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.

scholarly journals About the Inverse Theory and the Non-Unicity of the Film Thickness: Novel Approach Generating Equivalent Micro-Grooves and Roughness

2021 ◽  
Author(s):  
Mhammed ELGADARI ◽  
HAJJAM Mohamed
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Hydrodynamic Pressure ◽  
Inverse Theory ◽  
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 different ratios of the averaged film thickness by 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 with Patir and Cheng theory.

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.

The Numerical Analysis on Action Mechanism of Slurry in Free Abrasive Wiresaw Slicing

2007 ◽  
Vol 359-360 ◽  
pp. 455-459
Author(s):  
Pei Qi Ge ◽  
Bo Sang ◽  
Yu Fei Gao
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Pressure ◽  
Influence Coefficient ◽  
Main Method ◽  
Minimum Film Thickness ◽  
The Mathematical Model ◽  
Slurry Viscosity ◽  
Free Abrasive ◽  
Abrasive Size

Free abrasive wiresaw technology is the main method in slicing monocrystalline silicon wafers. The mathematical model of hydrodynamic action in the process of the free abrasive wiresaw slicing was founded, displacement caused under distributed radial load of every node on the wire is embodimented through self-compliance influence coefficient, which is beneficial to found the film thickness equation. The distributions of hydrodynamic pressure and film thickness in the free abrasive wiresaw slicing process are yielded by using the finite difference numerical methods to solve the two-dimension Reynolds equation. The results show that the minimum film thickness increases with the increase of wire speed, and slurry viscosity, while decreases with the increase of wire bow angle. The film thickness is greater than the average abrasive size so that the abrasives float in the slurry when the size of abrasive is small enough.

A Comparison of the Roughness Regimes in Hydrodynamic Lubrication

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
John Fabricius ◽  
Afonso Tsandzana ◽  
Francesc Perez-Rafols ◽  
Peter Wall
Keyword(s):  
Asymptotic Behavior ◽  
Stokes Flow ◽  
High Frequency ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Hydrodynamic Lubrication ◽  
Narrow Gap ◽  
Surface Textures ◽  
Lubrication Regimes ◽  
Generalized Reynolds Equation

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength μ, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/μ, denoted as λ, three different lubrication regimes exist: Reynolds roughness (λ = 0), Stokes roughness (0 < λ < ∞), and high-frequency roughness (λ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on λ. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter λ. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

Inverse Solution of Reynolds’ Equation of Lubrication Under Point-Contact Elastohydrodynamic Conditions

1981 ◽  
Vol 103 (4) ◽  
pp. 539-546 ◽  
Author(s):  
H. P. Evans ◽  
R. W. Snidle
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Inverse Solution ◽  
Heavy Loads

The paper describes a technique for solving the inverse lubrication problem under point contact elastohydrodynamic conditions, i.e. the calculation of a film thickness and shape corresponding to a given hydrodynamic pressure distribution by an inverse solution of Reynolds’ equation. The effect of compressibility and influence of pressure upon viscosity are included in the analysis. The technique will be of use in solving the point contact elastohydrodynamic lubrication problem at heavy loads.

Comparison of Experimental, Thermoelastohydrodynamic (TEHD) and Isothermal, Non-Deforming Computational Fluid Dynamics (CFD) Results for Thrust Bearings

2018 ◽  
Author(s):  
Xin Deng ◽  
Cori Watson ◽  
Minhui He ◽  
Houston Wood ◽  
Roger Fittro
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Reynolds Equation ◽  
Cfd Simulation ◽  
Hydrodynamic Lubrication ◽  
Operating Characteristics ◽  
Thrust Bearings ◽  
Load Combination ◽  
Ansys Cfx ◽  
Machine Elements

