Modified Reynolds Equation Research Articles

Non-Newtonian fluids effects on the steady-state performance of two-lobe journal bearings

This research aims to investigate the behavior of non-Newtonian fluid obeying the power law model in a laminar flow regime for a two-lobe journal bearing. The investigation involves calculating the static characteristics in terms; of load-carrying capacity, attitude angle, friction coefficient, friction force, and side leakage, for various values of the power law index and different eccentricity ratios. To determine the static characteristics, the pressure distributions are obtained by the numerical solution of the modified Reynolds equation considering the effect of non-Newtonian behavior of the fluids using the finite difference method. This study reveals that increasing both the eccentricity ratio and power law index produce an increase in the load-carrying capacity, friction force, and side leakage while lead to a decrease in the attitude angle and friction coefficient for the two-lobe journal bearing. In addition, compared to Newtonian fluid the results show that the using of non-Newtonian fluids as lubricants improves the static characteristics of the two-lobe journal bearing especially for the shear-thickening lubricants.

Effect of lubricant inertia on textured journal bearing implementing mass conserving (JFO) boundary conditions

Purpose Cavitation plays a significant role in the performance of textured journal bearings. Furthermore, because of the usage of low-viscosity lubricants and the high working speed of machines, it is pertinent to consider the lubricant inertia while analyzing the operating characteristics of bearings. This paper aims to investigate the influence of lubricant inertia in the case of a spherically textured journal bearing, considering both protrusion and dimple texturing and implementing the mass-conserving (JFO) boundary conditions. Design/methodology/approach A novel modified Reynolds equation has been developed to accommodate the effects of lubricant inertia and cavitation. The cavitation is treated by using mass-conserving (Jakobsson−Floberg−Olsson [JFO]) boundary conditions. The governing equation is solved by the Gauss−Seidel method with successive over-relaxation. To enhance computational efficiency and expedite the convergence process, the progressive mesh densification (PMD) method has been integrated into the solution process. Findings The current study indicates that the JFO boundary conditions result in higher load-carrying capacity and lesser friction variables for heavily loaded bearings, whereas the flow coefficient is reduced due to the application of JFO boundary conditions. The lubricant inertia effect enhances the flow coefficients for lightly loaded and protrusion-textured bearings. Originality/value It is crucial to understand the combined effects of lubricant inertia and cavitation for the effective design of textured journal bearings. The findings from this work will help in designing textured journal bearings more effectively and accurately, particularly when low-viscosity oil is used. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2024-0276/

Theoretical analysis of effect of MHD, couple stress and slip velocity on squeeze film lubrication of rough Triangular plates

In this study, Christensen's stochastic theory is utilized on rough surfaces' hydrodynamic lubricating effect to examine how surface roughness, couple stress fluid, slip velocity, magnetohydrodynamic (MHD), and the triangular surface interact. Modified Reynolds equation is derived analytically using combining theories of Stokes couple stresses, Lorentz forces, and Christensen's stochastic hypothesis about hydrodynamic lubrication. Pressure, load carrying capacity and squeeze film time expression is derived mathematically using Reynolds equation that accounts for surface roughness and coupling stress. For various parameters including rough parameter, slip velocity, Hartmann number, and couple stress, the lubricating characteristics are analysed graphically. Squeeze film time, load carrying capacity, and pressure are enhanced by an increase in slip velocity, couplestress and magnetic field. The lubrication characteristics decreases (increases) on squeeze film pressure, load carrying capacity and squeeze film time through increasing values of the longitudinal (transverse) roughness parameter.

Study of MHD on porous flat and curved circular plate lubricated with couple stress fluid-a slip velocity model

The current study achieved to explore novel of curved circular and porous flat plate under the existence of MHD and slip velocity. The gap between the plates is filled with conducting non-Newtonian lubricant as a couple stress fluids. We considered the phenomena of Darcy law is account for porous medium and Stokes theory is used to incorporate to couple stress effects. The effect of MHD slip velocity and couple stress lubricant is studied. 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 Reynolds equation is solved we obtain the derivation of non-dimensional pressure distribution, load carrying capacity and squeeze film time. Employing the Simpsons 1/3rd rule for numerical analysis in Mathematica tool and Origin Software to illustrate the behavior of pressure profile, load carrying capacity and squeeze film time in effect of Harmann number, couple stress parameter, slip velocity and permeability parameter. 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 and slip velocity are present. But reverse effect due to upsurge of permeability parameter.

