# TU Darmstadt ULB TUprints

# An analytical solution of the Reynolds Equation for the finite journal bearing and evaluation of the lubricant pressure

### Sfyris, Dimitris and Chasalevris, Athanasios (2012):An analytical solution of the Reynolds Equation for the finite journal bearing and evaluation of the lubricant pressure.Darmstadt, DE, Technische Universität Darmstadt, [Report]  Preview
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Item Type: Report
Title: An analytical solution of the Reynolds Equation for the finite journal bearing and evaluation of the lubricant pressure
Language: English
Abstract:

The Reynolds equation for the pressure distribution of the lubricant in a journal bearing with finite length is solved analytically. Using the method of the separation of variables in an additive and in a multiplicative form a set of particular solutions of the Reynolds equation is added in the general solution of the homogenous Reynolds equation and a closed form expression for the definition of the lubricant pressure is presented. The Reynolds equation is split in four linear ordinary differential equations of second order with non constant coefficients and together with the boundary conditions they form four Sturm-Liouville problems with the three of them to have direct forms of solution and one of them to be confronted using the method of power series. In this part of the work, the mathematical procedure is presented up to the point that the application of the boundaries for the pressure distribution yield the final definition of the solution with the calculation of the constants. The distributions of the pressure given from the particular solution and the solution of the homogeneous Reynolds equation are presented together with the resulting pressure. Also, the results of an approximate analytical solution using Bessels functions and linearization of the fluid film thickness function are also presented together with the results of the numerical solution using the finite differences method. Diagrams for the pressure profiles under the current study are compared with those from the approximate analytical and the numerical solution. The locations in which the maximum, the zero, and the minimum pressure are presented are given as a function of eccentricity rate with closed form expressions.

Alternative keywords:
Alternative keywordsLanguage
Journal bearing, Reynolds equation, pressure distribution, analytical solution, separation of variables, Sturm-Liouville, power seriesEnglish
Classification DDC: 500 Naturwissenschaften und Mathematik > 500 Naturwissenschaften
500 Naturwissenschaften und Mathematik > 510 Mathematik
600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 16 Department of Mechanical Engineering > Institute of Applied Dynamics (AD)
Date Deposited: 09 Feb 2012 08:37 View Item