Inertia Effects on Inclined Slider Bearings Lubricated by a Couple Stress Fluid

This article deals with a numerical investigation of fluid inertia effects on inclined slider bearings lubricated by couple stress fluids. Convective inertial forces are considered in the film fluid. A reduced version of the Navier-Stokes equations is thus derived. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing partial differential equations are discretized by finite differences based on boundary layer–type equations. The resulting algebraic equations are solved using a Gauss-Seidel method. Compared to the case of the non-inertia Newtonian lubricant, the couple effects of fluid inertia forces and non-Newtonian couple stresses provide a significant improvement in slider bearing load capacity.     

MHD couple stress squeeze film characteristics between sphere and plane surface

Abstract

In this paper, the effect of non-Newtonian couple stress fluids on the magnetohydrodynamic (MHD) squeeze film characteristics between a sphere and a plane surface is analysed. By taking into account the couple stresses due to the presence of microstructure additives in the lubricant and the magnetic effects due to the magnetisation of the couple stress fluid, the non-Newtonian couple stress MHD Reynolds type equation is derived. The numerical solutions for the MHD squeeze film characteristics are presented for various values of couple stress parameter, and magnetic Hartmann number. The results indicate that the influences of couple stresses and the magnetic effects on the squeeze film characteristics are significantly apparent. It is concluded that the MHD couple stress fluids have better lubricating qualities than the corresponding Newtonian case.     

Non-Newtonian couple stress poroelastic squeeze film

The aim of this paper is to develop a new model of the interaction of a fluid film with a porous medium. The model takes into account the fluid inertia in both the lubricant and the porous matrix. Non-Newtonian behavior of the fluid, viscous effects in the porous matrix, and poroelasticity of the matrix are also considered. The main concerns are modeling and simulation of the squeeze film lubrication between two discs when one has a porous facing. The fluid flow is described using a reduced version of the Navier–Stokes equations in the fluid film, and the Darcy–Brinkman–Forchheimer generalized model in the porous matrix.The present study focuses on the combined effects of the non-Newtonian fluid lubricant and porous matrix deformation. The non-Newtonian behavior of the lubricant is described by the so-called couple stress model. The porous interface deformation is obtained using the thin elastic layer approach. The partial differential equations established in this study are discretized by finite differences. The resulting algebraic equations are solved using the Gauss–Seidel relaxation method.The numerical results of the present simulations show that all these effects have a significant influence on the porous squeeze film performance.     

A Comparative Study of Static and Dynamic Characteristics of Parabolic and Plane Inclined Slider Bearings Lubricated with MHD Couple Stress Fluids

In this article the couple stress effects on the static and dynamic characteristics of parabolic and plane inclined slider bearings in the presence of an applied magnetic field with squeeze action is analyzed theoretically. The modified magnetohydrodynamic (MHD) couple stress Reynolds equation is derived. The closed-form solution for the film pressure of parabolic and inclined plane slider bearings is obtained and used to study the MHD couple stress static and dynamic characteristics of these bearings. The results predict a higher steady load-carrying capacity, dynamic stiffness, and damping coefficient for the bearings lubricated with MHD couple stress fluid than the corresponding Newtonian case. It is observed that the parabolic-shaped slider bearings provide greater steady load-carrying capacity, dynamic stiffness, and damping coefficients compared to the plane inclined slider bearings.     

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.     

Effects of couple stresses in the cyclic squeeze films of finite partial journal bearings

Based upon the microcontinuum theory, the present paper is to theoretically study the pure squeeze-film behavior of a finite partial journal bearing with non-Newtonian couple-stress lubricants operating under a time-dependent cyclic load. To take into account the couple stress effects resulting from the lubricant blended with various additives, the modified Reynolds equation governing the film pressure is obtained from Stokes equations of motion. The film pressure is numerically solved by using the Conjugate Gradient Method. Bearing characteristics are then calculated from the nonlinear motion equation of the journal. According to the results obtained, the effects of couple stresses result in a decrease in the value of eccentricity of the journal center. The finite partial bearing with a couple stress fluid as the lubricant yields an increase in the minimum permissible clearance and provides a longer time to prevent the journal-bearing contact.     

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.     

Inertia force effects in the non-Newtonian couple stress squeeze film between a sphere and a flat plate

On the basis of the Stokes micro-continuum theory together with the method of mean averaged inertia, the influences of fluid inertia forces on the non-Newtonian squeeze film characteristics between a sphere and a flat plate have been presented. Comparing with the case of a non-inertia non-Newtonian lubricant, the consideration of fluid inertia forces provides a longer squeeze film time especially for the squeeze film operating with a lower film height, and a larger non-Newtonian parameter and density parameter. It prolongs the life of squeeze films.     

