Steady-state performance of elliptical contact lubricated with micropolar fluids

In this work, the numerical investigation is done for the steady-state performance of elliptical contacts lubricated with micropolar fluids. The Eringen’s micro-continuum theory is applied to deduce the modified Reynolds equation for micropolar fluids. The modified Reynolds equation is discretized by the finite difference technique and evaluated by a multigrid technique for finding the steady-state pressure distribution; simultaneously, the elasticity equation is solved with the multilevel multi-integration method. The numerical solution is achieved under isothermal conditions and considering the exponential variation of viscosity with pressure. The effect of micropolar parameters, i.e. nondimensional characteristics length defines the molecular length of the blended additives, and coupling number measures the coupling between the angular and linear momentum of molecules, and operating parameters are studied. Owing to the analysis, the pronounced effect of the micropolar parameters on the elastohydrodynamic lubrication of elliptical contacts is observed and which cannot be avoided. Lubricants added with solid additives and coupling between linear and angular momentum improved the overall film thickness and pressure and enhanced the load-carrying capacity. Also, a nominal rise in the traction coefficient is noticed, but this increase in the traction coefficient is quite less when compared to Newtonian fluids.

Effects of adsorption layers and elastic deformation on thin-film lubrication of circular contacts with non-Newtonian lubricants

Purpose The modified Reynolds equation for non-Newtonian lubricant is derived using the viscous adsorption theory for thin-film elastohydrodynamic lubrication (TFEHL) of circular contacts. The proposed model can reasonably calculate the phenomenon in the thin-film lubrication (TFL) unexplained by the conventional EHL model. The differences between classical EHL and TFEHL with the non-Newtonian lubricants are discussed. Design/methodology/approach The power-law lubricating film between the elastic surfaces is modeled in the form of three layers: two adsorption layers on each surface and one middle layer. The modified Reynolds equation with power-law fluid is derived for TFEHL of circular contacts using the viscous adsorption theory. The finite difference method and the Gauss–Seidel iteration method are used to solve the modified Reynolds equation, elasticity deformation, lubricant rheology equations and load balance equations simultaneously. Findings The simulation results reveal that the present model can reasonably calculate the pressure distribution, the film thickness, the velocity distribution and the average viscosity in TFL with non-Newtonian lubricants. The thickness and viscosity of the adsorption layer and the flow index significantly influence the lubrication characteristics of the contact conjunction. Originality/value The present model can reasonably predict the average viscosity, the turning point and the derivation (log film thickness vs log speed) phenomena in the TFEHL under constant load conditions.

Combined effects of turbulence and elastic deformation on the performance of a journal bearing lubricated with a couple stress fluid

This paper presents a numerical study of the effect of turbulence and elastic deformation on the performance of a journal bearing operating with couple stress fluids, following Constantinescu’s turbulent lubrication theory. The modified Reynolds equation is derived taking into consideration the effect of turbulence and couple stresses. The modified Reynolds equation is solved using finite difference method. The results in terms of the load-carrying capacity, the attitude angle, friction coefficient and the side leakage are reported for various values of the couple stress parameter, the elastic coefficient, and Reynolds number. According to the obtained results, the couple stress fluid improves the performance characteristics of the rigid and deformed journal bearing in laminar and turbulent regimes. The results also show that bearing deformation and the turbulent regime cannot be neglected in calculating the performance characteristics of journal bearings lubricated with a Newtonian and a couple stress fluid.

Effect of non-Newtonian lubrication of squeeze film conical bearing with the porous wall operating with Rabinowitsch fluid model

In this article, a theoretical study is made to explore the effect of squeezing film in conical bearing for the permeable porous wall utilizing non-Newtonian lubricants. The Permeable medium impacts are characterized by modified Darcy’s law. The modified Reynolds equation representing the non-Newtonian properties following the cubic stress law condition is determined. After general contemplations on the flow in a bearing clearance and in a porous wall, the Cameron approximation is used to acquire modified Reynolds equation. The perturbation technique is used to solve the modified Reynolds equation and closed-form expressions are obtained for the fluid film pressure, load capacity, and response time. The results are illustrated by the graphical representation which shows that the introduction of porous on conical bearing with Rabinowitsch fluid, dilatant lubricant increases the film pressure, load capacity, and response time and decrease for pseudoplastic lubricant as compared to Newtonian fluid.

