The Accuracy of Short Bearing Theory for Newtonian Lubricants

1986 ◽  
Vol 108 (1) ◽  
pp. 73-79 ◽  
Author(s):  
R. H. Buckholz ◽  
B. Hwang
Keyword(s):  
Aspect Ratio ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Perturbation Expansion ◽  
Approximate Solutions ◽  
Matched Asymptotic Expansion ◽  
Eccentricity Ratio ◽  
Regular Perturbation ◽  
Slider Bearings

The accuracy of the short bearing approximation is analyzed in this discussion. The results apply to Newtonian lubricants, and they can also be extended to non-Newtonian power-law lubricants. Reynolds’ lubrication equation is first solved by applying a regular perturbation expansion in pressure to the π film journal bearing; after this, a matched asymptotic expansion is applied to linear slider bearings. Approximate solutions are then compared with numerical solutions, to estimate the accuracy of the short bearing approximation. Finally, the accuracy of fluid film pressures predicted via short bearing theory is shown to depend upon three factors: the bearing aspect ratio, eccentricity ratio, and the partial-arc extent. Ocvirk’s short bearing series approximation—for finite bearing aspect ratio—is shown to become singular in the limit as the eccentricity ratio approaches unity. The one term π film Ocvirk solution is shown to be a nonconservative approximation to the journal bearing load capacity. A method to extend the accuracy of the short bearing approximation for partial-arcs and slider bearings is then presented.

Dynamic Behavior of Pure Squeeze Films in Narrow Porous Bearings

1974 ◽  
Vol 96 (3) ◽  
pp. 361-364 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Dynamic Behavior ◽  
Cyclic Load ◽  
Journal Bearing ◽  
Load Capacity ◽  
Squeeze Film ◽  
Closed Form Expression ◽  
Cyclic Loads ◽  
Eccentricity Ratio ◽  
Form Expression ◽  
Bearing Material

The dynamic behavior of squeeze film in a narrow porous journal bearing under a cyclic load is analyzed. A thin-walled bearing with a nonrotating journal is considered and a closed form expression for the pressure distribution is derived. The locus of the journal center is found by numerical methods and it is established with an example that actual contact between the journal and bearing can be avoided by appropriate design of the bearing. Consequently, it is proved that pure squeeze films have a load capacity only under cyclic loads. The analysis also reveals that the permeability of the bearing material and the wall thickness of the bearing influence significantly the operating eccentricity ratio.

scholarly journals Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel

2012 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Timir Karmakar ◽  
Meraj Alam ◽  
G. P. Raja Sekhar
Keyword(s):  
Porous Medium ◽  
Approximate Solution ◽  
Existence And Uniqueness ◽  
Perturbation Expansion ◽  
Positive Semidefinite ◽  
Darcy Number ◽  
Momentum Equation ◽  
Matched Asymptotic Expansion ◽  
Regular Perturbation ◽  
Uniqueness Results

<p style='text-indent:20px;'>We present asymptotic analysis of Couette flow through a channel packed with porous medium. We assume that the porous medium is anisotropic and the permeability varies along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We developed existence and uniqueness results corresponding to the anisotropic Brinkman-Forchheimer extended Darcy's equation in case of fully developed flow using the Browder-Minty theorem. Complemented with the existence and uniqueness analysis, we present an asymptotic solution by taking Darcy number as the perturbed parameter. For a high Darcy number, the corresponding problem is dealt with regular perturbation expansion. For low Darcy number, the problem of interest is a singular perturbation. We use matched asymptotic expansion to treat this case. More generally, we obtained an approximate solution for the nonlinear problem, which is uniformly valid irrespective of the porous medium parameter values. The analysis presented serves a dual purpose by providing the existence and uniqueness of the anisotropic nonlinear Brinkman-Forchheimer extended Darcy's equation and provide an approximate solution that shows good agreement with the numerical solution.</p>

Numerical Investigation on the Mixed Lubrication Performance of Water-Lubricated Coupled Journal and Thrust Bearings

2019 ◽  
Author(s):  
Yanfeng Han ◽  
Guo Xiang ◽  
Jiaxu Wang
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Journal Bearing ◽  
Load Capacity ◽  
Hydrodynamic Pressure ◽  
Mixed Lubrication ◽  
Eccentricity Ratio ◽  
Thrust Bearings ◽  
Lubrication Performance

Abstract The mixed lubrication performance of water-lubricated coupled journal and thrust bearing (simplified as coupled bearing) is investigated by a developed numerical model. To ensure the continuity of hydrodynamic pressure and flow at the common boundary between the journal and thrust bearing, the conformal transformation is introduced to unify the solution domain of the Reynolds equation. In the presented study, the coupled effects between the journal and thrust bearing are discussed. The effects of the thrust bearing geometric film thickness on the mixed lubrication performance, including the load capacity, contact load and friction coefficient, of the journal bearing are investigated. And the effects of the journal bearing eccentricity ratio on the mixed lubrication performance of the thrust bearing are also investigated. The simulated results indicate the mutual effects between the journal and thrust bearing cannot be ignored in the coupled bearing system. The increasing thrust bearing geometric film thickness generates a decrease in load capacity of journal bearing. There exists an optimal eccentricity ratio of journal bearing that yields the minimum friction coefficient of the thrust bearing.

