Porous inclined stepped composite bearings with micropolar fluid

Abstract

This paper describes the theoretical analysis of the effect of micropolar fluid on the lubrication characteristics of porous inclined stepped composite bearing. The lubricant with additives in the film region and also in the porous region is modelled as Eringen's micropolar fluid, which is characterised by the presence of suspended rigid particles with microstructures. The generalised Reynolds type equation is derived for the most general porous bearing configuration (porous composite bearings) lubricated with micropolar fluid. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force and coefficient of friction. These expressions can be utilised to obtain the performance characteristics of four different bearing systems, namely, porous plane inclined slider, porous composite tapered land bearing, porous stepped bearing and composite porous tapered concave bearing. It is observed that the micropolar fluid lubricants provide an increased load carrying capacity and decreased coefficient of friction as compared to the corresponding Newtonian case.     

Hydrodynamic analysis of rough curved pivoted porous slider bearings with couple stress fluid

Abstract

The purpose of this paper is to study the effect of surface roughness on the performance of curved pivoted porous slider bearings lubricated with couple stress fluid. The modified B–J slip boundary condition is utilised at the porous/fluid film interface to derive the Reynolds type equation for the problem under consideration. To mathematically model the surface roughness due to non-uniform rubbing of bearing surfaces, a stochastic random variable with non-zero mean, variance and skewness is considered. The closed form solution is obtained for the averaged Reynolds equation, and the compact expressions for the mean fluid film pressure mean load carrying capacity, frictional force and the centre of pressure are obtained. The numerical computations of the results show the improved performance due to the couplestresses and the presence of negatively skewed surface roughness. However, the presence of porous facing and positively skewed surface roughness affects the performance of the pivoted porous slider bearing.     

Combined effects of surface roughness and couple stresses on static and dynamic behaviour of squeeze film lubrication of porous journal bearings

Abstract

The combined effects of surface roughness and the couple stresses on the static and dynamic characteristics of squeeze film lubrication in porous journal bearings with no journal rotation are theoretically studied. The Stokes couple stress fluid model is considered to model the lubricants with additives. The surface roughness on the porous journal bearing is mathematically modelled by a random variable with non-zero mean, variance and skewness. The generalised stochastic Reynolds type equation is derived for the problem under consideration. The applied load is considered as a sinusoidal function of time to simulate the bearings operating under cyclic loads. The closed form expressions for the bearing characteristics are obtained for the short porous journal bearings. It is observed that the negatively skewed surface roughness and couple stresses improve the performance of the porous journal bearings as compared to the smooth journal bearings with Newtonian lubricants. However, the presence of positively skewed surface roughness on the bearing surface affects its performance.     

Optimal film shape for two-dimensional slider bearings lubricated with couple stress fluids

The shape of a slider bearing is one of the major geometric conditions influencing the performance of the bearing. The aim of this study is to design the optimum shapes of the surfaces of sliders to meet the load and center of pressure demands specified by the designers. The design strategy uses COMSOL Multiphysics software package to solve the modified Reynolds equation derived on the basis of stokes microcontinuum theory. The sequential quadratic programming (SQP) is used to optimize the shape of the slider bearing. Results show that designers seeking to effectively reduce friction should consider a reducing the aspect ratio since it is the most significant parameter affecting optimal friction. In addition, slider bearings should be optimized with a polynomial profile of order 6 to reduce the computational effort and yield a solution that is very close to the solution of higher order polynomials.     

Static and dynamic characteristics of externally pressurized circular step thrust bearings lubricated with couple stress fluids

The combined effects of couple stresses, fluid inertia and recess volume fluid compressibility on the steady-state performance and the dynamic stiffness and damping characteristics of hydrostatic circular step thrust bearings are presented theoretically. Based on the micro-continuum theory, the modified Reynolds equation and the recess flow continuity equation are derived by using the Stokes constitutive equations to account for the couple stress effect resulting from a lubricant blended with various additives. Using a perturbation technique, results in terms of steady-state load-carrying capacity, oil flow rate, stiffness and damping coefficients are presented. A design example is also illustrated for engineering and industrial applications.     

Non-Newtonian effects on the dynamic characteristics of one-dimensional slider bearings: Rabinowitsch fluid model

The non-Newtonian effects of an isothermal incompressibe laminar-flow lubricant on the dynamic stiffness and damping characteristics of one-dimensional slider bearings are theoretically examined. On the basis of Rabinowitsch fluid (cubic equation) model, the modified Reynolds equation considering bearing-squeeze action is derived to take into account the transient motion of the slider, and the non-Newtonian properties of lubricants. Applying a small perturbation technique, both the steady-state performance and the dynamic characteristics are evaluated. According to the results, the steady film pressure, load-carrying capacity, and the dynamic stiffness and damping behaviors are significantly affected by the values of the dimensionless nonlinear factor accounting for non-Newtonian effects, the wedge parameter of a slider profile and the squeeze number of bearing-squeeze action.     

