Rostov na donu, Rostov-on-Don, Russian Federation
Kazan', Kazan, Russian Federation
Rostov-na-Donu, Rostov-on-Don, Russian Federation
Kazan', Kazan, Russian Federation
The article is devoted to the conclusion of resolving equations for solving the tasks of bulging rotating rods subject to the action of compressive co-centric forces taking into account uniformly distributed load along the axis. In this mode, for example, fast-moving shafts operate. The purpose of this article is to provide an engineer with a method for calculating drill pipes, tested diagrams and justification of conditions in rotary drilling. The new mathematical models describing stability of rods taking into account own weight and new software are proposed. Numerical simulation of load intensity distributions in the rod along the axis was carried out, at the same time different types of boundary conditions of rod fixation are used. Mathematical models and software for numerical simulation of stability of rotating rods under action of axial compressive forces have been improved. Note that the effect of torsion moment in the present case may not be considered as insignificant in comparison with the above loads. A new method of calculating stability of rotating rods, allowing to take into account any boundary conditions and taking into account own weight, has been developed and scientifically justified. There are proposed mathematical expressions convenient for practical use, which give very accurate results. Obtained results can be used in evaluation and diagnostics of state of samples of structural materials, in process of experimental investigations and in investigation of fast-flowing rotating processes in rod structures of variable stiffness, made of anisotropic composite materials in machine-building, shipbuilding, aircraft engineering, instrument-making, power engineering, etc.
Rotating rod, differential equations, greatest deflection, long modulus of elasticity, boundary conditions, frequency of transverse oscillations
1. Leybenzon L.S. Neustoychivost' napravleniya vraschatel'nogo bureniya. - Azerb. neft'. hoz-vo, 1922, M 8(9), s.67-72.
2. Dinnik A.N. Ob otklonenii burovyh skvazhin pri almaznom bure¬nii. - Gorn. zhurn., 1923, № 3/4, s.160-162.
3. Dinnik A.N. Prichiny iskrivleniya burovyh skvazhin pri vrascha¬tel'nom burenii. Gorn. zhurn., 1925, 10, s.823-630.
4. Simonyanc L.E. Ob uprugoy ustoychivosti vertikal'nogo vraschayuschegosya sterzhnya. - Tr. Grozn. neft. in-ta, 1953, sb. I. Vopr. Geologii neft. mestorozhdeniy i bureniya skvazhin, s.47-58.
5. Linevskiy A. Rol' napravleniy i udliniteley v provedenii vertikal'noy skvazhiny. -Azerb.neft. hoz-vo,1932, №2(122), s.64-74.
6. Panovko Ya.G., Gubanova I.I. Ustoychivost' i kolebaniya upru¬gih sistem.-M.: Nauka, 1964.-336 s.
7. Gulyaev V. I. Dinamika uprugih sistem pri slozhnom dvizhenii (obzor) // Prikl. mehanika. - 2003. - 39, № 5. - S. 28 - 51.
8. Gulyayev V. I., Gaidaichuk V. V., Solovjov I. L., and Gorbunovich I. V. The buckling of elongated rotating drill strings // J. Petrol. Sci. Eng. - 2009. - 67, No. 2. - P. 140 - 148.
9. Gulyayev V. I. and Borshch E. I. Free vibrations of drill strings in hyper deep vertical bore-wells // J. Petrol. Sci. Eng. - 2011. - 78, No. 3. - P. 759 - 764.
10. Gulyayev V. I., Hudoly S. N., and Glovach L. V. The computer simulation of drill column dragging in inclined bore-holes with geometrical imperfections // Int. J. Solids Struct. - 2011. - 48. - P. 110 - 118.
11. Gulyayev V. I., Khudoliy S. N., and Andrusenko E. N. Sensitivity of resistance forces to localized geometrical imperfections in movement of drill strings in inclined bore-holes // Int. Multiscale Mech. - 2011. - 4, No. 1. - P. 1 - 16.
12. Bodnar' T. A. Ustoychivost' vraschayuschegosya szhatogo sterzhnya //Prikladnaya mehanika i tehnicheskaya fizika. - 2000. - T. 41. - №. 4. - S. 190-197.
13. Ven'chzhe Ya. Ustoychivost' vraschayuschegosya sterzhnya, nagruzhennogo osevoy siloy i vstavlennogo v zhestkuyu trubu s zazorom //Vestnik Moskovskogo gosudarstvennogo universiteta lesa-Lesnoy vestnik. - 2002. - №. 5. - S. 179-181.
14. Sabirov R. A. Prodol'no-poperechnyy izgib sterzhnya pri ego vraschenii v centrifuge //Reshetnevskie chteniya. - 2014. - T. 1. - №. 18.
15. Chzhao Cze. Ustoychivost' stacionarnyh dvizheniy mehanicheskih sistem, soderzhaschih deformiruemye elementy. - M.: Inst. meh., 2008, dissertaciya na soiskanie uchenoy stepeni kand. fiz.-mat. nauk.
16. Mohiuddin M. A., Khan K., Abdulraheem A., et al. Analysis of wellbore instability in vertical, directional, and horizontal wells using field data // J. Petrol. Sci. Eng. - 2006. - 55, No. 1. - P. 83 - 92.
17. Cunha J. C. Buckling of tubulars inside wellbores: a review on recent theoretical and experimental works // SPE Drill. Compl. - 2006. - 19, No. 1. - P. 13 - 19.
18. Mitchell R. F. and Miska S. Helical buckling of pipe with connectors and torque // SPE Drill. Compl. - 2006. - 21, No. 2. - P. 108 - 115.
19. R. A. Kerr. Bumpy road ahead for world’s oil. Science, 18 Nov.2005, Vol. 310. International Energy Annual 2001 Edition (EIA, U.S. Department of Energy, Washington, DC, 2003).
20. W. R. Tucker, C. Wang. An integrated model for drill-string dynamics. Journal of Sound and Vibrations, 1999, 224 (1).
21. C. Sun, S. Lukasiewicz. A new model on the buckling of a rod in tubing. Journal of Petroleum Science and Engineering, 2006, Vol. 50.
22. J. C. Cunha. Buckling of tubulars inside wellbores: a review on recent theoretical and experimental works. SPE Drilling & Completion, 2004, Vol. 19, No. 1.
23. R. F. Mitchell. The twist and shear of helically buckled pipe, SPE Drilling & Completion, 2004, 19 (1).
24. Euler L. Methodus inveniendi lineas eurvas maximi minimive propietate gaudentes sive solution problematic isoperimetric lentissimo sensu accept. - Lausanne et Genevae, 1744, r.245-250.
