Analysis of coupled axial-torsional vibration of drill-string with an inclination angle

Drill-string vibration has a great negative influence on the safety and efficiency of geological drilling. Noticing that the influence of drill-string inclination is not well considered in the literature, this paper develops a novel drill-string vibration model for geological drilling with inclined drill-string. First, the correlation between the inclination angle of borehole and the axial and torsional forces on the drill-string is analyzed. Based on this, a drill-string motion model with the parameters of inclination angle is established. Then, the bit-rock interaction is considered as two processes, axial cutting and torsional friction, and an axial-torsional coupled bit-rock interaction model with state-dependent time delay is established. By combining the established drill-string motion model and bit-rock interaction model, a coupled axial-torsional vibration model of drill-string in inclined borehole is obtained with the effect of borehole wall friction taken into account. The drill-string vibration model proposed in this paper is more general, and includes the existing coupled drill-string vibration model of vertical borehole, which is closer to the actual situation.