In this work, we model and analyse drill-string vibrations. A special attention is paid to stick-slip and bit-bounce behaviours that are normally treated as the non-smooth dynamics. A two degrees-of-freedom lumped parameters model is employed to account for axial and torsional vibrations based on the model proposed by Christoforou and Yigit (J. Sound Vibr. 267:1029–1045, 2003). The coupling between both vibration modes is through contact with the formation, where the axial force is the catalyst to generate a resistive torque. The forces and torques are defined according the contact or non-contact scenarios, establishing a non-smooth system. Besides, the dry friction between the formation and the drill-bit introduces the other non-smoothness of the system. Here we adopt smoothened governing equations which are advantageous in terms of mathematical description and numerical analysis. Our studies have shown that the mathematical model is capable of predicting a full range of dynamic responses including the stick-slip and drill bit-bounce. A global analysis shows different scenarios related to parameter changes allowing to develop an in depth understanding of the drill-string dynamics and define critical behaviours of the system.
- non-linear dynamics
- drill string