Method of Theoretical Investigation of Externally Pressurized Gas-Lubricated Bearings

1969 ◽  
Vol 91 (1) ◽  
pp. 166-170 ◽  
Author(s):  
L. G. Stepanyants ◽  
N. D. Zablotsky ◽  
I. E. Sipenhov
Keyword(s):  
Numerical Integration ◽  
Theoretical Investigation ◽  
Reynolds Equation ◽  
Spherical Bearing

An “unevenly distributed supercharging” pattern is suggested for treating externally pressurized bearings. The scheme simplifies the problem and is applicable in calculating any type of externally pressurized bearings Results of numerical integration of Reynolds’ equation for a section spherical bearing using this treatment are given.

Reynolds Equation for Spherical Bearings

2002 ◽  
Vol 125 (1) ◽  
pp. 203-206 ◽  
Author(s):  
Donna Meyer
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Horizontal Position ◽  
Hemispherical Shell ◽  
Pressure Distributions ◽  
Spherical Bearing ◽  
Classical Paper ◽  
Fluid Film Thickness ◽  
Generalized Reynolds Equation

Osborne Reynolds’ classical paper on the theory of lubrication Reynolds (1886) produced the generalized Reynolds equation. For spherical bearing applications, the generalized Reynolds equation is transformed in order to obtain useful results when the hemispherical shell is not in a horizontal position. A new film thickness expression is also presented. These transformations permit the determination of pressure distributions and fluid film thickness for any orientation of the hemispherical shell including the horizontal position, for which the conventional description of Reynolds equation is well suited. The resulting equation in two-dimensional form, for an incompressible, variable viscosity fluid, with upper and lower sliding surfaces, in spherical coordinates, contains the inclination angle β, which accounts for non-horizontal positions of the shell.

The Accuracy of Short Bearing Theory in Presence of Cavitation

1990 ◽  
Vol 112 (4) ◽  
pp. 650-654 ◽  
Author(s):  
A. T. Prata ◽  
R. T. S. Ferreira
Keyword(s):  
Asymptotic Expansion ◽  
Numerical Integration ◽  
Reynolds Equation ◽  
Matched Asymptotic Expansion ◽  
Aspect Ratios ◽  
Very High

The accuracy of the short bearing approximation in presence of cavitation is tested for bearing aspect ratios (length/diameter) ranging from 0.1 to 1, and for eccentricity to clearance ratios from 0 to 1. Results for short bearings are obtained via the method of matched asymptotic expansion of [3]. These results are compared to those for finite bearings, which are calculated by numerical integration of the Reynolds equation utilizing boundary fitted coordinates that accommodate to the cavitation boundary. Except for very high eccentricities, the short bearing theory was shown to be accurate in predicting the load, within ten percent, for bearing aspect ratios up to 0.5. For large aspect ratios the short bearing theory overpredicts the load.

Theoretical investigation of surface texture effects on the performance characteristics of hydrodynamic two-lobe journal bearing

2020 ◽  
Vol 234 (11) ◽  
pp. 1712-1725
Author(s):  
Niranjan Singh ◽  
RK Awasthi
Keyword(s):  
Finite Element Method ◽  
Theoretical Investigation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Surface Texturing ◽  
Performance Characteristics ◽  
Performance Parameters ◽  
Eccentricity Ratio ◽  
Static Performance ◽  
Bearing System

In the present work, theoretical investigation has been performed to predict the influence of spherical textures on the performance characteristics of two-lobe journal bearing system. The flow of lubricant in the clearance space between the bearing and the journal is governed by the Reynolds equation assuming the flow is Newtonian and isoviscous. The Reynolds equation is solved using a finite element method and the static performance parameters of circular/two-lobe smooth/textured journal bearing system have been computed with variation in eccentricity ratio, dimple depth and its location. The numerically simulated results reveal that the partial surface texturing can provide better performance when the textures are created in the pressure build-up region of 126°–286° and the dimple aspect ratio is nearly 1.0.

scholarly journals Curvilinear Squeeze Film Bearing with Porous Wall Lubricated by a Rabinowitsch Fluid

2017 ◽  
Vol 22 (2) ◽  
pp. 427-441 ◽  
Author(s):  
A. Walicka ◽  
E. Walicki ◽  
P. Jurczak ◽  
J. Falicki
Keyword(s):  
Analytical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Porous Wall ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Numerical Examples ◽  
Load Carrying ◽  
Spherical Bearing

AbstractThe present theoretical analysis is to investigate the effect of non-Newtonian lubricant modelled by a Rabinowitsch fluid on the performance of a curvilinear squeeze film bearing with one porous wall. The equations of motion of a Rabinowitsch fluid are used to derive the Reynolds equation. After general considerations on the flow in a bearing clearance and in a porous layer using the Morgan-Cameron approximation the modified Reynolds equation is obtained. The analytical solution of this equation for the case of a squeeze film bearing is presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. Thrust radial bearing and spherical bearing with a squeeze film are considered as numerical examples.

scholarly journals Pressure Distribution in a Squeeze Film Spherical Bearing with Rough Surfaces Lubricated by an Ellis Fluid

2016 ◽  
Vol 21 (3) ◽  
pp. 593-610 ◽  
Author(s):  
P. Jurczak ◽  
J. Falicki
Keyword(s):  
Surface Roughness ◽  
Stochastic Model ◽  
Pressure Distribution ◽  
Analytical Solutions ◽  
Reynolds Equation ◽  
Rough Surfaces ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Plastic Fluid ◽  
Spherical Bearing

Abstract In this paper, the solution to a problem of pressure distribution in a curvilinear squeeze film spherical bearing is considered. The equations of motion of an Ellis pseudo-plastic fluid are presented. Using Christensen’s stochastic model of rough surfaces, different forms of Reynolds equation for various types of surface roughness pattern are obtained. The analytical solutions of these equations for the cases of externally pressurized bearing and squeeze film bearing are presented. Analytical solutions for the film pressure are found for the longitudinal and circumferential roughness patterns. As a result the formulae expressing pressure distribution in the clearance of bearing lubricated by an Ellis fluid was obtained. The numerical considerations for a spherical bearing are given in detail.

Static Performance Analysis of Orifice Compensated Externally Pressurized Gas Spherical Bearing Based on FEM

2006 ◽  
Vol 315-316 ◽  
pp. 860-863 ◽  
Author(s):  
Ying Xue Yao ◽  
Dong Li Qin ◽  
H.B. Zhang
Keyword(s):  
Reynolds Equation ◽  
Theoretical Study ◽  
Geometrical Parameters ◽  
Load Carrying Capacity ◽  
Weighted Residual Method ◽  
Load Carrying ◽  
Reasonable Range ◽  
Spherical Bearing ◽  
Static Performance ◽  
Derivatives Of

In order to optimize static performance of a new orifices compensated externally pressurized gas spherical bearing, the paper presents a theoretical study using finite element method (FEM). Galerkin weighted residual method is applied to reduce the order of derivatives of the transformed Reynolds equation. On the basis of theoretical analysis, the influence of supplying pressure and geometrical parameters to radial load carrying capacity and stiffness was analyzed. As a result, the reasonable range of the bearing’s parameters was proposed.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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