On Journal Bearings of Finite Length With Variable Viscosity

1959 ◽  
Vol 26 (2) ◽  
pp. 179-183
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Finite Length ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Load Capacity ◽  
Journal Bearings ◽  
Heun Functions ◽  
Load Vector ◽  
Constant Viscosity

Abstract An exact solution of the Reynolds equation for journal bearings of finite length with viscosity as a function of pressure is found. The analytical solution is expressed in terms of Heun functions. The load capacity and the attitude angle are derived. It is found that the load vector, in general, is not perpendicular to the line of journal and bearing centers as shown in the constant-viscosity case.

Analysis of Noncircular Gas Journal Bearings

1975 ◽  
Vol 97 (4) ◽  
pp. 616-623 ◽  
Author(s):  
O. Pinkus
Keyword(s):  
Reynolds Equation ◽  
Load Capacity ◽  
Full Range ◽  
Maximum Load ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Significant Advance ◽  
Arbitrary Direction ◽  
Isothermal Conditions ◽  
Load Vector

The compressible Reynolds Equation under isothermal conditions was solved for finite elliptical and 3-lobe bearings with the load vector acting in any arbitrary direction over the full range of 360 deg. Envelopes of minimum and maximum eccentricity for a given set of operating conditions are provided, the first to yield maximum load capacity, and the second to assist stability by a choice of the highest possible ε. Some values of the spring and damping forces are also given and it is shown that in comparison with conventional bearings, the non-circular designs offer a significant advance in stiffness, particularly for low ε, when instability is most often encountered.

An Improved Analytical Solution for Self-Acting, Gas-Lubricated Journal Bearings of Finite Length

1961 ◽  
Vol 83 (2) ◽  
pp. 188-192 ◽  
Author(s):  
J. S. Ausman
Keyword(s):  
Analytical Solution ◽  
Finite Length ◽  
Load Capacity ◽  
Journal Bearings ◽  
Perturbation Solution ◽  
Order Perturbation ◽  
Small Eccentricity ◽  
First Order ◽  
Bearing Load ◽  
First Order Perturbation

An improved analytical solution designated the “linearized ph” solution is obtained for gas-lubricated journal bearings of finite length. Whereas the older first-order perturbation solution is useful for small eccentricity ratios (ε < 1/2), the linearized ph solution may be used for high eccentricity ratios. As such it permits estimation of ultimate bearing load capacity. The linearized ph solution is expressed in the form of simple corrections to the first-order perturbation solution, and as such can be computed quickly and easily.

Lubrication of Porous Journal Bearings

1972 ◽  
Vol 94 (1) ◽  
pp. 69-73 ◽  
Author(s):  
C. Cusano
Keyword(s):  
Analytical Solution ◽  
Coefficient Of Friction ◽  
Load Capacity ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Eccentricity Ratio ◽  
Design Variables

An analytical solution for the performance characteristics of finite porous journal bearings is obtained. Results are presented which relate the eccentricity ratio and coefficient of friction as functions of load number for design variables of 0.0001, 0.001, 0.01, and 0.1. The load capacity obtained by using the finite bearing theory is compared to the load capacity obtained by using the short-bearing approximation and the infinite-bearing approximation.

Fixed Geometry Bearing Analysis Using 2 Dimensional Pad Data

2015 ◽  
Author(s):  
Wei Li ◽  
Manish Thorat
Keyword(s):  
Reynolds Equation ◽  
Dimensional Space ◽  
Journal Bearings ◽  
Analysis Method ◽  
Benchmark Study ◽  
Assembly Method ◽  
Turbulent Flow Regime ◽  
Load Vector ◽  
Vector Orientation ◽  
Rotor Dynamic

A fast and efficient method for evaluating bearing coefficients of the fixed geometry bearings is presented. In a typical industrial application, where the accuracy of the solution is desired, this paper presents a method whose accuracy is verified to be good by the benchmark study. Reynolds equation is solved to obtain non-dimensionalised static and rotor-dynamic characteristics for a pre-defined bearing pad geometry. The solution in the form of non-dimensional functions is obtained for a 2 dimensional space representing all possible journal loci for any load vector orientation. Laminar flow is considered in the analysis, although the method of analysis can be extended to Turbulent flow regime. The analysis method is most efficient for isoviscous boundary condition. A pad assembly method for the fixed pad journal bearings is presented. Any fixed pad bearing geometry including multi-pad bearings, preload with any load vector orientation can be evaluated using this method. In this paper, demonstrating cases for a four-pad bearing are presented.

