The effects of surface irregularities on the performance characteristics of flexible finite journal bearings lubricated with couple stress fluids

A numerical solution for the elastohydrodynamic lubrication of finite journal bearings is presented. Couple stress effects resulting from blending the lubricant with various additives are considered. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearings, is implemented in the solution scheme. A simple elastic model is used to describe the elastic deformation of the bearing liner. Furthermore, the effects of surface waviness on the performance of the bearing are incorporated into the analysis. A comprehensive study illustrates the effects of couple stress, liner flexibility, and surface waviness on the steady‐state performance of finite‐width journal bearings. The results show that these effects should be considered at higher values of the eccentricity ratio.     

Steady state solution of finite hydrostatic porous oil journal bearings with tangential velocity slip

A theoretical investigation has been made into the static characteristics of hydrostatic porous oil bearings with tangential velocity slip at the porous interface. A numerical method has been employed to solve the governing differential equations with a wide range of bearing parameters. Slip has been conventionally treated by choosing permeability factors and slip coefficients as independent parameters, and also more realistically by choosing practical values of shaft radius/radial clearance and slip coefficients as independent parameters. The effect of slip, eccentricity ratio, slenderness ratio, speed parameter and anisotropy of permeability on the load carrying capacity, friction coefficient, attitude angle and the oil flow rate has also been investigated. The results are presented in the form of graphs which may be useful for design of such bearings.     

Surface roughness effects in porous inclined stepped composite bearings lubricated with micropolar fluid

In this paper, the effect of surface roughness on the performance characteristic of porous inclined stepped composite bearings is studied. A generalised form of surface roughness is mathematically modelled by a stochastic random variable with non‐zero mean, variance and skewness. The generalised average Reynolds‐type equation is derived for the rough porous inclined stepped composite bearings with micropolar fluid. The closed‐form expressions are obtained for the fluid film pressure, load‐carrying capacity and frictional force. The results are presented for three different types of bearing system. The numerical computations of the results show that the negatively skewed surface roughness pattern increases fluid film pressure and load‐carrying capacity and decreases the coefficient of friction, whereas adverse effects were found for the positively skewed surface roughness pattern. Further, the rough porous inclined stepped composite bearing provides the largest load‐carrying capacity and the least coefficient of friction as compared with the porous plane slider and porous composite tapered concave bearings. Copyright © 2012 John Wiley & Sons, Ltd.     

Feed pressure flow in plain journal bearings

The purpose of this short technical note is to update the literature on feed pressure flow in plain bearings and to give a summary of suitable equations for predicting such flows. The work is part of a detailed study of feed pressure flow¹.     

Effects of lubricant additives on the performance of hydrodynamically lubricated journal bearings

A non-Newtonian rheological model to investigate theoretically the effects of lubricant additives on the steady state performance of hydrodynamically lubricated finite journal bearings is introduced. In this model, the non-Newtonian behavior resulting from blending the lubricant with polymer additives is simulated by Stokes couple stress fluid model. The formed boundary layer at the bearing surface is described through the use of a hypothetical porous medium layer that adheres to the bearing surface. The Brinkman-extended Darcy equations are utilized to model the flow in the porous region. A stress jump boundary condition is applied at the porous media/fluid film interface. A modified form of the Reynolds equation is derived and solved numerically using a finite difference scheme. The effects of bearing geometry, and non-Newtonian behavior of the lubricant on the steady-state performance characteristics such as pressure distribution, load carrying capacity, side leakage flow, and coefficient of friction are presented and discussed. The results showed that lubricant additives significantly increase the load carrying capacity and reduce both the coefficient of friction and the side leakage as compared to the Newtonian lubricants.     

Influence of surface roughness effects on the performance of non-recessed hybrid journal bearings

The effect of journal and bearing surface roughness on the performance of a capillary compensated hole-entry hybrid journal bearing system has been theoretically studied. The analysis considers the average Reynold’s equation for the solution of lubricant flow field in the clearance space of a rough surface journal bearing system. The finite element method and Galarkin’s technique has been used to derive the system equation for the lubricant flow field. The non-dimensional parameters Λ (surface roughness parameter) and γ (surface pattern parameter) have been defined to represent the magnitude of height distribution of surface irregularities and their orientation, respectively. The influence of surface roughness on the bearing performance has been studied for the transverse, isotropic and longitudinal surface patterns. The bearing performance characteristics have been computed for both symmetric and asymmetric capillary compensated hole-entry journal bearing configurations for the various values of surface roughness parameter (Λ), surface pattern parameter (γ) and restrictor design parameter ( ). The computed results indicate that the inclusion of surface roughness effects in the analysis affects the performance of a bearing quite significantly vis-à-vis smooth surface bearing. The study indicates that for generation of accurate bearing characteristic data, the inclusion of surface roughness effects in the analysis is essential.     

