A Solution of Reynolds Equation for a Full Finite Journal Bearing

1961 ◽  
Vol 83 (4) ◽  
pp. 589-593 ◽  
Author(s):  
S. Ramachandra
Keyword(s):  
Eigenvalue Problem ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Homogeneous Equation ◽  
Expansion Method ◽  
Eigenvalues And Eigenfunctions ◽  
Orthogonal Functions ◽  
Design Charts

Reynolds equation for the pressure in a full finite journal bearing which is nonhomogeneous has been reduced to a homogeneous equation. By separating the variables the problem is reduced to an eigenvalue problem. The orthogonal functions expansion method is used to determine the eigenvalues and eigenfunctions. First four eigenvalues are calculated. Design charts are prepared for the eccentricity ratios of 0.2, 0.4, 0.6, 0.8 and length to diameter ratios of 0.5, 1.0, 1.5, and 2.0.

Dynamic Stiffness and Damping Coefficients of Aerostatic, Porous, Journal Bearings

1978 ◽  
Vol 20 (5) ◽  
pp. 291-296 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Continuity Equation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Coefficients ◽  
Design Charts ◽  
Stiffness And Damping

A periodic (displacement) disturbance is imposed on an aerostatic, porous, journal bearing of finite length under steady-state conditions. The dynamic pressure distribution is obtained by a pressure perturbation analysis of Reynolds equation and a modified flow continuity equation in a porous medium. Dynamic stiffness and damping coefficients for different operating conditions are calculated numerically, using a digital computer, and presented in the form of design charts.

scholarly journals Theoretical investigation of porous hydrostatic journal bearing under micropolar fluid lubrication

2020 ◽  
Vol 234 (1-2) ◽  
pp. 11-18
Author(s):  
Biplab Bhattacharjee ◽  
Prasun Chakraborti ◽  
Kishan Choudhuri
Keyword(s):  
Carrying Capacity ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Low Flow ◽  
Load Carrying Capacity ◽  
Static Stiffness ◽  
Design Charts ◽  
Hydrostatic Bearings ◽  
Load Carrying

The features of micropolar fluid (a non-Newtonian fluid)–lubricated short single-layered porous hydrostatic journal bearing are analyzed theoretically by an iterative method. To investigate hydrostatic journal bearing characteristics, a modified Reynolds equation in the case of micropolar fluid is derived and solved numerically. The obtained results in this work are validated by comparing the same with previously published results with Newtonian and non-Newtonian lubricants in the form of design charts. The static stiffness and load-carrying capacity of the investigated bearing are 80% and 75% higher than conventional hydrostatic bearings. The porous hydrostatic journal bearing exhibits more economical performance as it requires 40% low flow rate and low pump power, and it generates 50% less heat in contrast with other hydrostatic bearings.

A Variational Approach to Lubrication Problems and the Solution of the Finite Journal Bearing

1959 ◽  
Vol 81 (1) ◽  
pp. 13-22 ◽  
Author(s):  
D. F. Hays
Keyword(s):  
Variational Approach ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Finite Width ◽  
Two Dimensional ◽  
Continuous Film ◽  
Design Charts ◽  
General Method

A general method is derived for the solution of the two-dimensional Reynolds’ equation. The method is applied to the solution of the full journal bearing of finite width with a continuous film and design charts are presented which describe the characteristics of this bearing.

A General Solution of Reynolds’ Equation for a Full Finite Journal Bearing

1967 ◽  
Vol 89 (2) ◽  
pp. 203-210 ◽  
Author(s):  
R. R. Donaldson
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Hill Equation ◽  
Eigenvalues And Eigenvectors ◽  
General Series ◽  
Bearing Load

Reynolds’ equation for a full finite journal bearing lubricated by an incompressible fluid is solved by separation of variables to yield a general series solution. A resulting Hill equation is solved by Fourier series methods, and accurate eigenvalues and eigenvectors are calculated with a digital computer. The finite Sommerfeld problem is solved as an example, and precise values for the bearing load capacity are presented. Comparisons are made with the methods and numerical results of other authors.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

Numerical and Experimental Investigations on Preload Effects in Air Foil Journal Bearings

2017 ◽  
Author(s):  
Marcel Mahner ◽  
Pu Li ◽  
Andreas Lehn ◽  
Bernhard Schweizer
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Compressible Fluids ◽  
Experimental Investigations ◽  
Hysteresis Curves ◽  
Numerical Predictions ◽  
Bearing Stiffness ◽  
Gasdynamic Model ◽  
Good Agreement

A detailed elasto-gasdynamic model of a preloaded three-pad air foil journal bearing is presented. Bump and top foil deflections are herein calculated with a nonlinear beamshell theory according to Reissner. The 2D pressure distribution in each bearing pad is described by the Reynolds equation for compressible fluids. With this model, the influence of the assembly preload on the static bearing hysteresis as well as on the aerodynamic bearing performance is investigated. For the purpose of model validation, the predicted hysteresis curves are compared with measured curves. The numerically predicted and the measured hysteresis curves show a good agreement. The numerical predictions exhibit that the assembly preload increases the bearing stiffness (in particular for moderate shaft displacements) and the bearing damping.

