Stick-Slip Patterns In Coupled Extensional/Torsional Vibrations Of Drill-Strings.

Abstract

In the present work a geometrically non-linear model is presented to study the coupling
of axial and torsional vibrations on a drill-string, which is described as a vertical slender
beam under axial rotation. The beam is subjected to distributed loads due to its own weight
and the reaction forces at the lower end. It is known that the geometrical nonlinearities play
an important role in the stiffening of a beam. The objective of this work is to understand the
geometrical stiffening/softening effects of axial-torsional coupled vibrations of drill-strings in
different operative conditions. Here, the geometrical stiffening is analyzed using a non-linear
finite element approximation, in which large rotations and nonlinear strain-displacements are
taken into account. The effect of structural damping is also included in the model. To help
to understand these effects comparisons of the present model with linear ones were simulated
and time responses and operative variables were compared. The analysis shows that linear and
non-linear models differ considerably after the first periods of stick-slip. The behavior is more
evident with the increase of the friction process in the lower part of the drill. One of the main
differences between the models is that the linear model predicts higher rotary speed peaks -in a
stick-slip situation- than the non-linear.