Stokes Roughness Effects on Hydrodynamic Lubrication. Part I—Comparison Between Incompressible and Compressible Lubricating Films

1986 ◽  
Vol 108 (2) ◽  
pp. 151-158 ◽  
Author(s):  
Y. Mitsuya ◽  
S. Fukui
Keyword(s):  
Carrying Capacity ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Navier Stokes ◽  
Load Carrying Capacity ◽  
Roughness Effects ◽  
Navier Stokes Equations ◽  
Large N ◽  
Significant Difference ◽  
Load Carrying

A perturbation method for the Navier-Stokes equations is presented for analyzing Stokes roughness effects on hydrodynamic lubrication in both incompressible and compressible films. The solution is obtained from direct numerical calculation by using an actual rough spacing, without applying the currently accepted assumption that the roughness height should be small. The roughness wavelength and height influences on flow rate, load carrying capacity and frictional force are clarified. Secondary quantities induced by Stokes effects are found to be proportional to wavenumber n squared for sufficiently large n values, so that the amount of the Stokes effect can be determined by the spacing to wavelength squared ratio. A significant difference between incompressible and compressible films is that Stokes roughness increases the flow resistance of and then enhances the load carrying capacity of incompressible films, while it inversely affects compressible films. The compressibility with respect to secondary pressure induced by the Stokes effects can be neglected for any compressibility number, no matter how large, as long as the local compressibility number, defined by the wavelength, is small.

Stokes Roughness Effects on Hydrodynamic Lubrication. Part II—Effects Under Slip Flow Boundary Conditions

1986 ◽  
Vol 108 (2) ◽  
pp. 159-166 ◽  
Author(s):  
Y. Mitsuya
Keyword(s):  
Flow Regime ◽  
Carrying Capacity ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Slip Flow ◽  
Load Carrying Capacity ◽  
Roughness Effects ◽  
Random Roughness ◽  
Load Carrying ◽  
Flow Effects

Stokes roughness effects on hydrodynamic lubrication are studied in the slip flow regime. Slip flow boundary conditions for Navier-Stokes equations are derived, assuming that the fluid on a surface slips due to the molecular mean free path along the surface, even if the surface is rough. The perturbation method for Navier-Stokes equations, which was derived in Part I of this report, is then applied. Slip flow effects on load carrying capacity and frictional force are numerically clarified for both Stokes and Reynolds roughnesses. In the slip flow regime, second-order quantities induced by Stokes effects, such as flow rate, load carrying capacity, and frictional force are in proportion to the wavenumber squared. This phenomenon relative to the quantities being proportional is also the same as that in the continuum flow regime. As a result of velocity slippage, the load carrying capacity in Stokes roughness is found to decrease more than in Reynolds roughness for incompressible films, while the relationship is reversed for compressible films having a high compressibility number. The simulation of random roughness, which is generated by numerical means, clarifies one important result: the average slip flow effects associated with random Stokes roughness become similar to the slip flow effects in deterministic sinusoidal Stokes roughness, whose wavelength and height are statistically equivalent to those of random roughness. Although attention should be given to the fact that Stokes effects on random roughness demonstrate considerable scattering with the continuum flow, such scattering diminishes with the slip flow.

Effects of Number of Porous Insert, Spindle Speed and Gap Thickness on Characteristics of a Partially Porous Aerostatic Journal Bearing

2015 ◽  
Vol 649 ◽  
pp. 30-37 ◽  
Author(s):  
Te Yen Huang ◽  
Shao Yu Hsu ◽  
Song Chiang Shen ◽  
Sheam Chyun Lin ◽  
Ta Hsin Chou
Keyword(s):  
Carrying Capacity ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Simple Algorithm ◽  
Navier Stokes ◽  
Coupling Scheme ◽  
Load Carrying Capacity ◽  
Navier Stokes Equations ◽  
Rotating Speed ◽  
Load Carrying

The effects of the rotating speed of the spindle, the number of the porous medium inserted into the partially porous aerostatic journal bearing and the thickness of the bearing gap on the characteristics of the bearing such as the pressure distribution, the load carrying capacity and the stiffness of the bearing were studied. Based on the finite volume method and the pressure-velocity coupling scheme of the SIMPLE algorithm with the standard k-ε turbulent model, the CFD software was used to solve the Navier-Stokes equations to calculate the pressure field in the bearing gap. The computed results revealed the faster the spindle rotated, the higher the gap pressure. As the gap thickness increased, the gap pressure, the load carrying capacity and the stiffness of the bearing decreased. The more the porous inserts, the higher the gap pressure and the load carrying capacity, but the less the bearing stiffness would be.

