Theoretical Pressure Distribution in Journal Bearings

1961 ◽  
Vol 28 (4) ◽  
pp. 497-506 ◽  
Author(s):  
Kichiye Habata
Keyword(s):  
Reynolds Equation ◽  
Variable Viscosity ◽  
Slenderness Ratio ◽  
Approximate Solutions ◽  
Journal Bearings ◽  
Oil Viscosity ◽  
Pressure Distributions ◽  
Hill’S Method ◽  
Ritz’S Method ◽  
Theoretical Pressure

By assuming oil viscosity constant, Reynolds’ equation for journal bearings has been solved in a manner similar to Hill’s method. Two approximate solutions using E. O. Waters’ method and Ritz’s method have been added. Numerical computations have been carried out for a centrally supported 120-deg bearing with a unity slenderness ratio. Isobarriers have been determined from the pressure distributions. In order to show a justification for assuming the viscosity constant, the Reynolds equation was solved for the infinitely long bearing with variable viscosity, and the solution compared with that of Sommerfeld.

Turborotor Instability: Effect of Initial Transients on Plane Motion

1969 ◽  
Vol 91 (4) ◽  
pp. 625-630 ◽  
Author(s):  
R. H. Badgley ◽  
J. F. Booker
Keyword(s):  
Reynolds Equation ◽  
Approximate Solutions ◽  
Initial Position ◽  
Plane Motion ◽  
Journal Bearings ◽  
Rigid Body Dynamics ◽  
Fluid Film ◽  
Body Dynamics ◽  
Instability Effect ◽  
Static Eccentricity

The rigid-body dynamics of rotors supported in plain, cylindrical, cavitated, fluid-film journal bearings are investigated numerically by Runge-Kutta extrapolation techniques. Expressions for journal force due to the fluid-film are developed for the short-bearing (Ocvirk), long-bearing (Sommerfeld), and finite-length-bearing (Warner) approximate solutions to the Reynolds equation. Stability of plane motion is investigated for each solution under the assumption of light initial impact. The long-bearing solution appears to be most conservative (that is, it predicts the onset of instability at lower angular velocity ratios than the other solutions) for static eccentricity ratios between 0 and 0.5, while the finite-bearing solution, with bearing length-to-diameter ratio L/D equal to 1, appears most conservative at higher static eccentricity ratios. Variations in L/D between 0.5 and 2.0 appear not to affect journal path shapes appreciably. Variations in initial journal center velocity are found to be important, at least with the short-bearing solution: large initial velocities are observed to produce instability for certain parameter combinations which are stable under small initial position or velocity disturbances. In all cases investigated, instability is not observed above static eccentricity ratios of 0.83.

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.

Adiabatic Solutions for Finite Journal Bearings

1979 ◽  
Vol 101 (4) ◽  
pp. 492-496 ◽  
Author(s):  
Oscar Pinkus ◽  
Sargit S. Bupara
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Initial Conditions ◽  
Variable Viscosity ◽  
Full Range ◽  
Journal Bearings ◽  
Maximum Temperature ◽  
Performance Results ◽  
Bearing Analysis

The paper offers a method of including variable viscosity in bearing analysis by the use of a simple energy equation uncoupled from the Reynolds equation. The relevant adiabatic solutions are made independent of the specifics of the kind of lubricant used and of its initial conditions. Performance results such as load, friction, maximum temperature, flow, etc. are given for the two axial-groove journal bearing covering three L/D ratios, three values of the adiabatic parameter E, and the full range of eccentricities. The effect of variable viscosity on the performance of misaligned bearings is also examined.

On Journal Bearings of Finite Length With Variable Viscosity

1959 ◽  
Vol 26 (2) ◽  
pp. 179-183
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Finite Length ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Load Capacity ◽  
Journal Bearings ◽  
Heun Functions ◽  
Load Vector ◽  
Constant Viscosity

Abstract An exact solution of the Reynolds equation for journal bearings of finite length with viscosity as a function of pressure is found. The analytical solution is expressed in terms of Heun functions. The load capacity and the attitude angle are derived. It is found that the load vector, in general, is not perpendicular to the line of journal and bearing centers as shown in the constant-viscosity case.

On The Role of a Non-Newtonian Fluid in Short Bearing Theory

1985 ◽  
Vol 107 (1) ◽  
pp. 68-74 ◽  
Author(s):  
R. H. Buckholz
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Asymptotic Expansions ◽  
Reynolds Equation ◽  
Slenderness Ratio ◽  
Fluid Film ◽  
Matched Asymptotic Expansions ◽  
Film Pressure ◽  
Boundary Shape ◽  
Pressure Distributions

The importance of rheological properties of lubricants has arisen from the realization that non-Newtonian fluid effects are manifested over a broad range of lubrication applications. In this paper a theoretical investigation of short journal bearings performance characteristics for non-Newtonian power-law lubricants is given. A modified form of the Reynolds’ equation for hydrodynamic lubrication is studied in the asymptotic limit of small slenderness ratio (i.e., bearing length to diameter, L/D = λ→0). Fluid film pressure distributions in short bearings of arbitrary azimuthal length are studied using matched asymptotic expansions in the slenderness ratio. The merit of the short bearing approach used in solving a modified Reynolds’ equation by the method of matched asymptotic expansions is emphasized. Fluid film pressure distributions are determined without recourse to numerical solutions to a modified Reynolds’ equation. Power-law rheological exponents less than and equal to one are considered; power-law fluids exhibit reduced load capacities relative to the Newtonian fluid. The cavitation boundary shape is determined from Reynolds’ free surface condition; and the boundary shape is shown to be independent of the bearing eccentricity ratio.

Machine learning-based performance analysis of two-axial-groove hydrodynamic journal bearings

2021 ◽  
pp. 135065012199289
Author(s):  
Biswajit Roy ◽  
Sudip Dey
Keyword(s):  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Performance ◽  
Support Vector ◽  
Oil Viscosity ◽  
Hydrodynamic Analysis ◽  
Supply Pressure ◽  
Input Parameters ◽  
Precise Prediction ◽  
Output Behavior

The precise prediction of a rotor against instability is needed for avoiding the degradation or failure of the system’s performance due to the parametric variabilities of a bearing system. In general, the design of the journal bearing is framed based on the deterministic theoretical analysis. To map the precise prediction of hydrodynamic performance, it is needed to include the uncertain effect of input parameters on the output behavior of the journal bearing. This paper presents the uncertain hydrodynamic analysis of a two-axial-groove journal bearing including randomness in bearing oil viscosity and supply pressure. To simulate the uncertainty in the input parameters, the Monte Carlo simulation is carried out. A support vector machine is employed as a metamodel to increase the computational efficiency. Both individual and compound effects of uncertainties in the input parameters are studied to quantify their effect on the steady-state and dynamic characteristics of the bearing.

Bifurcation Analysis of Self-Acting Gas Journal Bearings

2001 ◽  
Vol 123 (4) ◽  
pp. 755-767 ◽  
Author(s):  
Cheng-Chi Wang ◽  
Cha’o-Ku`ang Chen
Keyword(s):  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Rotational Velocity ◽  
Power Spectra ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Finite Differences Method ◽  
Subharmonic Response ◽  
Rotor Center ◽  
Rotor Mass

This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

Vibration of Rectangular Plates by the Ritz Method

1950 ◽  
Vol 17 (4) ◽  
pp. 448-453 ◽  
Author(s):  
Dana Young
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Modes Of Vibration ◽  
Ritz’S Method ◽  
Square Plate ◽  
Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

Sign in / Sign up

Export Citation Format

Share Document