Rayleigh Step Journal Bearing: Part 1—Compressible Fluid

1968 ◽  
Vol 90 (1) ◽  
pp. 271-280 ◽  
Author(s):  
B. J. Hamrock
Keyword(s):  
Compressible Fluid ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Pressure Profile ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Step Parameters ◽  
Bearing Part

A linearized PH solution to the Reynolds equation was obtained while neglecting side leakage. The analysis was divided into two parts—the step and ridge regions. The pressure profile across the step and ridge region of the various pads which are placed around the journal was obtained from the linearized PH Reynolds equation. Knowing the pressure, the load components and attitude angle were calculated. The resulting equations were found to be a function of the bearing parameters (the eccentricity and compressibility number) and the step parameters (ratio of the stepped clearance to the ridge clearance, ratio of the angle extended by the ridge to the angle extended by the pad, and number of pads placed around the journal). The maximum load capacity can be determined by numerically differentiating the load with respect to the step bearing parameters while finding where the slope is zero. A series of data was run while varying the bearing parameters. The attitude angle was calculated for the various cases which were run.

Rayleigh Step Journal Bearing, Part II—Incompressible Fluid

1969 ◽  
Vol 91 (4) ◽  
pp. 641-650 ◽  
Author(s):  
B. J. Hamrock ◽  
W. J. Anderson
Keyword(s):  
Theoretical Analysis ◽  
Film Thickness ◽  
Journal Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Single Step ◽  
Thickness Ratio ◽  
Infinite Length ◽  
One Step ◽  
Bearing Part

A theoretical analysis of the pressure distribution, load, capacity, and attitude angle for a single-step concentric as well as a multistep infinite length eccentric Rayleigh step journal bearing is performed. The results from the single-step concentric analysis indicated that the maximum load capacity is obtained when the film thickness ratio is 1.7 and the ratio of the angle subtended by the ridge to the angle subtended by the pad is 0.35. The results from the infinite length eccentric analysis indicated that one step placed around the journal was optimal. For eccentricity ratios greater than or equal to 0.2 the maximum load occurred for a bearing without a step or a Sommerfeld bearing. For eccentricity ratios less than 0.2 the optimal film thickness ratio is 1.7 while there are three optimal ratios of angle subtended by the ridge to the angle subtended by the pad of 0.4, 0.45, and 0.5 depending on whether load capacity or stability or both load capacity and stability is more important in the application being considered.

Rarefaction Effect on the Characteristics of Micro Gas Journal Bearings

2009 ◽  
Author(s):  
Haijun Zhang ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Slip Boundary Condition ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Clearance Ratio ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

Journal bearings, which are used to support radial loads in a rotating machine, have somewhat unusual requirements in MEMS deriving from the extremely shallow structures. Thus, the micro gas journal bearings are characterized by a very small length-diameter ratio, defined as the ratio of the bearing length to its diameter and a paradoxically large bearing clearance ratio, defined as the ratio of the average radial clearance to the bearing radius. Given the definition of the reference Knudsen number for micro gas journal bearings, the range of the reference Knudsen number is illustrated according to the viscosity values of air under different temperatures. With the reference Knudsen number being included, the modified Reynolds equation for micro gas journal bearings based on Burgdorfer’s first order slip boundary condition is put forward. The finite difference method (FDM) is employed to solve the modified Reynolds equation to obtain the pressure distribution, load capacities and attitude angles for micro gas journal bearings under different reference Knudsen numbers, bearing numbers and eccentricity ratios. Numerical analysis shows that the pressure profiles and non-dimensional load capacities decrease obviously with gas rarefaction strengthened, and the attitude angle changes conversely. Moreover, when the bearing number is smaller, the effect of gas rarefaction on the non-dimensional load capacity and attitude angle is less.

A General Solution of Reynolds’ Equation for a Full Finite Journal Bearing

1967 ◽  
Vol 89 (2) ◽  
pp. 203-210 ◽  
Author(s):  
R. R. Donaldson
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Hill Equation ◽  
Eigenvalues And Eigenvectors ◽  
General Series ◽  
Bearing Load

Reynolds’ equation for a full finite journal bearing lubricated by an incompressible fluid is solved by separation of variables to yield a general series solution. A resulting Hill equation is solved by Fourier series methods, and accurate eigenvalues and eigenvectors are calculated with a digital computer. The finite Sommerfeld problem is solved as an example, and precise values for the bearing load capacity are presented. Comparisons are made with the methods and numerical results of other authors.

