Bearing Of Finite Length Research Articles

Thermo-hydrodynamic study of the journal bearing under static load

A number of studies have been carried out on the hydrodynamic lubrication of journal bearings. This article seeks to summarize this work, presenting it in the form of a flow chart. The treatment of rupture and reformation of the film fluid in the contact region, for a steady loaded circular journal bearing, are accomplished using the Reynolds and the Jakobsson—Floberg and Olsson (JFO) boundary conditions. A flow chart taking into account the resolution of some of the hydrodynamic lubrication problems is elaborated. A computer code is carried out for solving the Reynolds equation and for calculating the most important parameters relating to a hydrodynamic contact. The obtained results for a finite-length bearing are compared with those obtained from the short-bearing hypothesis. In addition, a global thermal study is carried out in order to evaluate the effect of temperature.

Computer-aided design (CAD) of full hydrodynamic journal bearings

Since the equations involved in solving bearing problems are tedious to work with, calculations are most easily made by the use of bearing performance charts. However, the design of journal bearings is still a relatively cumbersome iterative process that involves the use of various data charts and tables, thus leading to time consuming and less accurate results. Therefore, a complete computer-aided design (CAD) procedure covering the basic methods for designing a full hydrodynamic journal bearing of finite length is developed and presented. The theoretical data and relevant empirical charts are collected and presented in appropriate formats. Also, the design variables of load per unit of projected bearing area, and bearing clearance in industrial applications, needed in the bearing design, are derived and incorporated in the design process. However, when designing a bearing for a given application, an infinite number of solutions is possible. Thus, certain limitations are imposed on the values of the bearing performance variables including stability, based on empirical guidelines. Consequently, one may select the solution for optimum conditions, say of maximum load capacity, or the minimum power loss (i.e. minimum friction). Finally, the CAD programme developed and constructed is general, fully automated, flexible, extendable, interactive and friendly to use.

Numerical solution for tilted hydrostatic multi-pad thrust bearings of finite length

The effect of the bearing shape functions on the self-aligning action of tilted hydrostatic thrust bearings of finite length is studied. Furthermore an alternative method is described, to select the restrictor coefficients, without flow computation. Tilted plane bearing surfaces and laminar flow condition in the film are assumed. Orifice restriction is considered. Numerical results are verified by exact solutions of the infinite bearing length.

Vibration Analysis of Squeeze Film Damper-Flexible Rotor System Subjected to Base Excitation.

The purposes of this study are to clarify the characteristics of fluid film of a squeeze film damper (SFD) which consists of fluid film and centering springs, and to develop an analytical method which can simulate vibration phenomena of a flexible rotor system supported by the SFD's. It is also supposed that a squeeze film damper∼flexible rotor system is subjected to a base excitation, such as an earthquake with a vertical shock. The fluid film forces of the SFD were computed by solving the Reynolds equation for finite-length bearings. In the formulation of a rotating shaft, a finite-element method (FEM) was used to consider the elasticity and arbitrary shape of the shaft. We show the calculated results for the properties of the fluid films, vibration modes of the rotor system and time history responses in the case when the rotor system was subjected to a base excitation. The results of the calculations show that usage of the SFD's can effectively reduce the rotor vibration caused by both unbalance of the rotor and the base excitation.

On the Performance of Finite Journal Bearings Lubricated with Micropolar Fluids

A study of the performance parameters for a journal bearing of finite length lubricated with micropolar fluids is undertaken. Results indicate that a significantly higher load carrying capacity than Newtonian fluids may result depending on the size of material characteristic length and the coupling number. It is also shown that although the frictional force associated with micropolar fluid is in general higher than that of a Newtonian fluid, the friction coefficient of micropolar fluids tends to be lower than that of the Newtonian.

Numerical Prediction of Cavitation in Noncircular Journal Bearings

A numerical investigation of gaseous cavitation in noncircular journal bearings of finite length is presented in this paper. Four bearing profiles are considered: circular, worn-circular, two-lobe (lemon) and elliptical. The alternating direction implicit (ADI) method is used to numerically solve a single partial differential equation that is valid throughout the bearing, i.e., both in full film and cavitated regions. The equation is part of the Elrod algorithm which is used to simulate bearing cavitation. This procedure, which conserves mass throughout the bearing, automatically implements boundary conditions at rupture and reformation that are thought to model moderately to heavily loaded bearings. Performance predictions are compared to results obtained from a variety of earlier papers. Presented at the 43rd Annual Meeting in Cleveland, Ohio May 9–12, 1988

Stability of a Rigid Rotor in Finite Externally Pressurized Oil Journal Bearings With Slip

A theoretical analysis has been carried out to determine the stability characteristics of externally pressurized porous oil journal bearings of finite length considering the tangential velocity slip at the bearing-film interface. The stability curves have been drawn for different slip parameters, eccentricity ratios, slenderness ratios, bearing speed parameters etc.

