A SIMPLE COSSERAT MODEL FOR THE DYNAMICS OF DRILL-STRINGS Robin W Tucker, Charles Wang Lancaster University, Department of Physics Lancaster LA1 4YB, UK r.tucker@lancaster.ac.uk Abstract Some of the vibrational states experienced by the active components of a drilling assembly (as used in the oil or gas industry) are discussed in the context of an integrated mathematical model. A control mechanism designed to ameliorate the sustained excitation of torsional relaxation oscillations due to frictional torques generated by an active bit during drilling operations with an extended drill-string is discussed. Analytic and numerical simulations indicate that many of the volatilities suffered by existing soft-torque feed-back approaches used to combat slip-stick can be eliminated by the alternative mentioned herein. INTRODUCTION Despite continuing efforts to control the vibrational states experienced by on-shore drilling-assemblies a comprehensive understanding of their genesis and interaction remains an important challenge for the engineer and applied mathematician. Although numerous control strategies have been devised to ameliorate unwanted vibrations practical implementations often rely on anecdotal evidence and the experience of generations of drilling engineers. The dynamics of a long slender rotating drill-string under a compressive load of several hun- dred kN linking a source of surface torque to a heavy drillbit that cuts into rock, ejecting fluid “mud” at high pressure, is inherently unstable under lateral, axial and torsional perturbations. Ef- fective stable drilling over a range of configurations can only be achieved by feedback control of drive-torque and active monitoring of the dynamic environment of the drill-string and bit. The presence of frictional torques that depend non-linearly on the angular speed of the drillbit and its reaction force to the rock-surface (“weight on bit”) is responsible for the excitation of torsional relaxation oscillations that in turn can excite axial and flexural modes that result in the phenomena of “bit-bounce” and drill-string collisions with the walls of the bore-cavity. The existence of these dangerous dynamical states is responsible for much of the continuing effort [4] to find more effec- tive control strategies that address the drilling assembly in its entirety rather than separate controls for the torsional, flexural and axial instabilities of its various components. A programme to address this issue has recently been initiated [1] by modeling the assembly in terms of the special Cosserat theory of rods [2] and their interactions with the environment.