The Excitation and Control of Torsional Slip-Stick In the Presence of Axial-Vibrations

The interaction between friction and vibration is a widely recognised source of inefciency in all mechanical systems. The nature of this interaction is very dependent on the dynamic environment and its control requires a detailed understanding of the mathematical structure governing the stability of this environment. Although the fundamental causes of friction-induced intermittent motion have been known since the pioneering studies by S Thomas, and F Bowden and L Leben on slip-stick, the detailed predictions of such e ects in complex mechanical systems have often been limited by ignoring the signi cance of factors such as the coupling between normal and tangential oscillations relative to the sliding interface. Modern drilling technology in the oil and gas industry relies on the understanding and e ective control of non-linear vibration phenomena A typical drill assembly consists of a heavy rotating \drill-bit" attached by a exible \drill-string" to a torque generator at the well head. The system is monitored for torque uctuations produced by the ambient frictional and cutter forces and torsional, axial and lateral motion induced by the borehole, string and drill-bit. If these motions cause the bit to slip or stick repeatedly in the bore hole, catastrophic bit failure can occur. Only careful monitoring of the dynamic environment can warn the drilling engineer when dangerous operational regimes are about to be encountered and bit-failure often necessitate a major re-installation of the entire drilling operation. Most existing mathematical models of such phenomena ignore the e ects of essential non-linearities inherent in the stress-strain constitutive relations, the nature of frictional forces between string, bit and bore-hole, large amplitude excitations and the e ects produced by combined axial, exural and torsional wave propagation along the drill-string. The importance of dynamic non-linear interactions is fully recognised by drilling engineers but little detailed theoretical understanding of their origin exits.