A simplified model to explore the root cause of stick–slip vibrations in drilling systems with drag bits

In this paper a study of the self-excited stick–slip oscillations of a rotary drilling system with a drag bit, using a discrete model that takes into consideration the axial and torsional vibration modes of the system, is described. Coupling between these two vibration modes takes place through a bit–rock interaction law, which accounts for both the frictional contact and the cutting processes. The cutting process introduces a delay in the equations of motion that is responsible for the existence of self-excited vibrations, which can degenerate into stick–slip oscillations and/or bit bouncing under certain conditions. From analysis of this new model it is concluded that the experimentally observed decrease of the reacting torque with the angular velocity is actually an expression of the system response, rather than an intrinsic rate dependence of the interface laws between the rock and the drill bit, as is commonly assumed.