Modified Reynolds Equation Research Articles

Experimental and numerical studies of positive texture effect on friction reduction of sliding contact under mixed lubrication

Textured surfaces have been remarkable in improving the frictional performance of sliding contacts, particularly at instances such as boundary or mixed lubrication regimes. This article reports the results of an experimental and numerical study carried out by introducing surface textures in the form of protrusions to investigate its effects on friction performance under a mixed lubrication regime. The surface textures produced by the chemical etching process are tested on the pin on disc test rig by varying area density and height of the texture. In numerical simulation, the modified Reynolds equation (Patir–Cheng flow model) and asperity contact model (Greenwood–Tripp model) are solved for hydrodynamic and asperity pressures, respectively. The results indicate that the experimental measurements are qualitatively in good agreement with numerical predictions. Furthermore, the simulations are performed for different texture shapes by varying texture area density, height, and sliding velocity. The results depict that a maximum friction reduction of 87% with elliptical textures compared to the un-textured case.

Lubricating condition evaluation of the rotary compressor under high ambient temperature

Abstract Propane has been suggested as one of the alternative working fluids for room air conditioners in hot climate areas because of its excellent environmental properties and lower discharge temperature though there still is concern about its flammability. The lubricating condition of rotor bearings system should also be emphasized because a heavier load and lower viscosity in the oil sump could impair the reliability of rotary compressor under high ambient temperature. In this study, in order to obtain the input of simulation, the dynamic pressures and viscosity of a R290 air conditioner are experimentally measured under several conditions. On these bases, lubricating characteristics are numerically simulated by coupling the dynamics equation of crank shaft and the modified Reynolds equation of oil film using finite element method. The results show that the load on crank under 50 °C is twice as large as that of 30 °C while the viscosity of bottom oil sump decreases from 1.89 to 1.59 mPa⋅s. Simulation results imply that the minimum oil film thickness decreased to 0.44 µm under 50 °C, in which asperity contact force peaks at 3 N when arithmetic mean roughness is 0.2 µm. Asperity contact force would significantly increase to 174 N if surface roughness is 0.6 µm and boundary lubrication regime is reached. Strategies to increase oil sump viscosity is recommended to avoid adhesive wear in this case.

Numerical Optimization of Surface Texture for Hydrophobic Textured Slider Bearing

To reduce a significant energy waste in industry due to the friction and wear in mechanical components, there is an increasing demand for durable thrust bearing under extreme operational conditions. Surface texturing, combined with the application of hydrophobic material, has been proven to be an effective and economical means to enhance the tribological lubrication performance of sliding surfaces. Therefore, in the present work, an exact optimization method is presented to optimize the surface texture in terms of the texture depth for enhancing the load-carrying capacity. Furthermore, the texture shapes, including ellipse and triangle, are investigated under different arrangements of hydrophobic materials. The lubrication characteristics are established by solving the modified Reynolds equation with means of finite volume method. For modeling the hydrophobic behavior, the critical shear stress model is employed to assure more real boundary conditions of bearing. The simulation results show that for any type of groove shape, the highest load-carrying capacity can be achieved under unique hydrophobic placement. The main interesting finding is the fact that the optimal texture with the groove shape of ellipse shows a better impact on the performance of slider bearing irrespective of the hydrophobic placements.

Performance of novel air foil thrust bearings with taper-groove on surface of top foil

To improve the load capacity of air foil thrust bearing, the micro taper-grooves on the surface of top foil was introduced and studied. A modified Reynolds equation considering the gas rarefaction effect was established, in which the Knudsen number was affected by the film thickness and pressure. A new bump stiffness model was built with the consideration of bump rounding, friction, and bending stiffness of foil. By considering the variation of gas film thickness, the load capacity, friction torque, and power loss of novel bearing with grooves were calculated by the finite difference method. Moreover, the effect law of groove parameters, groove shape and grooves number on the novel bearing performance was studied systematically. The results show that the predicted axial load capacity considering gas rarefaction effect is decreased slightly in smaller clearance and more consistent with the actual test data. The novel air foil thrust bearing with taper-groove can weaken the air end leakage and enhance the local dynamic pressure efficiently in the parallel portion of top foil, thus improving the static characteristics of bearing. For the novel air foil thrust bearing with taper-groove depth of 10 µm, the load capacity can be increased by about 13.33%, compared with traditional bearing. With the increments of taper-groove depth and length on top foil, the load capacity can be increased. However, the friction torque is decreased when there is a longer taper-groove in the circumferential direction. Meanwhile, the optimal groove width ratio is about 0.5, and the structure of multi-grooves is beneficial to the decreased friction torque. The validity of presented theoretical model has been verified by the literature data, and the results are expected to be helpful to bearing designers, researchers, and academicians concerned.

