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Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control

Nonlinear Dynamics volume 78, pages 1891–1906 (2014)Cite this article

Abstract

Nonlinear motions of a rotary drilling mechanism are considered, and a two degree-of-freedom model is developed to study the coupled axial-torsional dynamics of this system. In the model development, state-dependent time delay and nonlinearities that arise due to dry friction and loss of contact are considered. Stability analysis is carried out by using a semi-discretization scheme, and the results are presented in terms of stability volumes in the three-dimensional parameter space of spin speed, cutting depth, and a cutting coefficient. These stability volume plots can serve as a guide for choosing parameters for rotary drilling operations. A control strategy based on state and delayed-state feedback is presented with the goal of enlargening the stability region, and the effectiveness of this strategy to suppress stick-slip oscillations is illustrated.

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Acknowledgments

The authors from Shanghai Jiao Tong University gratefully acknowledge the support received through 973 Grant No. 2011CB706803 and No. 2014CB04660.

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Authors and Affiliations

  1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai , 200240, China

    Xianbo Liu, Xinhua Long & Guang Meng

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD , 20742, USA

    Nicholas Vlajic & Balakumar Balachandran

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  1. Xianbo Liu
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  2. Nicholas Vlajic
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  3. Xinhua Long
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  4. Guang Meng
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  5. Balakumar Balachandran
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Correspondence to Balakumar Balachandran.

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Liu, X., Vlajic, N., Long, X. et al. Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control. Nonlinear Dyn 78, 1891–1906 (2014). https://doi.org/10.1007/s11071-014-1567-y

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  • DOI: https://doi.org/10.1007/s11071-014-1567-y

Keywords

  • Drill string
  • State-dependent time delay
  • Stability analysis
  • Semi-discretization method
  • Stick-slip vibrations
  • Vibration control