The Validity of the Reynolds Equation in Modeling Hydrostatic Effects in Gas Lubricated Textured Parallel Surfaces

2005 ◽  
Author(s):  
Yuri Feldman ◽  
Yuri Kligerman ◽  
Izhak Etsion ◽  
Shimon Haber
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Surface Texturing ◽  
Laser Surface Texturing ◽  
Navier Stokes ◽  
Load Carrying Capacity ◽  
Navier Stokes Equations ◽  
Load Carrying ◽  
Parallel Surfaces

The pressure distribution and load carrying capacity for a single 3D dimple, representing laser surface texturing (LST) of gas-lubricated tribological components with parallel surfaces, were obtained via two different methods of analysis: 1) a numerical solution of the exact full Navier-Stokes equations; 2) an approximate solution of the much simpler Reynolds equation. Comparison between the two solutions illustrated that the differences in load carrying capacity were negligible for clearances that are 3% or less of the dimple diameter. At larger realistic clearances the error in the load carrying capacity may reach a maximum of 10%.

Simulation of Static Performance of Air Foil Bearings Using Coupled Finite Element and Computational Fluid Dynamics Techniques

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Leonidas I. Paouris ◽  
Dimitrios A. Bompos ◽  
Pantelis G. Nikolakopoulos
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Pressure Distribution ◽  
Carrying Capacity ◽  
Stokes Equations ◽  
Element Model ◽  
Elastic Behavior ◽  
Navier Stokes ◽  
Load Carrying Capacity ◽  
Load Carrying

The main objective of the current work is to determine a relationship between the top and bump foil's geometry and load-carrying capacity in a journal compliant generation I air foil bearing, as well as determining the effect of the thermohydrodynamic phenomena in the performance of the air foil bearing (AFB). Static and steady-state operation is assumed throughout the analysis. A finite element model is adopted in order to investigate the operational characteristics of the specific bearing. Bump foil's elastic behavior is modeled using two node linear link spring elements. During the hydrodynamic analysis, incompressible viscous steady state Navier–Stokes equations are numerically solved, due to the low bearing compressibility number. During the thermohydrodynamic analysis, compressible, viscous, steady-state Navier–Stokes equations were solved, coupled with the energy equation. The material used during the structural analysis is Inconel X750, and it is assumed that it has linear and elastic behavior. Constant ambient pressure is applied at the free faces of the fluid as well as no slip condition at the surface of the fluid that faces the top foil. Computational fluid dynamics (CFD) and structural models are solved separately. At the beginning of the analysis, the CFD problem is solved with the assumption that the top foil has not yet been deformed. After the solution of the CFD problem, the pressure distribution at the surface of the fluid that faces the top foil is applied at the top foil and then the structural problem is solved. Consequently, the deflections of the top foil are applied on the corresponding surface of the CFD model and the algorithm continues until convergence is obtained. As soon as the converged solution for the pressure distribution is obtained, numerical integration is performed along the surface of the bearing in order to calculate its load-carrying capacity. Static bearing performance characteristics, such as pressure distribution, bump foil deflection, and load capacity are calculated and presented. Furthermore, fluid film thickness, top foil deflection, and fluid pressure are investigated as functions of the bearing angle as well as load-carrying capacity as a function of the bump and top foil stiffness. The same procedure is repeated for the thermohydrodynamic analysis. Moreover, in order to estimate the heat flux from the top foil to the bump foil channel as a function of the top foil temperature, a simple finite element model of the bump foil–cooling channel is constructed.

scholarly journals Two-scale homogenization of hydrodynamic lubrication in a mechanical seal with isotropic roughness based on the Elrod cavitation algorithm