Characteristics of Externally Pressurized Journal Bearings with Membrane-Type Variable-Flow Restrictors as Compensating Elements

1974 ◽  
Vol 188 (1) ◽  
pp. 527-536 ◽  
Author(s):  
C. Cusano Ms
Keyword(s):  
Aspect Ratio ◽  
Load Capacity ◽  
Pressure Ratio ◽  
Journal Bearings ◽  
Eccentricity Ratio ◽  
Rotating Shaft ◽  
Variable Flow ◽  
Type Variable ◽  
Bearing Stiffness ◽  
Membrane Type

The characteristics of externally pressurized journal bearings with four recesses and with membrane-type variable-flow restrictors as compensating elements are analytically investigated by using the bearing model of Raimondi and Boyd. The effects of the ratio of the recess pressure at zero eccentricity to the supply pressure (pressure ratio), the eccentricity ratio, the compliance of the membrane and the shaft rotation on the lubricant flow rate, the load capacity and the stiffness of these bearings are presented for a given aspect ratio and inter-recess*** land width-to-diameter ratio. For a non-rotating shaft, it is shown that when the bearing operates at zero eccentricity there is a pressure ratio that gives an optimum bearing stiffness. This pressure ratio is a function of the aspect ratio of the bearing only. Using this pressure ratio, data for the load capacity and stiffness of the bearing are presented for an eccentricity ratio that varies from 0 to 0·1. For these data, the membrane compliances used are those that would give an infinite bearing stiffness if the bearing were operating at zero eccentricity.

On the Load Capacity of the MHD Journal Bearing

1968 ◽  
Vol 90 (1) ◽  
pp. 139-144 ◽  
Author(s):  
S. J. Dudzinsky ◽  
F. J. Young ◽  
W. F. Hughes
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Journal Bearing ◽  
Hartmann Number ◽  
Load Capacity ◽  
External Source ◽  
Diameter Ratio ◽  
Experimental Results ◽  
Eccentricity Ratio ◽  
Applied Current

An analysis and experimental results are presented for a magnetohydrodynamic partial journal bearing using a liquid metal lubricant. An external magnetic field is applied axially along the journal, and current is permitted to flow between the journal and bearing. The analysis shows that increased load capacity can be achieved by supplying current from an external source. In addition, the analysis reveals the existence of an optimum Hartmann number at which the load capacity peaks for a given applied current. This optimum value is about 5 for a dimensionless current I¯ = −5 applied to a bearing with a width/diameter ratio of 1 and an eccentricity ratio of 0.6. Experimental results which demonstrate the increase in load capacity resulting from an externally applied current are presented graphically and compared with the theory.

The Load Capacity of Short Journal Bearings With Oscillating Effective Speed

1964 ◽  
Vol 86 (2) ◽  
pp. 348-353 ◽  
Author(s):  
B. K. Gupta ◽  
R. M. Phelan
Keyword(s):  
Significant Contribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Journal Bearings ◽  
Squeeze Film ◽  
Major Conclusion ◽  
Angular Velocities ◽  
Effective Speed

The development of the Reynolds equation for the general case of dynamically loaded journal bearings is extended to include the concept of an effective speed that combines in one term the angular velocities of the journal, bearing, and load. Numerical solutions for the short-bearing approximation are presented for the case of an oscillating effective speed and a load that is constant or varying sinusoidally. Results are compared with available experimental data. The major conclusion is that for those cases involving an oscillating effective speed and a reversing load, the only significant contribution to load capacity comes from the squeeze film and the wedge film can safely be ignored when designing such bearings.

