Combined effects of piezo-viscous dependency and non-Newtonian couple stresses in wide parallel-plate squeeze-film characteristics

According to the Stokes micro-continuum theory of couple stress fluids together with the consideration of viscosity variation with pressure, the combined effects of piezo-viscous dependency, and non-Newtonian couple stresses in wide parallel rectangular-plate squeeze-film characteristics have been presented. An approximate analytical solution is obtained using a small perturbation method. Comparing with the iso-viscous and Newtonian case, the squeeze film performance is apparently improved. In addition, the improved characteristics are further emphasized for the squeeze film plates operating with a larger viscosity-pressure parameter, a non-Newtonian couple stress parameter and a lower film thickness.     

Combined effects of piezo-viscous dependency and non-Newtonian couple stresses in wide parallel-plate squeeze-film characteristics

According to the Stokes micro-continuum theory of couple stress fluids together with the consideration of viscosity variation with pressure, the combined effects of piezo-viscous dependency, and non-Newtonian couple stresses in wide parallel rectangular-plate squeeze-film characteristics have been presented. An approximate analytical solution is obtained using a small perturbation method. Comparing with the iso-viscous and Newtonian case, the squeeze film performance is apparently improved. In addition, the improved characteristics are further emphasized for the squeeze film plates operating with a larger viscosity–pressure parameter, a non-Newtonian couple stress parameter and a lower film thickness.     

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.     

A Study of Dynamically Loaded Journal Bearings Lubricated with Non-Newtonian Couple Stress Fluids

This paper is to theoretically investigate the behavior of dynamically loaded journal bearings lubricated with non-Newtonian couple stress fluids. To take into account the couple stress effects due to the lubricants blended with various additives, the modified Reynolds equation for dynamic loads governing the film pressure is derived. The film pressure is solved numerically with Reynolds boundary conditions and then various bearing characteristics are calculated. The effects of couple stresses on bearing performance characteristics are analyzed. The results conclude that couple stress fluids lubrication improves the bearing performance under dynamic loads.     

Static Performance of Finite Hydrodynamic Journal Bearings Lubricated by Magnetic Fluids with Couple Stresses

Based upon the Stokes micro-continuum theory, the problem of lubrication of finite hydrodynamic journal bearing lubricated by magnetic fluids with couple stresses is investigated. By taking into account the couple stresses due to the microstructure additives and the magnetic effects due to the magnetization of the magnetic fluid, modified Reynolds equation is obtained. The effects of couple stresses are studied by defining the couple stress parameter L that can be considered as a measure of the chain length of the additive molecule. The magnetic effects of the magnetic fluid are investigated by the magnetic coefficient γ. Using the finite-difference technique and for different values of couple stress parameter and magnetic coefficient, the Reynolds equation is solved, and pressure distributions are obtained. The bearing static characteristics namely load carrying capacity, attitude angle, friction coefficient, and side leakage flow are determined. The results indicate that the influence of couple stresses and magnetic effects on the bearing characteristics are significantly apparent. It is concluded that fluids with couple stresses are better than Newtonian fluids. The improvement of the bearing characteristics is enhanced if the magnetic effects are present.     

Modified Reynolds Equation for Different Types of Finite Plates with the Combined Effect of MHD and Couple Stresses

We make an effort to analyze the behavior of squeeze film characteristics of different finite plates with couple stress fluid in the presence of a transverse magnetic field. On the basis of the Stokes couple stress fluid model and hydromagnetic flow model, a modified Reynold's equation is derived, which is solved by using appropriate boundary conditions to obtain squeeze film pressure, load-carrying capacity, and squeeze film time. The graphical representation of the results suggests that the different bearing systems register an enhanced performance with couple stresses compared to that of a bearing system working with a conventional lubricant in the presence of a transverse magnetic field. It is observed that the effect of applied magnetic field on the squeeze film lubrication between different finite plates with conducting couple stress fluids is to increase the load-carrying capacity significantly and to delay the time of approach compared to the corresponding nonconducting Newtonian case. It is seen that for all of the finite plates of different shapes, the circular shape gives the maximum load and time.     

