Nondimensional Presentation of Frictional Tractions in Elastohydrodynamic Lubrication—Part I: Fully Flooded Conditions

1975 ◽  
Vol 97 (3) ◽  
pp. 398-410 ◽  
Author(s):  
J. F. Archard ◽  
K. P. Baglin
Keyword(s):  
Elastic Modulus ◽  
Elastohydrodynamic Lubrication ◽  
Analytic Solutions ◽  
Glassy Polymers ◽  
Exponential Relationship ◽  
Low Elastic Modulus ◽  
Pressure Dependent Viscosity ◽  
Wide Range ◽  
Computer Based ◽  
Dependent Viscosity

Using several sources, analytic and semi-analytic solutions for frictional tractions of a lubricated line contact are presented in the appropriate non-dimensional form which is similar to that previously used by Moes for film thickness. A Newtonian lubricant with an exponential relationship between viscosity and pressure is assumed and, at this stage, the treatment is confined to fully flooded conditions. The components of frictional tractions arising from rolling (Poisseiulle) and sliding (Couette) flows are distinguished and sliding tractions in the outlet cavitated region are separated from those in the main pressure zone. Three main regimes of lubrication are studied: classical (isoviscous, undeformed), low elastic modulus (isoviscous, heavily deformed) and high elastic modulus (pressure dependent viscosity, heavily deformed). The results presented here provide a broad background of approximate results, covering a very wide range of conditions against which the results of more precise computer-based analyses can be judged. Thus the treatment reveals the existence of a range of conditions (typical of the lubrication of glassy polymers by hydrocarbon lubricants) which has been little studied and is, as yet, imperfectly understood.

Nondimensional Presentation of Frictional Tractions in Elastohydrodynamic Lubrication—Part II: Starved Conditions

1975 ◽  
Vol 97 (3) ◽  
pp. 412-421 ◽  
Author(s):  
J. F. Archard ◽  
K. P. Baglin
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Sliding Friction ◽  
Elastohydrodynamic Lubrication ◽  
Rolling Friction ◽  
Analytic Treatment ◽  
Low Elastic Modulus ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity ◽  
Negligible Influence

Part I of this paper presented a broad semi-analytic treatment of frictional tractions in nondimensional terms; this was confined to the fully flooded situation and the present paper extends the analysis to include starved conditions. As in Part I three major conditions are considered in detail: classical (isoviscous, undeformed) low elastic modulus (isoviscous, heavily deformed) and high elastic modulus (pressure dependent viscosity, heavily deformed). The influence of starvation is presented as a series of correction curves for the rolling and sliding friction derived for fully flooded conditions. Starvation influences friction both through the extent to which the gap between the surfaces is filled by lubricant and through its influence upon the film thickness. Both factors affect rolling friction which is therefore markedly reduced by starvation so mild that there is negligible influence upon the film thickness. In contrast, sliding friction (arising either in the main pressure zone or the cavitated region) is most strongly influenced by the film thickness and is therefore markedly affected only by relatively severe starvation.

Elastohydrodynamic Lubrication—Improvements in Analytic Solutions

1986 ◽  
Vol 200 (4) ◽  
pp. 281-291 ◽  
Author(s):  
J F Archard ◽  
K P Baglin
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Analytic Solutions ◽  
Physical Explanation ◽  
Inlet Condition ◽  
Low Elastic Modulus ◽  
Tilting Pad ◽  
Computer Analyses ◽  
The Relationship