MHD steady and dynamic characteristics of wide tapered-land slider bearings

Based on the magneto-hydrodynamic (MHD) thin-film lubrication theory, steady load capacity and dynamic characteristics of wide tapered-land slider bearings lubricated with an electrically conducting fluid by the application of an external magnetic field are presented. Compared with the non-conducting lubricant (NLC) tapered-land bearing by Lin et al. (2006), the MHD bearing provides higher values of load capacity and dynamic coefficients. Compared with the MHD inclined-plane bearing by Lin et al. (2009), the MHD tapered-land bearing how an increase in load capacity and dynamic coefficients as well as a reduction in the steady friction parameter.     

Squeeze film characteristics of finite journal bearings: couple stress fluid model

A theoretical study of squeeze film behaviour for a finite journal bearing lubricated with couple stress fluids is presented. On the basis of the microcontinuum theory, the modified Reynolds equation is obtained by using the Stokes equations of motion to account for the couple stress effects due to the lubricant blended with various additives. With the Conjugate Gradient Method of iteration the built-up pressure is calculated, and then applied to predict the squeeze film characteristics of the system. According to the results evaluated, the rheological influence of couple stress fluids is physically apparent. Compared with the case of a Newtonian lubricant, the couple stress effects increase the load-carrying capacity significantly and lengthen the response time of the squeeze film behaviour. On the whole, the presence of couple stresses improves the characteristics of finite journal bearings operating under pure squeeze film motion. The rheological effects of couple stress fluids agree with previous works.     

Squeeze film characteristics of long partial journal bearings lubricated with couple stress fluids

On the basis of microcontinuum theory, a theoretical analysis of hydrodynamic squeeze film behaviour for long partial journal bearings lubricated by fluids with couple stresses is presented. To take into account the couple stress effects due to the lubricant containing additives or suspended particles, the modified Reynolds equation governing the film pressure is derived by using the Stokes constitutive equations. Various bearing characteristics are then calculated. According to the results obtained, the influence of couple stress effects on the performance of the system is physically apparent and not negligible. Compared with the Newtonian lubricant case, the couple stress effects provide an enhancement in the load-carrying capacity and lengthen the response time of the squeeze film action. On the whole, the presence of couple stresses signifies an improvement in the squeeze film characteristics of the system.     

Numerical analysis of journal bearings lubricated with micropolar fluids including thermal and cavitating effects

A numerical study of the non-Newtonian behavior for a finite journal bearing lubricated with micropolar fluids is undertaken considering both thermal and cavitating effects. The modified Reynolds equation and energy equation are derived based on Eringen's micropolar fluid theory. The solution to the modified Reynolds equation is determined using the Elord's cavitation algorithm. The effects of the size of material characteristic length and the coupling number on the thermohydrodynamic performance of a journal bearing are investigated. It is shown, compared with Newtonian fluids, that micropolar fluids exhibit the increase in load capacity and temperature, but the decrease in coefficient of friction and side leakage flow. It is also indicated that, in the full film region, micropolar fluids increase the values of non-dimensional density, while in the cavitated region, both micropolar fluids and Newtonian fluids yield the same values of the fractional film content.     

Static and dynamic characteristics of short wavy journal bearings

A general analysis has been done to investigate the static and dynamic performance of short wavy journal bearing. Reynolds equation is solved for both steady‐ and unsteady‐state operations. The steady‐state analysis has been done and compared with circular bearing with respect to their load capacity, flow rate, pressure distribution and friction factor. The unsteady‐state analysis has been used to determine the rotor dynamic coefficients for various eccentricity ratios. These coefficients are used to determine the stability parameters, such as critical mass and whirl ratio, and prove that wave bearing has not only better load carrying capacity but also provides better stability at high speed than circular bearing. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of magnetic fields on the dynamic characteristics of wide parallel step slider bearings with electrically conducting fluids

By the use of electrically conducting fluids as lubricants together with the application of externally magnetic fields, the dynamic lubrication problems of parallel step slider bearings lubricated with a nonconducting fluid are extended in this paper. A closed‐form solution has been derived for the magneto‐hydrodynamic characteristics of wide parallel step slider bearings. Comparing with the bearing lubricated with nonconducting fluids, the magneto‐hydrodynamic parallel step slider bearings signify an improvement in the load capacity, as well as the dynamic stiffness and damping coefficients. A numerical example and calculated values are also provided in tables for engineers in bearing selection and designing. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Static and dynamic analysis of elastohydrodynamic elliptical journal bearing with micropolar lubricant

In this paper the effect of deformation of the bearing liner on the static and dynamic performance characteristics of an elliptical (two-lobe) journal bearing operating with micropolar lubricant is presented. Lubricating oil containing additives and contaminants is modeled as micropolar fluid. A generalized form of Reynold's equation is derived from the fluid flow and diffusion equations. Finite element technique is used to solve the modified Reynold's equation governing the flow of micropolar lubricant in the clearance space of the journal bearing and the three-dimensional elasticity equations governing the displacement field in the bearing shell. The static and dynamic characteristics of the bearing are computed for a wide range of deformation coefficient which takes into accountant the flexibility of bearing liner by treating operating lubricant as (i) Newtonian and (ii) micropolar. The computed results show that the increasing volume concentration of additives and mass transfer of additives produce significant changes on the performance characteristics.     

