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.     

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.     

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.     

Lubrication of a narrow porous journal bearing with a couple stress fluid

This paper describes a theoretical investigation of the rheological effects of couple stress fluids on the performance of narrow porous journal bearings. A most general modified Reynolds equation is derived for narrow porous journal bearings using the Stokes constitutive equations for couple stress fluids. The fluid in the film region and in the porous region has been modelled as a couple stress fluid. The analysis takes into account velocity slip at the porous interface using the Beavers‐Joseph criterion. A closed‐form expression for field pressure is obtained for narrow journal bearings. Eigen‐type expressions for field variations are obtained. The dimensionless load‐carrying capacity, attitude angle, and coefficient of friction are presented for different operating parameters. It is observed that narrow porous journal bearings with couple stress fluids as lubricant show a significant increase in load‐carrying capacity with reduced coefficient of friction as compared to the Newtonian case. The present study predicts the effects of the percolation of polar additives (microstructures) into the porous matrix on the bearing performance.     

Linear stability analysis of hydrodynamic journal bearings under micropolar lubrication

The dynamic characteristics of hydrodynamic journal bearings lubricated with micropolar fluids are presented. The modified Reynolds equation is obtained using the micropolar lubrication theory. Applying the first order perturbation of the film thickness and steady state film pressure, the dynamic characteristics in terms of the components of stiffness and damping coefficients, critical mass parameter and whirl ratio are obtained with respect to the micropolar property for varying eccentricity ratios and slenderness ratios. The results show that micropolar fluid exhibits better stability in comparison with Newtonian fluid.     

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.     

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.     

Approximate closed‐form solution for the dynamical analysis of short bearings with couple stress fluid

The film forces in journal bearings may cause self‐exciting oscillations under particular operating conditions; if the amplitude of these oil‐whirl oscillations becomes too large, it may involve unsafe machinery dynamics. Thus, there is a need to understand the dynamic characteristics of the journal bearings evaluating the performances of the couple stress lubricants used to minimise the friction losses in steady operating conditions. The purpose of this paper was to illustrate a method to formulate with closed‐form solutions the non‐steady fluid film forces, and the stiffness and damping coefficients for ‘short’ liquid‐lubricated couple stress journal bearings, assuming the micro‐continuum Stokes' model. It is shown that the model allows the advantage of minimising the computational time required for the non‐linear dynamic analysis of couple stress journal bearings without any significant loss of accuracy, while the analytical form of the solution involves a better readability of the parameter effects on the system unsteady behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of Noncircular Hole-Entry Capillary-Compensated Hybrid Journal Bearing with Micropolar Lubrication

This article presents the analysis of a two-lobe hole-entry hybrid journal bearing operating with micropolar lubrication. The modified Reynolds equation governing the laminar flow of isoviscous, incompressible micropolar lubricant in the clearance space of a journal bearing system has been solved using a finite element model incorporating appropriate boundary conditions. A comparative analysis between circular and noncircular two-lobe hybrid journal bearings with capillary restrictor under Newtonian and micropolar lubrication has been presented. It is concluded that bearing performance characteristics are significantly influenced by micropolar lubrication.     

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.     

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.     

计入轴瓦弹性的应力偶流体润滑分析

推导了计入轴瓦弹性的应力偶流体润滑轴承的变形雷诺方程。数值分析表明,刚性轴瓦的最大油膜压力值比弹性轴瓦的最大油膜压力值大,且随着应力偶参数的增大,最大油膜压力提高明显;润滑油分别为牛顿流体和应力偶流体时,弹性系数越大轴承的承载力越小,应力偶参数越大轴承的承载力越大,且轴承的偏心率越大,应力偶参数对承载力的影响越明显,应力偶参数对刚性轴瓦材料的影响比对弹性轴瓦材料的影响大。     

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.     

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.     

Influence of lubricants on the performance of journal bearings – a review

ABSTRACT

The lubricant properties have a significant influence on the static and dynamic performance characteristics of journal bearing such as load-carrying capability, minimum fluid film thickness, maximum pressure, lubricant flow rate, damping coefficients, stiffness coefficients, etc. The present document reviews the behaviour of various lubricants such as power-law lubricants, couple stress lubricants, micropolar lubricants, ionic liquid lubricants and space lubricants. The influence of these lubricants on the performance of hydrostatic, hydrodynamic and hybrid journal bearings is discussed. An effort is made to develop the understanding to choose the suitable lubricant for journal bearings for different journal bearing configurations. Journal bearings operated with non-Newtonian lubricants have shown better performance compared to Newtonian lubricants. Ionic liquid lubricants have shown high potential in vacuum applications and extreme temperature environment such as in bearings of spacecraft moving mechanical assemblies.     

Theoretical characteristics of hydrodynamic journal bearings lubricated with soybean‐based oil

Vegetable‐based oils are not only biodegradable but also environmentally advantageous, and the range of lubrication applications offered by them continues to grow. Recently, vegetable‐based oils have been combined with synthetic esters to produce modified vegetable‐based oils. This paper presents an investigation of the theoretical characteristics of hydrodynamic journal bearings lubricated with non‐Newtonian soybean‐based oil. The soybean‐based oil was mixed with synthetic esters and silicone oil. The relationship between the shear stress and shear strain rate of the oil was obtained experimentally. The time‐dependent modified Reynolds equation including non‐Newtonian effects was formulated for short circular journal bearings. The perturbation technique was applied to the Reynolds equation to obtain zero‐ and first‐order pressure equations. The finite difference method was used to calculate the pressure distribution numerically. The static and dynamic characteristics, such as pressure distribution, Sommerfeld number, attitude angle, and spring and damping coefficients, were obtained numerically. It was found that the nonlinear factors of the non‐Newtonian soybean‐based oil strongly affected the performance characteristics of the journal bearings.     

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.     

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.