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.

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.

Theoretical Analysis of Externally Pressurized Air Journal Bearing

1970 ◽  
Vol 12 (2) ◽  
pp. 123-129 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Experimental Data ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Design Parameters ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Dimensional Parameters ◽  
Bearing Design

A theoretical investigation is made to predict the performance of an externally pressurized air journal bearing having several pressure sources. The pressure distribution, which leads to the determination of load-carrying capacity and flow requirement, is obtained by solving Reynolds equation numerically. The load and flow, expressed in non-dimensional parameters, are presented for different bearing design parameters (dimensionless). The results predicted by this method are compared with others' experimental data.

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.

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.

Steady-state performance of a circular journal bearing lubricated with a non-Newtonian fluid considering the elastic deformation of the liner

2019 ◽  
Vol 233 (9) ◽  
pp. 1389-1396
Author(s):  
Boualem Chetti ◽  
Hamid Zouggar
Keyword(s):  
Friction Coefficient ◽  
Elastic Deformation ◽  
Power Law ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Carrying Capacity ◽  
Static Characteristics ◽  
Load Carrying ◽  
Power Law Index

In this work, a numerical study of the effect of elastic deformation on the static characteristics of a circular journal bearing operating with non-Newtonian fluids obeying to the power law model is presented. The modified Reynolds equation has been derived taking into consideration the effect of non-Newtonian behavior of the fluids. To obtain the pressure distribution, the Reynolds equation has been solved using finite difference technique with appropriate iterative technique incorporating Reynolds boundary conditions. The static performance characteristics for finite-width journal bearing in terms of the load-carrying capacity, the attitude angle, friction coefficient, and the side leakage have been studied for various values of the non-Newtonian power law index n and the elastic coefficient. The results show that the increase of the power law index produces a higher load-carrying capacity, a higher side leakage, a lower attitude angle, and a lower friction coefficient. From this study, it can be concluded that the elastic deformation has an important influence on the static characteristics of the journal bearing lubricated with a non-Newtonian fluid, and this influence is more significant for the journal bearing operating at larger values of the eccentricity ratio.

Effect of Nanoparticle Additives on Journal Bearing Lubricated with Non-Newtonian Carreau Fluid

2015 ◽  
Vol 751 ◽  
pp. 137-142 ◽  
Author(s):  
W. Gunnuang ◽  
C. Aiumpornsin ◽  
Mongkol Mongkolwongrojn
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Research Work ◽  
Load Carrying Capacity ◽  
Static Characteristics ◽  
Carreau Fluid ◽  
Load Carrying ◽  
Nanoparticle Additives

This research work presents the influence of Al2O3 nanoparticle additives on the performance characteristics of a journal bearing. Non-Newtonian fluid based on Carreau viscosity model was represented for SAE10W50 oil blended with Al2O3 nanoparticles in this work. Reynolds equation and energy equation have been formulated and solved numerically using finite difference method and multigrid multilevel techniques with boundary conditions. The static characteristics of the journal bearing under isothermal and adiabatic conditions were examined. The results show that the addition of Al2O3 nanoparticles improve load-carrying capacity of the journal but almost no change on film temperature due to good thermal property of Al2O3 nanoparticles.

scholarly journals Effect of Viscosity Variation on the Micropolar Fluid Squeeze Film Lubrication of a Short Journal Bearing

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
N. B. Naduvinamani ◽  
Archana K. Kadadi
Keyword(s):  
Carrying Capacity ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Closed Form Solution ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Viscosity Variation ◽  
Modified Reynolds Equation

A theoretical study of the effect of the viscosity variation on the squeeze film performance of a short journal bearing operating with micropolar fluid is presented. The modified Reynolds equation accounting for the viscosity variation in micropolar fluid is mathematically derived. To obtain a closed form solution, the short bearing approximation under constant load is considered. The modified Reynolds equation is solved for the fluid film pressure and then the bearing characteristics, such as obtaining the load carrying capacity and the squeeze film time. According to the results evaluated, the micropolar fluid as a lubricant improves the squeeze film characteristics and results in a longer bearing life, whereas the viscosity variation factor decreases the load carrying capacity and squeezes film time. The result is compared with the corresponding Newtonian case.

Study on Lubrication Simulation and Capability of Three-Lobe Journal Bearing

2014 ◽  
Vol 709 ◽  
pp. 210-214
Author(s):  
Kun Qian ◽  
Wei Gang Guo
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Rotation Speed ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Bearing Load ◽  
The Stability ◽  
Eccentric Distance

The lubrication state of three-lobe bearing is simulated by using Reynolds equation. It concluded that the load-carrying capability of three-lobe bearing increases with the eccentric distance between the centers of axis and bearing with a nonlinear way. The largest bearing load-carrying capacity occurs in the eccentric direction of 30 °and making sure the eccentric direction can improve the stability of the system. To improve the rotation speed of the axis is beneficial to promote the load-carrying capacity.

scholarly journals Comparative study of spherical dimple and bump effects on the tribological performances of journal bearing

2018 ◽  
Vol 233 (1) ◽  
pp. 139-157 ◽  
Author(s):  
Chao Gui ◽  
Fanming Meng
Keyword(s):  
Friction Force ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Pressure ◽  
Load Carrying Capacity ◽  
Transform Method ◽  
Cavitation Effect ◽  
Fast Fourier Transform Method ◽  
Load Carrying

In the present study, tribological performances of journal bearings with the representative spherical dimples and bumps are compared numerically. In doing so, the hydrodynamic pressure of the lubricant is solved by the Reynolds equation considering the lubricant cavitation effect. Meanwhile, the elastic deformation is calculated by the continuous convolution fast Fourier transform method. The enhanced load-carrying capacity and the reduced friction force occur only when the dimples are located at pressure rising part of the bearing. The bumps located at the pressure falling part can enhance the load-carrying capacity but increase the friction force. The above dimple and bump effects change at the varied feature sizes and intervals.

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