An equation in lubricant pressure is derived, based on Prandtl's mixing-length theory, under general loading conditions. This non-homogeneous partial differential equation is amenable to reduction by separation of variables. One of the resulting ordinary equations is integrated directly, while the other is solved by a direct method. The solution is subject to zero pressure boundary conditions; for the long bearing both the pressure and its gradient vanish at the trailing edge. The approximate eigenfunctions are given as truncated sine series and the eigenvalues are bounded. Design figures are presented for journal bearings under static loading in both laminar and turbulent regimes.
Get full access to this article
View all access options for this article.
References
1.
ReynoldsO.‘On the theory of lubrication …’, Phil. Trans. R. Soc.1886177 (Pt 1).
2.
DuBoisG. B.OckvirkF. W.‘Analytical derivation and experimental evaluation of short bearing approximation for full journal bearings’, N.A.S.A. Report 1157, 1953.
3.
PinkusO.SternlichtB.Theory of hydrodynamic lubrication1961 (McGraw-Hill Book Co. Inc.).
4.
RaimondiA. A.BoydJ.‘A solution for the finite journal bearing and its application to analysis and design: III’, Trans. Am. Soc. lubric. Engrs19581.
5.
PaiS.Viscous flow theory—II1958 (D. Van Nostrand Co. Inc., Princeton).