2021 ◽  
pp. 135065012110176
Author(s):  
Yanxiang Han ◽  
Qingen Meng ◽  
Gregory de Boer
Keyword(s):  
Surface Topography ◽  
Carrying Capacity ◽  
Hydrodynamic Lubrication ◽  
Tribological Performance ◽  
Stribeck Curve ◽  
Polar Coordinate System ◽  
Load Carrying Capacity ◽  
Mechanical Seal ◽  
Macro Scale ◽  
Load Carrying

A two-scale homogenization method for modelling the hydrodynamic lubrication of mechanical seals with isotropic roughness was developed and presented the influence of surface topography coupled into the lubricating domain. A linearization approach was derived to link the effects of surface topography across disparate scales. Solutions were calculated in a polar coordinate system derived based on the Elrod cavitation algorithm and were determined using homogenization of periodic simulations describing the lubrication of a series of surface topographical features. Solutions obtained for the hydrodynamic lubrication regime showed that the two-scale homogenization approach agreed well with lubrication theory in the case without topography. Varying topography amplitude demonstrated that the presence of surface topography improved tribological performance for a mechanical seal in terms of increasing load-carrying capacity and reducing friction coefficient in the radial direction. A Stribeck curve analysis was conducted, which indicated that including surface topography led to an increase in load-carrying capacity and a reduction in friction. A study of macro-scale surface waviness showed that the micro-scale variations observed were smaller in magnitude but cannot be obtained without the two-scale method and cause significant changes in the tribological performance.

The Validity of the Reynolds Equation in Modeling Hydrostatic Effects in Gas Lubricated Textured Parallel Surfaces

2005 ◽  
Vol 128 (2) ◽  
pp. 345-350 ◽  
Author(s):  
Y. Feldman ◽  
Y. Kligerman ◽  
I. Etsion ◽  
S. Haber
Keyword(s):  
Carrying Capacity ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Surface Texturing ◽  
Laser Surface Texturing ◽  
Physical Parameters ◽  
Load Carrying Capacity ◽  
Wide Range ◽  
Load Carrying ◽  
Parallel Surfaces

Microdimples generated by laser surface texturing (LST) can be used to enhance performance in hydrostatic gas-lubricated tribological components with parallel surfaces. The pressure distribution and load carrying capacity for a single three-dimensional dimple, representing the LST, were obtained via two different methods of analysis: a numerical solution of the exact full Navier-Stokes equations, and an approximate solution of the much simpler Reynolds equation. Comparison between the two solution methods illustrates that, despite potential large differences in local pressures, the differences in load carrying capacity, for realistic geometrical and physical parameters, are small. Even at large clearances of 5% of the dimple diameter and pressure ratios of 2.5 the error in the load carrying capacity is only about 15%. Thus, for a wide range of practical clearances and pressures, the simpler, approximate Reynolds equation can safely be applied to yield reasonable predictions for the load carrying capacity of dimpled surfaces.

The Granular Lubricated Journal Bearing: Evidence of Lift Formation

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Venkata K. Jasti ◽  
Martin C. Marinack ◽  
Deepak Patil ◽  
C. Fred Higgs
Keyword(s):  
Carrying Capacity ◽  
Granular Flow ◽  
High Speed ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Flow Behavior ◽  
Extreme Environments ◽  
Granular Flows ◽  
Load Carrying Capacity ◽  
Load Carrying

This work demonstrates that granular flows (i.e., macroscale, noncohesive spheres) entrained into an eccentrically converging gap can indeed actually exhibit lubrication behavior as prior models postulated. The physics of hydrodynamic lubrication is quite well understood and liquid lubricants perform well for conventional applications. Unfortunately, in certain cases such as high-speed and high-temperature environments, liquid lubricants break down making it impossible to establish a stable liquid film. Therefore, it has been previously proposed that granular media in sliding convergent interfaces can generate load carrying capacity, and thus, granular flow lubrication. It is a possible alternative lubrication mechanism that researchers have been exploring for extreme environments, or wheel-regolith traction, or for elucidating the spreadability of additive manufacturing materials. While the load carrying capacity of granular flows has been previously demonstrated, this work attempts to more directly uncover the hydrodynamic-like granular flow behavior in an experimental journal bearing configuration. An enlarged granular lubricated journal bearing (GLJB) setup has been developed and demonstrated. The setup was made transparent in order to visualize and video capture the granular collision activity at high resolution. In addition, a computational image processing program has been developed to process the resulting images and to noninvasively track the “lift” generated by granular flow during the journal bearing operation. The results of the lift caused by granular flow as a function of journal rotation rate are presented as well.

