Perturbation Solution of the 1-D Reynolds Equation With Slip Boundary Conditions

1978 ◽  
Vol 100 (1) ◽  
pp. 70-73 ◽  
Author(s):  
Aron Sereny ◽  
Vittorio Castelli
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Load Carrying Capacity ◽  
Slip Boundary Conditions ◽  
Slider Bearing ◽  
Slip Boundary ◽  
Load Carrying ◽  
Bearing Number

The method of matched asymptotic expansion is applied to obtain the pressure distribution and the load carrying capacity for an infinitely long slider bearing, operating under high-speed, low-height, with slip boundary conditions. The pressure distribution is easily applicable as the starting solution for the iterative numerical solution of Reynolds equation. Two examples given show extremely good correlation between this expansion and the numerical solution. It is shown that, for a tapered slider bearing with a bearing number above 100, the reduction in load because of slip is minimal and that, for a parabolic slider, there exists a certain unique bearing number for which the load carrying capacity is independent of the parabolic crown of the slider. It is shown that for a wide slider bearing with large bearing number, the effect of slip is on the order of 1/A.

Hydrodynamic Lubrication of Finite Slider Bearings: Effect of One Dimensional Film Shape, and Their Computer Aided Optimum Designs

1983 ◽  
Vol 105 (1) ◽  
pp. 48-63 ◽  
Author(s):  
C. Bagci ◽  
A. P. Singh
Keyword(s):  
Numerical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Design Data ◽  
Slider Bearings ◽  
Load Carrying ◽  
Computer Aided

The effect of the film shape on the load carrying capacity of a hydrodynamically lubricated bearing has not been considered an important factor in the past. Flat-faced tapered bearing and the Raileigh’s step bearing of constant film thickness have been the primary forms of film shapes for slider bearing studies and design data developments. This article, by the computer aided numerical solution of the Reynolds equation for two dimensional incompressible lubricant flow, investigates hydrodynamically lubricated slider bearings having different film shapes and studies the effect of the film shape on the performance characteristics of finite bearings; and it shows that optimized bearing with film shapes having descending slope toward the trailing edge of the bearing has considerably higher load carrying capacity than the optimized flat-faced tapered bearing of the same properties. For example the truncated cycloidal film shape yields 26.3 percent higher load carrying capacity for Lz/Lx = 1 size ratio, and 44 percent higher for Lz/Lx = 1/2. The article then presents charts for the optimum designs of finite slider bearings having tapered, exponential, catenoidal, polynomial, and truncated-cycloidal film shapes, and illustrates their use in numerical bearing design examples. These charts also furnish information on flow rate, side leakage, temperature rise, coefficient of friction, and friction power loss in optimum bearings. Appended to the article are analytical solutions for infinitely wide bearings with optimum bearing characteristics. The computer aided numerical solution of the Reynolds equation in most general form is presented by which finite or infinitely wide hydrodynamically or hydrostatically lubricated bearings, externally pressurized or not, can be studied. A digital computer program is made available.

Numerical Solution of Reynolds Equation With Slip Boundary Conditions for Cases of Large Bearing Number (Λ > 300)

1979 ◽  
Vol 101 (1) ◽  
pp. 64-66 ◽  
Author(s):  
A. Sereny ◽  
V. Castelli
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Slip Boundary Conditions ◽  
Grid Spacing ◽  
Slip Boundary ◽  
Finite Differencing ◽  
Bearing Number

The behavior of two numerical discretizations for the solution of Reynolds equation with slip boundary conditions for cases of large bearing number is described. The narrow boundary layer caused by the large bearing number is well handled by a variable grid spacing. The performance of these methods is compared against exact solutions for the ∞-wide case. It is clearly demonstrated that discretization which satisfies integral conservation is preferable to the differential procedure of finite differencing.

Higher Order Approximations in the Asymptotic Solution of the Reynolds Equation for Slider Bearings at High Bearing Numbers

1969 ◽  
Vol 91 (1) ◽  
pp. 45-51 ◽  
Author(s):  
R. C. DiPrima
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Higher Order ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Load Carrying ◽  
Higher Order Terms ◽  
Parabolic Shape ◽  
Bearing Number

The methods of matched asymptotic expansions are used in a systematic manner to obtain the load-carrying capacity of an infinitely long slider bearing correct through terms 0 (1/Λ) where Λ is the bearing number. The expression for the load is extremely simple. It is shown that the error is 0 (1/Λ2), and the procedure for obtaining higher order terms is discussed. Results are given for the case of a converging film thickness with a parabolic shape and for a partial arc journal bearing.