The paper develops a statement of film shape within an elastohydrodynamic conjunction and shows that the Grubin (parallel conjunction, high elastic modulus) and the Baglin and Archard (tilting pad conjunction, low elastic modulus) models are its asymptotes. A film thickness equation is presented for low values of the parameter N3 = αE′(η0[Formula: see text]/ E′R)1/4. The relationship between inlet pressure [Formula: see text] and maximum Hertzian pressure p0 is explored and it is shown that [Formula: see text]/p0 is primarily a function of N3. Evaluation of the modified inlet condition, [Formula: see text] = (1/α)(1 − e−α[Formula: see text]), allows a limit to be placed on the validity of the Grubin model and provides a physical explanation for the differences between the Grubin and the Dowson and Higginson formulae for film thickness. In this way it is shown that, although film thickness may be evaluated to within a few per cent by the condition [Formula: see text] = 1/α, it does not follow that the conjuction is parallel or that [Formula: see text] = ∞. The model thus provides a link between the simpler analytic theories of elastohydrodynamic lubrication and those based on computer analyses.

Two Dimensional Modified Reynolds Equation Including Pressure Dependent Viscosity Effect

2012 ◽  
Author(s):  
Jung Gu Lee ◽  
Alan Palazzolo
Keyword(s):  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Fluid Film ◽  
Maximum Pressure ◽  
Elastic Solids ◽  
Pressure Distributions ◽  
Pressure Dependent Viscosity ◽  
Modified Reynolds Equation ◽  
Dependent Viscosity ◽  
Modified Equation

The Reynolds equation plays an important role for predicting pressure distributions for fluid film bearing analysis, One of the assumptions on the Reynolds equation is that the viscosity is independent of pressure. This assumption is still valid for most fluid film bearing applications, in which the maximum pressure is less than 1 GPa. However, in elastohydrodynamic lubrication (EHL) where the lubricant is subjected to extremely high pressure, this assumption should be reconsidered. The 2D modified Reynolds equation is derived in this study including pressure-dependent viscosity, The solutions of 2D modified Reynolds equation is compared with that of the classical Reynolds equation for the ball bearing case (elastic solids). The pressure distribution obtained from modified equation is slightly higher pressures than the classical Reynolds equations.

Elastohydrodynamic Lubrication of Spherical Surfaces of Low Elastic Modulus

1976 ◽  
Vol 98 (4) ◽  
pp. 524-529 ◽  
Author(s):  
S. Biswas ◽  
R. W. Snidle
Keyword(s):  
Elastic Modulus ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
High Elastic Modulus ◽  
Spherical Surfaces ◽  
Low Elastic Modulus ◽  
Alternative Approach ◽  
Low Modulus ◽  
Theoretical Results

The paper presents a numerical solution for the elastohydrodynamic lubrication of low modulus point contacts which is broadly equivalent to the theory of Grubin for materials of high elastic modulus. The theoretical results obtained for the variation of minimum film thickness using this approach are therefore expected to apply to conditions of high load and low speed. For less severe conditions in which elastic deformation is less significant an alternative approach has been developed. Results of this analysis show the transition from undeformed to heavily loaded conditions. The effect of lubricant starvation has been examined for heavily loaded conditions and the theoretical results are compared with those obtained previously for high elastic modulus point contact.

Remarks on the Reynolds problem of elastohydrodynamic lubrication

1993 ◽  
Vol 4 (1) ◽  
pp. 83-96 ◽  
Author(s):  
José-Francisco Rodrigues
Keyword(s):  
Free Boundary ◽  
A Priori ◽  
Elastohydrodynamic Lubrication ◽  
Small Data ◽  
Existence Of A Solution ◽  
Pressure Dependent Viscosity ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Dependent Viscosity ◽  
The Mathematical Model

The mathematical model of the flow of a viscous lubricant between elastic bearings leads to the study of a highly non-linear and non-local elliptic variational inequality. We discuss the existence of a solution by using an a prioriL∞-estimate. This method allows us to solve a large class of problems, including those arising from the linear Hertzian theory, and yields new existence results for the cases of a pressure-dependent viscosity or the inclusion of a load constraint. For small data the uniqueness of the solution holds, and we show that in the cylindrical journal bearing problem with small eccentricity ratio, the free boundary is given by two disjoint differentiable arcs close to the free boundary of the first-order approximate solution.