Modelling and analysis of slip conditions in hydrodynamic lubrication of a piston skirt-cylinder contact

Purpose After more than a century of agreement with the postulate of non-slip condition (adhesion to the wall), the study of fluid-solid boundary conditions has shown renewed interest over the past two decades. Although numerous studies have not yet been arrived to a complete description of slip phenomena, however, it appears that the influence of wetting and/or surface roughness results in a weak interaction between fluid and solid; thus, the presence of the slip phenomenon is observed at the fluid-solid interface. The purpose of this paper is to highlight the presence of the slip phenomenon at the lubricated piston skirt-cylinder contact. Design/methodology/approach For this proposal, a modified Reynolds equation and operating characteristics are determined by taking into account the slip conditions at the interface between oil-film and entire cylinder surface. Findings The findings indicate that the operating characteristics are strongly influenced when the slip conditions are taken into account at the interface between oil-film and cylinder surface. The friction force and dissipated power might be reduced to improve diesel engine performances. Originality/value Various research studies have been conducted to model the slip phenomenon in different lubricated contacts over the past two decades. However, there are no studies available concerning the piston-cylinder system. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0483/

Surface virtual texturing of the journal bearings of a three-cylinder ethanol engine

PurposeThis paper aims to numerically investigate the surface texturing effects on the main bearings of a three-cylinder ethanol engine in terms of the power loss and friction coefficient for dynamic load conditions.Design/methodology/approachThe mathematical formulation considers the Partir-Cheng modified Reynolds equation. The mass-conserving Elrod-Adams p-θ model with the JFO approach is used to deal with cavitation. A fluid-structure coupling procedure is considered for the elastohydrodynamic lubrication. Accordingly, a 3-D linear-elastic substructured finite element model obtained from Abaqus is appliedFindingsSimulations were carried out considering different dimple texture designs in terms of location, depth and radius. The results suggested that there are regions where texturing is more effective. In addition, distinct journal rotation speeds are studied and the surface texture was able to reduce friction and the power loss by 7%.Practical implicationsThe surface texturing can be a useful technique to reduce the power loss on the crankshaft bearing increasing the overall engine efficiency.Originality/valueThe surface texturing performance in a three-cylinder engine using ethanol as fuel was investigated through numerical experimentation. The results are supported by previous findings.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-09-2019-0380/

Interaction of inertia and cavitation in textured hydrodynamically lubricated bearing in very low sliding velocity considering slip

Surface texturing is becoming an effective way for increasing the performance of hydrodynamic bearings. However, introducing the texture on the lubricated sliding contact may lead to the presence of the inertia effect as well as the cavitation effect. In this study, the correlation between the inertia and the cavitation in textured bearing is investigated in terms of hydrodynamic pressure and load support. The Navier-Stokes equation based on CFD and modified Reynolds equation are applied. In addition, the use of slip condition and its effect on the performance of bearing is of particular interest. The simulations are conducted in very low sliding velocity to address the low inertia effect. The result shows that increasing inertia effect can increase the load support, but the cavitation effects is not found in the bearing pattern in which the inertia is not significant. The other interesting result concludes that slip reduces the load support, but on the other hand slip also increases the load support depending on the texture length.

