Evaluation on Applicability of Reynolds Equation for Squared Transverse Roughness Compared to CFD

2007 ◽  
Vol 129 (4) ◽  
pp. 963-967 ◽  
Author(s):  
Jiang Li ◽  
Haosheng Chen
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Roughness Height ◽  
Obvious Effect ◽  
Disk Interface ◽  
Transverse Roughness ◽  
The Difference ◽  
Cfd Method

A discrete probability distribution function is used to represent the squared transverse roughness effect in a modified Reynolds equation, and the Reynolds equation is used to calculate the hydrodynamic lubrication in a slider-disk interface compared to the CFD method. When the roughness height is below 1% of the film thickness, the results acquired by the two methods are the same and the surface roughness does not show obvious effect on the lubrication results compared to that on the smooth surface. The load capacity and friction force increase as the roughness height increases when the roughness height exceeds 1% of the film thickness. Moreover, the forces acquired by Reynolds equations are smaller than those acquired by CFD, and the difference between them exceeds 10% when the roughness height is higher than 10% of the film thickness. Sidewall effect is considered to be the main reason for the difference, and the Reynolds equation is believed not suitable for calculating the effect of the squared transverse roughness in the hydrodynamic lubrication.

A Theoretical Analysis Considering Cavitation Occurrence in Oil-Lubricated Spiral-Grooved Journal Bearings With Experimental Verification

2004 ◽  
Vol 126 (3) ◽  
pp. 490-498 ◽  
Author(s):  
Tomoko Hirayama ◽  
Takeo Sakurai ◽  
Hiroshi Yabe
Keyword(s):  
Reynolds Equation ◽  
Flow Model ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Theoretical Studies ◽  
Bearing Stiffness ◽  
Hydrodynamic Lubrication Theory ◽  
The Difference ◽  
Theoretical Results

Performances of an oil-lubricated spiral-grooved journal bearing are investigated in this paper with special attention paid to cavitation occurrence. The “equivalent flow model,” which is a theoretical scheme for taking the cavitation occurrence into hydrodynamic lubrication theory, is applied to the analyses by a finite difference treatment of the Reynolds equation that deals with the geometry of a finite number of grooves. The calculated results are compared with experimental results under eccentric states, and verified in terms of cavitation map and pressure distribution. The cavitated area ratio, load capacity and bearing stiffness are also theoretically calculated. The difference between the theoretical results with and without consideration of the cavitation occurrence is considerable, and thus the influence of cavitation occurrence should not be ignored in theoretical studies on bearing characteristics.

Analysis of a Hydrodynamic Spiral Grooved Upstream Pumping Face Seal Considering Cavitation

2015 ◽  
Vol 799-800 ◽  
pp. 671-680
Author(s):  
Ding Hua Liu ◽  
Bin Zhang ◽  
Juan Zhao ◽  
Kai Ge ◽  
Shun Zhang
Keyword(s):  
Boundary Condition ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Logarithmic Spiral ◽  
Groove Depth ◽  
Frictional Torque ◽  
Face Seal ◽  
The Difference ◽  
Rotary Speed

A numerical analysis of an oil-lubricated spiral grooved upstream pumping face seal, accounting for the occurrence of cavitation, have been performed in this paper. The “equivalent flow model”, which is a theoretical scheme for taking the JFO boundary condition into hydrodynamic lubrication theory, was applied to the analyses by a finite difference treatment of the Reynolds equation that dealt with the geometry of logarithmic spiral groove. The calculated results were compared respectively based on Reynolds model and JFO model. The load capacity, cavitation ratio, frictional torque and leakage rate were also theoretically calculated. The difference between the theoretical results based on two boundary conditions for cavitation occurrence is considerable. The JFO boundary condition should be used in theoretical studies on sealing characteristics rather than Reynolds equation, especially in the conditions of less groove depth and high rotary speed.

