Modelling of Nonlinear Torsional-Flexural Vibrations of Drill Strings
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Keywords:
drill-string, dynamics, torsional-flexural vibrations, finite deformations, nonlinear model.Abstract
Nonlinear flexural-torsional vibrations of shallow drill-strings are investigated. The drill-string is represented as an elastic rod rotating at constant angular velocity under the action of the longitudinal compressive force. The nonlinear model of flexural and torsional vibrations of drill-string is constructed on the basis of the theory of finite deformations of V.V. Novozhilov and its second system of simplifications. The numerical analysis of the model is carried out in the environment of symbolic mathematical computations - Wolfram Mathematica. The dominance of flexural vibrations of the drill-string over torsional vibrations is established. The influence of drill-string parameters on its oscillatory processes is investigated. It will allow to build up the modes of the drill-string movements to improve the quality of drilling of wells.References
1. Muller P. Torsional-flexural waves in thin-walled open beams // Journal of Sound and Vibration. – 1983. – Vol. 87, Issue 1. – P. 115-141.
2. Erofeev V.I., Orekhova O.I. Dispersion of flexural-torsional wave propagating in the beam. Parts 1,2 // Privolzhsky scientific journal. – 2011. – Vol 2. – P. 7–15; Vol 3. – P. 20–26. (in Russian)
3. Raspopov A.S. Improved calculation of flexural-torsional vibrations of continuous beams and frames // Transport construction. – 2007. – №18. – P. 161-166. (in Russian)
4. Anfilofyev A.V. Geometric properties of an elastic rod in the varieties of simple bending (concentrated load) // Bulletin of the Tomsk Polytechnic University. – 2008. – Vol. 313,No 2. – P. 12–17. (in Russian)
5. Timoshenko S.P., Gudter Dzh. The theory of elasticity / transl. from English; ed. Shapiro G.S. – M: Nauka, 1975. – 576 p.
6. Timoshenko S.P. Vibrations in engineering. – M.: Fizmatgiz, 1959. – 450 p.
7. Vorobyov Yu.S., Shorr B. F. The theory of twisted rods. – Kiev: Nauk. dumka, 1983. – 188 p.
8. Vorobyov Yu.S. Refinement of equations of free vibrations of rotating rods // Working processes in turbomachines and durability of their elements. – Kiev: Nauk. dunka, 1965. – P. 11–27.
9. Avramov K.V., Galas O.S., Morachkovsky O.K., Pierre K. Analysis of nonlinear flexural - flexural-torsional vibration of rotating twisted rods taking into account the cross-sectional warping // Problems of Strength. – 2009. – Vol 2. – P. 112–124. (in Russian)
10. Verichev N.N., Erofeev V.I., Vedyaykina O.I. Nonlinear stationary flexural and torsional waves in an elastic rods // Bulletin of scientific and technological development. – 2013. – № 11(75). – P. 17-24. (in Russian)
11. Erofeev V. I., Kazhaev V. V., and Orekhova O. I. Intense Flexural and Torsional Waves in an Elastic Bar // Journal of Machinery Manufacture and Reliability. – 2012. – Vol. 41, No 1. – P. 7–10.
12. Hodges D.H. and Dowell E.H. Nonlinear Equations of Motions for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades. – NASA TND-7818, 1974. – P. 52.
13. Novozhilov V.V. Foundations of the Nonlinear Theory of Elasticity. - M.- L.: OGIZ, 1948. – 211 p.
14. Vibrations in equipment. Reference book: in 6 volumes. – M.: Mashinostroenie, 1978. - Vol. 1. – 352 p.
15. Khulief Y.A., Al-Sulaiman F.A., Bashmal S. Vibration Analysis of drillstrings with self-excited stick-slip oscillations. // Journal of Sound and Vibration. – 2007. – Vol. 299. – P. 540-558.
16. Vaz M.A., Patel M.N. Analysis of drill strings in vertical and deviated holes using the Galerkin technique. // Engineering structures. – 1995. – Vol. 17(6). – P. 437-442.
17. Khajiyeva L., Kudaibergenov A., Kudaibergenov A., Kydyrbekuly A. Analysis of drill string motion in a gas stream // Proc. 8th European Nonlinear Dynamics Conf. (ENOC 2014). – Vienna, Austria, 2014.
18. Hayrer E., Vanner G. Solution of the ordinary differential equations. Stiff and differential-algebraic problems: transl. from English. – M: Mir, 1999. – 685 p.