Simulating tribological characteristics of Palm Methyl Ester (PME) lubricated contact

The study simulates the lubricant Stribeck curve for Palm Methyl Ester (PME) by coupling modified Reynolds solution with Greenwood and Tripp’s rough surface contact model. The predicted lubricant Stribeck curves for PME is validated with measured data from a pin-on-disc tribometer. The Reynolds equation is modified to accommodate for the lubricant properties of PME (e.g. viscosity and density), which is mathematically described using Gibbs energy additivity approach. Solving the modified Reynolds equation would then provide the fluid film formation behaviour of PME, such as the contact pressure and film thickness. These fluid film parameters are then used as the input to determine the boundary and viscous friction of the investigated lubricated contact using Greenwood and Tripp’s rough surface contact model. The proposed mathematical solution correlates well with experimental data and is shown to be capable of predicting lubricant Stribeck, capturing the frictional behavior for the whole range of lubrication regimes. The findings of the present study prepare for a mathematical foundation to further explore the use of biodiesel as an alternative biodegradable lubricant to mineral-based ones.

The Gas Squeeze Film Characteristics of Acoustic Levitation with Various Excitation Disc Shapes Based on the Modified Reynolds Equation

In order to simulate the characteristics of acoustic levitation for freely floating states with a larger ratio between the excitation radius and film thickness, a group of governing equations including a modified Reynolds, movement, and vibration equations were derived in this article. The inertia effect was considered in the modified Reynolds equation (MRE) and compared to experimental vibration curves. The vibration curves were interpolated from the experimental data on disc modal shapes with the standing wave’s excitation. The effect of wave numbers and amplitudes on floating height and bearing capacity are discussed in this article. The results indicate that the amplitudes of the excitation disc are approximately linear with the floating height, and the larger wave number along R direction can induce not only better bearing capacity but also floating stability. It is concluded that there would be more accurate results for floating height calculated by the MRE considering inertia effects. This squeeze film model with the MRE can aid in the design of actuators.

Theoretical investigation of porous hydrostatic journal bearing under micropolar fluid lubrication

The features of micropolar fluid (a non-Newtonian fluid)–lubricated short single-layered porous hydrostatic journal bearing are analyzed theoretically by an iterative method. To investigate hydrostatic journal bearing characteristics, a modified Reynolds equation in the case of micropolar fluid is derived and solved numerically. The obtained results in this work are validated by comparing the same with previously published results with Newtonian and non-Newtonian lubricants in the form of design charts. The static stiffness and load-carrying capacity of the investigated bearing are 80% and 75% higher than conventional hydrostatic bearings. The porous hydrostatic journal bearing exhibits more economical performance as it requires 40% low flow rate and low pump power, and it generates 50% less heat in contrast with other hydrostatic bearings.

An overlapped electrical double layer model for aqueous electrolyte lubrication with asymmetric surface electric potentials

We developed an aqueous electrolyte lubrication model with asymmetric surface electric potentials using the Poisson equation with no simplification to determine electric field and using the Nernst equation to determine ionic concentrations. The site-dissociation of water was considered and modeled using equilibrium dissociation equations. Electric field strength was modeled by assuming that the streaming current balances the conduction current. An electro viscosity term was obtained in our modified Reynolds equation. Our model was validated by comparing with data from literatures and with the Debye-Hückel model and Poisson-Boltzmann model. The effects κh (κ is Debye length and h is film thickness) and surface electric potential on the electro viscosity are explored using our overlapped EDL model.

Research on Static and Dynamic Characteristics of Gas-lubricated Microbearings for Microfluidic Devices

Aerodynamic journal microbearings with microtribological phenomena significantly influence the operating stability of microfluidic devices. The modified Reynolds equations including different rarefaction models are derived and are solved by the partial derivative method and relaxation iteration algorithm. The effects of Knudsen number and bearing parameters on the static and dynamic characteristics of microbearings are investigated in detail. The results show that the rarefaction effect plays a crucial role in the ultra-thin gas film lubrication. The maximum film pressure of Fukui–Kaneko (FK) model is lowest and the result in Boltzmann model is largest in small Knudsen number regions. As the Knudsen number increases further, the curve of FK model is coincident with that of the Boltzmann model in the transition regime. The direct stiffness coefficients of Boltzmann model increase with the increase of eccentricity ratio and aspect ratio, whereas the effect of Knudsen number on the damping coefficients yields a relatively complicated trend.

