A Theoretical Investigation of Compliant Surface Journal Bearings

1971 ◽  
Vol 93 (1) ◽  
pp. 191-201 ◽  
Author(s):  
M. K. Benjamin ◽  
V. Castelli
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Mathematical Problem ◽  
Ritz Method ◽  
Newton Iteration ◽  
Journal Bearings ◽  
Elasticity Problem ◽  
Algebraic Equations ◽  
Compliant Surface ◽  
Nonlinear Algebraic Equations

The problem of the compliant surface journal bearing is investigated. The mathematical problem is divided into two parts, the elasticity problem and the fluid problem. The equations of linear elasticity, which represent the elasticity problem, are solved; (a) by expansion of the solution in eigenfunctions (b) by the Raleigh Ritz method, and (c) by a collocation method. Reynolds’ equation, which represents the fluid problem, is then coupled with the solution to the elasticity problem. The corresponding finite difference representation of Reynolds’ equation, which is a set of fourth-order nonlinear algebraic equations, is inverted by Newton iteration. Finally, numerical results are presented.

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.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

Numerical and Experimental Investigations on Preload Effects in Air Foil Journal Bearings

2017 ◽  
Author(s):  
Marcel Mahner ◽  
Pu Li ◽  
Andreas Lehn ◽  
Bernhard Schweizer
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Compressible Fluids ◽  
Experimental Investigations ◽  
Hysteresis Curves ◽  
Numerical Predictions ◽  
Bearing Stiffness ◽  
Gasdynamic Model ◽  
Good Agreement

A detailed elasto-gasdynamic model of a preloaded three-pad air foil journal bearing is presented. Bump and top foil deflections are herein calculated with a nonlinear beamshell theory according to Reissner. The 2D pressure distribution in each bearing pad is described by the Reynolds equation for compressible fluids. With this model, the influence of the assembly preload on the static bearing hysteresis as well as on the aerodynamic bearing performance is investigated. For the purpose of model validation, the predicted hysteresis curves are compared with measured curves. The numerically predicted and the measured hysteresis curves show a good agreement. The numerical predictions exhibit that the assembly preload increases the bearing stiffness (in particular for moderate shaft displacements) and the bearing damping.

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.

Dynamic stability of micropolar lubricated hydrodynamic offset-halves journal bearings

2020 ◽  
pp. 135065012093685
Author(s):  
Sanyam Sharma ◽  
Chimata M Krishna
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Critical Mass ◽  
Journal Bearings ◽  
Aspect Ratios ◽  
Input Parameters ◽  
Output Characteristics ◽  
The Stability ◽  
Offset Factor

The plain circular journal bearings are not found to be stable by researchers when used in high speed rotating machineries. Hence, extensive research in the study of stability characteristics of non-circular bearings or lobed bearings assumed importance, of late. Present article deals with the stability analysis of non-circular offset bearing by taking selected set of input and output parameters. Modified Reynolds equation for micropolar lubricated rigid journal bearing system is solved using finite element method. Two kinds of input parameters namely, offset factors (0.2, 0.4) and aspect ratios (1.6, 2.0) have been selected for the study. The important output characteristics such as load, critical mass, whirl frequency ratio, and threshold speed are computed and plotted for various set of values of input parameters. The results obtained indicate that micropolar lubricated circular offset bearing is highly stable for higher offset factor and higher aspect ratio.

scholarly journals Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 224 ◽  
Author(s):  
Harendra Singh ◽  
Rajesh Pandey ◽  
Hari Srivastava
Keyword(s):  
Chebyshev Polynomials ◽  
Jacobi Polynomials ◽  
Ritz Method ◽  
Variational Problems ◽  
Algebraic Equations ◽  
The Third ◽  
Fractional Variational Problems ◽  
Nonlinear Algebraic Equations ◽  
Non Linear ◽  
Fourth Kind

The aim of this paper is to solve a class of non-linear fractional variational problems (NLFVPs) using the Ritz method and to perform a comparative study on the choice of different polynomials in the method. The Ritz method has allowed many researchers to solve different forms of fractional variational problems in recent years. The NLFVP is solved by applying the Ritz method using different orthogonal polynomials. Further, the approximate solution is obtained by solving a system of nonlinear algebraic equations. Error and convergence analysis of the discussed method is also provided. Numerical simulations are performed on illustrative examples to test the accuracy and applicability of the method. For comparison purposes, different polynomials such as 1) Shifted Legendre polynomials, 2) Shifted Chebyshev polynomials of the first kind, 3) Shifted Chebyshev polynomials of the third kind, 4) Shifted Chebyshev polynomials of the fourth kind, and 5) Gegenbauer polynomials are considered to perform the numerical investigations in the test examples. Further, the obtained results are presented in the form of tables and figures. The numerical results are also compared with some known methods from the literature.

scholarly journals On Error Torques of Squeeze-Film Cylindrical Journal Bearings

1968 ◽  
Vol 90 (1) ◽  
pp. 191-198
Author(s):  
C. H. T. Pan ◽  
T. Chiang
Keyword(s):  
Radial Displacement ◽  
High Performance ◽  
Journal Bearing ◽  
Rotational Symmetry ◽  
Mathematical Problem ◽  
Journal Bearings ◽  
Squeeze Film

The squeeze-film bearing has been considered for the output axis of high performance gyroscopes. Viewing this application, it is important that the parasitic torque of the bearing be very small. In the case of a squeeze-film journal bearing, parasitic torque can result from tolerance effects which disrupt rotational symmetry of the bearing. This problem has been studied by assuming ellipses for the tolerances of the journal and bearing surfaces as well as the squeeze motion, respectively. Each tolerance effect is assumed to be axially uniform. The mathematical problem is linearized with respect to each of the tolerances and the radial displacement of the journal. It was found that the parasitic torques do not depend on the radial displacement of the journal. The parasitic torques result from interactions among the three types of tolerance effects while each of the tolerances alone will not lead to any torque. Numerical estimates based on the geometry of a typical gyroscope and current fabrication practice shows such parasitic torques can seriously impair the accuracy of the gyroscope.

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.

A Numerical Solution for the Incompressible Hybrid Journal Bearing With Cavitation

1969 ◽  
Vol 91 (3) ◽  
pp. 508-515 ◽  
Author(s):  
Stanley Heller ◽  
Wilbur Shapiro
Keyword(s):  
Vapor Pressure ◽  
Pressure Gradient ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Supply Circuit ◽  
Hydrodynamic Bearing

A numerical solution is presented for determining performance for hybrid journal bearings with arbitrary clearance distribution and cavitation. Regions of cavitation are determined by solution of the incompressible Reynolds’ equation. The pressures in the cavitated regions are immediately adjusted to a specified vapor pressure with zero pressure gradient. The continuity of mass equation permits coupling the influence of the external supply circuit and the methods of recess compensation to the Reynolds’ equation. Results are presented for geometrically similar hydrodynamic, hydrostatic, and hybrid bearings. Favorable comparisons are made with previously published results for the hydrodynamic bearing.

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.

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