Shabnam Tashakori - Department of Mechanical Engineering, Sharif University of Technology
Gholamreza Vossoughi - Department of Mechanical Engineering, Sharif University of Technology
Hassan Zohoor - Department of Mechanical Engineering, Sharif University of Technology
Ehsan Azadi Yazdi - Department of Mechanical Engineering, Shiraz University

Drill strings, used for oil and gas exploration and extraction, are subjected to complex coupled dynamics that involves axial, torsional and lateral vibrations. In this paper, the distributed axial-torsional dynamics of such systems is studied to investigate the root cause ofthese vibrations and as a basis for further studies on stability analysis and control design. In this regard, the neutral-type time delay model is modified, where both the cutting process and frictional contact are considered in the bit-rock interaction. Moreover, the damping effect of the drilling mud is considered in the boundary conditions. The resulting equations of motion, which are obtained directly from the distributed parameter model, are neutral-type delay differential equations with constant state and input delays, introduced by theoscillatory behavior of the drill string, and a statedependent delay, induced by the bit-rock interaction.Illustrative simulation results are presented for the nonlinear system which demonstrate intense axial and torsional vibrations that may lead to system failure.

Drill sting; Neutral-type time-delay dynamic model; Coupled axial-torsional vibrations; Bit-bounce phenomenon; Stick-slip oscillations