Influence of magnetic field on a curved circular plate and flat plate lubricated with non-Newtonian fluid

This paper presents a Analytical study of the effect of magnetic field on the performance of flat and curved circular plate with Non-Newtonian fluids. From the Stokes theory a Modified Reynolds equation is derived. The solution for pressure, load capacity and squeeze time is obtained to study the influence of transverse magnetic field and couple stress parameter on these characteristics. The non-dimensional pressure, load and squeeze film time is computed numerically and presented graphically. The results predicts that, the effect of Hartmann number M 0 and Non-Newtonian fluid l * is improved in pressure, load carrying capacity significantly whereas delay in squeezing time as compared to the non-magnetic(NMC) and Newtonian(NC) cases.

Effects of oil film thickness and viscosity on the performance of misaligned journal bearings with couple stress lubricants

This paper investigated the performance characteristics of misaligned journal bearing lubricated using couple stress fluids. Based on micro-continuum theory, the modified Reynolds equation for couple stress lubricants was developed, in which viscosity-pressure effect was considered. By setting the critical oil film thickness, the region with couple stress effect can be recognized. The ratio of the critical oil film thickness to couple stress parameter was referred to as film thickness coefficient. It was found from results that increase of film thickness coefficient can significantly improve the maximum film pressure and high-pressure area, when film thickness coefficient was smaller than 4. Viscosity-pressure effect was capable of enhancing viscosity, friction coefficient and the maximum film pressure, and reducing couple stress parameter, especially for large misalignment angle.

Numerical investigation on the high‐speed wheel/rail adhesion under the starved interfacial contaminations with surface roughness

AbstractThis paper presents a new numerical model of wheel/rail in rolling contact to study the adhesion mechanism under the starved interfacial contaminations at high speed considering surface roughness. A thermal starved mixed elastohydrodynamic lubrication (EHL) theory is hired in the model. The empirical equations for analysing the contact force of rough surfaces that are based on amount of accurate finite element analysis (FEA) of an elastic‐plastic single‐asperity contact over a rigid flat are proposed. Multilevel method is used to solve the modified Reynolds equations, and sweeping column method is used to solve energy and heat conduction equations. The pressure field, the fractional film content, and the temperature field are obtained through the present model. In addition, the influences of train speed, surface roughness amplitudes, and inlet film thickness on the adhesion coefficient are investigated. The results from the present model have been compared with those from flooded analyses for water and oil‐contamination cases. The numerical results show that the inlet film thickness and the train speed had a significant effect on the wheel/rail adhesion ability.

Non-Newtonian couple-stress squeeze film behaviour between oscillating anisotropic porous circular discs with sealed boundary

The thrust of this paper is to investigate theoretically the non-Newtonian couple stress squeeze film behaviour between oscillating circular discs based on V. K. Stokes micro-continuum theory. The lubricant squeezed out between parallel porous and rigid facings is supposed to be a concentrated suspension which consists of small particles dispersed in a Newtonian base fluid (solvent). The effective viscosity of the suspension is determined by using the Krieger-Dougherty viscosity model for a given volume fraction of particles in the base fluid. For low frequency and amplitude of sinusoidal squeezing where cavitation as well as turbulence are unlikely, the governing equations including the modified Reynolds equation coupled with the modified Darcy's equation are derived and solved numerically using the finite difference method and a sub-relaxed iterative procedure. The slip velocity at the porous-fluid interface is directly evaluated by means of the modified Darcy's law considering laminar and isothermal squeezing flow. For a given volume fraction, the couple stress effects on the squeeze film characteristics are analyzed through the dimensionless couple stress parameterℓ˜considering sealed and unsealed boundary of the porous disc. The obtained relevant results reveal that the use of couple stress suspending fluids as lubricants and the effect of sealing the boundary of the porous matrix improves substantially the squeeze film behaviour by increasing the squeeze film force. On the other hand, side leakage flow calculated in the sealed case remains constant in comparison to that of open end (unsealed) porous disc for all values of couple stress parameter and volume fraction of particle.