Investigation the combined effects of wear and turbulent on the performance of hydrodynamic journal bearing operating with couple stress fluids

2019 ◽  
Vol 10 (6) ◽  
pp. 825-837
Author(s):  
Mushrek A. Mahdi ◽  
Ahmed Waleed Hussein
Keyword(s):  
Couple Stress ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Performance Characteristics ◽  
Turbulent Regime ◽  
Hydrodynamic Bearings ◽  
Content Type ◽  
Hydrodynamic Journal Bearing ◽  
Local Reynolds Number ◽  
Couple Stress Fluids

Purpose The purpose of this paper is to investigate the combined effect of wear and turbulence on the performance of a hydrodynamic journal bearing operating under Newtonian and couple stress fluids (CSF). Design/methodology/approach The analysis consists of a modified Reynolds equation of incompressible thin viscous films, and the film thickness model taking into account the wear effect. The governing equation was solved numerically using the finite difference approach. Findings The effect of both the wear parameter and the local Reynolds number on the performance characteristics of bearing has been presented and discussed. The obtained results observed that the characteristics of the intact and worn bearing in turbulent and laminar have been enhanced due to the non-Newtonian fluid (CSF) effect. Also, the results display that bearing worn and the turbulent regime cannot be neglected in calculating the performance characteristics of the bearing lubricated with Newtonian and non-Newtonian fluids. The results achieved from this study, specify that the bearing characteristics are significantly affected by these effects. Originality/value The paper investigates the behavior of hydrodynamic bearings considering different aspects simultaneously is interesting, and the application meets the current needs of improvement in modeling hydrodynamic bearings under different conditions.

scholarly journals 3D Numerical study on the effect of shaft eccentricity on the tribological performance of lubricated sliding contact

2018 ◽  
Vol 159 ◽  
pp. 02042
Author(s):  
Mohammad Tauviqirrahman ◽  
Bayu Kurniawan ◽  
Jamari
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Study ◽  
Wall Slip ◽  
Sliding Contact ◽  
Eccentricity Ratio ◽  
3D Numerical Modelling ◽  
Hydrodynamic Journal Bearing ◽  
Wedge Effect ◽  
Lubricated Sliding

Recently, a growing interest is given to the wall slip and the artificial texturing for improving the performance of lubricated sliding contact. The use of wall slip, artificial texturing, and the combination of slip and texturing can be the effective approach to enhance the performance of the bearing. The present study examines the effect of shaft eccentricity ratio on the hydrodynamic journal bearing performance. 3D numerical modelling based on modified Reynolds equation is used to analyse the effect of texturing and the wall slip on the characteristics of a hydrodynamically lubricated sliding contact. The analysis results point out that with respect to the load support and the power loss of the bearing, the use of wall slip on smooth surface is the most excellent configuration compared to other patterns (i.e. slip-texturing, pure texturing and conventional patterns). It is also confirmed that the wedge effect due to the shaft eccentricity has a significant role in altering the lubricant behaviour. Thus, a particular care must be taken in choosing the pattern of lubricated sliding contact as well as the shaft eccentricity.

scholarly journals An Analytical Method for the Determination of Temperature Distribution in Short Journal Bearing Oil Film

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 539
Author(s):  
Nebojsa Nikolic ◽  
Zivota Antonic ◽  
Jovan Doric ◽  
Dragan Ruzic ◽  
Stjepan Galambos ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Oil Film ◽  
Symmetric Geometry ◽  
Experimental Values ◽  
Operating Regimes ◽  
Level Of Agreement

The aim of this paper is to derive an equation for the temperature distribution in journal bearing oil film, in order to predict the thermal load of a bearing. This is very important for the prevention of critical regimes in a bearing operation. To achieve the goal, a partial differential equation of the temperature field was first derived, starting from the energy equation coupled with the Reynolds equation of hydrodynamic lubrication for a short bearing of symmetric geometry. Then, by solving the equation analytically, the function of temperature distribution in the bearing oil film has been obtained. The solution is applied to the journal bearing, for which the experimental data are available in the references. Finally, the obtained results have been compared to the corresponding experimental values for two operating regimes, and a good level of agreement was achieved.

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