Empirical Treatment of Hydrodynamic Journal Bearing Performance in the Superlaminar Regime

1970 ◽  
Vol 12 (2) ◽  
pp. 116-122 ◽  
Author(s):  
H. F. Black
Keyword(s):  
Reynolds Number ◽  
Field Equation ◽  
Experimental Work ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Theoretical Treatment ◽  
Hydrodynamic Journal Bearing

The application of a perturbation in terms of simple correlations for friction in turbulent Couette and ‘screw’ flows, together with a further empirical assumption consonant with the experimental work of Smith and Fuller (1), leads to a pressure field equation identical in form with the Reynolds equation. The load capacity of journal bearings throughout most of the superlaminar range may be represented by a single curve, and existing laminar solutions may be applied with the parameters modified by Reynolds number. The theory is compared with published experimental results, and with the most successful theoretical treatment (4). The correlations obtained confirm the adequacy of the theory to predict performance in the superlaminar régime.

A New Analytic Approximation for the Hydrodynamic Forces in Finite-Length Journal Bearings

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Yaser Bastani ◽  
Marcio de Queiroz
Keyword(s):  
Finite Length ◽  
Reynolds Equation ◽  
Computational Study ◽  
Hydrodynamic Forces ◽  
Journal Bearings ◽  
Closed Form Expression ◽  
Impedance Method ◽  
Analytic Approximation ◽  
State Behavior ◽  
Order Polynomial

A new method for determining a closed-form expression for the hydrodynamic forces in finite-length plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely long (IL) or infinitely short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. A comparative computational study is presented for the steady-state behavior of the bearing system under static and unbalance loads. The results show the proposed models outperforming the standard limiting approximations as well as a model based on the finite-length impedance method.

scholarly journals Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui-Hui Feng ◽  
Chun-Dong Xu ◽  
Jie Wan
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Eccentricity Ratio ◽  
Dynamic Coefficients ◽  
Pressure Fields ◽  
Dynamic Performances ◽  
Rotary Speed

The water-lubricated bearings have been paid attention for their advantages to reduce the power loss and temperature rise and increase load capacity at high speed. To fully study the complete dynamic coefficients of two water-lubricated, hydrostatic journal bearings used to support a rigid rotor, a four-degree-of-freedom model considering the translational and tilting motion is presented. The effects of tilting ratio, rotary speed, and eccentricity ratio on the static and dynamic performances of the bearings are investigated. The bulk turbulent Reynolds equation is adopted. The finite difference method and a linear perturbation method are used to calculate the zeroth- and first-order pressure fields to obtain the static and dynamic coefficients. The results suggest that when the tilting ratio is smaller than 0.4 or the eccentricity ratio is smaller than 0.1, the static and dynamic characteristics are relatively insensitive to the tilting and eccentricity ratios; however, for larger tilting or eccentricity ratios, the tilting and eccentric effects should be fully considered. Meanwhile, the rotary speed significantly affects the performance of the hydrostatic, water-lubricated bearings.

A Contribution to the Analysis of the Thermo-Hydrodynamic Lubrication of Porous Self-Lubricating Journal Bearings

2010 ◽  
Vol 297-301 ◽  
pp. 618-623 ◽  
Author(s):  
S. Boubendir ◽  
Salah Larbi ◽  
Rachid Bennacer
Keyword(s):  
Thermal Effects ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Matrix ◽  
Journal Bearings ◽  
Governing Equations ◽  
Hydrodynamic Analysis ◽  
Result Show

In this work the influence of thermal effects on the performance of a finite porous journal bearing has been investigated using a thermo-hydrodynamic analysis. The Reynolds equation of thin viscous films is modified taking into account the oil leakage into the porous matrix, by applying Darcy’s law to determine the fluid flow in the porous media. The governing equations were solved numerically using the finite difference approach. Obtained result show a reduction in the performance of journal bearings when the thermal effects are accounted for and, this reduction is greater when the load capacity is significant.

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