Effect of journal misalignment and coupled-stress lubricant on the film pressure of a double-layered porous journal bearing

PurposeIn the application of hydrostatic double-layered porous journal bearings, misalignment of bearing systems is a major problem. On the other hand, the use of coupled-stress fluid as a lubricant is more practical in the present days. Furthermore, in case of porous bearing, neglecting slip effect and percolation effect of additives into the pores may lead to erroneous result. Hence, this paper aims to address the effect of journal misalignment and coupled-stress lubricant on the steady-state film pressure of the double-layered porous journal bearing with tangential velocity slip and percolation effect.Design/methodology/approachFirst, considering the tangential velocity slip, the most general modified Reynolds type equation has been derived for the film region and the governing equations for flow in the coarse and fine layers of porous medium, incorporating the percolation effect for a double-layered porous bearing. Here, considering the misalignment caused by shaft displacement. Film thickness expression established considering the effect of misalignment. Steady-state film pressures are obtained by solving modified Reynolds equation based on the coupled-stress lubrication theory. Effects of journal misalignment and coupled-stress lubricant on the pressure profiles in the film region are discussed and demonstrated in the graphical form.FindingsIn this paper, effects of journal misalignment and coupled-stress lubricant on the pressure profiles in the film region are obtained. In general, higher degree of misalignment gives higher steady-state pressure value in the film region, and this pressure increases due to increase in coupled-stress parameter up to a certain limit.Originality/valueTo the best of the author’s knowledge, there is no literature available, so far, that addresses the analysis of the steady-state pressure in the film region of a doubled–layered porous journal bearing under misaligned condition with coupled-stress lubricant. But in this paper all these points are included, which makes this article valuable in design purpose.

Computational investigation on the performance of hydrodynamic micro-textured journal bearing lubricated with micropolar fluid using mass-conserving numerical approach

The tribological characteristic of journal bearing systems can be enhanced with the integrating of textures in the contact interfaces, or using the lubricating effect of non-Newtonian fluids. In this study, the combined effects of bearing surface texturing and non-Newtonian lubricants behavior, using micropolar fluid model, on static characteristics of hydrodynamic circular journal bearings of finite length are highlighted. The modified Reynolds equation of micropolar lubrication theory is solved using finite differences scheme and Elrod's mass conservation algorithm, taking into account the presence of the cylindrical texture shape on full and optimum bearing surfaces. The optimization textured area is carried out through particle swarm optimization algorithm, in order to increase the load lifting capacity. Preliminary results are in good agreement with the reference ones, and present an enhancement in the performances of micro-textured journal bearings (load carrying capacity and friction). The results suggest that texturing the bearing convergent zone significantly increases the load carrying capacity and reduce friction coefficient, while fully texturing causes bad performances. It is also shown that the micropolar fluids exhibit better performances for smooth journal bearings than a Newtonian fluid depending on the size of material characteristic length and the coupling number. The combined effects of fully surface textured with micropolar fluids reduce the performance of journal bearing, especially at lower eccentricity ratios. Considering the optimal arrangement of textures on the contact surface, a significant improvement in terms of load capacity and friction can be achieved, particularly at high eccentricity ratios, high material characteristic lengths and high values of the coupling numbers of micropolar fluids.

Modified Reynolds Equations for High Viscosity Surface Layer and Thin Film Lubrication Analysis of Tapered/Tapered Land Bearings as Models of Surface Texture

Modified Reynolds Equations for High Viscosity Surface Layer and Thin Film Lubrication Analysis of Tapered/Tapered Land Bearings as Models of Surface Texture

Effect of bearing materials on journal bearings under TEHL with lubricant based on Carreau model

ABSTRACTThis work presents a transient analysis of journal bearings under thermal elastohydrodynamic lubrication (TEHL) based on the Carreau model. The effects of the elastic modulus of the bearing liner have been investigated using numerical simulations. A time-dependent modified Reynolds equation and an adiabatic energy equation based on the Carreau model have been formulated and numerically solved to examine the performance of the journal bearings. The results show that the minimum film thickness and the friction coefficient both increase with decreasing bearing liner elastic modulus. In contrast, the dimensionless load carrying capacity, dimensionless maximum film temperature, and dimensionless maximum film pressure all decrease with decreasing bearing liner elastic modulus. The stability regions tend to decrease in size for journal bearings under TEHL, especially for journal bearings composed of soft materials.