Non Linear Dynamic Stability Analysis of Finite Flexible Oil Journal Bearings Including Fluid Inertia Effects

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
  
© 2017 by IJETT Journal
Volume-49 Number-4
Year of Publication : 2017
Authors : K.C Ghosh, S.K.Mazumder, M.C.Majumdar
DOI :  10.14445/22315381/IJETT-V49P232

Citation 

K.C Ghosh, S.K.Mazumder, M.C.Majumdar "Non Linear Dynamic Stability Analysis of Finite Flexible Oil Journal Bearings Including Fluid Inertia Effects", International Journal of Engineering Trends and Technology (IJETT), V49(4),195-205 July 2017. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group

Abstract
The aim of this study is to analyse the Non-linear transient stability of finite oil journal bearing including the effect of fluid inertia and bearing liner surface deformations. The inertia effect is usually ignored in view of its negligible contribution compared to viscous force. However, fluid inertia effect is to be taken in the analysis when modified Reynolds number is around one. This investigation deals with the stability of finite isoviscous oil journal bearing with fluid film inertia effect using finite difference method. An attempt has been made to evaluate the critical mass parameter. A non-linear time transient method is used to simulate the journal centre trajectory to estimate the stability parameter, which is a function of speed. In the present work, a modified form of Reynolds equation is developed to include the combined influence of fluid inertia and bearing liner surface deformation for the analysis of finite isoviscous oil journal bearing. The modified average Reynolds equation considering inertia effect with bearing liner surface deformation is solved by a finite difference method with a successive over-relaxation scheme (Gauss-Siedel),while the equation of motion of the journal is solved by the fourth-order Runge-Kutta method. The stability increases with the increase of eccentricity ratio and modified Reynold’s numbers.

 References

1. Pinkus, O. and Sternlicht, B., Theory of Hydrodynamic Lubrication, New York, McGraw-Hill (1961).
2. V. N. Constantinescu and S. Galetuse “On the Possibilities of Improving the Accuracy of the Evaluation of Inertia Forces in Laminar and Turbulent Films” J. Tribol. Vol 96 (1), 69-77 (Jan 01, 1974) (9 pages), ASME, Journal of Tribology | Volume 96 | Issue 1 |
3. Banerjee Mihir B .,Shandil R.G.,and Katyal S.P.A “Nonlinear Theory of Hydrodynamic Lubrication” Journal of Mathematical Analysis and Applications 117,48-56(1986)
4. Kakoty S. K. and Majumdar B. C., “Effect of Fluid Inertia on Stability of Oil Journal Bearing”. ASME Journal of Tribology, Vol 122, pp 741-745, October 2000
5. Chen, C.H. and Chen, C.K., “The influence of fluid inertia on the operating characteristics of finite journal bearings”, Wear, Vol. 131, (1989), pp. 229-240.
6. Higginson, G. R., "The Theoretical Effects of Elastic Deformation of the Bearing Liner on Journal Bearing Performance," ElastohydrodynamicLubrication, Proc. Inst. Mech. Eng., Vol. 180, Part 3B, 1965-1966, pp. 31-37.
7. B.C.Majumder, D.E.Brewe and M.M.Khonsari, “Stability of a rigid rotor supported on flexible oil Journal bearings,” Journal of Tribology Trans Vol 110, 1988, pp 181 - 187.
8. J.O`Donoghue, D.K.Brighton and C.J.K.Hooke, “The effect of elastic distortions on Journal bearing performance,” Journal of Lubrication Technology, Vol 89, n4, 1967, pp 409 -417.
9. D.K.Brighton, C.J.K.Hooke and J.O`Donoghue , “A theoretical and experimental investigation on the effect of elastic distortions on the performance of Journal bearing,” Tribology convention 1968, Proc. of Institute of Mechanical Engineers, Vol 182,Part 3N, 1967 - 1968, pp 192 - 200.
10. H.N.Chandrawat and R Sinhasan, “A study of steady state and transient performance characteristics of a flexible shell Journal bearing,” Tribology International, V21, n3, Jun 1988, pp 137 - 148.
11. H.D.Conway, H.C.Lee., “The Analysis of the Lubrication of a flexible Journal Bearing” Transaction of ASME, Journal of Lubrication Technology, October 1975, pp 599-604
12. Oh, K. P., and Huebner, K. H., "Solution of the Elastohydrodynamic Finite Journal Bearing Problem," ASME JOURNAL OF LUBRICATION TECHNOLOGY, Vol. 95, No. 3, 1973, pp. 342-352.
13. Katory, S. K., and Majumdar, B. C., 1997, „„The Influence of Fluid Inertia on the Steady-state Characteristics and Stability of Journal Bearings,?? Proceedingsof 9th National Conference on Machines and Mechanisms ~NACOMM-97!, IIT, Kanpur, India, pp. B-15–B-26.
14. B.C.Majumder and D.E.Brewe, “Stability of a rigid rotor supported on oil film journal bearings under dynamic load,” NASA TM, 102309, 1987.
15. S.C.Jain, R.Sinhasan and D.V.Singh, “Elastohydrodynamic analysis of a cylindrical Journal bearing with a flexible bearing shell,” Wear, March 1981, pp 325 - 335.
16. .D.Conway, H.C.Lee., “The Analysis of the Lubrication of a flexible Journal Bearing” Transaction of ASME, Journal of Lubrication Technology, October 1975, pp 599-604
17. E. Sujith Prasad, T. Nagaraju & J. Prem Sagar “ Thermohydrodynamic performance of a journal bearing with 3d-surface roughness and fluid inertia effects” International Journal of Applied Research in Mechanical Engineering (IJARME) ISSN: 2231 –5950, Volume-2, Issue-1, 2012
18. Constantinescu, V. N., and Galetuse, S., 1974, „„On the Possibilities of Improving the Accuracy of the Evaluation of Inertia Forces in Laminar and Turbulent Films,?? ASME J. Lubr. Technol., 96, pp. 69–79.
19. Cameron, “Basic Lubrication theory,” Longman Group Ltd., 1970
20. M. K. Ghosh, B.C.Majumder & Mihir Sarangi, “Theory of Lubrication”, Tata McGraw Hill company.
21. B.C.Majumder, “Introduction to Tribology of Bearings,” A.H.Wheeler & Co., 1986.
22. Bernard J. Hamrock, “Fundamentals of Fluid flim Lubrication,” McGraw Hill International edition, 1994
23. S.P.Timoshenko and J.N.Goodier, “Theory of Elasticity,” McGraw Hill Book Company, 1987

Keywords
Modified Reynolds number, slenderness ratio, attitude angle, sommerfeld number, eccentricity ratio, journal bearings, inertia, and deformation factor.