Analysis of hydrodynamic journal bearings lubricated with non-Newtonian fluids

A procedure for solving the Navier-Stokes equations for the steady, three-dimensional flow of a non-Newtonian fluid within a finite-breadth hydrodynamic journal bearing is described. The method uses a finite-difference approach, together with a technique known as SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) which has now become established in the field of computational fluid dynamics. The concept of ‘effective viscosity’ to describe the non-linear dependence of shear stress on shear rate is used to predict the performance of bearings having a single full-width axial inlet groove situated at the position of maximum film thickness. To illustrate the capabilities of the procedure, results are obtained for a range of non-linearity factors, and lead to the conclusion that the pressure distribution, attitude angle, end-leakage rate, shear force and load capacity can all be predicted for a variety of non-Newtonian lubricants using the SIMPLE numerical integration technique.     

Performance of flexible shell journal bearings with variable viscosity lubricants

In heavily loaded rotating machines, both the deformation of the elastic bearing shell and the dependence of lubricant viscosity on pressure become significant and may result in an appreciable change in the performance of the journal bearing system. In this paper, stable solutions for bearing deformation and the lubricant flow field are obtained which combine the effects of the elastic deformation of the bearing shell with the pressure-viscosity dependence of the lubricant. Two elastic models were tried for deformation calculations in the bearing. One which was computationally economical and consistent in accuracy was adopted for the detailed computation. The effects of bearing deformation on the performance characteristics of the journal bearing system are reported for both isoviscous and variable viscosity lubricants.     

Stability of a rigid rotor in turbulent hybrid porous journal bearings

Stability characteristics of hybrid porous journal bearings with a turbulent fluid film have been investigated theoretically following Constantinescu's turbulent lubrication theory. The stability curves have been drawn for different Re, eccentricity ratios, slenderness ratios and bearing speed parameters. In the absence of any experimental data, laminar flow results obtained by this analysis have been compared and found to be in excellent agreement with the previous results. It is observed that turbulence deteriorates the stability of the rotor and for better performance the value of the bearing feeding parameter, β, should be kept small.     

Conical whirl instability of turbulent flow hybrid porous journal bearings

An analysis of conical whirl instability of an unloaded rigid rotor supported in a turbulent flow hybrid porous journal bearing has been presented, following Constantinescu's turbulent lubrication theory. The effect of bearing feeding parameter (β), Reynolds number (Re), ratio of wall thickness to journal radius (H/R) and anisotropy of porous material on the stability of rotor-bearing system has been investigated. It is observed that higher values of β gives better stability and higher stability is predicted if the porous bush is considered to be isotropic.     

Lubrication performance of finite journal bearings considering effects of couple stresses and surface roughness

To inspect the performance characteristics of finite journal-bearing systems, the combined effects of couple stress due to a Newtonian lubricant blended with additives and the presence of roughness on journal-bearing surfaces are studied in this article. Basing on the Stokes theory and Christensen’s stochastic model, the stochastic generalized Reynolds equation is deduced. The film pressure distribution equation is numerically solved by using the conjugate gradient method of iterations. According to the results, the couple stress effects can raise the film pressure of the lubricant fluid, improve the load-carrying capacity and reduce the friction parameter, especially at high eccentricity ratio. The surface roughness effect is dominant in long bearing approximation and the influence of transverse or longitudinal roughness to the journal bearing is in reverse trend. In general, the critical value of length-to-diameter is 1.1.     

Stability analysis of externally-pressurized gas-lubricated porous bearings with journal rotation Part 1. Cylindrical whirl

Whirl stability (cylindrical) of externally-pressurized gas-lubricated porous journal bearings, considering one-dimensional flow through the porous matrix, is analysed by a first-order perturbation method. The effect of supply pressure, feeding parameter, porosity parameter and length-to-diameter ratio on the stability is also investigated.     

Stability analysis of externally-pressurized gas-lubricated porous bearings with journal rotation Part 2. Conical whirl

The stability analysis of externally pressurized gas journal bearings under conical mode of vibration has been obtained using a first-order perturbation method. The effect of journal speed, feeding parameter, supply pressure, porosity parameter and length-to-diameter ratio on the conical whirl and whirl ratio has been investigated.     

Ferrofluid lubrication of finite journal bearings using Jenkins model

The present study investigates hydrodynamic lubrication by ferrofluids of finite journal bearings using the Jenkins model. A magnetic field created by displaced finite wire is used. A numerical solution for the modified Reynolds equation using the finite difference method is obtained. Static characteristics of finite journal bearings are analyzed using 2 control parameters: magnetic force coefficient and Jenkins viscosity. The obtained results are compared to those from Neurenger‐Rosensweig model. It is shown that pressure, load capacity, attitude angle, and side leakage increase and friction factor decreases when increasing the value of each control parameter at low and medium eccentricity ratios. However, the Jenkins viscosity parameter decreases the load capacity and increases the friction factor at high eccentricity ratios.     