Static characteristics of hydrostatic doubled-layered porous journal bearings with slip flow including additives percolation into pores under coupled stress lubrication

A theoretical analysis of the steady-state characteristics of finite hydrostatic double-layered porous journal bearings dealing with the effects of slip flow at the fine porous layer–film interface and percolation of additives into pores under the coupled stress fluid lubrication is presented. Based on the Beavers–Joseph’s criterion for slip flow, the modified Reynolds equation applicable to finite porous journal bearings lubricated with coupled stress fluids have been derived. The governing equations for flow in the coarse and fine layers of porous medium incorporating the percolation of polar additives of lubricant and the modified Reynolds equation are solved simultaneously using finite difference method satisfying appropriate boundary conditions to obtain the steady-state performance characteristics for various parameter namely percolation factor, slip coefficient, bearing feeding parameter, coupled stress parameter, and eccentricity ratio. The results are exhibited in the form of graphs, which may be useful for design of such bearing.

On the study of Rayleigh step slider bearings lubricated with non-Newtonian Rabinowitsch fluid

Purpose Nowadays, the use of Newtonian fluid as a lubricant is diminishing day by day, and the use of non-Newtonian fluids has gained importance. This paper presents an analysis of the static characteristics of Rayleigh step slider bearing lubricated with non-Newtonian Rabinowitsch fluid, which has not been studied so far. The purpose of this paper is to derive the modified Reynolds equation for Rabinowitsch fluids for two regions and to obtain the optimum bearing parameters for the Rayleigh step slider bearings. Design/methodology/approach The governing equations relevant to the problem under consideration are derived. The modified Reynolds equation is derived, and it is found to be highly non-linear and hence small perturbation method is adopted to find solution. Findings From this study it is found that there is an increase in the load-carrying capacity, pressure and frictional coefficients for dilatant fluids as compared to the corresponding Newtonian case. Further, for dilatant lubricants the maximum load-carrying capacity is attained for the slightly larger values of entry region length of Rayleigh step bearing as compared to Newtonian and pseudoplastic lubricants. Originality/value Rabinowitsch fluid is used for the study of lubrication characteristics of Rayleigh step bearings. The author believes that the paper presents these results for the first time.

Pressure Distribution in a Porous Squeeze Film Bearing Lubricated with a Herschel-Bulkley Fluid

The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated with a lubricant being a viscoplastic fluid of a Herschel-Bulkley type is considered. After general considerations on the flow of the viscoplastic fluid (lubricant) in a bearing clearance and in a porous layer the modified Reynolds equation for the curvilinear squeeze film bearing with a Herschel-Bulkley lubricant is given. The solution of this equation is obtained by a method of successive approximation. As a result one obtains a formula expressing the pressure distribution. The example of squeeze films in a step bearing (modeled by two parallel disks) is discussed in detail.

Behaviors of the wedge-shaped gas-lubricated film using the finite difference lattice Boltzmann method

In this article, the finite difference lattice Boltzmann method (FDLBM) is successfully applied to analyze the hydrodynamic properties of the wedge-shaped gas film lubrication for the high speed micro gas bearings by comparing with the macroscopic methods (solving the modified Reynolds equation coupled with the simplified energy (modified Reynolds equation) and the Navier–Stokes equations coupled with the energy equation). By comparison, it is found that the vertical flow across the gas film can weaken the gas backflow and thus improves the gas film pressure, as the Navier–Stokes equation and FDLBM are used to analyze the wedge-shaped film lubrication. The continuum assumption in the macroscopic methods leads to a larger gas film pressure, compared with the value predicted by the FDLBM. And, the high temperature and speed enlarge this difference between them. Furthermore, the FDLBM provides a good warm-up for the multiscale simulation on the complex flow in the micro gas bearings.