Analysis of an arbitrarily misaligned self-acting gas film journal bearing of finite length

To date, there has been no comprehensive study of the pressure distribution and related features of the operation and design of gas film journal bearings of finite length undergoing arbitrary misalignment. In this paper the afore-named study is presented. Direct application of the finite difference method to the non-linear partial differential equation of Reynolds, governing the phenomenon of lubrication, proved to be very effective in handling the geometry of “double-planed” misalignment. The results of the study reveal a very smooth asymmetric pressure distribution, strongly affected by the misalignment parameters. The load capacity, attitude angle and misaligning moment vs. the operational and design variables are presented in dimensionless form. This investigation reveals that the load capacity increases with the misalignment severity ratio — an unexpected feature of gas-lubricated journal bearings — providing that the rupture of the gas film at the ends is effectively prevented. The effect of the misalignment orientation angle is almost insignificant, except for the minimum film thickness at the ends.

Steady state and dynamic characteristics of partial journal bearings with variable viscosity effects

A method of including variable viscosity in journal bearing analysis by the use of a simple energy equation uncoupled from the Reynolds equation is presented. By means of a numerical technique the static and dynamic behaviour of a journal bearing of finite length is investigated. Performance results such as load, maximum temperature, stiffness and damping coefficients, threshold speeds are evaluated for 180° and 60° journal bearings covering two b/d ratios (0.5. 1), three values of the adiabatic parameter E and the full range of eccentricity ratios. Typical results are presented in non-dimensional form and will also be useful for design calculations of the critical speeds and stability of a practical rotor.

On the Stability of a Rigid Rotor in Finite Porous Journal Bearings With Slip

This investigation deals with the stability characteristics of oil filled porous journal bearings of finite length and with velocity slip. The stability curves are drawn for different slip parameters, eccentricity ratios, slenderness ratios, and in the absence of any experimental data, the theoretical results for the solid bearings obtained by this analysis have been compared with the available results of solid bearing.

Computer-Aided Study of Journal Bearings With Undulating Surfaces

This paper presents the results of an analytical study of the performance of a cylindrical journal bearing of finite length as influenced by undulations intentionally produced on the surface. With the aid of a digital computer, the analysis has been applied to some common cases to obtain relevant numerical solutions. Compared with journal bearings having perfectly smooth surfaces, wavy bearings may well run at lower values of journal eccentricities and attitude angles. Wavy bearings may thus operate with higher safety. It is herein also established that, with load criterion as parameter, the higher the wave amplitude ac and the number of waves along the bearing circumference nc, the lower would be the eccentricity ratio. Moreover, when running at same eccentricity, higher values of ac and nc show a tendency of the journal center to move closer to the load line, thus leading to lower attitude angles.

Dynamic Characteristics of Finite Porous Journal Bearings Considering Tangential Velocity Slip

A theoretical investigation to find out the dynamic characteristics of porous journal bearings of finite length has been carried out considering the Beavers-Joseph crierion of velocity slip at the bearing film interface. It has been shown that the effect of velocity slip on the dynamic characteristics is small.

The calculation of the characteristics of journal slider bearings

In this paper a procedure is presented for calculating the characteristics of journal slider bearings operating in conditions of fluid friction. The equations describing the oil flow in the bearing interspace were solved with the method of finite differences. The adiabatic oil flow was examined in a bearing of finite length and arbitrary interspace geometry that was fed from the outside at an arbitrary point of the bush. p ]The presented procedure allows the following to be determined: the angle of the line of centres corresponding to the journal equilibrium position, the load-carrying capacity of the oil film, the distribution of the pressure and the temperature in the oil film, the coefficient of resistance to motion, the oil discharge and the mean temperature of the oil film. The program serves for both the precalculation of the bearing characteristics as well as the examination of the influence of the bearing geometry and supply oil parameters on the characteristics. Some examples of calculated characteristics of the bearings are presented.

Hydrodynamic instability of self-acting journalbearings of infinite length in the turbulent regime

An analysis for the determination of the conditions of dynamic stability of hydrodynamically lubricated plain circular bearings of finite length with turbulent flow is presented. The conditions for both static and dynamic stability were calculated from the response to a small random disturbance. The study of static stability was necessary as a first step. The dynamic stability was investigated with the Routh-Hurwitz criterion by using the perturbation (or linearization) technique. The results are fully analytical and are in the closed form. This allows the computation of data and the construction of stability charts for a wide range of parameters involved for the determination of the stability threshold.

