Stability analysis of a state dependent delayed, coupled two DOF model of drill-stringvibration

K. Nandakumar, Marian Wiercigroch

Research output: Contribution to journalArticle

60 Citations (Scopus)

Abstract

Stick-slip and bit-bounce are dangerous dynamic phenomena encountered during rotary drilling of oil-wells, but their exact origins and interplay are far from obvious. In this paper, we consider a fully coupled two degrees-of-freedom model, which assumes a state-dependent time delay and a viscous damping for both the axial and torsional motions. Without making any asymptotic assumptions, we have conducted a detailed linear stability analysis of the resultant mathematical model, which is composed of two coupled delay differential equations. The main significance of our work lies in providing practically useful results, which are in the form of stability charts in the plane of drilling rates and rotary speeds.

Original languageEnglish
Pages (from-to)2575-2592
Number of pages18
JournalJournal of Sound and Vibration
Volume332
Issue number10
Early online date8 Feb 2013
DOIs
Publication statusPublished - 13 May 2013

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drilling
Drilling
viscous damping
Linear stability analysis
Stick-slip
Oil wells
charts
mathematical models
Time delay
Differential equations
slip
differential equations
time lag
degrees of freedom
Damping
oils
Mathematical models

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Condensed Matter Physics
  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Stability analysis of a state dependent delayed, coupled two DOF model of drill-stringvibration. / Nandakumar, K.; Wiercigroch, Marian.

In: Journal of Sound and Vibration, Vol. 332, No. 10, 13.05.2013, p. 2575-2592.

Research output: Contribution to journalArticle

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