Hydrodynamic Lubrication of Finite Slider Bearings: Effect of One Dimensional Film Shape, and Their Computer Aided Optimum Designs

1983 ◽  
Vol 105 (1) ◽  
pp. 48-63 ◽  
Author(s):  
C. Bagci ◽  
A. P. Singh
Keyword(s):  
Numerical Solution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Design Data ◽  
Slider Bearings ◽  
Load Carrying ◽  
Computer Aided

The effect of the film shape on the load carrying capacity of a hydrodynamically lubricated bearing has not been considered an important factor in the past. Flat-faced tapered bearing and the Raileigh’s step bearing of constant film thickness have been the primary forms of film shapes for slider bearing studies and design data developments. This article, by the computer aided numerical solution of the Reynolds equation for two dimensional incompressible lubricant flow, investigates hydrodynamically lubricated slider bearings having different film shapes and studies the effect of the film shape on the performance characteristics of finite bearings; and it shows that optimized bearing with film shapes having descending slope toward the trailing edge of the bearing has considerably higher load carrying capacity than the optimized flat-faced tapered bearing of the same properties. For example the truncated cycloidal film shape yields 26.3 percent higher load carrying capacity for Lz/Lx = 1 size ratio, and 44 percent higher for Lz/Lx = 1/2. The article then presents charts for the optimum designs of finite slider bearings having tapered, exponential, catenoidal, polynomial, and truncated-cycloidal film shapes, and illustrates their use in numerical bearing design examples. These charts also furnish information on flow rate, side leakage, temperature rise, coefficient of friction, and friction power loss in optimum bearings. Appended to the article are analytical solutions for infinitely wide bearings with optimum bearing characteristics. The computer aided numerical solution of the Reynolds equation in most general form is presented by which finite or infinitely wide hydrodynamically or hydrostatically lubricated bearings, externally pressurized or not, can be studied. A digital computer program is made available.

The Axial Load-Carrying Capacity of Radial Cylindrical Roller Bearings

1970 ◽  
Vol 92 (1) ◽  
pp. 129-134 ◽  
Author(s):  
H. Korrenn
Keyword(s):  
Carrying Capacity ◽  
Hydrodynamic Lubrication ◽  
Experimental Investigations ◽  
Load Carrying Capacity ◽  
Oil Viscosity ◽  
Application Range ◽  
Roller Bearings ◽  
Load Carrying ◽  
Thrust Load ◽  
Cylindrical Roller

Thrust load transmission at the contact areas of roller ends and flanges occurs under conditions of pure sliding. Recent theoretical and experimental investigations showed that with adequately designed roller ends and flanges and with a satisfactory lubricant high thrust loads can be accommodated over a wide speed range with fully hydrodynamic lubrication. The conventional methods used for the determination of the safe thrust load should be revised and supplemented. Oil viscosity should be introduced as an important parameter. Contrary to present opinion the hydrodynamic load-carrying capacity at the flange increases with increasing speed. This new knowledge broadens the application range of radial cylindrical roller bearings.

Numerical Computation of Roughness Effects on Heat Transfer and Hydrodynamic Characteristics in Microchannels

2006 ◽  
Author(s):  
Heming Yun ◽  
Lin Cheng ◽  
Liqiu Wang ◽  
Binjian Chen
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Hydrodynamic Characteristics ◽  
Roughness Effects ◽  
Navier Stokes Equations ◽  
Experimental Heat ◽  
Macro Scale

In the present paper we focus our attention on the analysis of surface roughness effects. In the process of numerical simulation, a finite-volume method was used to solve the three-dimensional Navier-Stokes equations and energy equation. In turbulent region, wall-function was used to solve the temperature and velocity of coolant in the area near the wall. In all computational regions, the fluid-solid Conjugate heat transfer is used to solve the microchannel heat transfer problems. In conclusion the effect of surface roughness on heat transfer and pressure drop can not be neglected. And one should be very careful in ascribing the roughness effect to the discrepancies between experimental heat transfer and the prediction for standard macro scale channels.

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