Static Characteristics of Gas Foil Thrust Bearing Based on Gas Rarefaction Model

2015 ◽  
Author(s):  
Jiajia Yan ◽  
Guanghui Zhang ◽  
Zhansheng Liu ◽  
Fan Yang
Keyword(s):  
Film Thickness ◽  
Optimization Design ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Rarefied Gas ◽  
Load Capacity ◽  
Structural Parameters ◽  
Lubricating Film ◽  
Lift Off ◽  
Foil Thrust Bearing

A modified Reynolds equation for bump type gas foil thrust bearing was established with consideration of the gas rarefaction coefficient. Under rarefied gas lubrication, the Knudsen number which was affected by the film thickness and pressure was introduced to the Reynolds equation. The coupled modified Reynolds and lubricating film thickness equations were solved using Newton-Raphson Iterative Method and Finite Difference Method. By calculating the load capacity for increasing rotor speeds, the lift-off speed under certain static load was obtained. Parametric studies for a series of structural parameters and assembled clearances were carried out for bearing optimization design. The results indicate that with gas rarefaction effect, the axial load capacity would be decreased, and the lift-off speed would be improved. The rarefied gas has a more remarkable impact under a lower rotating speed and a smaller foil compliance coefficient. When the assembled clearance of the thrust bearing rotor system lies in a small value, the lift-off speed increases dramatically as the assembled clearance decreases further. Therefore, the axial clearance should be controlled carefully in assembling the foil thrust bearing. It’s worth noting that the linear uniform bump foil stiffness model is not exact for large foil compliance ∼0.5, especially for lift-off speed analysis, due to ignoring the interaction between bumps and bending stiffness of the foil.

On the effects of two-dimensional Reynolds roughness in hydrodynamic lubrication

1978 ◽  
Vol 364 (1716) ◽  
pp. 89-106 ◽  
Keyword(s):  
Surface Roughness ◽  
Numerical Computation ◽  
Autocorrelation Function ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
The Other ◽  
Roughness Height ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Dimensional Surface

The hydrodynamic lubrication of rough surfaces is analysed with the Reynolds equation, whose application requires the roughness spacing to be large, and the roughness height to be small, compared with the thick­ness of the fluid film. The general two-dimensional surface roughness is considered, and results applicable to any roughness structure are obtained. It is revealed analytically that two types of term contribute to roughness effects: one depends on the shape of the autocorrelation function and the other does not. The former contribution was neglected by previous workers. The numerical computation of an example shows that these two contributions are comparable in magnitude.

An Investigation Into the Influence of Fluid Viscoelasticity in a Squeeze Film Bearing

1978 ◽  
Vol 100 (1) ◽  
pp. 56-64 ◽  
Author(s):  
John A. Tichy ◽  
Ward O. Winer
Keyword(s):  
Molecular Weight ◽  
Film Thickness ◽  
High Molecular Weight ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Surface Film ◽  
Free Fall ◽  
Squeeze Film ◽  
Delayed Response ◽  
High Molecular Weight Polymers

This investigation concerns a prediction of the behavior of viscoelastic fluids in a parallel circular squeeze film with a constant approach velocity, and a comparison to experimental results. The squeeze film geometry has direct application to unsteady hydrodynamic lubrication. The analysis predicts that load capacity of a viscoelastic fluid may be increased due to normal stress effects or decreased due to a delayed response of shear stress to a change in shear rate. Ten tested fluids include Newtonian control fluids, silicone fluids, high molecular weight polymers in petroleum oils, and extremely high molecular weight polymers in water and glycerin. The experimental squeezing is accomplished by the free fall of a cylindrical steel rod along its axis toward a stationary opposing surface. Film thickness, velocity of approach and load are measured. The velocity of approach is essentially constant in the range of film thickness considered. The water-glycerin-polymer solutions exhibited load capacity increases up to 33 percent, while the petroleum-polymer and silicone fluids showed decreases to 23 percent. It appears that viscoelastic effects cannot account for the reported improved bearing performance of polymer-additive lubricants.

EHL Film Thickness Computations at Low Speeds: Risk of Artificial Trends as a Result of Poor Accuracy and Implications for Mixed Lubrication Modelling

2005 ◽  
Vol 219 (4) ◽  
pp. 285-290 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Validity Of Results ◽  
Erroneous Conclusion ◽  
Low Speeds ◽  
Lubrication Models ◽  
Circular Contact

When numerical and experimental results are compared to validate elasto-hydrodynamic lubrication (EHL) models, it is of utmost importance that grid-converged results are used. In particular at low speeds and high loads, solutions obtained using grids that are not sufficiently dense will exhibit an artificial trend that does not represent the behaviour of the continuous modelling equations. As it coincides with a trend observed in experiments this may lead to the erroneous conclusion that the theoretical model on which the numerical simulations are based is accurate. This risk is illustrated in detail. It is further shown that EHL models based on the Reynolds equation in a steady state circular contact predicts a positive film thickness as long as the grid used in the calculations is sufficiently dense. This has significant implications for the validity of results obtained using mixed lubrication models based on a Reynolds model and a film thickness threshold.