Inertial MHD Couple Stress Effects on Infinitely Wide Slider Bearings

This article presents a numerical study of magnetohydrodynamic (MHD) infinitely wide plane inclined slider bearings including both fluid inertia and non-Newtonian couple stress effects. Fluid inertia forces are considered in the film fluid using a simplified form of the Navier-Stokes equations. The non-Newtonian couple stress behavior of the lubricant is described based on the microcontinuum Stokes theory. The governing equations are discretized by finite differences using a boundary layer–type equations resolution. The resulting algebraic equations are solved using the Gauss-Seidel method. It is found that the couple effects of fluid inertia forces, MHD, and non-Newtonian couple stresses provide a significant improvement in the slider bearing load capacity compared to the case of the noninertia Newtonian nonconducting lubricant. The use of conducting lubricant diminishes the negative effect of inertia forces on the friction coefficient.     

Micropolar fluid squeeze film lubrication between rough anisotropic poroelastic rectangular plates: special reference to synovial joint lubrication

Abstract

The effect of anisotropic permeability on micropolar squeeze film lubrication between poroelastic rectangular plates is studied. The non-Newtonian synovial fluid is modelled by Eringen’s micropolar fluid, and the poroelastic nature of cartilage is taken in to account. The stochastic modified Reynolds equation, which incorporates the elastic as well as randomised surface roughness structure of cartilage with micropolar fluid as lubricant, is derived. Modified equations for the mean fluid film pressure, mean load carrying capacity and squeeze film time are obtained using the Christensen’s stochastic theory for the study of roughness effects. The effects of surface roughness, micropolar fluid and anisotropic permeability on the squeeze film characteristics of synovial joint are discussed. It is found that the surface roughness effects are more pronounced for micropolar fluids as compared to the Newtonian fluids, and the anisotropic nature of permeability of cartilage off-squares the plate size for optimum 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.     

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.     

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.     

Effect of Piezoviscous Dependency and Couple Stress on Squeeze Film Lubrication Between Parallel Stepped Plates

Theoretical analysis of the effect of piezoviscous dependency and couple stress on squeeze film lubrication between parallel stepped plates is presented in this article. According to the Stokes microcontinuum theory of couple stress fluids, the modified Reynolds equation is derived by considering viscosity variation along the film thickness. The standard perturbation technique is used to solve the nonlinear Reynolds equation and an approximate analytical solution for the film pressure is obtained. It is found that the effect of couple stresses and pressure-dependent viscosity variation increases the load-carrying capacity and lengthens the squeeze film time.     

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.     

Squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and non-Newtonian couple stresses

In this paper, the analysis of squeeze film characteristics of conical bearings with combined effects of piezo-viscous dependency and couple stress fluid is presented. On the basis of the Stokes microcontinuum theory of couple stress fluid model and Barus experimental research, a modified Reynolds equation is derived, the standard perturbation technique is used to solve the highly non-linear Reynolds equation and approximate analytical solution is obtained for the squeeze film pressure, load carrying capacity and squeeze film time. According to the results obtained, the effect of viscosity pressure dependency on the squeeze film lubrication of conical bearings with couple stress fluids is to improve the load carrying capacity significantly and lengthen the squeeze film time as compared to iso-viscous Newtonian case.     

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.     

Numerical solution of couplestress finite Reynolds equation for squeeze film lubrication of partial porous journal bearings

Abstract

In this paper, the general Reynolds equation of finite porous journal bearing lubricated with couplestress fluid is solved numerically for the assessment of dynamic characteristics of the bearings. The Reynolds type equation governing the steady performance is obtained and solved numerically by finite difference technique. From the numerical results, it is observed that the effect of couple stresses is to increase the load carrying capacity and to lengthen the squeeze film time as compared to the corresponding solid case. The effect of permeability is to reduce the load capacity and to decrease the squeeze film time as compared to the solid case.     

Squeeze film lubrication of a short porous journal bearing with couple stress fluids

This paper presents the theoretical investigations of the rheological effects of the couple stress fluids on the static and dynamic behaviour of the pure squeeze films in the porous journal bearings. The present study predicts the effects of percolation of the polar additives (microstructures) into the porous matrix on the performance of squeeze films in the porous journal bearings. The most general modified Reynolds-type equation is derived for a porous journal bearing with no journal rotation. The analysis takes into account of the tangential velocity slip at the porous interface by using the BJ-slip condition. The cases of a short porous journal bearing under a constant applied load and that under an alternating load are analyzed. As compared to the Newtonian lubricants, the lubricants which sustain the couple stresses yield an increase in the load carrying capacity. Under a cyclic load the couple stress fluids provide a reduction in the journal velocity and an increase in the minimum permissible height of squeeze films.     

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.     

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.