Influence of magneto-hydrodynamic and couple stress squeeze film lubrication on conical bearing-a slip velocity model

This paper explores the impact of MHD couple stress and slip velocity over a conical bearing in the presence of magnetic field. The flow is considered as incompressible. A uniform magnetic field is imposed perpendicular to the bearing alongy-axis. The modified Reynolds equation is solved using appropriate boundary conditions in dimensionless form to find the pressure distribution which is then used to obtain the expression for load carrying capacity paving the way for the calculation of response time. Numerical computations of the results show that the MHD couple stress on the conical bearings indicates that enhances the pressure distribution, load carrying capacity and squeeze film time of the conical bearings. Further, decrease in these characteristics was observed for the increased values of slip velocity and cone angle.

Tilt effect on squeeze-film damping in electrostatic micro-actuators

In this study, we theoretically explore the impact of tilt on the switching dynamics of a MEMS device operated by a pair of electrostatic actuators and subject to pronounced squeeze-film damping in the transition and free molecular flow regimes. Our investigation reveals that inducing tilt, achieved through the application of uneven voltages on the electrodes, introduces additional source terms in the modified Reynolds equation governing the pressure distribution in the squeeze-film gap. These added terms result in an accelerated decay of the squeeze film force, facilitating faster device switching between the initial and target configurations.To analyze the device dynamics, we develop a coupled numerical model and employ evolutionary multi-objective optimization to determine an optimal actuation scheme. This optimization is carried out for scenarios where initially different voltages are applied to the electrodes during a certain pre-defined time interval before transitioning to the steady voltage corresponding to the target gap size at equilibrium. Our findings highlight that the suggested actuation strategy leads to substantial improvements in the switching time of the device. Furthermore, we provide insights into the conditions favoring tilt actuation over parallel-motion actuation where the initially applied voltages are equal.

Combined Effect of Surface Irregularities and Applied Voltage on the Behavior of Hole-Entry Spherical Hybrid Journal Bearings Lubricated with an Electro-Rheological Fluid

Abstract Surface irregularities substantially affect the performance of tribological systems. The influence of three-dimensional surface irregularities has been investigated on the behavior of hole-entry spherical hybrid journal bearings. Recently, smart fluids have been employed in several applications to improve their performance. The interactive effect of electro-rheological (ER) fluid and surface irregularities have also been studied. The modified Reynolds equation and restrictor flow equation have been solved using the finite element technique with appropriate boundary conditions. The results show that consideration of surface irregularities on bearing surface enhances bearing stability. Spherical hybrid journal bearings lubricated by ER fluid increase minimum fluid film thickness and minimize the possibility of metal-to-metal contact. It is found that the combined effect of surface irregularities and ER fluid significantly improved the bearing performance parameters than individual behavior. The bearing designer is anticipated to benefit from the current model.

Controlling stick–slip in low-speed motion with a lifting force of magnetic fluid

Stick–slip is a standard friction-induced self-excited vibration that usually occurs in the boundary or mixed lubrication regimes. Broadening of the hydrodynamic lubrication regime is conducive to suppressing stick–slip motion. In this paper, the load carrying capacity of a magnetic fluid (MF) film in the presence of a magnetic field is derived based on the modified Reynolds equation. An additional lifting force produced by MF under the magnet was applied between the tribopairs to achieve the full fluid lubrication. Thus, the stick–slip is expected to be inhibited in a lower speed scope. The effect of magnet thickness on the lifting force is investigated experimentally and theoretically. Special attention is given to the influence of the lifting force on the friction and the critical transition speed of the hydrodynamic lubrication regime. Results demonstrate that the lifting force increases with the increment of the magnet thickness. The presence of the additional lifting force expands the hydrodynamic lubrication and makes the critical transition speed move left, as shown by the friction transitions on the Stribeck curve. Therefore, stick–slip motion can be suppressed at a lower sliding speed. Such beneficial effects are more pronounced in thicker magnets. It can be confirmed that, so long as the lifting force is higher than the normal load, the friction will invariably operate in the full film lubrication and the stick-slip motion may be eliminated theoretically.

