Non Linear Model For Coupled Vibrations Of Drill-Strings.

Marcelo T. Piovan, Rubens Sampaio


In the present work a continuous model is presented to study, by means of finite element
discretization, the coupling of extensional, flexural and torsional vibrations on a drillstring, which is described
as a vertical slender beam under axial rotation. The structure is subjected to distributed loads
due to its own weight, the reaction force and perturbation moments at the lower end. The beam structure
is also confined to move inside a rigid cylinder, which simulates the borehole. The impacts and
friction of the drill-string with the borehole are modeled employing simplified forms. It is known that
the accounting of geometrical non-linearities affects the dynamics of slender beams. The vibrations of
drill-strings are frequently analyzed by means of lumped parameter models. Normally, these models employ
equivalent lumped parameters which are obtained from experimental field data or from continuous
models assuming one-mode approximation for extensional, flexural and torsional vibrations. However,
the lumped parameter models do not include dynamical effects due to geometrical non-linearities. In
this context, the objective of present work is to analyze the effects of geometrical non-linearities in the
vibration of drill-strings together with the patterns of vibroimpact and comparing the results with the
predictions of linear models. The beam model is discretized using a finite element with 12 degrees of
freedom. The results have shown an important influence of the geometric non-linearities (when compared
with the predictions of a linear model) in the dynamic responses of the drill-strings, especially
when the beam undergoes impact patterns with the borehole or the rock formation. This influence can
be observed in the calculation of reaction forces at top position as well as the time histories of radial

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