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Shock and Vibration
Volume 2014 (2014), Article ID 429164, 8 pages
Research Article

Chaotic Vibration Analysis of the Bottom Rotating Drill String

1College of Petroleum Engineering, China University of Petroleum, Qingdao 266580, China
2Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4
3Drilling Technology Research Institute, Sinopec Shengli Oil field Administration, Dongying 257000, China

Received 13 August 2013; Accepted 23 January 2014; Published 27 February 2014

Academic Editor: Nuno Maia

Copyright © 2014 Qilong Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Drill string vibration is a widely studied topic. This paper developed a real-time measurement system near the drilling bit and extracted the lateral vibration, longitudinal vibration time series of bottom rotating drill string. In order to reconstruct the phase space, we estimated the delay time with mutual information and calculated the embedding dimension through Cao’s method. Finally, the chaotic characterization of the system is analyzed by calculating the correlation dimension and the largest Lyapunov exponent. The results show that such system can exhibit positive finite-time Lyapunov exponents and a clear convergence toward the correlation dimension, which is a strong indicator for the chaotic behavior of the system. It is expected that the new dynamics found in this paper could be of potential implication to the control methods of the drill string vibration.