Design of herringbone grooved thrust bearing for locomotive turbocharger rotor

The herringbone texture exhibited excellent tribological performance to minimize friction and wear. However, the application of this texture in the development of grooved thrust bearings is limited. Therefore, in this study, an attempt was made to design an oil-lubricated herringbone grooved thrust bearing for high-speed locomotive turbochargers. The designed bearing accommodates the axial load generated due to the pressure difference between the turbine and compressor wheel. The bearing design starts with applying Newton’s second law to predict the thrust load acting on the locomotive turbocharger rotor. The thrust load is calculated analytically and is found to be 4.54 kN for a design rotor speed of 1,00,000 rpm. Further, the herringbone grooved thrust bearing has been modeled numerically using non-linear Reynolds equation. The modified Reynolds equation is discretized using the finite volume method (FVM) and solved by successive over-relaxation (SOR) methodology to determine the static characteristics over the bearing surface. The developed HGTB is found to have a suitable load-carrying capacity of 4.6 kN, frictional torque of 0.25 N.m, and power loss of 2.98 kW. Further, a parametric analysis has been carried out to study the influence of design parameters such as the number of grooves, helix angle, angular groove width, groove depth, and speed on load-carrying capacity, frictional torque, and power loss.

Numerical Investigation of Short Bearing Lubricated with Copper Oxide Nanolubricants

Performance of short hydrodynamic journal bearing lubricated with Copper oxide (CuO) nanoparticle suspensions in base oil (nanolubricants) is investigated numerically. Dimensionless pressure, load carrying capacity and friction parameter are calculated by numerical solution of the modified Reynolds equation by means of finite difference method. The particular values of couple stress parameter for nanolubricants are evaluated and used for finding pressure distribution. Modified Krieger Dougherty equation is used to predict the viscosity of nanolubricant. Two short bearing configurations with aspect ratio 0.25 and 0.5 are analyzed by evaluating the pressure profile, load carrying capacity and friction parameter. The comparative results between plain lubricants and nanolubricants are presented. The results reveal improved pressure and load carrying capacity accompanied by decrease in friction parameter of short bearing. The shorter bearing configuration with aspect ratio of 0.25 shows better results than the others.

On the static performance of aerostatic elements

Porous aerostatic bearings and seals offer several advantages in precision engineering applications. The static performance of aerostatic elements, i.e., bearings and seals, is investigated both experimentally and numerically. This study presents a method, a test setup, and a measurement of the air gap pressure distribution with high spatial and temporal resolution. This study presents experimental and numerical results of the load capacity, air gap height, static stiffness, air consumption, and air gap pressure distribution. The experimental results are compared to a numerical model based on the modified Reynolds equation. Furthermore, boundaries for the operating parameter space of the investigated seal are determined by stiffness and leakage. The experimental results and the numerical model showed good correlation, providing corroborative evidence for the accuracy of the measurement setup and the feasibility of the pressure measurement method.

Effect of textured shapes on slot entry hybrid conical journal bearing with ER lubricant behavior

This article investigates the influence of textured shapes and electrorheological fluid (ERF) behavior on slot entry hybrid conical journal bearing system (HCJBs). The slot entry restrictor is used as a compensating element to supply the lubricant in the clearance space. Spherical, rectangular, and triangular textured shapes over the surface of conical bearings have been employed. Furthermore, the intelligent properties of ERF on the behavior of textured slot entry HCJBs have been analyzed. The finite element method (FEM) and the successive iteration-based Gauss-Seidel method have been used to solve the modified Reynolds equation. The results drawn from this study show different influences on the bearing performance for different textured shapes. Using textured surfaces and ERF improves the minimum fluid film thickness, stability, and bearing stiffness compared to the non-textured bearing.

