A simple model of bit whirl for deep drilling applications

A simple analytical model of bit whirl is presented. In contrast to the previous works, which consider bottom hole assembly mass imbalance to model bit whirl, the model here takes into account the history-dependent boundary conditions at the bit–rock interface as well as the bit geometry. In particular, an analytical expression for the bit–rock interaction is derived. It is shown that the bit geometry affects the bit–rock interaction only through three dimensionless parameters. Depending on the value of these parameters the system can be stable or undergo forward or backward whirl.