Finite Porous Journal Bearings Research Articles

MICROPOLAR FLUID LUBRICATION OF FINITE ROUGH POROUS JOURNAL BEARING WITH SQUEEZING EFFECT

In this paper, a theoretical analysis of the effect of surface roughness on the squeeze film lubrication of finite porous journal bearings with micropolar fluids is studied. A more generalized form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The generalized average Reynolds type equation is derived for the squeeze film lubrication of finite rough porous journal bearings with micropolar fluids as lubricant. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, journal centre velocity and locus of the journal centre. The cases of a constant applied load and an alternating applied load are analyzed under a cyclic load the micropolar fluids provide a reduction in the journal centre velocity. Further, it is numerical computations of the results show that the negatively skewed surface roughness pattern increase fluid film pressure, load carrying capacity and decreases the journal centre velocity. Where as adverse effects were found for the positively skewed surface roughness pattern. The effect of porous parameter causes reduction in fliud film pressure, load carrying capacity and enhances the journal centre velocity.

Influence of roughness on porous finite journal bearing with heterogeneous slip/no-slip surface

A numerical study of effect of surface roughness on finite porous journal bearing with heterogeneous slip/no-slip surface is presented. Generalized Reynolds type equations are derived for both types of uni-dimensional roughness structure. The well established Christensen stochastic theory is used to study the roughness effect. The governing differential equation can be solved by finite difference method. The effect of surface roughness parameter, slip parameter, permeability parameter and eccentricity ratio on pressure and hydrodynamic load is investigated. It has been shown that pressure and load carrying capacity increases with surface roughness for the bearing with slip/no-slip surface.

Elastic Deformation Effects on the Thermo-Hydrodynamic Aspect of Porous Journal Bearings

In this paper, the effects of porous bush elastic deformation on the static characteristics of finite porous journal bearing are investigated using Darcy’s law. The modified Reynolds equation applied to thermo-hydrodynamic problems is modified by considering the viscosity variation along the film thickness. The film pressure distribution and other characteristics such as the load carrying capacity and attitude angle are obtained by solving the governing equations numerically. Obtained results showed that deformation is considerable in the maximum pressure zone, and the elastic deformation will decrease the load carrying capacity. The viscosity variation parameter tends also to decrease the load carrying capacity.

Micropolar fluid squeeze film lubrication of finite porous journal bearing

In this paper, the effect of micropolar fluid on the static and dynamic characteristics of squeeze film lubrication in finite porous journal bearings is studied. The finite modified Reynolds equation is solved numerically using the finite difference technique and the squeeze film characteristics are obtained. According to the results obtained, the micropolar fluid effect significantly increases the squeeze film pressure and the load-carrying capacity as compared to the corresponding Newtonian case. Under cyclic load, the effect of micropolar fluid is to reduce the velocity of the journal centre. Effect of porous matrix is to reduce the film pressure, load-carrying capacity and to increase the journal centre velocity.

A Contribution to the Analysis of the Thermo-Hydrodynamic Lubrication of Porous Self-Lubricating Journal Bearings

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.

Numerical solution of finite modified Reynolds equation for couple stress squeeze film lubrication of porous journal bearings

In this paper, the rheological effect of couple stress fluids on the static and dynamic characteristics of squeeze film lubrication in finite porous journal bearings is studied. The finite modified Reynolds equation is derived from the Stokes constitutive equations for couple stress fluids and is solved numerically by using the finite difference technique. The applied load is considered as a sinusoidal function of time to simulate the bearings operating under cyclic loads. Under a cyclic load, the effect of couple stress is to reduce the velocity of the journal centre and to increase the minimum permissible height of the squeeze film.

Approximate model for unsteady finite porous journal bearings fluid film force calculation

This article focuses on an analytical approximate fluid film pressure solution in finite porous journal bearings. Exploring the dynamic behaviour of a rotor on porous bearings, such as the fluid film force, the authors find in an analytical model an effective approach to provide a more readable description of the interaction between rotor and bearings. Furthermore, this kind of method for analysing the behaviour of a system is more effective than a numerical procedure and allows covering not only the individual case, but also the whole class to which the system in question belongs. The proposed model provides a quick analytical calculation of the fluid film force for different values of the permeability factor, aspect ratio, and eccentricity ratio in the whole domain of dynamic states. The results are in good agreement with those achieved using the numerical solutions.

Surface roughness effect on finite journal bearings with flexible porous liners

The effects of surface roughness on the static characteristics of finite porous journal bearings under hydrodynamic lubrication conditions are investigated in this paper. The well-established Christensen stochastic theory of hydrodynamic lubrication of rough surfaces is used to incorporate the effects of surface roughness into the Reynolds equation. The analysis takes into account the flexibility of the porous liner by using a thin liner model. The effects of velocity slip at the surface of the porous medium are considered in the analysis by using the Beavers-Joseph criterion. The mathematical model is then solved numerically by finite-difference methods for mean hydrodynamic pressure, which in turn gives the hydrodynamic load. The effects of the surface roughness parameter, surface pattern, eccentricity ratio, length-to-diameter ratio, permeability parameter, and flexibility parameter on the hydrodynamic load-carrying capacity, attitude angle, and friction factor are discussed.