ELASTOHYDRODYNAMIC EFFECTS IN LUBRICATION OF JOURNAL BEARINGS UNDER TURBULENT CONDITIONS

The current paper is aimed to investigate the deformability effects of the bearing surface on the lubrication performance of cylindrical journal bearing with finite length under turbulent conditions. The bush is coated with a thin resilient layer with a smooth surface, the radial distortions of which are of the same order of magnitude as the film thickness. The elastohydrodynamic problem is studied under elasticity conditions in accordance with the plain strain hypothesis (Winkler model). The modified Reynolds equation is carried out on the base of the turbulent lubrication model of Hirs (bulk flow model). The partial differential equation is solved numerically by successive over-relaxation technique on a finite difference grid, considering different values of coating materials, lubricant viscosity, and journal speed. Results for the performance characteristics of the bearing are given for several selected values of Reynolds number and elasticity parameters of the soft liner on the bush.

Analysis of turbulent cavitation effects on water-lubricated bearing in single screw compressors

PurposeTo guide the stable radius clearance choice of water-lubricated bearings for single screw compressors, this paper aims to analyze the effects of turbulence and cavitation on bearing performance under two conditions of specified external load and radius clearance.Design/methodology/approachA modified Reynolds equation considering turbulence and cavitation is adopted, based on the Jakobsson–Floberg–Olsson boundary condition, Ng–Pan model and turbulent factors. The equation is solved using the finite difference method and successive over-relaxation method to investigate the bearing performance.FindingsThe turbulent effect can increase the hydrodynamic pressure and cavitation. In addition, the turbulent effect can lead to an increase in the equilibrium radius clearance. The turbulent region exhibits a higher load capacity and cavitation rate. However, the increased cavitation negatively impacts the frictional coefficient and end flow rate. The impact of turbulence increases as the radius clearance decreases. As the rotating speed increases, the turbulence effect has a greater impact on the bearing characteristics.Originality/valueThe research can provide theoretical support for the design of water-lubricated journal bearings used in high-speed water-lubricated single screw compressors.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-01-2024-0029/

Effect of texture parameters on the lubrication performance of static and dynamic pressure thrust bearings and multi-objective optimization

PurposeThis paper aims to study the influence of cylindrical texture parameters on the lubrication performance of static and dynamic pressure thrust bearings (hereinafter referred to as thrust bearings) and to optimize their lubrication performance using multiobjective optimization.Design/methodology/approachThe influence of texture parameters on the lubrication performance of thrust bearings was studied based on the modified Reynolds equation. The objective functions are predicted through the BP neural network, and the texture parameters were optimized using the improved multiobjective ant lion algorithm (MOALA).FindingsCompared with smooth surface, the introduction of texture can improve the lubrication properties. Under the optimization of the improved algorithm, when the texture diameter, depth, spacing and number are approximately 0.2 mm, 0.5 mm, 5 mm and 34, respectively, the loading capacity is increased by around 27.7% and the temperature is reduced by around 1.55°C.Originality/valueThis paper studies the effect of texture parameters on the lubrication properties of thrust bearings based on the modified Reynolds equation and performs multiobjective optimization through an improved MOALA.

Experimental and numerical analysis of flow through a natural rough fracture subject to normal loading

Fractured crystalline rocks have been chosen or are under consideration by several countries as host rock formations for deep geological repositories for spent nuclear fuel. In such geological formations, flow and solute transport are mostly controlled by a network of connected natural fractures, each of them being characterised by internal heterogeneity, also denoted as roughness. Fractures are, in turn, subject to variable load caused by various factors, such as the presence of thick ice sheets formed during glaciation periods. Understanding how coupled hydro-mechanical (HM) processes affect flow and transport at the scale of a single natural fracture is crucial for a robust parameterisation of large-scale discrete fracture network models, which are not only used for nuclear waste disposal applications but are also of interest to problems related to geothermics, oil and gas production or groundwater remediation. In this work, we analyse and model an HM experiment carried out in a single natural fracture and use the results of both, the experimental and the modelling work, to get insights into fundamental questions such as the applicability of local cubic law or the effect of normal load on channeling. The initial fracture aperture was obtained from laser scanning of the two fracture surfaces and an equivalent initial aperture was then defined by moving the two fracture surfaces together and comparing the results obtained using a Navier–Stokes based computational fluid dynamics (CFD) model with the experimental flowrate obtained for unloaded conditions. The mechanical effect of the different loading stages was simulated using a high-resolution contact model. The different computed fracture apertures were then used to run groundwater flow simulations using a modified Reynolds equation. The results show that, without correction, local cubic law largely overestimates flowrates. Instead, we show that by explicitly acknowledging the difference between the mechanical aperture and the hydraulic aperture and setting the latter equal to 1/5 of the former, cubic law provides a very reasonable approximation of the experimental flowrates over the entire loading cycle. A positive correlation between fluid flow channeling and normal load is also found.

