State Dependent Delayed Drill-string Vibration: Theory, Experiments and New Model

We have reviewed the development and the analysis of the coupled two degrees-of-freedom model of drill-string vibration, which assumes a state-dependent time delay and a viscous damping for both the axial and torsional vibration. This model corrects the instability deficiencies of the previous models but it is still based on a uniform angular distribution of blades on a drill-bit, which can lead to unrealistic regenerative types of instability. However, the model sheds some lights on the origin and the interplay between stick-slip and bit-bounce, the dangerous dynamic phenomena encountered during rotary drilling. The experimental rig developed by the Centre of Applied Dynamics Research at the University of Aberdeen is used to show some shortcomings of this model and to develop a new more realistic one. The new model assuming a non-uniform distribution of blades for drag type drill-bits is proposed.