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.     

Analysis of viscosity interaction on the misaligned conical–cylindrical bearing

Viscosity is an essential property in hydrodynamic lubrication. In general, the lubricant is not considered to have uniform viscosity within a given bearing. The viscosity of the lubricant is affected by both pressure and temperature. The viscosity of the lubricant increases with pressure and for most lubricants, this effect is much larger than that of temperature or shear when the pressure is significantly above than the atmospheric pressure. This study analyzes the thermal effect of conical–cylindrical bearing performance parameters via the viscosity–pressure–temperature relationships of lubricants. The results reveal that pressure increases both the film viscosity and temperature as well.     

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.     

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.     

On the steady-state performance of misaligned hydrodynamic journal bearings lubricated with micropolar fluids

The present work deals with the micropolar lubrication theory to the problem of the steady-state characteristics of hydrodynamic journal bearings considering two types of misalignment, e.g. axial (vertical displacement) and twisting (horizontal displacement). Using a finite difference method, the steady-state film pressures are obtained by solving modified Reynolds equation based on the micropolar lubrication theory. With the help of the steady-state film pressures, the steady-state performance characteristics in terms of load-carrying capacity, misalignment moment and friction parameter of a journal bearing are obtained at various values of eccentricity ratio, degree of misalignment and micropolar fluid characteristic parameters viz. coupling number and non-dimensional characteristic length.     

The effect solid particle lubricant contamination on the dynamic behavior of compliant journal bearings

The proposed work concerns a theoretical and numerical investigation of the effect of solid particle contamination of lubricant oils on the static and dynamic characteristics of a finite length compliant journal bearing operating under isothermal conditions with laminar flow. In the present investigation, we use simple models based on the Einstein's mixture theory, which is characterized by the presence of suspended rigid particles in a fluid. Using the classical assumptions of lubrication, a Reynolds equation is derived and solved numerically by the finite difference method. The displacement field at the fluid film bearing liner interface due to pressure forces is determined using the elastic thin layer model. The results obtained show that the presence of suspended rigid particles in the lubricating oil (solid contamination) has significant effects on the hydrodynamic performance characteristics such as the pressure field, friction force, flow rate, elastic surface deformation as well as stability maps of the rotor‐bearing system (critical mass and whirl frequency) especially at high volumetric concentration.     

Thermal effects in cylindrical journal bearings of high‐speed gearboxes

The high rotational speeds and loads of gears operating in acceleration gearboxes causes problems related to the correct choice and design of journal or rolling bearings. In the case of journal bearings, these problems are connected with thermoelastohydrodynamic lubrication theory and the dynamics of the bearing system. However, of major importance is the problem of thermal effects in journal bearings. This has been considered for bearings used in a double‐helical gearbox with the pinion and output shaft operating in cylindrical journal bearings. The oil film pressure, temperature, viscosity distributions, and maximum and mean oil film temperatures have been determined. In calculations, laminar adiabatic and turbulent adiabatic models of oil films have been applied. The results of the calculations can be used in the design of cylindrical or other types of journal bearing in rotating machinery, including acceleration or reduction gearboxes.     

Transient thermo‐elastohydrodynamic lubrication of gear teeth

During a gear mesh cycle, load, rolling and sliding velocities, curvature, and temperature change rapidly. In this paper, a transient, thermo‐elastohydrodynamic lubrication model is presented that has been used to study the lubrication parameters at 250 contact points along the path of a contact. The working flanks were assumed to be smooth. The line load was calculated at every contact point, using the finite‐element method. Dynamic loading was not considered. The steady‐state temperature field of the working flanks was used to obtain the surface temperature at the inlet of each contact point, determined by an experimental‐analytical method presented previously. In this model, the lubricant is considered to follow the Ree‐Eyring constitutive equation. The influences of both pressure and temperature on density, thermal conductivity, and specific heat of the lubricant are also taken into account. Results are presented for an FZG type A gear pair lubricated with an FVA No. 4 reference oil; these include film shape, pressure and temperature distributions, as well as friction coefficient.     

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.     

Coupled couple stress and surface roughness effects on elasto‐hydrodynamic contact

This paper deals with the combined effects of couple stress and surface roughness to inspect the elasto‐hydrodynamic performance of slider bearing systems. On the basis of the couple stress Stokes theory and homogenisation method, the homogenised generalised Reynolds equation including the slider bearing stationary surface deformation is derived. The total deformation include the deformation of smooth surface, taken into account by the elastic thin layer model, and the deformation of roughness corresponding to a sinusoidal normal displacement on an elastic half space of identical wavelength. The governing equations are discretised by the finite difference method, and the obtained algebraic equations are solved using the iterative overrelaxation Gauss–Seidel technique. The load‐carrying capacity and friction coefficient are presented for transverse, longitudinal and anisotropic roughness patterns for different values of the couple stress parameter in both rigid and deformable cases. The simulation results indicate that the interaction between couple stress, surface roughness and elastic deformation effects is significant. Copyright © 2013 John Wiley & Sons, Ltd.     

