-bounce.