Nonlinear Dynamic Stability Analysis of Flexibly Supported Finite Oil Journal Bearings with Variable Viscosity Including Bearing Liner Surface Deformation

 International Journal of Engineering Trends and Technology (IJETT) © 2017 by IJETT Journal Volume-48 Number-3 Year of Publication : 2017 Authors : Manoj Kundu, S.K Mazumder, M.C Mazumdar DOI :  10.14445/22315381/IJETT-V48P222

Citation

Manoj Kundu, S.K Mazumder, M.C Mazumdar "Nonlinear Dynamic Stability Analysis of Flexibly Supported Finite Oil Journal Bearings with Variable Viscosity Including Bearing Liner Surface Deformation", International Journal of Engineering Trends and Technology (IJETT), V48(3),120-129 June 2017. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group

Abstract
This paper analyses the stability characteristics of a rigid rotor mounted in flexibly supported hydrodynamic finite oil journal bearings considering pressure depended viscosity including the effect of elastic distortion on the surface of bearing liner. This theoretical analysis is intended to show how the effect of elastic distortion along with the flexible support on the journal bearing performance considering pressure depended viscosity, which can be calculated for three-dimensional bearing geometries. The deformation equations for bearing surface will be solved simultaneously with hydrodynamic equations considering variable viscosity. A Non-linear time transient method is used to simulate the journal and bearing centre trajectory and thereby to estimate the stability parameter. In this analysis forth order Runge-Kutta method is used to determine the locus of the journal and the bearing centre for the various operating conditions. The stability of the system is determined from the combined stability effect in journal and bearing centre. It has been found that stability decreases with increase of the elasticity parameter of the bearing and stability improves with increase of the viscosity parameter.

References

1) N.P.Petroff, “ Friction in machines and the effect of lubricant,” Engg. Journal, St. Petersburg, No. 1,2,3,4, 1983.
2) B.Tower, “1st report on friction experiments, “Proc. Inst. Mech. Engrs., 1883, 632-664, 1884, 29-35; Part II: 1885, 58-70; Part III: 1888, 173-205; Part IV:1891, 111-140.
3) O.Reynolds, “On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of Olive oil,” Phil. Trans. Royal Soc., London, 177, 1886, 157-234.
4) A.Sommerfeld, ”Zur hydrodynamische theorie der schmiermitterlreiburg,” Zeitschrieft fur mathematische Physik, 50, 1904, 97-155.
5) 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.
6) R. Pai and B.C.Majumder, “Stability of submerged oil Journal bearing under dynamic load,” Wear V146, n1, May 30, 1991, pp 125 - 135.
7) B.C.Majumder and M.K.Ghosh, “Stability of a rigid rotor supported on rough oil journal bearings,” Trans. ASME, J.Tribology, 112, 1990, pp 73-77.
8) H.D.Conway and H.C.Lee, “The analysis of the lubrication of a flexible Journal bearing,”ASME Journal of Lubrication Technology, Vol 97, n4, 1975, pp 599–604.
9) 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.
10) 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.
11) 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.
12) 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.
13) 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.
14) 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
15) Jose´ A. Va´zquez, Lloyd E. Barrett, Ronald D. Flack “A Flexible Rotor on Flexible Bearing Supports: Stability and Unbalance Response” Transactions of the ASME, Journal of Vibration and Acoustics, APRIL 2001, Vol. 123 pp 137-144
16) D. Benasciutti, M. Gallina, M. Gh. Munteanu, F. Flumian,2012 “A Numerical Approach for Static and Dynamic Analysis of Deformable Journal Bearings” World Academy of Science, Engineering and Technology 67 , 2012,pp-778-783
17) D.G.Christopherson, “A new mathematical model for solution of film lubrication problems,” Proc. Inst. Mech. Engrs., London, 146, 1942, 126-135.
18) A.A.Raimondi and J.Boyd, “A solution for the finite journal bearing and its application to analysis and design,” I, II, III, ASLE Trans., 1958, 159-209.
19) 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.
20) J. F. Booker, “ Dynamically loaded Journal bearings; Mobility method of solution,” Trans ASME, J. Basic Engg., 87, 1965, 537-546.
21) J. F. Booker, “ Dynamically loaded Journal bearings; Numerical application of the mobility method,” Journal of lubrication Technology Trans ASME V93, n1, Jan 1971, pp 168 - 176.
22) C.M.Woods and D.E.Brewe,“The solution of the Elrod algorithm for a dynamically loaded journal bearing using multi-grid techniques,” Trans. ASME, J. Lub. Tech., 111, 1989, 302-308.
23) H.G.Elrod, “A cavitation algorithm,” Trans. ASME, J. Lub. Tech., 103, 1981, 350-354.
24) E. Capone, “Oil whirl in Journal bearing under no load conditions,” Wear V26, n2, Nov 1973 pp 207 - 217.
25) Akers, S. Michaelson and A. Cameron, “Stability contours for whirling finite Journal bearing,” Journal of lubrication technology ASME V93, n1, Jan 1971, pp 177-190.
26) Cameron, “Basic Lubrication theory,” Longman Group Ltd., 1970
27) M. K. Ghosh, B.C.Majumder & Mihir Sarangi, “Theory of Lubrication”, Tata McGraw Hill company.
28) B.C.Majumder, “Introduction to Tribology of Bearings,” A.H.Wheeler & Co., 1986.
29) Bernard J. Hamrock, “Fundamentals of Fluid flim Lubrication,” McGraw Hill International edition, 1994
30) S.P.Timoshenko and J.N.Goodier, “Theory of Elasticity,” McGraw Hill Book Company, 1987

Keywords
Journal bearing, surface deformation, variable viscosity, eccentricity ratio, Reynolds equation.