Effects of Misalignment on the Performance of Flexible Porous Journal Bearings

A mathematical model is introduced to study the effects of journal misalignment on the hydrodynamic lubrication performance of finite flexible porous journal bearings. A modified form of Reynolds equation, which was derived from the Brinkman-extended Darcy equations and Stokes' equations, is utilized in the present study. The journal misalignment is allowed to vary in magnitude as well as in direction with respect to the bearing boundaries. The predicted performance characteristics of porous journal bearings are compared with available theoretical and experimental results. The effects of the degree and angle of misalignment, and the permeability of the porous liner on the pressure distribution, load-carrying capacity, friction coefficient and misalignment moment are presented and discussed.

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.

Direct and Inverse Solutions for Elastohydrodynamic Lubrication of Finite Porous Journal Bearings

In this paper a numerical solution for the elastohydrodynamic lubrication of a finite porous journal bearing is presented. The Brinkman–extended Darcy model was applied within the porous layer to incorporate the viscous shear stresses into the analysis. A simple elastic model is used to describe the elastic deformation of the liner. An inverse model is introduced to estimate the permeability parameter and/or the eccentricity ratio from experimentally obtained pressure data. As experimental measurements were not conducted, these data were simulated numerically. It consists of a direct solution for the pressure, for given parameters (permeability parameter and/or the eccentricity ratio), to which a normally distributed random error is added. The least-squares optimization technique is used to solve the proposed inverse problem. A unique solution was obtained for one-parameter estimation. The two-parameter estimation case, however, leads to multiple solutions lying on a constant load line.

Hydrodynamic lubrication of finite porous journal bearings—Use of the Brinkman-extended Darcy model

This paper applies the Brinkman-extended Darcy model (BEDM) to investigate the hydrodynamic lubrication of finite porous journal bearings. A finite difference technique employing the Preconditioned Conjugate Gradient method (PCGM) of iteration is used to solve the modified Reynolds equation. The results show that the influences of viscous shear stresses on the lubrication performance of porous journal-bearing systems are apparent and not negligible. Comparing with those of the Darcy model (DM), the effects of viscous shear stresses of the BEDM provide an increase in the load capacity, as well as a reduction in the friction parameter; and the quantitative effects of the viscous shear stresses on the static characteristics are more pronounced for the cases of large length-to-diameter ratios.

Linear stability analysis of finite porous journal bearings—Use of the Brinkman-extended Darcy model

On the basis of the Brinkman-extended Darcy model (BEDM), this paper examines the effects of viscous shear stresses on the linear stability of finite porous journal bearings. The result shows that the influences of viscous shear stresses on the dynamic performance of porous journal-bearing systems are apparent and not negligible. In certain regions of parameter space the BEDM predicts quite different stability characteristics to those derived using either the slip-flow model (SFM) or Darcy model (DM). In particular, a higher threshold speed (increased stability) is predicted using the BEDM for porous bearings with (i) small length-to-diameter ratios ( λ < 1) or (ii) low permeability parameters and high steady-state eccentricity ratios.

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.

A Refined Numerical Solution for the Hydrodynamic Lubrication of Finite Porous Journal Bearings

A refined numerical solution for the hydrodynamic performance of finite porous journal bearings is presented. The solution takes into account the curvature of the bearing wall, interfacial slip of the fluid across the pore mouths, and employs the Reynolds boundary conditions at the oil film extremities. Based upon the results obtained, bearing design charts are shown for a wide range of L/D, ε and ψ values enabling design and performance characteristics to be evaluated for these bearings over and beyond the range normally required by the industrial engineer.

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.

Gas-Lubricated Porous Bearings—Infinitely Long Journal Bearings, Steady-State Solution

The general governing equations for finite porous journal bearings with compressible lubricants and slip-flow are derived. A mass content rule is developed for infinitely long porous bearings; an exact solution is established for a gas-lubricated porous bearing with very large bearing number consistent with the mass content rule. An analytic-numerical technique which takes advantage of the linearity of the pressure equation in the porous medium is developed to solve the problem for finite values of compressibility. The results approach those for the solid bearing case as the defined poro-slip parameter β becomes very large.

A Numerical Solution for the Hydrodynamic Lubrication of Finite Porous Journal Bearings

We present a numerical solution for the operating conditions of a hydrodynamic porous journal bearing. The numerical method allows for the possibility of variable porosity in the bearing matrix, but the solution has been achieved on the assumption of matrix homogeneity. The relation between the various bearing parameters have been shown for a variety of bearing geometries and permeabilities enabling the operating conditions for this type of bearing to be better appreciated. A comparison of the present solution with approximate solutions used by other authors has been made, which indicates the useful working range of the approximate solutions.

A Numerical Solution for the Hydrodynamic Lubrication of Finite Porous Journal Bearings

We present a numerical solution for the operating conditions of a hydrodynamic porous journal bearing. The numerical method allows for the possibility of variable porosity in the bearing matrix, but the solution has been achieved on the assumption of matrix homogeneity. The relation between the various bearing parameters have been shown for a variety of bearing geometries and permeabilities enabling the operating conditions for this type of bearing to be better appreciated. A comparison of the present solution with approximate solutions used by other authors has been made, which indicates the useful working range of the approximate solutions.

Lubrication of Porous Journal Bearings

An analytical solution for the performance characteristics of finite porous journal bearings is obtained. Results are presented which relate the eccentricity ratio and coefficient of friction as functions of load number for design variables of 0.0001, 0.001, 0.01, and 0.1. The load capacity obtained by using the finite bearing theory is compared to the load capacity obtained by using the short-bearing approximation and the infinite-bearing approximation.