Theoretical investigation of transient elastohydrodynamic lubrication with newtonian solid–liquid lubricants

This paper reports a theoretical investigation of transient elastohydrodynamic lubrication of a line contact. A time‐dependent Reynolds equation and elasticity equations for compressible solid–liquid lubricants were solved using finite volume and multigrid techniques. The lubricants used were mineral oils mixed with very small solid particles, MoS2 and PTFE which can be treated as Newtonian fluids. The two surfaces were initially at rest and in contact. The transient oil film pressure and oil film thickness were calculated numerically. This simulation showed the significant effects of solid particles on the lubrication characteristics. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

液体动压径向滑动轴承润滑状态的可靠性分析

文章分析了影响轴承液体润滑状态,可靠性因素,提出了用预测相对间隙变异系数的方法确定轴承直径间隙和制造公差,从而保证轴承润滑状态达到预期的可靠度要求。     

On the effective length of the top piston ring involved in hydrodynamic lubrication

This paper describes a simple analytical model for top piston ring lubrication. The model is constructed using the open‐end boundary condition hypothesis, with an assumption of minimum hydrodynamic pressure in the effective ring length equal to the saturation pressure. The analysis confirms that not all of the ring length is involved in the case of hydrodynamic lubrication, and the effective length is found to be less than 40–50% under some operating conditions. The results are in agreement with previous investigations.     

Micropolar lubricant effects on the performance of noncircular lobed bearings

The noncircular bearing configurations considered for the present study are two, three and four-lobe bearings lubricated with micropolar fluids. The modified Reynolds equation is obtained based on the theory of micropolar fluids and solving it by using finite element method, the steady state film pressures are obtained. Then the effects of the size of material characteristic length and the coupling number on the static performance are investigated. The results show that micropolar lubricants can produce significant enhancement in the static performance characteristics. The effects are more pronounced at larger coupling numbers. The trend of effects depends on the bearing configurations.     

Load‐carrying capacity of lubricated and dry sliding elements

The factors influencing the load‐carrying capacity of tribological contacts are reviewed. The load‐carrying capacity depends in part on the lubrication regime, and hydrodynamic, hydrostatic, and elastohydrodynamic lubrication are discussed. In some circumstances, lubrication is not possible. The parameters of dry rubbing are described, and approaches to the design and operation of dry bearings are discussed, particularly the choice of suitable non‐metallic materials for use in the wear couple.     

Linear stability performance analysis of finite hydrostatic porous journal bearings under the coupled stress lubrication with the additives effects into pores

A theoretical investigation into the stability performance characteristics of a finite externally pressurized porous journal bearing has been undertaken with the slip flow of coupled stress fluid. The analysis deals with the modified Darcy-type equation incorporating the additive effect in the porous bush. A modified form of Reynolds equation is obtained using Stokes micro-continuum theory of coupled stress fluids as lubricant. Applying the first-order perturbation of the film thickness and steady-state film pressure, the stability parameters are obtained under various parametric conditions. The results reveal that stability deteriorates with increase in coupled stress parameter for a value of percolation factor under full slip condition.     

Pressure distribution in small hydrodynamic journal bearings considering cavitation: a numerical approach based on the open‐source CFD code OpenFOAM®

Hydrodynamic journal bearings are traditionally designed using the half‐Sommerfeld theory. This consists in a semi‐analytical solution of the continuity and momentum conservation equations substituting negative pressures with the ambient pressure. This hypothesis provides acceptable results, but a better understanding of the phenomena considering the effective pressure distribution including 3D and cavitation effects can be achieved only by using numerical methods. For this reason, some different solvers and cavitation models were applied to different geometries for which literature provides experimental data. Once the numerical model was validated, a parametric analysis was performed in order to better understand the influence of the rotational speed and the relative eccentricity on the attitude angle, the reaction forces, the pressure distribution and the power losses of a small journal bearing. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings with couple stress fluids

This paper presents the theoretical study of the effect of surface roughness on the hydrodynamic lubrication of porous step-slider bearings. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The generalized average Reynolds-type equation is derived for the rough porous step-slider bearing lubricated with Stokes couple stress fluid. The closed-form expressions for the mean load carrying capacity, frictional force and the coefficient of friction are obtained. The performance of the rough porous step-slider bearing is compared with a corresponding smooth porous step-slider bearing. The numerical computations of the results show that the negatively skewed surface roughness pattern increases the load carrying capacity and decreases the coefficient of friction whereas the adverse effects were found for the positively skewed surface roughness pattern.