Theoretical characteristics of hydrodynamic journal bearings lubricated with soybean‐based oil

Vegetable‐based oils are not only biodegradable but also environmentally advantageous, and the range of lubrication applications offered by them continues to grow. Recently, vegetable‐based oils have been combined with synthetic esters to produce modified vegetable‐based oils. This paper presents an investigation of the theoretical characteristics of hydrodynamic journal bearings lubricated with non‐Newtonian soybean‐based oil. The soybean‐based oil was mixed with synthetic esters and silicone oil. The relationship between the shear stress and shear strain rate of the oil was obtained experimentally. The time‐dependent modified Reynolds equation including non‐Newtonian effects was formulated for short circular journal bearings. The perturbation technique was applied to the Reynolds equation to obtain zero‐ and first‐order pressure equations. The finite difference method was used to calculate the pressure distribution numerically. The static and dynamic characteristics, such as pressure distribution, Sommerfeld number, attitude angle, and spring and damping coefficients, were obtained numerically. It was found that the nonlinear factors of the non‐Newtonian soybean‐based oil strongly affected the performance characteristics of the journal bearings.     

Numerical study of the thermo-hydrodynamic lubrication phenomena in porous journal bearings

In this work, a numerical simulation is presented for the thermo-hydrodynamic self-lubrication aspect analysis of porous circular journal bearing of finite length with sealed ends. It consists in analyzing the thermal effects on the behavior of circular porous journal bearings. The Reynolds equation of thin viscous films is used 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 presented results are in good agreement with those cited in the literature. The effects of dimensionless permeability parameter and eccentricity ratio on performance parameters are presented and discussed. The results showed that the temperature influence on the journal bearings performance is important in some operating cases, and that a progressive reduction in the pressure distribution, in the load capacity and attitude angle is a consequence of the increasing permeability.     

The effect solid particle lubricant contamination on the dynamic behavior of compliant journal bearings

The proposed work concerns a theoretical and numerical investigation of the effect of solid particle contamination of lubricant oils on the static and dynamic characteristics of a finite length compliant journal bearing operating under isothermal conditions with laminar flow. In the present investigation, we use simple models based on the Einstein's mixture theory, which is characterized by the presence of suspended rigid particles in a fluid. Using the classical assumptions of lubrication, a Reynolds equation is derived and solved numerically by the finite difference method. The displacement field at the fluid film bearing liner interface due to pressure forces is determined using the elastic thin layer model. The results obtained show that the presence of suspended rigid particles in the lubricating oil (solid contamination) has significant effects on the hydrodynamic performance characteristics such as the pressure field, friction force, flow rate, elastic surface deformation as well as stability maps of the rotor‐bearing system (critical mass and whirl frequency) especially at high volumetric concentration.     

A numerical analysis method based on flow continuity for hydrodynamic journal bearings

A numerical method of hydrodynamic bearing analysis is presented which is simple in concept, yet capable of development to handle complex situations such as dynamic misalignment. It is similar to the finite difference solution of Reynolds equation, but incorporates a more realistic modelling of cavitation. The approach to a numerical solution is direct, and should facilitate a better ‘feel’ for the way in which the physical processes are modelled. Results produced with this analysis are compared with other published data for aligned crankshaft bearings and misaligned sterntube bearings.     

Roughness effects in a narrow porous journal bearing with arbitrary porous wall thickness

The paper uses Christensen's stochastic theory to study the effects of surface roughness in a narrow porous journal bearing. An exact solution, valid for arbitrary wall thickness, is given for the film pressure and pressure in the bearing material. The results are compared with the approximate solutions, and the range of various influencing parameters, for which the approximate analysis is satisfactory from a practical point of view is determined.     

Experimental study of journal bearings with undulating journal surface

A journal bearing test rig was designed and constructed to test the behaviour of journals with wavy surfaces, the circumferential undulations being varied both in amplitude and in number. Results show that wavy journal surfaces may well enhance the load carrying capacity of a bearing. Moreover, surface undulations are shown to move the journal centre locus closer to the load line, ie cause a lower attitude angle. These effects are found to be more pronounced with larger wave amplitudes, and with higher numbers of waves around the journal circumference. In general, friction is found to be reduced with increase in surface wave amplitude.Good agreement is shown to exist between test results and a computer aided analysis conducted by the authors to predict wavy journals performance¹. It has been established that a wavy journal surface may, under certain conditions, display higher load capacity, lower friction and permit safer running of journal than bearings with perfectly smooth surfaces.