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.     

Hydrodynamic lubrication of rough slider bearings with couple stress fluids

The combined effects of couple stresses and surface roughness on the performance characteristics of hydrodynamic lubrication of slider bearings with various film shapes, such as plane slider, exponential, secant and hyperbolic, are studied. A stochastic random variable with non-zero mean, variance and skewness is used to mathematically model the surface roughness of the slider bearing’s. The Stokes couple stress fluid model is used to characterize the rheological behavior of the lubricant with polymer additives. The modified expressions for the bearing characteristics, namely pressure, load carrying capacity, center of pressure, frictional force are obtained for the general lubrication film shape on the basis of Stokes microcontinuum theory for couple stress fluids. Results are computed numerically for various film shapes under consideration. It is observed that, for all the lubricant film shapes under consideration, the negatively skewed surface roughness increases the load carrying capacity, frictional force and temperature rise, while it reduces the coefficient of friction. On the contrary, the reverse trend is observed for positively skewed surface roughness. Further, these effects are more pronounced for the couple stress fluids.     

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.     

The influence of couple stresses in squeeze films

A theoretical study of non-Newtonian flow effects in a squeeze film configuration is carried out with special reference to synovial joints. The material model taken is that of the Stokes' couple stress fluid. It is found that the bearings with couple stresss fluid as lubricant provide significant load supporting capacities which result in longer bearing life. The squeeze film time is found to be considerably longer for couple stress fluid than in the case of Newtonian fluid of the same viscosity. These are the most desirable advantages which render the model close to the natural characteristics of synovial joints.     

规则形貌作用下非牛顿流体润滑的数值分析

利用Navier-Stockes方程和有限体积法,求解斜面滑块润滑模型的承载力和摩擦力,研究形貌高度较大时,表面形貌影响下非牛顿介质的润滑效果,获得用传统的包含表面形貌统计模型的雷诺方程方法难以获得的流场的细节信息。数值结果显示：在规则横向条纹形貌的作用下,形貌突变处出现压力突变;当形貌高度大于1%油膜厚度时才对润滑结果有较大影响,承载力和压差阻力随形貌高度的增加而增加,摩擦阻力随之下降,总阻力基本保持不变;当形貌高度大于油膜厚度的10% 时,摩擦阻力随之上升,总阻力迅速增加。非牛顿介质幂律模型参数对润滑结果的影响远大于形貌参数的影响,但其并不影响承载力等结果随形貌高度变化的趋势,选择合适的润滑材料参数是改善润滑的关键因素。     

Frequency-domain analysis of non-Newtonian fluid behavior in head-disk interface lubrication

A lubricant in a head-disk interface is considered as a non-Newtonian fluid. Properties of non-Newtonian lubricants are specified by three nonlinear functions and a modified Reynolds equation is derived for the varied film thickness in the interface. The shear dependent viscosity is the principal factor and it is expressed by a first order transfer function. Its amplitude frequency response describes the process of the viscosity variation and indicates that the shear dependent viscosity is affected not only by the lubricant material parameters, but also by the shear frequency. Based on the modified Reynolds equation, the numerical result of lubrication is given. The load capacity is not always higher or always lower than that of the Newtonian fluid. The effect of the first normal stress difference is enlarged with the slider flying height varies.     

Effect of surface roughness on static and dynamic characteristics of MHD couple stress lubrication of parabolic slider bearing

The effect of surface roughness on static and dynamic characteristics of parabolic slider bearing lubricated with couple stress fluid in the presence of magnetic field is theoretically analysed in this paper. The modified stochastic MHD couple stress Reynolds-type equation is derived on the basis of Christensen stochastic theory and considered two types of roughness pattern namely longitudinal and transverse. Expressions for steady pressure and load, dynamic stiffness and damping coefficients are obtained for both roughness patterns. Compared to smooth surface, transverse roughness pattern provides larger load-carrying capacity, dynamic stiffness and damping coefficients, whereas longitudinal roughness pattern has adverse effects. The presence of couple stress and applied magnetic field improves the bearing performance.     

Combined thin-film and Navier–Stokes analysis in high Reynolds number lubrication

The classical theory of hydrodynamic lubrication assumes that the flow regime is laminar and the inertia forces in the fluid film are negligible. For large bearings using low viscosity lubricant or for high speed, the inertia forces could be important and non laminar flow occurs. In that presentation a general view of non-laminar lubrication is presented. The different flow regimes, which occur in bearings and seals, are shown. The theories to obtain the characteristics of bearings operating in turbulent flow regime are presented. The effects of inertia forces in laminar and in turbulent flows are shown. Finally results obtained using the complete Navier Stokes equations are presented and it is shown how they are included in the classic lubrication theory.     