Study on Load Capacity and Dynamic Characteristics of the Wave Bearing at Infinite Compressibility Number

2014 ◽  
Author(s):  
Baisong Yang ◽  
Haipeng Geng ◽  
Jian Zhou ◽  
Lie Yu ◽  
Shemiao Qi ◽  
...  
Keyword(s):  
Continuous Wave ◽  
Journal Bearing ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Computational Method ◽  
Wave Number ◽  
Algebraic Equations ◽  
Eccentricity Ratio ◽  
Operation Speed ◽  
Stiffness And Damping

The wave bearing developed by Dimofte in the 1990’s features a continuous wave profile and presents numerous advantages compared to plain journal bearings. One of the main advantages of the wave bearing is that it has a higher degree of stability than the plain journal bearing and this load capacity is close to the load capacity of the plain journal bearing. Predicting these coefficients for the wave bearing with high bearing numbers is difficult, although there are many studies on the aerodynamic bearing. This paper presents an analytical method for calculating the limiting values of load capacity, dynamic stiffness and damping coefficients of the wave bearing for compressible fluids by simplifying the compressible Reynolds equation at high journal operation speed. A computational method is submitted which is derived from simple algebraic equations combined with infinitesimal perturbation method. The limiting characters of the wave bearing are compared with the plain journal bearing for all eccentricity ratios. Special emphasis is placed on investigating the effects of wave number, wave eccentricity ratio and wave starting angle on the limiting characteristics. Numerical results obtained indicate that the load capacity and stiffness of the wave bearing is better than the plain journal bearing at the same eccentricity ratio.

scholarly journals Bending of Rectangular Plates With Finite Deflections

1965 ◽  
Vol 32 (4) ◽  
pp. 821-825 ◽  
Author(s):  
Frances Bauer ◽  
Louis Bauer ◽  
William Becker ◽  
Edward L. Reiss
Keyword(s):  
Aspect Ratio ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Normal Pressure ◽  
Rectangular Plates ◽  
Membrane Stress ◽  
Wide Range ◽  
Loading Parameter ◽  
Range Of Values ◽  
Membrane Displacement

A previously developed iterative procedure is applied to obtain numerical solutions of the von Ka´rma´n equations for rectangular plates subjected to a uniform normal pressure. On the simply supported boundary, it is assumed that the normal membrane stress and the tangential membrane displacement vanish. Solutions are obtained for a wide range of values of the loading parameter and the aspect ratio. Boundary layers develop both as the loading parameter and the aspect ratio increase. The stresses and deflections are examined and compared with an “asymptotic” solution which can be valid only in the interiors of long plates. A comparison is also made with previously obtained approximate solutions.

On the Analytical Evaluation of the Lubricant Pressure in the Finite Journal Bearing

2012 ◽  
Author(s):  
Athanasios Chasalevris ◽  
Dimitris Sfyris
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Closed Form Expression ◽  
Linear Ordinary Differential Equations ◽  
Definition Of

The Reynolds equation for the pressure distribution of the lubricant in a journal bearing with finite length is solved analytically. Using the method of the separation of variables in an additive and in a multiplicative form, a set of particular solutions of the Reynolds equation is added in the general solution of the homogenous Reynolds equation and a closed form expression for the definition of the lubricant pressure is presented. The Reynolds equation is split in four linear ordinary differential equations of second order with non constant coefficients and together with the boundary conditions they form four Sturm-Liouville problems with the three of them to have direct forms of solution and one of them to be confronted using the method of power series. The mathematical procedure is presented up to the point that the application of the boundaries for the pressure distribution yields the final definition of the solution with the calculation of the constants. The current work gives in detail the mathematical path with which the analytical solution is derived, and it ends with the pressure evaluation and a comparison with past numerical solutions and an approximate analytical solution for a finite bearing. Also the parameters of primary interest to the bearing designer, such as load capacity, attitude angle, and stiffness and damping coefficients are evaluated and compared with numerical results.

Effects of Power—Law, Non-Newtonian Lubricants on Load Capacity and Friction for Plane Slider Bearings

1986 ◽  
Vol 108 (1) ◽  
pp. 86-91 ◽  
Author(s):  
R. H. Buckholz
Keyword(s):  
Power Law ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Lagrange Equation ◽  
Load Capacity ◽  
Approximate Solutions ◽  
Finite Width ◽  
Aspect Ratios ◽  
Modified Reynolds Equation ◽  
Power Law Index

The lubrication of a conventional, finite width plane bearing, using a power-law, non-Newtonian lubricant, is studied. The basic assumptions in this analysis are: thin fluid-film, no thermal effects, and a modified Reynolds’ equation for small bearing aspect ratios. Results from this study include bearing pressure, load, and friction formulas. Similar results for the not-so-small bearing aspect ratios are found via an Euler-Lagrange equation. This Euler-Lagrange equation is derived from the optimization integral for the modified Reynolds’ equation. Approximate solutions to the modified Reynolds’ equation and to the Euler-Lagrange equation are contrasted with numerical solutions for the modified Reynolds equation. Bearing aspect ratios in the range 0.1 to 0.6, clearance ratios in the range 1.2 to 4.0, and non-Newtonian power-law index in the range 0.4 to 1.0 are considered.

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