Fully coupled vibrations of actively controlled drillstrings

A fully coupled model for axial, lateral, and torsional vibrations of actively controlled drillstrings is presented. The proposed model includes the mutual dependence of these vibrations, which arises due to bit/formation and drillstring/borehole wall interactions as well as other geometric and dynamic non-linearities. The active control strategy is based on optimal state feedback control designed to control the drillstring rotational motion. It is demonstrated by simulation results that bit motion causes torsional vibrations, which in turn excite axial and lateral vibrations resulting in bit bounce and impacts with the borehole wall. It is also shown that the results are in close qualitative agreement with field observations regarding stick-slip and axial vibrations and that the proposed control is effective in suppressing them. However, care must be taken in selecting a set of operating parameters to avoid transient instabilities in the axial and lateral motions.