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.

Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part IV—Starvation Results

1977 ◽  
Vol 99 (1) ◽  
pp. 15-23 ◽  
Author(s):  
B. J. Hamrock ◽  
D. Dowson
Keyword(s):  
Film Thickness ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Contact Center ◽  
Minimum Film Thickness ◽  
Pressure Spike ◽  
Contour Plots

Utilizing the theory and numerical procedure developed by the authors in an earlier publication the influence of lubricant starvation on minimum film thickness was investigated. This study of lubricant starvation was performed simply by moving the inlet boundary closer to the contact center. From the results it was found that for the range of conditions considered the value of dimensionless inlet distance at the boundary between fully flooded and starved conditions (m*) can be expressed simply as m*=1+3.06Rxb2Hc,F0.58 or m*=1+3.34Rxb2Hmin,F0.56 that is, for a dimensionless 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 central and minimum film thickness for a starved condition as Hc,S=Hc,Fm−1m*−10.29Hmin,S=Hmin,Fm−1m*−10.25 Contour plots of the pressure and film thickness in and around the contact are shown for the fully flooded and starved lubricant condition. From these contour plots it was observed that the pressure spike becomes suppressed and the film thickness decreases substantially as starvation increases.

Isothermal Elastohydrodynamic Lubrication of Point Contacts: Part III—Fully Flooded Results

1977 ◽  
Vol 99 (2) ◽  
pp. 264-275 ◽  
Author(s):  
B. J. Hamrock ◽  
D. Dowson
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Load Parameter ◽  
Mineral Oils ◽  
Minimum Film Thickness ◽  
Pressure Spike ◽  
Contour Plots ◽  
Order Of Magnitude ◽  
Speed Parameter ◽  
Ellipticity Parameter

Utilizing the theory developed by the authors in an earlier publication, the influence of the ellipticity parameter, the dimensionless speed, load, and material parameters on minimum film thickness was investigated. The ellipticity parameter was varied from one (a ball on a plate configuration) to eight (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. The dimensionless load parameter was varied over a range of one order of magnitude. Conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of paraffinic and naphthenic mineral oils were considered in obtaining the exponent in the dimensionless material parameter. Thirty-four different cases were used in obtaining the minimum film thickness formula given below as H¯min=3.63U0.68G0.49W−0.073(1−e−0.68k) A simplified expression for the ellipticity parameter was found where k=1.03RyRx0.64 Contour plots were also shown which indicate in detail the pressure spike and two side lobes in which the minimum film thickness occurs. These theoretical solutions of film thickness have all the essential features of the previously reported experimental observations based upon optical interferometry.

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.

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.

Influence of Surface Waviness on the Thermal Elastohydrodynamic Lubrication of an Eccentric-Tappet Pair

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
J. Wang ◽  
C. H. Venner ◽  
A. A. Lubrecht
Keyword(s):  
Film Thickness ◽  
Elastohydrodynamic Lubrication ◽  
Surface Waviness ◽  
Film Pressure ◽  
Oil Film ◽  
Working Cycle ◽  
Temperature Oscillations ◽  
Minimum Film Thickness ◽  
Traction Coefficient ◽  
Oil Film Pressure

The effect of single-sided and double-sided harmonic surface waviness on the film thickness, pressure, and temperature oscillations in an elastohydrodynamically lubricated eccentric-tappet pair has been investigated in relation to the eccentricity and the waviness wavelength. The results show that, during one working cycle, the waviness causes significant fluctuations of the oil film, pressure, and temperature, as well as a reduction in minimum film thickness. Smaller wavelength causes more dramatic variations in oil film. The fluctuations of the pressure, film thickness, temperature, and traction coefficient caused by double-sided waviness are nearly the same compared with the single-sided waviness, but the variations are less intense.

Film thickness in elastohydrodynamically lubricated slender elliptic contacts: Part I – numerical studies of central film thickness

2021 ◽  
pp. 135065012110477
Author(s):  
Marius Wolf ◽  
Sergey Solovyev ◽  
Fatemi Arshia
Keyword(s):  
Film Thickness ◽  
State Of The Art ◽  
Experimental Studies ◽  
Elastohydrodynamic Lubrication ◽  
Large Parameter ◽  
Numerical Studies ◽  
Minimum Film Thickness ◽  
Subsequent Publication ◽  
New Formula ◽  
Increasing Load

In this paper, analytical equations for the central film thickness in slender elliptic contacts are investigated. A comparison of state-of-the-art formulas with simulation results of a multilevel elastohydrodynamic lubrication solver is conducted and shows considerable deviation. Therefore, a new film thickness formula for slender elliptic contacts with variable ellipticity is derived. It incorporates asymptotic solutions, which results in validity over a large parameter domain. It captures the behaviour of increasing film thickness with increasing load for specific very slender contacts. The new formula proves to be significantly more accurate than current equations. Experimental studies and discussions on minimum film thickness will be presented in a subsequent publication.

Roughness Amplitude Reduction Under Non-Newtonian EHL Conditions

2005 ◽  
Author(s):  
A. D. Chapkov ◽  
C. H. Venner ◽  
A. A. Lubrecht
Keyword(s):  
Film Thickness ◽  
Pressure Fluctuations ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Quantitative Prediction ◽  
Point Contacts ◽  
Minimum Film Thickness ◽  
Roughness Amplitude ◽  
Average Film Thickness ◽  
Ehl Contact

The influence of surface roughness on the performance of bearings and gears operating under ElastoHydrodynamic Lubrication (EHL) conditions has become increasingly important over the last decade, as the average film thickness decreased due to various influences. Surface features can reduce the minimum film thickness and thus increase the wear. They can also increase the temperature and the pressure fluctuations, which directly affects the component life. In order to describe the roughness geometry inside an EHL contact, the amplitude reduction of harmonic waviness has been studied over the last ten years. This theory currently allows a quantitative prediction of the waviness amplitude and includes the influence of wavelength and contact operating conditions. However, the model assumes a Newtonian behaviour of the lubricant. The current paper makes a first contribution to the extension of the roughness amplitude reduction for EHL point contacts including non-Newtonian effects.

A thermal EHL investigation on plate-pin hinge pairs in silent chains using a narrow finite line contact

2020 ◽  
Vol 72 (10) ◽  
pp. 1139-1145
Author(s):  
Mingyu Zhang ◽  
Jing Wang ◽  
Jinlei Cui ◽  
Peiran Yang
Keyword(s):  
Film Thickness ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Radius Of Curvature ◽  
Line Contact ◽  
Equivalent Radius ◽  
Content Type ◽  
Finite Line Contact ◽  
Pressure Peak ◽  
Finite Line

Purpose The purpose of this paper is to numerically study the variations of oil film pressure, thickness and temperature rise in the contact zone of plate-pin pair in silent chains. Design/methodology/approach A steady-state thermal elastohydrodynamic lubrication (EHL) model is built using a Ree–Eyring fluid. The contact between the plate and the pin is simplified as a narrow finite line contact, and the lubrication state is examined by varying the geometry and the plate speed. Findings With increase in the equivalent radius of curvature, the pressure peak and the central film thickness increase. Because the plate is very thin, the temperature rise can be neglected. Even when the influence of the rounded corner region is less, a proper design can beneficially increase the minimum film thickness at both edges of the plate. Under a low entraining speed, strong stress concentration results in close-zero film thickness at both edges of the plate. Originality/value This study reveals the EHL feature of the narrow finite line contact in plate-pin pairs for silent chains and will support the future works considering transient effect, surface features and wear.

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