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.
Bibliographical noteFunding Information:
The research was supported by grants from BP-Amoco (UK), Security-DBS (USA), Diamant Drilling Services (Belgium), and CSIRO (Australia) and by a Sommerfeld fellowship from the Department of Civil Engineering of the University of Minnesota. The authors are in particular indebted to Martyn Fear from BP-Amoco for bringing them the reality of field data and for his confidence in the research team. The authors would also like to recognize the contributions of Dr. T. Insperger (Budapest University of Technology and Economics) and Prof. R. Sepulchre (University of Liège) in the formulation of the linear stability analysis. Finally the authors would like to thank one of the reviewers for his careful critique of the original manuscript and for valuable comments which have enabled us to improve the paper.