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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Hidden Oscillations in Drilling Systems: Torsional Vibrations

Journal of Applied Nonlinear Dynamics 2(1) (2012) 83--94 | DOI:10.5890/JAND.2012.09.006

G.A. Leonov; M.A. Kiseleva; N.V. Kuznetsov; P. Neittaanmäki

Department of Applied Cybernetics, Saint-Petersburg State University, Universitetsky pr. 28, Saint-Petersburg, Russia, 198504

Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), Jyväskylä, Finland, FI-40014

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Study of drilling systems plays important role in drilling industry. During the operation mode these systems experience different kinds of vibration, which may cause malfunctioning (i.e. dissipation of kinetic energy, noise, excessive wear, machine parts premature failure etc). In this article the most common type of vibrations is considered - torsional vibrations. The two mass model of a drilling system and modified version of it, supplemented by equations of induction motor, are studied. Both systems experience so-called hidden oscillations. It is extremely difficult to analyze such hidden oscillations since they cannot be found with the help of standard analytical procedures of trajectory modeling in the equilibrium state domain. Hidden oscillations correspond to torsional vibrations in real systems, thus they may cause breakdowns.


This work was partly supported by the Government of the Russian Federation (Ministry of Education and Science of the Russian Federation), Russian Foundation for Basic Research, Saint-Petersburg State University, Academy of Finland and Finnish Doctoral Programme in Computational Science.


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