Influence of bit-rock interaction on stick-slip vibrations of PDC bits

This paper describes a new approach to understand the causes of stick-slip vibrations experienced by PDC bits. This new model takes into consideration not only the axial and torsional modes of vibration, but also the coupling between these two modes through bit-rock interaction laws, which are consistent with laboratory results from single cutter experiments. These interaction laws, which account for both frictional contact and cutting processes at the bit-rock interface, are formulated in terms of the depth of cut, a variable that brings into the equations the position of the bit at a previous a priori unknown time. They also account for potential loss of frictional contact between the wear-flats and the rock. The delayed and coupled nature of this interaction is ultimately responsible for the occurrence of self-excited vibrations, which can degenerate into stick-slip oscillations under certain conditions. The features of the torsional vibrations that are predicted with this model are well in accordance with field observations. Furthermore, the results reveal that the model predicts apparent rate effects as an inherent outcome of the nature of the bit-rock interface.