Bearings are machine elements that allow components to move with respect to each other. A thrust bearing is a particular type of rotary bearing permitting rotation between parts but designed to support a predominately axial load. Oil-lubricated bearings are widely used in high speed rotating machines such as those found in the aerospace and automotive industries. With the increase of velocity, the lubrication regime will go through boundary lubrication, mixed lubrication, and hydrodynamic lubrication (full film). In this paper, the analysis was in the hydrodynamic lubrication region. THRUST is used to predict the steady-state operating characteristics of oil-lubricated thrust bearings. As a thermoelastohydrodynamic prediction tool, THRUST assumes a 3D turbulence model, 3D energy equation, and 2D Reynolds equation. Turbulence is included by obtaining average values of eddy momentum flux (Reynolds stress) and averaging the influence down to a 2D Reynolds equation. Convergence is achieved by iterating on the pad tilt angles and pivot film thickness until the integrated pressure matches the load applied to the pad. Despite the multiple experimental, CFD, and TEHD studies of thrust bearings that have been performed to date, no validation has yet been performed to confirm the accuracy of TEHD methods in modeling the performance of thrust bearings by both experimental and advanced computational means simultaneously. This study addresses this need by comparing TEHD and CFD simulation results of film thickness, temperature, power loss, and pressure in thrust bearings taken from the literature at multiple speeds and loads with results from experimental data. Starting from the case of the lowest speed and load, it was verified that this case is indeed laminar and with negligible thermal and elastic effects. Four cases were run in THRUST, a TEHD solver, combining thermal and deformation in each rotational speed and load combination. Additionally, a CFD study was performed in ANSYS CFX with the assumptions of isothermal, non-deforming. The average viscosity from THRUST was used in CFD to follow the effects of the isoviscous assumption. Then, the experimental, TEHD and CFD results were compared at each case. Experimental, TEHD, and CFD results show acceptable agreement when turbulence is negligible.

Numerical Calculation and Analysis of Water-Lubricated Stern Bearing Considering Elastic Hydrodynamic

2014 ◽  
Vol 1061-1062 ◽  
pp. 653-657
Author(s):  
Gang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Calculation ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Water Film ◽  
Polymer Materials ◽  
The Finite Element Method ◽  
Metal Materials

The deformation of marine water-lubricated stern bearing which the lining materials are polymer materials is much bigger than the bearing built with metal materials. So, in order to improve the calculate accuracy of elastic hydrodynamic, it is necessary to consider the deformation of the lining. Both pressure and thickness distributions of water film which contrasts with the hydrodynamic lubrication are presented by the Reynolds equation, and combining with the elastic deformation of the stern bearing solved by using the finite element method theory. The result shows that the stern bearing water film pressure of elastic hydrodynamic lubrication is lower than that of hydrodynamic lubrication, while the water film thickness is larger.

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.

Profile Design for Misaligned Journal Bearings Subjected to Transient Mixed Lubrication

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Thomas Gu ◽  
Q. Jane Wang ◽  
Shangwu Xiong ◽  
Zhong Liu ◽  
Arup Gangopadhyay ◽  
...  
Keyword(s):  
Film Thickness ◽  
Performance Metrics ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Industrial Applications ◽  
Mixed Lubrication ◽  
Asperity Contact ◽  
Minimum Film Thickness ◽  
Profile Design

Misalignment between the shaft and the bearing of a journal bearing set may be inevitable and can negatively impact journal bearing performance metrics in many industrial applications. This work proposes a convex profile design of the journal surface to help counteract the negative effects caused by such a misalignment. A transient mass-conserving hydrodynamic Reynolds equation model with the Patir–Cheng flow factors and the Greenwood–Tripp pressure–gap relationship is developed to conduct the design and analysis. The results reveal that under transient impulse loading, a properly designed journal profile can help enhance the minimum film thickness, reduce mean and peak bearing frictions, and increase bearing durability by reducing the asperity-related wear load. The mechanism for the minimum film thickness improvement due to the profile design is traced to the more even distribution of the hydrodynamic pressure toward the axial center of the bearing. The reason for the reductions of the friction and wear load is identified to be the decreased asperity contact by changing the lubrication regime from mixed lubrication to nearly hydrodynamic lubrication. Parametric studies and a case study are reported to highlight the key points of the profile design and recommendations for profile height selection are made according to misalignment parameters.

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