A Simplified Model for the Elastohydrodynamic Traction Between Rollers

1976 ◽  
Vol 98 (3) ◽  
pp. 357-361 ◽  
Author(s):  
Charles W. Allen
Keyword(s):  
Preliminary Analysis ◽  
High Pressures ◽  
Elastohydrodynamic Lubrication ◽  
Rolling Contact ◽  
Experimental Investigations ◽  
Pressure Dependent Viscosity ◽  
Linear Shear ◽  
Dependent Viscosity ◽  
Low Pressures ◽  
Good Agreement

The elastohydrodynamic lubrication of two rollers in combined rolling and sliding is considered. A simple rheological model to predict the traction is presented. The model is based upon an exponential pressure dependent viscosity at low pressures and a linear shear stress/pressure relationship at high pressures. The slope of the latter is assumed to be a function of the rolling and sliding velocities. The model is used to analyze the traction data of two recently published experimental investigations of other authors and good agreement is achieved in most cases. The model should be of considerable use to designers in the preliminary analysis of rolling contact systems in combined rolling and sliding.

Mixed lubrication of soft contacts: An engineering look

2016 ◽  
Vol 231 (2) ◽  
pp. 263-273 ◽  
Author(s):  
M Masjedi ◽  
MM Khonsari
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Load Ratio ◽  
Soft Materials ◽  
Line Contact ◽  
Soft Contact ◽  
Lubrication Regime ◽  
Low Elastic Modulus ◽  
Stribeck Curves

Mixed elastohydrodynamic lubrication of materials with low elastic modulus (soft materials) is investigated. Expressions for prediction of film thickness and the asperity load ratio in soft line-contact elastohydrodynamic lubrication are presented. The traction behavior of soft contact in mixed elastohydrodynamic lubrication regime is also studied in terms of the Stribeck curves.

Water Lubricated Bearing Lubrication Model Based on Multilayer Gridding

2011 ◽  
Vol 101-102 ◽  
pp. 623-627
Author(s):  
Jin Min Peng ◽  
Jiang Bo Yu
Keyword(s):  
Elastic Modulus ◽  
Numerical Calculation ◽  
Numerical Model ◽  
Elastohydrodynamic Lubrication ◽  
Water Film ◽  
Contact Theory ◽  
Frictional Surface ◽  
Model Based ◽  
Low Elastic Modulus ◽  
High Elasticity

The principle of the multilayer gridding algorithm, as well as its applications to the numerical calculation of water lubricated plastic alloy bearing elastohydrodynamic lubrication (EHL), was described. The computation of water lubricated plastic alloy bearing EHL was carried out by the numerical model based on the linear contact theory. A cuneiform water film on the frictional surface between bearing and spindle is formed because the plastic alloy has a high elasticity and low elastic modulus, which lead the water lubricated bearing easy to be distorted.

Oil Film Thickness and Shape for a Ball Sliding in a Grooved Raceway

1972 ◽  
Vol 94 (3) ◽  
pp. 199-208 ◽  
Author(s):  
N. Thorp ◽  
R. Gohar
Keyword(s):  
General Theory ◽  
Film Thickness ◽  
Contact Area ◽  
Elastohydrodynamic Lubrication ◽  
Surface Velocity ◽  
Oil Film ◽  
Pressure Dependent Viscosity ◽  
Ball Surface ◽  
Lubricated Contact ◽  
Dependent Viscosity

The behavior in the lubricated contact area of a driven ball sliding in a conforming glass groove, is studied. Interferometry is used to measure the oil film. Coupled ball surface velocity components are provided by angling the drive, while loads and speeds are varied in order to cover a range of conditions from undistorted surfaces to elastohydrodynamic lubrication. A general theory for lubrication with, no distortion and pressure-dependent viscosity, is developed and compared with experiment. Ball spin is found to have only a small effect on the oil film thickness.

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