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

K. Nandakumar, Marian Wiercigroch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

112 Citations (Scopus)


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
Issue number10
Early online date8 Feb 2013
Publication statusPublished - 13 May 2013

Bibliographical note

Dr. Pankaj Wahi of IIT Kanpur is gratefully acknowledged for the technical discussions and suggestions on modelling aspects and stability analysis of delay differential equations.


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