Example of Instability in Drive Mechanisms

Abstract

Stability of rotation of a drillstring in curved oil wellbores is studied. The drillstring is considered as a Cosserat rod and the equations for a spatially curved drillstring and hole are derived and studied in detail for circular cross sections. The cases which allow for the solution in closed form are analysed. The rotation with a constant angular velocity is shown to be feasible only for a straight drillstring. In all other cases the rotation is unstable and for some relations between the parameters it is accompanied by a quasi-static transition to a new configuration. The instability is caused by the energy exchange between the torsional and bending modes. The increasing torque on the end of the drillstring improves the rotational stability at expenses of the increasing stresses in the string.