19. Petzold L. Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations // SIAM J. Sci. Stat. Comput. – 1983. – Vol. 4, No. 1. – P. 136-148.
20. Kudaibergenov A.K., Kudaibergenov Ask.K. Comparative analysis of numerical methods for modeling of drill string nonlinear dynamics// Bulletin of NAN RK, phys.-mat. Series. – 2015. – №3 (301). – P. 37-42. (in Russian)
2. Erofeev V.I., Orekhova O.I. Dispersion of flexural-torsional wave propagating in the beam. Parts 1,2 // Privolzhsky scientific journal. – 2011. – Vol 2. – P. 7–15; Vol 3. – P. 20–26. (in Russian)
3. Raspopov A.S. Improved calculation of flexural-torsional vibrations of continuous beams and frames // Transport construction. – 2007. – №18. – P. 161-166. (in Russian)
4. Anfilofyev A.V. Geometric properties of an elastic rod in the varieties of simple bending (concentrated load) // Bulletin of the Tomsk Polytechnic University. – 2008. – Vol. 313,No 2. – P. 12–17. (in Russian)
5. Timoshenko S.P., Gudter Dzh. The theory of elasticity / transl. from English; ed. Shapiro G.S. – M: Nauka, 1975. – 576 p.
6. Timoshenko S.P. Vibrations in engineering. – M.: Fizmatgiz, 1959. – 450 p.
7. Vorobyov Yu.S., Shorr B. F. The theory of twisted rods. – Kiev: Nauk. dumka, 1983. – 188 p.
8. Vorobyov Yu.S. Refinement of equations of free vibrations of rotating rods // Working processes in turbomachines and durability of their elements. – Kiev: Nauk. dunka, 1965. – P. 11–27.
9. Avramov K.V., Galas O.S., Morachkovsky O.K., Pierre K. Analysis of nonlinear flexural - flexural-torsional vibration of rotating twisted rods taking into account the cross-sectional warping // Problems of Strength. – 2009. – Vol 2. – P. 112–124. (in Russian)
10. Verichev N.N., Erofeev V.I., Vedyaykina O.I. Nonlinear stationary flexural and torsional waves in an elastic rods // Bulletin of scientific and technological development. – 2013. – № 11(75). – P. 17-24. (in Russian)
11. Erofeev V. I., Kazhaev V. V., and Orekhova O. I. Intense Flexural and Torsional Waves in an Elastic Bar // Journal of Machinery Manufacture and Reliability. – 2012. – Vol. 41, No 1. – P. 7–10.
12. Hodges D.H. and Dowell E.H. Nonlinear Equations of Motions for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades. – NASA TND-7818, 1974. – P. 52.
13. Novozhilov V.V. Foundations of the Nonlinear Theory of Elasticity. - M.- L.: OGIZ, 1948. – 211 p.
14. Vibrations in equipment. Reference book: in 6 volumes. – M.: Mashinostroenie, 1978. - Vol. 1. – 352 p.
15. Khulief Y.A., Al-Sulaiman F.A., Bashmal S. Vibration Analysis of drillstrings with self-excited stick-slip oscillations. // Journal of Sound and Vibration. – 2007. – Vol. 299. – P. 540-558.
16. Vaz M.A., Patel M.N. Analysis of drill strings in vertical and deviated holes using the Galerkin technique. // Engineering structures. – 1995. – Vol. 17(6). – P. 437-442.
17. Khajiyeva L., Kudaibergenov A., Kudaibergenov A., Kydyrbekuly A. Analysis of drill string motion in a gas stream // Proc. 8th European Nonlinear Dynamics Conf. (ENOC 2014). – Vienna, Austria, 2014.
18. Hayrer E., Vanner G. Solution of the ordinary differential equations. Stiff and differential-algebraic problems: transl. from English. – M: Mir, 1999. – 685 p.
19. Petzold L. Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations // SIAM J. Sci. Stat. Comput. – 1983. – Vol. 4, No. 1. – P. 136-148.
20. Kudaibergenov A.K., Kudaibergenov Ask.K. Comparative analysis of numerical methods for modeling of drill string nonlinear dynamics// Bulletin of NAN RK, phys.-mat. Series. – 2015. – №3 (301). – P. 37-42. (in Russian)
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Sergaliyev, A. S., & Khajiyeva, L. A. (2015). Modelling of Nonlinear Torsional-Flexural Vibrations of Drill Strings. International Journal of Mathematics and Physics, 6(2), 41–48. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/147
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