Stiffness and damping characteristics of finite width journal bearings with a non-newtonian film and their application to instability prediction

Starting from the most general fluid flow equation of the power law type expressing rate of shear in terms of powers of shear stress for non-Newtonian lubricants a modified form of Reynolds'equation is derived for dynamically loaded finite width journal bearings. The finite difference technique with successive over relaxation is used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution. From the equations of fluid film forces, the values of stiffness and damping coefficients are obtained for a linearised case. The shear thinning effect of non-Newtonian lubricants at higher shear rates is shown to decrease the stiffness and damping values. Finally, the stability limit for such a bearing is obtained for different values of the nonlinear factor.     

Effect of pressure dependent viscosity on squeeze film characteristics of micropolar fluid in convex curved plates

In this paper, the effect of pressure dependent viscosity on the squeeze film characteristics between convex curved plates of a cosine form is presented. Micropolar fluid theory, which is a possible non-Newtonian model of a suspension of rigid particle additives, is applied to the study of the lubrication of cosine form convex curved plates. The modified Reynolds equation is solved for the fluid film pressure and then the cosine form by considering the exponential relationship in the viscosity variation. For iso-viscous lubricants, the effects of pressure dependent viscosities signify an increase in the values of the squeeze film pressure, the load capacity and the elapsed time. It provides useful information in designing the mechanisms of squeeze film plates for engineering application.     

Misalignment effects on steady‐state and dynamic behaviour of compliant journal bearings lubricated with couple stress fluids

This work concerns the steady‐state and dynamic analysis of misaligned compliant journal bearings considering the effects of couple stresses arising from the lubricant blended with polymer additives. Based on the Stokes micro‐continuum theory, a modified form of the Reynolds equation is derived. The displacement field at the fluid film–bearing liner interface due to pressure forces is determined using the elastic thin liner model. The effects of the misalignment and the couple stress parameters on static and dynamic performances such as pressure distribution, load‐carrying capacity, power loss, side leakage flow, misalignment moment, critical mass and whirl frequency are presented and discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

A theoretical and experimental study into the steady-state performance characteristics of industrial air lubricated thrust bearings

The effect of pocket length on the steady-state performance characteristics of a single orifice industrial aerostatic bearing has been studied experimentally. For a given air gap the pocket length is found to have an important influence on stiffness. A further theoretical and experimental study of the performance of the twin orifice version of the bearing has been made. Load capacity and film stiffness are found to improve at the expense of flowrate. There is considered to be satisfactory agreement between predicted and observed performance.     

Squeeze film characteristics between a sphere and a rough porous flat plate with micropolar fluids

The effects of surface roughness on the squeeze film characteristics between a sphere and flat plate covered with a thin porous layer are investigated in this paper. The sphere and the plate are separated with a non‐Newtonian lubricant of a micropolar fluid. 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 film pressure distribution is solved and other squeeze film characteristics, such as the load‐carrying capacity,and time–height relationship, are obtained. The results indicate that lubrication by a micropolar fluid will increase the load‐carrying capacity and lengthen the squeeze film time, regardless to the surface rough and porosity of the flat plate. It is also found that excessive permeability of the porous layer causes a significant drop in the squeeze film characteristics and minimises the effect of surface roughness. For the case of limited or no permeability, the azimuthal roughness is found to increase the load‐carrying capacity and squeeze time, whereas the reverse results are obtained for the case of radial roughness.     

Derivation of dynamic couple-stress Reynold’s equation of sliding-squeezing surfaces and numerical solution of plane inclined slider bearings

Deriving a general dynamic Reynold’s equation of sliding-squeezing surfaces with non-Newtonian fluids is necessary for the assessment of dynamic characteristics of a lubricating system. Taking into account the transient squeezing-action effect and considering the effects of couple stresses resulting from the lubricant blended with various additives, the non-Newtonian dynamic Reynold’s equation applicable to the general film shape is derived by using the Stokes micro-continuum theory. As an application, the numerical analysis of a two-dimensional plane inclined slider bearing is illustrated. Based upon the small perturbation technique, two Reynold’s-type equations responsible for both the steady performance and the perturbed characteristics are obtained. The steady and perturbed pressures are then numerically calculated by using the conjugate gradient method. From the results obtained, the effects of couple stresses provide an improvment on both the steady-state performance and the dynamic stiffness and damping characteristics especially for the bearing with a higher value of aspect ratio.