State Dependent Delayed Drill-string Vibration: Theory, Experiments and New Model

Marian Wiercigroch, Nandakumar Krishnan, Lijun Pei, Marcin Tomasz Kapitaniak, Vahid Vaziri

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)
28 Downloads (Pure)


We have reviewed the development and the analysis of the coupled two degrees-of-freedom model of drill-string vibration, which assumes a state-dependent time delay and a viscous damping for both the axial and torsional vibration. This model corrects the instability deficiencies of the previous models but it is still based on a uniform angular distribution of blades on a drill-bit, which can lead to unrealistic regenerative types of instability. However, the model sheds some lights on the origin and the interplay between stick-slip and bit-bounce, the dangerous dynamic phenomena encountered during rotary drilling. The experimental rig developed by the Centre of Applied Dynamics Research at the University of Aberdeen is used to show some shortcomings of this model and to develop a new more realistic one. The new model assuming a non-uniform distribution of blades for drag type drill-bits is proposed.
Original languageEnglish
Pages (from-to)39-50
Number of pages12
JournalProcedia IUTAM
Early online date30 Aug 2017
Publication statusPublished - 2017
EventIUTAM Symposium on Nonlinear and Delayed Dynamics of Mechatronic Systems - Minggugong Campus, Nanjing University of Aeronautics and Astronautics, Nanjing, China
Duration: 17 Oct 201621 Oct 2016


  • drill-string
  • vibration
  • state dependent delay
  • modelling
  • experiments


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