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

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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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References

  1. Bommer, P.: A Primer of Oilwell Drilling. The University of Texas at Austin, Austin (2008)

    Google Scholar 

  2. Dufeyte, M.-P., Henneuse, H., Elf, A.: Detection and monitoring of the slip-stick motion: field experiments. In: SPE/IADC Drilling Conference, pp. 429–438, 11–14 March 1991

  3. Pavone, D. R., Desplans, J. P.: Application of high sampling rate downhole measurements for analysis and cure of stick-slip in drilling, pp. 335–345. Number SPE 28324. (1994)

  4. Navarro-Lopez, E. M., Suarez, R.: Practical approach to modelling and controlling stick-slip oscillations in oilwell drillstrings. In: Control Applications, 2004. Proceedings of the 2004 IEEE International Conference on, vol. 2, pp. 1454–1460, Sept 2004

  5. Brett, J.F.: The genesis of bit-induced torsional drillstring vibrations. SPE Drill. Eng. 7(3), 168–174 (1992)

    Article  Google Scholar 

  6. Mihajlović, N., van Veggel, A.A., van de Wouw, N., Nijmeijer, H.: Analysis of friction-induced limit cycling in an experimental drill-string system. ASME J. Dyn. Syst. Meas. Control 126(4), 709–720 (2004)

    Article  Google Scholar 

  7. Liu, X., Vlajic, N., Long, X., Meng, G., Balachandran, B.: Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects. Nonlinear Dyn. 72(1–2), 61–77 (2013)

    Article  MathSciNet  Google Scholar 

  8. Liao, C.-M., Balachandran, B., Karkoub, M., Abdel-Magid, Y.L.: Drill-string dynamics: reduced-order models and experimental studies. ASME J. Vib. Acoust. 133(4), 041008 (2011)

    Article  Google Scholar 

  9. Long, X.H., Balachandran, B., Mann, B.: Dynamics of milling processes with variable time delays. Nonlinear Dyn. 47, 49–63 (2007)

    Article  MATH  Google Scholar 

  10. Insperger, T., Stépán, G., Hartung, F., Turi, J.: State dependent regenerative delay in milling processes. ASME IDETC/CIE 2005, (DETC2005-85282), 2005 (2005)

  11. Insperger, T., Stépán, G., Turi, J.: State-dependent delay in regenerative turning processes. Nonlinear Dyn. 47, 275–283 (2007)

    Article  MATH  Google Scholar 

  12. Stépán, G.: Modelling nonlinear regenerative effects in metal cutting. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 359(1781), 739–757 (2001)

    Article  MATH  Google Scholar 

  13. Balachandran, B.: Nonlinear dynamics of milling processes. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 359(1781), 793–819 (2001)

    Article  MATH  Google Scholar 

  14. Balachandran, B., Kalmar-Nagy, T., Gilsinn, D.E.: Delay Differential Equations: Recent Advances and New Directions. Springer, New York (2009)

    Google Scholar 

  15. Richard, T., Germay, C., Detournay, E.: Self-excited stick-slip oscillations of drill bits. Comptes Rendus Mcanique 332(8), 619–626 (2004)

    Article  MATH  Google Scholar 

  16. Richard, T., Germay, C., Detournay, E.: A simplified model to explore the root cause of stickslip vibrations in drilling systems with drag bits. J. Sound Vib. 305(3), 432–456 (2007)

    Article  Google Scholar 

  17. Besselink, B., van de Wouw, N., Nijmeijer, H.: A semi-analytical study of stick-slip oscillations in drilling systems. ASME J. Comput. Nonlinear Dyn. 6(2), 021006 (2011)

    Article  Google Scholar 

  18. Aldred, W. D., Sheppard, M. C.: Anadrill. Drillstring vibrations: A new generation mechanism and control strategies. In: SPE Annual Technical Conference and Exhibition, pp. 353–453, 4–7 Oct 1992

  19. Jansen, J.D., van den Steen, L.: Active damping of self-excited torsional vibrations in oil well drillstrings. J. Sound Vib. 179(4), 647–668 (1995)

    Article  Google Scholar 

  20. Tucker, W.R., Wang, C.: An integrated model for drill-string dynamics. J. Sound Vib. 224(1), 123–165 (1999)

    Article  Google Scholar 

  21. Kreuzer, E., Struck, H.: Active damping of spatio-temporal dynamics of drill-strings. In: IUTAM Symposium on Chaotic Dynamics and Control of Systems and Processes in Mechanics 122, 407–417 (2005)

  22. Yigit, A.S., Christoforou, A.P.: Stick-slip and bit-bounce interaction in oil-well drillstrings. ASME J. Energy Resour. Technol. 128(4), 268–274 (2006)

    Article  Google Scholar 

  23. Khulief, Y.A., Al-Sulaiman, F.A., Bashmal, S.: Vibration analysis of drillstrings with self-excited stickslip oscillations. J. Sound Vib. 299(3), 540–558 (2007)

    Article  Google Scholar 

  24. de Bruin, J.C.A., Doris, A., van de Wouw, N., Heemels, W.P.M.H., Nijmeijer, H.: Control of mechanical motion systems with non-collocation of actuation and friction: a popov criterion approach for input-to-state stability and set-valued nonlinearities. Automatica 45(2), 405–415 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Karkoub, M., Abdel-Magid, Y.L., Balachandran, B.: Drill-string torsional vibration suppression using ga optimized controllers. J. Can. Pet. Technol. 48(12), 1–7 (2009)

  26. Insperger, T., Stépán, G.: Semi-discretization method for delayed systems. Int. J. Numer. Method. Eng. 55(5), 503–518 (2002)

    Article  MATH  Google Scholar 

  27. Insperger, T., Stépán, G.: Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int. J. Numer. Method. Eng. 61(1), 117–141 (2004)

    Article  MATH  Google Scholar 

  28. Liu, X., Vlajic, N., Long, X., Meng, G., Balachandran, B.: Multiple regenerative effects in cutting process and nonlinear oscillations. Int. J. Dyn. Control 2(1), 86–101 (2014)

    Article  Google Scholar 

  29. Germay, C., van de Wouw, N., Nijmeijer, H., Sepulchre, R.: Nonlinear drillstring dynamics analysis. SIAM J. Appl. Dyn. Syst. 8(2), 527–553 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. Germay, C., Denol, V., Detournay, E.: Multiple mode analysis of the self-excited vibrations of rotary drilling systems. J. Sound Vib. 325(12), 362–381 (2009)

    Article  Google Scholar 

  31. Detournay, E., Defourny, P.: A phenomenological model for the drilling action of drag bits. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 29(1), 13–23 (1992)

    Article  Google Scholar 

  32. Detournay, E., Richard, T., Shepherd, M.: Drilling response of drag bits: theory and experiment. Int. J. Rock Mech. Min. Sci. 45(8), 1347–1360 (2008)

    Article  Google Scholar 

  33. Insperger, T., Stépán, G.: Semi-Discretization for Time-Delay Systems: Stability and Engineering Applications, vol. 178. Springer, New York (2011)

    Google Scholar 

  34. Nayfeh, A.H., Balachandran, B.: Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods. WILEY-VCH Verlag GmbH, Weinheim (1995)

    Book  MATH  Google Scholar 

  35. Elbeyli, O., Sun, J.Q.: On the semi-discretization method for feedback control design of linear systems with time delay. J. Sound Vib. 273(12), 429–440 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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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

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