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


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

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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).

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