Analysis of Infinitely Short and Infinitely Long Hydrodynamic Journal Bearings Under Micro-Polar Fluid by Direct Integration Method

2017 ◽  
Author(s):  
Bikash Routh
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Integration Method ◽  
Pressure Profile ◽  
Journal Bearings ◽  
Direct Integration ◽  
Polar Fluid ◽  
Direct Integration Method

In the present paper Reynolds equation of lubrication under micro-polar fluid for journal bearing is solved by direct-integration method under infinitely long and infinitely short journal bearing assumptions [1]. Infinitely long-bearing and infinitely short bearing solutions are the two available approximate closed form solutions for journal bearings. In the present investigation, solution of Reynolds equation i.e. pressure profile is compared with pressure profile obtained by previously used approximate method like finite difference method (FDM). Mentionable here that any approximation method needs lots of calculation and computer programing to get the result. In the present work it has been found that direct-integration method leads the almost same result as the conventionally used complex finite difference method. CFD analysis is also presented in the present work to justify the profile obtained by direct numerical method. It has seen here that theoretical and simulation results are in good agreement to each other’s.

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.

The Characteristics of a Statically Loaded Journal Bearing with Superlaminar Flow

1980 ◽  
Vol 22 (2) ◽  
pp. 79-94 ◽  
Author(s):  
R. E. Hinton ◽  
J. B. Roberts
Keyword(s):  
Friction Factor ◽  
Journal Bearing ◽  
Load Capacity ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Experimental Results ◽  
Empirical Theory ◽  
Clearance Ratio ◽  
Friction Factors ◽  
Theoretical Predictions

Experimental results are presented, relating to the friction factor, load capacity and attitude angle, for a plain, cylindrical journal bearing with a central, circumferential inlet groove. The length to diameter ratio of the journal bearing was 1/3 and the clearance ratio was 0.011. By the use of various lubricants, including water, Reynolds numbers ranging from 40 to 50 000 were attained. Comparisons with various theoretical predictions are given. It is shown that a simple, empirical theory, which incorporates measured friction factors, gives better agreement with the experimental load capacity results than previous theories.

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.

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.

Static Characteristics of the Regular and Reversible Rotation Type Herringbone Grooved Journal Bearing

1989 ◽  
Vol 111 (3) ◽  
pp. 484-490 ◽  
Author(s):  
Nobuyoshi Kawabata ◽  
Yasumi Ozawa ◽  
Shuji Kamaya ◽  
Yutaka Miyake
Keyword(s):  
Numerical Analysis ◽  
Journal Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Radial Load ◽  
Static Characteristics ◽  
Oil Film ◽  
New Type ◽  
Load Component ◽  
Reversible Rotation

A new type herringbone grooved journal bearing, which produces an oil film bearing pressure with a shaft or bearing rotation in either direction, is proposed in this paper. A numerical analysis of the bearing parameters using the narrow groove theory and the Gu¨mbel condition confirmed that the load capacity of this bearing and the radial load component (related to stability) do not differ greatly from those of a conventional bearing. The values of the bearing parameters which give maximum load capacity, and the values of the load capacity and its direction angle are also determined numerically for the case of either grooved member or smooth member rotation.

Modified Reynolds Equation for Non-Newtonian Fluid With Rheological Model in Frequency Domain

2005 ◽  
Vol 127 (4) ◽  
pp. 893-898 ◽  
Author(s):  
Chen Haosheng ◽  
Chen Darong
Keyword(s):  
Frequency Domain ◽  
Newtonian Fluid ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Pressure Profile ◽  
Thickness Variation ◽  
Lubrication Equation ◽  
Shear Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity

The purpose of this paper is to provide a lubrication equation for non-Newtonian fluid. Three nonlinear functions instead of common power law model are used to describe non-Newtonian properties more completely. They are shear dependent viscosity, first normal stress difference and stress relaxation. After the coordinate conversion which is needed for the lubricant film thickness variation, the functions are involved in the modified Reynolds equation and show their effects on the lubrication results. As the principle factor in lubrication, viscosity is expressed by a first order transfer function in frequency domain. Its variation process is described by the function’s amplitude frequency response curve, which is validated by rheological experiment. Numerical results of the modified Reynolds equation show that non-Newtonian lubricant’s load capacity is not always higher or lower than Newtonian lubricant’s, and non-Newtonian lubricant has flatter pressure profile at high working speed.

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