On the study of Rayleigh step slider bearings lubricated with non-Newtonian Rabinowitsch fluid

2017 ◽  
Vol 69 (5) ◽  
pp. 666-672
Author(s):  
N.B. Naduvinamani ◽  
Siddharam Patil ◽  
S.S. Siddapur
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Maximum Load ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Content Type ◽  
Slider Bearings ◽  
Load Carrying ◽  
Modified Reynolds Equation ◽  
Frictional Coefficients

Purpose Nowadays, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of non-Newtonian fluids has gained importance. This paper presents an analysis of the static characteristics of Rayleigh step slider bearing lubricated with non-Newtonian Rabinowitsch fluid, which has not been studied so far. The purpose of this paper is to derive the modified Reynolds equation for Rabinowitsch fluids for two regions and to obtain the optimum bearing parameters for the Rayleigh step slider bearings. Design/methodology/approach The governing equations relevant to the problem under consideration are derived. The modified Reynolds equation is derived, and it is found to be highly non-linear and hence small perturbation method is adopted to find solution. Findings From this study it is found that there is an increase in the load-carrying capacity, pressure and frictional coefficients for dilatant fluids as compared to the corresponding Newtonian case. Further, for dilatant lubricants the maximum load-carrying capacity is attained for the slightly larger values of entry region length of Rayleigh step bearing as compared to Newtonian and pseudoplastic lubricants. Originality/value Rabinowitsch fluid is used for the study of lubrication characteristics of Rayleigh step bearings. The author believes that the paper presents these results for the first time.

An Analysis of Powder Lubricated Slider Bearings

1996 ◽  
Vol 118 (1) ◽  
pp. 206-214 ◽  
Author(s):  
K. T. McKeague ◽  
M. M. Khonsari
Keyword(s):  
Boundary Conditions ◽  
Carrying Capacity ◽  
Parametric Study ◽  
Experimental Measurements ◽  
Load Carrying Capacity ◽  
General Boundary Conditions ◽  
Slider Bearing ◽  
Slider Bearings ◽  
Load Carrying ◽  
Theoretical Predictions

A theory for predicting the behavior of powder lubricated slider bearings based on the collisional characteristics of the grain particles and their interactions at the boundaries is presented. General boundary conditions that account for the effects of powder slippage are applied to the slider bearing configuration. Theoretical predictions are presented with comparison to published experimental measurements. An extensive parametric study is also conducted to illustrate the behavior of the flow and the response of the bearing’s load-carrying capacity and friction factor to changes in various powder material and boundary parameters.

The Magnetohydrodynamic Slider Bearing

1962 ◽  
Vol 84 (1) ◽  
pp. 197-202 ◽  
Author(s):  
William T. Snyder
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Boundary Conditions ◽  
Carrying Capacity ◽  
Load Capacity ◽  
Numerical Data ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Electrically Conducting ◽  
Load Carrying

An analysis is presented of the slider bearing using an electrically conducting lubricant, such as a liquid metal, in the presence of a magnetic field. The solution permits the calculation of the load-carrying capacity of the bearing. A comparison is made with the classical slider bearing solution. It is shown that the load capacity of the bearing depends on the electromagnetic boundary conditions entering through the conductivity of the bearing surfaces. Numerical data are presented for nonconducting surfaces with the emphasis on a comparison between the classical bearing and the magnetohydrodynamic bearing characteristics. It is shown that a significant increase in load capacity is possible with liquid metal lubricants in the presence of a magnetic field.

The Thermally Boosted Oil Lubricated Sliding Thrust Bearing

1974 ◽  
Vol 96 (3) ◽  
pp. 322-328 ◽  
Author(s):  
C. M. Rodkiewicz ◽  
J. C. Hinds ◽  
C. Dayson
Keyword(s):  
Boundary Conditions ◽  
Carrying Capacity ◽  
Thrust Bearing ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Governing Equations ◽  
Temperature Ratio ◽  
Thrust Bearings ◽  
Temperature Boundary ◽  
Load Carrying

