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.     

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.     

An inverse solution for finite journal bearings lubricated with couple stress fluids

This paper presents an inverse solution for finite journal bearings lubricated with couple stress fluids to estimate the eccentricity ratio and the couple stress parameter for a given experimentally measured pressure distribution. The least-squares optimization technique is used to solve the inverse problem. An efficient numerical scheme is developed to solve the direct lubrication problem, which consists of the modified Reynolds equation, the film thickness equation, and the boundary conditions for the pressure field. The flexibility of the bearing liner is considered in the film thickness equation by a simple elastic model. The proposed inverse algorithm was tested using numerically simulated pressure distribution. The results showed that as the percentage of random error added to the numerically calculated pressure data points increases, the number of iterations required for convergence increases slightly, and the accuracy of the predictions decreases especially in the case of elastic liner.     

On the performance of dynamically loaded journal bearings lubricated with couple stress fluids

A numerical study of the performance for a dynamically loaded journal bearing lubricated with couple stress fluids is undertaken. First of all, on the basis of micro-continuum theory, the generalized Reynolds equation for dynamic loads is derived. Then it is simultaneously solved with the force balance equation of the journal, thus obtaining the transient oil film pressure, the transient position and velocity of the journal center. Results from this analysis are presented for a typical engine crankshaft bearing. It is shown, compared with Newtonian lubricants, that under a dynamic loading lubricants with couple stress yield an obvious increase in oil film pressure and oil film thickness, but a decrease in the side leakage flow. Moreover, the effects of couple stress on friction force and friction coefficient vary considerably with time.     

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.     

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.     

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.     

Thermohydrodynamic analysis of journal bearings lubricated with couple stress fluids

Thermohydrodynamic analysis of journal bearings is extended to include couple stress effects in lubricants blended with high polymer additives. Based on the micro-continuum theory, a modified energy equation is derived and then is simultaneously solved with the heat transfer equation as well as the modified Reynolds equation. The effects of couple stress on the key performance of a finite journal bearing, such as maximum temperature, shaft temperature, load capacity, friction force, friction coefficient, and side leakage flow, are presented. The results have shown that lubricants with couple stresses, compared with Newtonian lubricants, not only yield an obvious increase in load capacity and decrease in friction coefficient, but also produce a lower bearing temperature field. Thus it can be concluded that the lubricant with couple stress does improve the performance of journal bearings.     

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.     

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 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.     

A study of optimum load capacity of slider bearings lubricated with power law fluids

A general theoretical study of an infinitely wide lubricated slider bearing is presented, considering the lubricant to be an incompressible, isothermal, power law fluid. A set of algebraic equations is developed to obtain the pressure gradient for any value of the power law index. To illustrate the mathematical development, the set of equations is used to calculate the pressure gradient for two special forms of slider bearings, viz., inclined and parabolic slider bearings. In these two cases, the variation of pressure, load capacity, coefficient of friction, etc. for a range of fluid- and bearing-parameters is presented. In order to obtain optimum load capacity for an inclined and a parabolic slider bearing, the variations of load capacity, coefficient of friction, etc., with respect to the simultaneous changes of the inlet–oulet film height ratio and of the power law index of lubricants are also analysed. The results are presented both numerically and graphically. The results reveal that in the cases of an inclined and a parabolic slider bearings the inlet–outlet film height ratio for the optimum load capacity depends on the power law index of lubricants. Further, for each value of power law index, there exists a value of inlet–outlet film height ratio for which the frictional coefficient is minimum.     

An analytical approach for analysis and optimisation of slider bearings with infinite width parallel textures

This paper introduces an analytical approach to study the textured surfaces in hydrodynamic lubrication regime. For this purpose, a method of integrating the Reynolds equation for slider bearings with surface discontinuities is presented. By introducing appropriate dimensionless parameters, analytical relations for various texture profiles in both indented and projected forms are delivered. These relations express the nature of mathematical dependence between textured bearing performance measures and geometrical/operational parameters. An optimisation procedure is employed to achieve the optimum texturing parameters promoting maximum load capacity, load capacity to lubricant flow rate ratio and minimum friction coefficient for asymmetric partially textured slider bearings.