Modified Reynolds Equation for Thin Film Lubrication with Arbitrarily Enhanced Viscosity Surface Layers and Lubrication Analysis of Micro-Tapered Pad Bearing

Modified Reynolds Equation for Thin Film Lubrication with Arbitrarily Enhanced Viscosity Surface Layers and Lubrication Analysis of Micro-Tapered Pad Bearing

Effect of magnetic field and slip velocity on the performance of bearings lubricated by couple stress fluid on long cylinder and infinite plate — A theoretical analysis

In this research, the combined effect of magnetohydrodynamics (MHD) and slip velocity on squeeze film lubrication of long cylinders and infinite plates with couple stress fluid has been studied. Combining the Stokes couple stress theory and the Lorentz force theory yields analytical solutions for the modified Reynolds equation. Using the Reynolds equation, the mathematical expressions for squeeze film pressure, load-carrying capacity and squeeze film time are obtained. The pressure, load carrying capacity and squeeze film time increase with the combined effect of MHD, couple stress fluids and slip velocity.

Numerical Modeling and Simulation of a Poroelastic Journal Bearing Lubricated By Nanofluids with Couple-Stresses

In this paper we present a numerical simulation of a porous journal bearing considering the fluid film – poroelastic matrix interaction and the non-Newtonian rheological behavior of nanolubricant consisting of base fluid and nanoparticles (NPs). The flow of nanolubricant in the bearing clearance space is described by the Vijay Kumar Stokes micro-continuum theory which considers the characteristic size of nanoparticles such as fullerenes dispersed in a base oil. The flow of the nanolubricant in the porous medium is modeled by the modified Darcy’s law where the Beavers–Joseph slip conditions are applied at the fluid film-porous matrix interface. The deformation of the fluid-film porous matrix interface due to hydrodynamic pressure is calculated by using a simplified analytical thin elastic liner model. The hydrodynamic behavior of lubricating film is governed by the modified Reynolds equation obtained from the momentum, moment of momentum, and mass conservation laws using the classical Reynolds derivation process. The bearing porosity is introduced into the governing modified Reynolds equation by means of the Morgan-Cameron approximation. The steady-state analysis shows that for an imposed operating eccentricity, the load capacity increases with the characteristic size and the concentration of NPs while the attitude angle, the leakage flow rate, and the coefficient of friction decrease. On the other hand, the permeability decreases the hydrodynamic pressure, the load capacity, and the leakage flow rate, and increases the attitude angle and the coefficient of friction.

Performance of rough secant slider bearing lubricated with couple stress fluid in the presence of magnetic field

The effect of surface roughness, magnetic field, and couple stress on the performance of secant slider bearing is studied in this paper. The effectiveness of the bearing is assessed by using a couple stress liquid as the lubricant in the process. Because of microstructural impacts, couple stress fluids have distinctive rheological characteristics. These features have the potential to make a major impact on the bearing’s performance. The novel aspect of this study is that the roughness of the secant slider is taken into consideration. The modified Reynolds equation is derived using Christensen’s stochastic theory for roughness. Here, both transverse and longitudinal roughness patterns are considered. The analytical solutions are obtained for steady-state pressure, load-carrying capacity, film stiffness, and damping coefficient. The results are presented for various parameters through graphs and tables. The combined effect of the magnetic field and couple stress is significant on bearing characteristics. It is noticed that the bearing features increase with the longitudinal roughness parameter, and the reverse phenomenon is observed with the transverse roughness parameter. When a transverse roughness pattern is assumed on a secant slider bearing, characteristics like pressure, load, stiffness of the film, and damping coefficient increase significantly.