Two-dimensional finite difference solution for externally pressurized journal bearings of finite length

A two-dimensional finite difference solution was used to predict the performance of finite length externally pressurized oil-lubricated journal bearings with several supply holes. The generalized Reynolds equation was solved numerically to obtain the effects of the bearing design parameter, eccentricity ratio and speed parameter on bearing performance. Performance curves are presented for a double-feeding plane bearing compensated by orifice restrictors. The bearing load-carrying capacity, stiffness, lubricant flow rate and frictional torque due to bearing rotation increase with increase in the bearing design parameter, eccentricity ratio and speed parameter. The attitude angle increases with increase in the bearing design parameter and is generally stable at high values of the eccentricity ratio and speed parameter. Hydrodynamic and centrifugal actions are present at higher values of the eccentricity ratio and speed parameter.

A re-examination of the performance of partial plain laminar journal bearings of finite length

The effect of C R on the performance of partial plain laminar film journal bearings of finite length with a newtonian lubricant was determined. The non-dimensionalized Reynolds lubrication equation was solved by the method of separation of variables under zero boundary conditions using the infinite Fourier series and the collocation technique. The performance characteristics were determined analytically from this solution. For C R < 10 −4 , the characteristics do not change, implying that the effect of C R can be neglected and that conventional theory is adequate. For C R between 10 −3 and 10 −4, as found in practice, the analysis presented here must be used. For C R > 10 −3 , the characteristics change very sharply, indicating a transitional or turbulent flow to which the non-inertial laminar theory discussed here is not applicabe.

Friction coefficient and oil flow in plain finite partial journal bearings during turbulent operation

Plain partial journal bearings of finite length with a turbulent hydrodynamic film of a newtonian lubricant were analysed to determine the friction coefficient and the total oil flow. The coefficient of friction, which is a performance characteristic, is presented analytically in the closed form. The total oil flow through superlaminar bearings is also treated as a bearing performance characteristic. The results of interest, which are dimensionless and available in the closed form, are simple yet exact over a wide range of the parameters involved.

The finite journal bearing considering film separation

The Reynolds equation is solved numerically for a journal bearing of finite length considering separation of the film of lubricant at the trailing edge of the pressure zone. The performance characteristics of the bearing are calculated. The solution is compared with that obtained using the conventional Swift-Stieber boundary conditions.

Hydrodynamic load capacity of a full porous journal bearing of finite length in the turbulent regime considering slip flow and curvature

The hydrodynamic lubrication of a 360° finite porous metal journal bearing of arbitrary wall thickness press fitted in a solid housing and working with a turbulent film of newtonian lubricant was analysed in a closed form using a new generalized pressure equation. Bearings of undefined axial length and narrow bearings have been considered previously. For finite bearings the flow of lubricant in the axial clearance space is of the same order as in the azimuth. Therefore the governing differential equation is three dimensional and difficult to solve. However, Warner's method was used to reduce this equation to two second-order ordinary linear differential equations with analytically known variable coefficients which are simpler to solve. Analytical solutions of these were obtained as a boundary value problem in terms of the end conditions defining the start and termination of the load-supporting film. The half Sommerfeld boundary conditions were used for the azimuthal film extent since they are mathematically simpler, and the results obtained in the laminar regime were close to those obtained using the more complex (but realistic) Reynolds boundary conditions. Film curvature effects were included by using C/ R 1 in the expression for film thickness. The curvature effect of the thick porous bearing matrix, which allows it to have an arbitrary wall thickness, was taken into account by a new direct approach which makes it possible to use the separation of variables. The collocation technique was utilized to determine the hydrodynamic pressure from which the bearing characteristics were evaluated. The results are fully analytical in nature, simple and yet exact and accurate; they permit easy and economical calculation of numerical data over a very wide range of parameters.

Coefficient of friction and oil flow in plain finite partial journal bearings during turbulent operation

Bearings which have been properly designed with respect to the provision of a hydrodynamic oil film can sometimes fail by overheating. Hence the complete analysis of journal bearings requires the evaluation of friction and oil flow. Plain partial journal bearings of finite length with a turbulent hydrodynamic film of a newtonian lubricant were analysed to obtain the coefficient of friction and the total oil flow. The coefficient of friction, which is a performance characteristic, is presented analytically in the closed form. The total oil flow through superlaminar bearings is also considered as a bearing performance characteristic. All the results of interest are dimensionless and available in a closed form which is simple yet exact over the wide range of parameters involved.