scholarly journals Hydrodynamic lubrication of rough surfaces

1982 ◽  
Vol 383 (1785) ◽  
pp. 439-446 ◽  
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Rough Surfaces ◽  
Homogenization Method ◽  
Squeeze Film ◽  
Spatial Average

Using the two-space homogenization method we derive an averaged Reynolds equation that is correct to O (< H 6 > — < H 3 > 2 ), where H is the total film thickness and the angle brackets denote a spatial average. Applications of this mean Reynolds equation to a squeeze-film bearing with a sinusoidal or an isotropic surface roughness are discussed.

A Contribution to the Analysis of the Thermo-Hydrodynamic Lubrication of Porous Self-Lubricating Journal Bearings

2010 ◽  
Vol 297-301 ◽  
pp. 618-623 ◽  
Author(s):  
S. Boubendir ◽  
Salah Larbi ◽  
Rachid Bennacer
Keyword(s):  
Thermal Effects ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Matrix ◽  
Journal Bearings ◽  
Governing Equations ◽  
Hydrodynamic Analysis ◽  
Result Show

In this work the influence of thermal effects on the performance of a finite porous journal bearing has been investigated using a thermo-hydrodynamic analysis. The Reynolds equation of thin viscous films is modified taking into account the oil leakage into the porous matrix, by applying Darcy’s law to determine the fluid flow in the porous media. The governing equations were solved numerically using the finite difference approach. Obtained result show a reduction in the performance of journal bearings when the thermal effects are accounted for and, this reduction is greater when the load capacity is significant.

Hydrodynamic Lubrication of Partial Porous Metal Bearings

1966 ◽  
Vol 88 (1) ◽  
pp. 53-60 ◽  
Author(s):  
C. A. Rhodes ◽  
W. T. Rouleau
Keyword(s):  
Series Solution ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Porous Metal ◽  
Operating Conditions ◽  
Two Dimensional ◽  
Bearing Material ◽  
Porous Bearing ◽  
The Galerkin Method

Partial porous metal bearings are analyzed to determine their performance during steady-state operating conditions with a full film of lubricant. The pressure distribution is determined by a simultaneous solution of the two-dimensional Reynolds equation in the film region and the Laplace equation within the porous bearing material. An infinite-series solution is obtained for pressure utilizing the Galerkin method to determine coefficients. Numerical values of load capacity and coefficient of friction are presented for bearing arcs of 180, 150, and 120 deg.

scholarly journals The Non-Unicity of the Film Thickness in the Hydrodynamic Lubrication: Novel Approach Generating Equivalent Micro-Grooves and Roughness

2021 ◽  
Vol 26 (3) ◽  
pp. 44-61
Author(s):  
M. El Gadari ◽  
M. Hajjam
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Hydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
New Approach ◽  
Initial Film ◽  
Surface Finishes ◽  
Novel Approach ◽  
The 1960S

Abstract Since the 1960s, all studies have assumed that a film thickness “h” provides a unique pressure field “p” by resolving the Reynolds equation. However, it is relevant to investigate the film thickness unicity under a given hydrodynamic pressure within the inverse theory. This paper presents a new approach to deduce from an initial film thickness a widespread number of thicknesses providing the same hydrodynamic pressure under a specific condition of gradient pressure. For this purpose, three steps were presented: 1) computing the hydrodynamic pressure from an initial film thickness by resolving the Reynolds equation with Gümbel’s cavitation model, 2) using a new algorithm to generate a second film thickness, 3) comparing and validating the hydrodynamic pressure produced by both thicknesses with the modified Reynolds equation. Throughout three surface finishes: the macro-shaped, micro-textured, and rough surfaces, it has been demonstrated that under a specific hydrodynamic pressure gradient, several film thicknesses could generate the same pressure field with a slight difference by considering cavitation. Besides, this paper confirms also that with different ratios of the averaged film thickness to the root mean square (RMS) similar hydrodynamic pressure could be generated, thereby the deficiency of this ratio to define the lubrication regime as commonly known from Patir and Cheng theory.

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