Lubricant Flow and Accumulation on the Slider’s Air-Bearing Surface in a Hard Disk Drive

Lubricant accumulation on the slider’s surface of a hard disk drive (HDD) has a detrimental effect on its read/write performance. Air flow through the slider-disk clearance moves some of the lubricant from the air-bearing surface (ABS) toward the slider’s lateral walls where it accumulates. In this article, we show by numerical simulations that the lubricant accumulation characteristics are strongly dependent on the slider’s flying height, skew angle and ABS design. The lubricant flow on the slider’s surface is quantified numerically. Air shear stress, air pressure and disjoining pressure are used as driving forces in the simulations. The lubricant thickness profile and volume evolution are calculated for two states of the HDD: operating and at rest. In the first state, lubricant is driven by air shear stress toward the trailing edge of the slider where it accumulates on the deposit end. In the second state, lubricant from the deposit end flows back into the ABS driven by the action of disjoining pressure. Lubricant accumulation on the four lateral walls of the slider is taken into account. The lateral walls are unfolded to study the flow using a two-dimensional lubrication model. The effects of flying height, skew angle and slider design on the accumulation removal of lubricant from the ABS are determined for the two states of the drive.     

Investigation of couple stress effects on poroelastic squeeze film of parallel plates

The couple stress effects on hydrodynamic performances of poroelastic squeeze film in the case of infinitely long parallel plates are examined in this paper. The lower plate is a poroelastic matrix saturated by a Newtonian fluid. The poroelasticity is taken into account by the means of homogenisation method. The rheological behaviour of the lubricant is described by the Stokes couple stress fluid theory. The modified Reynolds equation accounting for the couple stress, the elasticity of the poroelastic plate and the slip velocity condition at the film–poroelastic plate interface is derived. The governing equations in the fluid film and poroelastic plate are discretised by finite difference method and solved iteratively by using Gauss–Seidel method. The fluid film and poroelastic plate coupling is managed by the iterative fixed point technique. A computer program is developed in this study. The result analysis shows that couple stress effects on poroelastic squeeze film performances are significant. Copyright © 2016 John Wiley & Sons, Ltd.     

A theoretical study of combined effects of non-Newtonian rheology and viscosity-pressure dependence in the sphere-plate squeeze-film system

A theoretical study of the combined effects of non-Newtonian couple-stress lubricants and variation of viscosity with pressure in the squeeze-film motion between a sphere and a flat plate is presented. To account for the couple stress effect arising from a lubricant blended with various additives and to consider the viscosity-pressure dependence, the nonlinear non-Newtonian Reynolds-type equation is derived in accordance with the Stokes microcontinuum constitutive equations cooperated with the Barus formula. Through a small perturbation technique, the analytical approximate solution for the film pressure is obtained. According to the results, the combined effects of couple stresses produced by the spin of microelements and viscosity-pressure dependence provide an enhancement in the load-carrying capacity and lengthen the response time as compared to the classical iso-viscous Newtonian-lubricant case. On the whole, the sphere-plate squeeze-film characteristics are improved, especially for higher values of couple stress parameter and viscosity parameter. An application to a lubrication problem is also illustrated for to assess the extent to design the sphere-plate squeeze-film system considering the combined effects of non-Newtonian couple stresses and viscosity-pressure dependence.     

Effect of non-Newtonian lubrication on the separation of a sphere from a flat

A numerical analysis is presented to study the effect of lubrication with non-Newtonian fluid on the separation flow of a fully flooded sphere from a flat under the condition of constant applied load. Different non-Newtonian fluid models were utilized to account for the microstructure and rheology of additives suspended in the film lubricant, namely those models for couple stress, micropolar, and power-law fluids. The equation of motion of the sphere was used to examine the effect of the sphere inertia on accelerating the separation process as the film viscous force decreases. This required solving the film pressure field, which is derived from a modified Reynolds equation and later computed numerically by a forth-order Runge-Kutta integration scheme. Several parameters were examined such as the time to complete separation, the length scale of the additives, the variation in lubricant's viscosity due to the presence of the additives, the sphere mass and radius, and the applied force on the sphere. Compared to the Newtonian fluid case, the results of the numerical solution indicated that there is a delay on the separation time for large non-Newtonian parameters, i.e., parameters representing additives characteristic length, additives concentration, and power-law indices.