A Variational Approach to Lubrication Problems and the Solution of the Finite Journal Bearing

1959 ◽  
Vol 81 (1) ◽  
pp. 13-22 ◽  
Author(s):  
D. F. Hays
Keyword(s):  
Variational Approach ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Finite Width ◽  
Two Dimensional ◽  
Continuous Film ◽  
Design Charts ◽  
General Method

A general method is derived for the solution of the two-dimensional Reynolds’ equation. The method is applied to the solution of the full journal bearing of finite width with a continuous film and design charts are presented which describe the characteristics of this bearing.

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.

Effect of non-Newtonian magneto-elastohydrodynamic on performance characteristics of slider-bearings

2019 ◽  
Vol 71 (10) ◽  
pp. 1158-1165
Author(s):  
Mouhcine Mouda ◽  
Mohamed Nabhani ◽  
Mohamed El Khlifi
Keyword(s):  
Friction Coefficient ◽  
Design Methodology ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Transverse Magnetic ◽  
Finite Width ◽  
Two Dimensional ◽  
Content Type ◽  
Slider Bearings ◽  
First Time

Purpose This study aims to examine the magneto-elastohydrodynamic effect on finite-width slider-bearings lubrication using a non-Newtonian lubricant. Design/methodology/approach Based on the magneto-hydrodynamic (MHD) theory and Stokes micro-continuum mechanics, the modified two-dimensional Reynolds equation including bearing deformation was derived. Findings It is found that the bearing deformation diminishes the load-capacity and increases the friction coefficient in comparison with the rigid case. However, the non-Newtonian effect increases load-capacity but decreases the friction coefficient. Moreover, the use of a transverse magnetic field increases both the friction coefficient and load capacity. Originality/value This study combines for the first time MHD and elastic deformation effects on finite-width slider-bearings using a non-Newtonian lubricant.

Partial Journal Bearing Performance in the Laminar Regime

1975 ◽  
Vol 97 (1) ◽  
pp. 94-100 ◽  
Author(s):  
T. S. Yu ◽  
A. Z. Szevi
Keyword(s):  
Heat Conduction ◽  
Radial Direction ◽  
Journal Bearing ◽  
Two Dimensional ◽  
Approximate Analysis ◽  
Laminar Regime ◽  
Design Charts ◽  
Numerical Iteration ◽  
Equation Of Heat Conduction ◽  
Energy Equations

In this approximate analysis of laminar journal bearing operations both the momentum and the energy equations are two dimensional, the shaft operates at a constant temperature and the bearing conducts heat in the radial direction only. Via the last of these assumptions, the equation of heat conduction is eliminated from consideration. The remaining equations are solved by a numerical iteration method. A parametric study of therohydrodynamic journal bearing operations is performed and design charts are given for a 100 deg arc bearing.

The Comparison of Four Pressure-Thermal Models of Oil Film Bearing With the Non-Newtonian and Temperature-Viscosity Effects

2016 ◽  
Author(s):  
Feng Liang ◽  
Quanyong Xu ◽  
Xudong Lan ◽  
Ming Zhou
Keyword(s):  
Temperature Field ◽  
Numerical Model ◽  
High Speed ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Oil Film ◽  
Viscosity Effects

The thermohydrodynamic analysis of oil film bearing is essential for high speed oil film bearing. The temperature field is coupled with the pressure field. The numerical model can be built or chosen according to the complexity of the objects and requirement of the accuracy. In this paper, four pressure-thermal (P-T) models are proposed, which are zero-dimensional temperature field coupled with Reynolds equation (0D P-T model), two-dimensional temperature field coupled with Reynolds equation (2D P-T model), two-dimensional temperature with third dimensional correction coupled with Dawson equation (2sD P-T model), three-dimensional temperature field coupled with Dawson equation (3D P-T model). The non-Newtonian and temperature-viscosity effects of the lubrication oil are considered in all the four models. Two types of cylindrical journal bearing, the bearing with/without axial grooves, are applied for the simulation. All the simulated cases are compared with the solutions of the CFX. The results show that the 0D P-T model fails to predict the behavior of high speed bearing; The 2D and 2sD P-T model have an acceptable accuracy to predict the performance of the bearing without grooves, but are not able to simulate the P-T field of the bearing with grooves because of the under-developed thermal boundary layer; The 2sD P-T model shows a great improvement when calculating the pressure field compared with the 2D P-T model; the 3D P-T model coincides well with the CFX at any condition. The comparison of these four models provides a reference to help designer choose a proper numerical model for a certain project.

Dynamic Stiffness and Damping Coefficients of Aerostatic, Porous, Journal Bearings

1978 ◽  
Vol 20 (5) ◽  
pp. 291-296 ◽  
Author(s):  
N. S. Rao ◽  
B. C. Majumdar
Keyword(s):  
Continuity Equation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Dynamic Pressure ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Damping Coefficients ◽  
Design Charts ◽  
Stiffness And Damping

A periodic (displacement) disturbance is imposed on an aerostatic, porous, journal bearing of finite length under steady-state conditions. The dynamic pressure distribution is obtained by a pressure perturbation analysis of Reynolds equation and a modified flow continuity equation in a porous medium. Dynamic stiffness and damping coefficients for different operating conditions are calculated numerically, using a digital computer, and presented in the form of design charts.

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.

A Solution of Reynolds Equation for a Full Finite Journal Bearing

1961 ◽  
Vol 83 (4) ◽  
pp. 589-593 ◽  
Author(s):  
S. Ramachandra
Keyword(s):  
Eigenvalue Problem ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Homogeneous Equation ◽  
Expansion Method ◽  
Eigenvalues And Eigenfunctions ◽  
Orthogonal Functions ◽  
Design Charts

Reynolds equation for the pressure in a full finite journal bearing which is nonhomogeneous has been reduced to a homogeneous equation. By separating the variables the problem is reduced to an eigenvalue problem. The orthogonal functions expansion method is used to determine the eigenvalues and eigenfunctions. First four eigenvalues are calculated. Design charts are prepared for the eccentricity ratios of 0.2, 0.4, 0.6, 0.8 and length to diameter ratios of 0.5, 1.0, 1.5, and 2.0.

Calculation of the Dynamic Coefficients of a Journal Bearing, Using a Variational Approach

1986 ◽  
Vol 108 (3) ◽  
pp. 421-424 ◽  
Author(s):  
P. Klit ◽  
J. W. Lund
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Approach ◽  
Numerical Evaluation ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Temperature Dependency ◽  
The Finite Element Method ◽  
Dynamic Coefficients ◽  
The Individual

The dynamic bearing coefficients are obtained from a solution to the variational equivalent of Reynolds equation. A perturbation method is applied to find the individual dynamic coefficients. The Finite Element Method is used in the numerical evaluation of the equations. The flow is assumed to be laminar, the lubricant is Newtonian. Allowance is made for viscosity-temperature dependency in circumferential and axial directions.

Squeeze Films: A Finite Journal Bearing With a Fluctuating Load

1961 ◽  
Vol 83 (4) ◽  
pp. 579-586 ◽  
Author(s):  
Donald F. Hays
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Sinusoidal Load ◽  
Curve Form ◽  
General Method

A general method is derived for the solution of the Reynolds equation including the effects of tangential and normal velocities. It is applied to the solution of a full journal bearing under a fluctuating load with no journal rotation. The characteristics of a finite journal bearing under a cyclic sinusoidal load are shown in curve form.

Sign in / Sign up

Export Citation Format

Share Document