The effect of varying the ratio of slider to pad temperature boundary conditions and the influence of varying inlet to outlet ratio of a plane infinitely wide slider bearing is examined. The lubricant is assumed to be incompressible and the variation of viscosity with temperature is taken into account. The nondimensionalized governing equations, transformed in terms of the stream function, are solved numerically. The results show that maintaining a lower slider temperature to pad temperature ratio causes an increase in the load carrying capacity of the bearing. A means of which advantage could be taken of this effect in the design of thrust bearings is suggested.

scholarly journals Analysis of Heat Transfer and Lifting Force in a Ferro-Nanofluid Based Porous Inclined Slider Bearing with Slip Conditions

2019 ◽  
Vol 8 (1) ◽  
pp. 206-215 ◽  
Author(s):  
Paras Ram ◽  
Anil Kumar
Keyword(s):  
Thermal Effects ◽  
Load Carrying Capacity ◽  
Slip Boundary Conditions ◽  
Slider Bearing ◽  
Slip Boundary ◽  
Lifting Force ◽  
Mean Temperature ◽  
Governing System ◽  
Load Carrying ◽  
Fluid Film Thickness

Abstract Thermal effects have been investigated in a porous inclined slider bearing together with the slip boundary conditions. Using Jenkins model, the governing system of equations pertaining to the flow is solved analytically to yield the various bearing characteristics. The expressions for mean temperature, pressure and the lifting force (load carrying capacity) have been derived as a function of slip, magnetic, permeability, material and thermal parameters. Furthermore, the term pertaining to the co-rotational derivative of magnetization is expected to influence the lifting force significantly. Therefore its effect on the bearing characteristics is also considered. The lubricant is assumed to be incompressible, and its viscosity varies exponentially with the temperature. The behavior of mean temperature with other bearing characteristics across the fluid film thickness has also been investigated. The variations in the lifting force and mean temperature w.r.t. various bearing parameters have been analyzed graphically.

A Comparison of Porous Structures on the Performance of a Slider Bearing with Surface Roughness in Couple Stress Fluid Film Lubrication

2015 ◽  
Vol 813-814 ◽  
pp. 921-937
Author(s):  
P.S. Rao ◽  
Santosh Agarwal
Keyword(s):  
Surface Roughness ◽  
Carrying Capacity ◽  
Couple Stress ◽  
Type Equation ◽  
Random Variable ◽  
Couple Stress Fluid ◽  
Load Carrying Capacity ◽  
Porous Structures ◽  
Slider Bearing ◽  
Load Carrying

This paper presents the theoretical study and analyzes the comparison of porous structures on the performance of a couple stress fluid based on rough slider bearing. The globular sphere model of Kozeny-Carman and Irmay’s capillary fissures model have been subjected to investigations. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The stochastically averaged Reynolds type equation has been solved under suitable boundary conditions to obtain the pressure distribution in turn which gives the expression for the load carrying capacity, frictional force and coefficient of friction. The results are illustrated by graphical representations which show that the introduction of combined porous structure with couple stress fluid results in an enhanced load carrying capacity more in the case of Kozeny-Carman model as compared to Irmay’s model.

The Validity of the Reynolds Equation in Modeling Hydrostatic Effects in Gas Lubricated Textured Parallel Surfaces

2005 ◽  
Vol 128 (2) ◽  
pp. 345-350 ◽  
Author(s):  
Y. Feldman ◽  
Y. Kligerman ◽  
I. Etsion ◽  
S. Haber
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Surface Texturing ◽  
Laser Surface Texturing ◽  
Physical Parameters ◽  
Load Carrying Capacity ◽  
Wide Range ◽  
Load Carrying ◽  
Parallel Surfaces

Microdimples generated by laser surface texturing (LST) can be used to enhance performance in hydrostatic gas-lubricated tribological components with parallel surfaces. The pressure distribution and load carrying capacity for a single three-dimensional dimple, representing the LST, were obtained via two different methods of analysis: a numerical solution of the exact full Navier-Stokes equations, and an approximate solution of the much simpler Reynolds equation. Comparison between the two solution methods illustrates that, despite potential large differences in local pressures, the differences in load carrying capacity, for realistic geometrical and physical parameters, are small. Even at large clearances of 5% of the dimple diameter and pressure ratios of 2.5 the error in the load carrying capacity is only about 15%. Thus, for a wide range of practical clearances and pressures, the simpler, approximate Reynolds equation can safely be applied to yield reasonable predictions for the load carrying capacity of dimpled surfaces.

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