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.

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.

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.

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.

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.

Effect of Surface Roughness on Elastohydrodynamic Line Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 401-407 ◽  
Author(s):  
B. C. Majumdar ◽  
B. J. Hamrock
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Strain Analysis ◽  
Elastohydrodynamic Lubrication ◽  
Asperity Contact ◽  
Pressure Dependent Viscosity ◽  
Surface Irregularities ◽  
Dependent Viscosity ◽  
Contact Pressures ◽  
Effect Of Surface

A numerical solution of an elastohydrodynamic lubrication (EHL) contact between two long, rough surface cylinders is obtained. A theoretical solution of pressure distribution, elastohydrodynamic load, and film thickness for given speeds and for lubricants with pressure-dependent viscosity, material properties of cylinders, and surface roughness parameters is made by simultaneous solution of an elasticity equation and the Reynolds equation for two partially lubricated rough surfaces. The pressure due to asperity contact is calculated by assuming a Gaussian distribution of surface irregularities. The elastic deformation is found from hydrodynamic and contact pressures by using plane strain analysis. The effect of surface roughness on EHL loads, speeds, and central film thicknesses is studied. The results indicate that for a constant central film thickness (1) increasing the surface roughness decreases the EHL load and (2) there is little variation in minimum film thickness as the surface roughness is increased.

Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus: II—Starved Conjunction

1979 ◽  
Vol 101 (1) ◽  
pp. 92-98 ◽  
Author(s):  
B. J. Hamrock ◽  
D. Dowson
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Rolling Direction ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Radius Of Curvature ◽  
Low Elastic Modulus ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Lubrication Conditions

By using the theory and numerical procedure developed by the authors in earlier publications, the influence of lubricant starvation upon minimum film thickness in starved elliptical elastohydrodynamic conjunctions for low-elastic-modulus materials has been investigated. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction. The results show that the location of the dimensionless inlet boundary m* between the fully flooded and starved conditions can be expressed simply as m* = 1 + 1.07 [(Rx/b)2Hmin,F]0.16, where Rx is the effective radius of curvature in the rolling direction, b is the semiminor axis of the contact ellipse, and Hmin,F is the dimensionless mimimum film thickness for the fully flooded condition. That is, for a dimension-less inlet distance m less than m*, starvation occurs; and for m ≥ m*, a fully flooded condition exists. Furthermore, it has been possible to express the minimum film thickness for a starved condition as Hmin,S = Hmin,F [(m − 1)/(m* − 1)]0.22. Contour plots of the pressure and film thickness in and around the contact are presented for both the fully flooded and starved lubrication conditions. It is evident from the contour plots that the inlet pressure contours become less circular and that the film thickness decreases substantially as the severity of starvation increases. The results presented in this report, when combined with the findings previously reported, enable the essential features of starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus to be ascertained.

Elastohydrodynamic Lubrication of Elliptical Contacts for Materials of Low Elastic Modulus I—Fully Flooded Conjunction

1978 ◽  
Vol 100 (2) ◽  
pp. 236-245 ◽  
Author(s):  
Bernard J. Hamrock ◽  
Duncan Dowson
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Low Elastic Modulus ◽  
Minimum Film Thickness ◽  
Contour Plots ◽  
Order Of Magnitude ◽  
Ellipticity Parameter

Our earlier studies of elastohydrodynamic lubrication of conjunctions of elliptical form are applied to the particular and interesting situation exhibited by materials of low elastic modulus. By modifying the procedures we outlined in an earlier publication, the influence of the ellipticity parameter k and the dimensionless speed U, load W, and material G parameters on minimum film thickness for these materials has been investigated. The ellipticity parameter was varied from 1 (a ball-on-plate configuration) to 12 (a configuration approaching a line contact). The dimensionless speed and load parameters were varied by 1 order of magnitude. Seventeen different cases were used to generate the following minimum- and central-film-thickness relations: H˜min=7.43(1−0.85e−0.31k)U0.65W−0.21H˜c=7.32(1−0.72e−0.28k)U0.64W−0.22 Contour plots are presented that illustrate in detail the pressure distribution and film thickness in the conjunction.

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.

Contact Stress Analysis of NCD Coating on Cemented Carbide

2010 ◽  
Vol 431-432 ◽  
pp. 98-101
Author(s):  
Jia Jing Yuan ◽  
Wen Zhuang Lu ◽  
Dun Wen Zuo ◽  
Feng Xu
Keyword(s):  
Shear Stress ◽  
Elastic Modulus ◽  
Stress Distribution ◽  
Film Thickness ◽  
Contact Stress ◽  
Maximum Shear Stress ◽  
Shear Stress Distribution ◽  
Cemented Carbide ◽  
Low Elastic Modulus ◽  
Film Layer

The contact stress of cemented carbide with NCD coating in elastic contact was analyzed using ANSYS. Factors such as elastic modulus and thickness of NCD film and elastic modulus of interlayer which affect the shear stress distribution of NCD film on cemented carbide substrate were investigated. The results show that the maximum shear stress point moves towards the interface with the increase of film elastic modulus. Film thickness has a significant effect on shear stress distribution of NCD film. High shear stress develops in the film layer with the increase of film thickness. Interlayer with low elastic modulus will cause shear stress concentration in NCD film.

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.

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