Multiple Regenerative Effects of the Bit-Rock Interaction in a Distributed Drill-String System

In this paper, a distributed model in terms of neutral-type time-delay equations is presented to investigate the global nonlinear axial-torsional dynamical behavior of a drilling string. A rate-independent bit-rock interaction law is employed for both cutting and frictional forces at the bit. A model is proposed for the estimation of the depth of cut which is valid in the case of bit bouncing and the bit reverse rotation. Illustrative simulation results are presented for a representative case study, which demonstrate the existence of the bit-bounce and reverse-rotation in some practical operating conditions, and indicates the need for taking the resulting multiple regenerative effects into account.