Analytical study of the velocity of the lubricating fluid in the hydrodynamic journal bearing with the effect of centrifugal force for short bearing type
The paper aims to obtain the expression of the velocity of lubricating fluid in the hydrodynamic journal bearings by analytical method. In the classical short-bearing theory, the fluid flow was studied by ignoring the effect of centrifugal force of the lubricating fluid film. However, the self-oscillation of the shaft of high-power motors does not follow the rules in classical hydrodynamic lubrication theory. To explain this phenomenon, a modified form of Reynolds equation, in which the influence of centrifugal force of the lubricant is not ignored, is established. The study aims to establish the modified Reynolds equation by including the effect of centrifugal forces for the case of the short bearing type. Integration of the Navier-Stokes equations, yield the expressions for the components of velocity of the lubricating fluid in the gap. The oil’s pressure in the hydrodynamic journal bearing is obtained by solving the modified Reynolds equation. The numerical results are considered in the case of the stable equilibrium position of the motion of the shaft, i.e. the symmetry axis of the shaft does not move. The plots of the velocity components in the tangential axial direction are displayed too. The theoretical results of a parabolic velocity distribution similar to that of a Newtonian fluid, derived from a Bingham plastic flow model. The flow in the gap, which are obtained by analytical method, are completely consistent with its boundary conditions and its physical properties. Further, with these results, the paper as a lemma to solve the dynamics problem in floating ring bearing with the influence of the centrifugal force of the lubricant
Loytsyanskiy, L. G. (1987). Mekhanika zhidkosti i gaza. Moscow: Nauka, 823. Available at: https://www.rfbr.ru/rffi/ru/books/o_26855#1
Hori, Y. (2002). Hydrodynamic Lubrication. Springer Tokyo, 231. doi: https://doi.org/10.1007/4-431-27901-6
Belyaev, A. K., Krommer, M., Irschik, H., Nguyen, V. T. (2008). Forces and moments acting on the rapidly rotating floating bearing. XXXVI International Summer School-Conference “Advanced Problems in Mechanics”, 104–111.
Nguyen, V. T. (2011). Sily i momenty, deystvuyuschie na rotor v upornom podshipnike skol'zheniya, s uchetom gidrodinamiki smazki i tsentrobezhnykh sil. Nauchno-tekhnicheskie vedomosti Sankt-Peterburgskogo gosudarstvennogo politekhnicheskogo universiteta. Fiziko-matematicheskie nauki, 1, 116–122. Available at: https://cyberleninka.ru/article/n/sily-i-momenty-deystvuyuschie-na-rotor-v-upornom-podshipnike-skolzheniya-s-uchetom-gidrodinamiki-smazki-i-tsentrobezhnyh-sil
Tondl, A. (1971). Dinamika rotorov turbogeneratorov. Leningrad: Energiya, 387.
Boyaci, A., Hetzler, H., Seemann, W., Proppe, C., Wauer, J. (2008). Analytical bifurcation analysis of a rotor supported by floating ring bearings. Nonlinear Dynamics, 57 (4), 497–507. doi: https://doi.org/10.1007/s11071-008-9403-x
Dubois, G. B. (1953). Analytical derivation and experimental evaluation of short-bearing approximation for full journal bearing. Report 1157. Available at: https://digital.library.unt.edu/ark:/67531/metadc60530/m1/1/
Hatakenaka, K., Tanaka, M., Suzuki, K. (2002). A Theoretical Analysis of Floating Bush Journal Bearing With Axial Oil Film Rupture Being Considered. Journal of Tribology, 124 (3), 494–505. doi: https://doi.org/10.1115/1.1454104
Kirk, R. G., Alsaeed, A. A., Gunter, E. J. (2007). Stability Analysis of a High-Speed Automotive Turbocharger. Tribology Transactions, 50 (3), 427–434. doi: https://doi.org/10.1080/10402000701476908
Li, C.-H. (1982). Dynamics of Rotor Bearing Systems Supported by Floating Ring Bearings. Journal of Lubrication Technology, 104 (4), 469–476. doi: https://doi.org/10.1115/1.3253258
Mutuli, S., Bonneau, D., Frene, J. (1986). Velocity Measurements in the Grease-Lubricating Film of a Sliding Contact. A S L E Transactions, 29 (4), 515–522. doi: https://doi.org/10.1080/05698198608981715
Li, J. X., Höglund, E., Westerberg, L. G., Green, T. M., Lundström, T. S., Lugt, P. M., Baart, P. (2012). μPIV measurement of grease velocity profiles in channels with two different types of flow restrictions. Tribology International, 54, 94–99. doi: https://doi.org/10.1016/j.triboint.2012.03.007
Guo, H., Xia, B. Q., Cen, S. Q. (2011). Performance Analysis of High Speed Floating Ring Hybrid Bearing in the Laminar and Turbulent Regimes. Advanced Materials Research, 197-198, 1776–1780. doi: https://doi.org/10.4028/www.scientific.net/amr.197-198.1776
Copyright (c) 2022 Nguyen Van Thang
This work is licensed under a Creative Commons Attribution 4.0 International License.
Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.