A Generalized Reynolds Equation for Non-Newtonian Thermal Elastohydrodynamic Lubrication

1990 ◽  
Vol 112 (4) ◽  
pp. 631-636 ◽  
Author(s):  
Yang Peiran ◽  
Wen Shizhu
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Generalized Reynolds Equation ◽  
Newtonian Behavior

A new generalized Reynolds equation, which can incorporate most of the rheological laws found in the literature, is derived in this paper. A number of numerical solutions of the line contact thermal elastohydrodynamic lubrication problem has been obtained by using five rheological laws. The results show that, the influence of the non-Newtonian behavior of lubricant is not as important as that of the thermal one, when Roelands’ viscosity is used in the study.

The Elastohydrodynamic Lubrication of Heavily Loaded Point Contacts

1980 ◽  
Vol 22 (4) ◽  
pp. 183-187 ◽  
Author(s):  
C. J. Hooke
Keyword(s):  
Exact Solution ◽  
Film Thickness ◽  
Close Agreement ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Substantial Part ◽  
Line Contact ◽  
Point Contacts ◽  
Contact Width ◽  
Inlet Zone

It is shown that the film thickness in heavily loaded point contacts can be accurately calculated by comparing the inlet and exit zones of the contact with those of an equivalent line contact. The results become increasingly accurate as the extent of the inlet and exit regions is reduced and in the limit yields an exact solution. Even for moderately loaded contacts in which the inlet zone occupies a substantial part of the contact width the results are in close agreement with existing numerical solutions.

Study on Photoelastic Method for Measuring Elastohydrodynamic Lubrication Pressure in Line Contact

2013 ◽  
Vol 281 ◽  
pp. 329-334
Author(s):  
Jun He ◽  
Huang Ping ◽  
Qian Qian Yang
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Friction Pair ◽  
Elastohydrodynamic Lubrication ◽  
Ccd Camera ◽  
Measuring System ◽  
Line Contact ◽  
Basic Equations ◽  
Plastic Disk

In the present paper, a new method for measuring elastohydrodynamic lubrication (EHL) pressure in line contact is proposed, which is based on the photoelastic technique. The pressure distribution of EHL film and the inner stresses in the friction pairs are fundamental issues to carry out EHL research. The film thickness, pressure and temperature have been successfully obtained with solving the basic equations such as Reynolds equation and energy equation simultaneously or separately, with numerical model of EHL problem. The film thickness can be also measured with the optical interference technique. However, the pressure measurement is still a problem which has not been well solved yet, so as the inner stresses inside the friction pairs. With the experimental mechanics, the photoelastic technique is a possible method to be used for measuring the pressure distribution of EHL film and inner friction pair in the line contact. Therefore, A flat plastic disk and a steel roller compose the frictional pairs of the photoelastic pressure measuring rig with combining the monochromatic LED light source, polarizer CCD camera and stereomicroscope to form the whole pressure measuring system of the line contact EHL. The experimental results with the rig display the typical features of EHL pressure. This shows that the method is feasible to be used for measuring the pressure of EHL film and the inner stresses of the friction pairs in the line contact.

Film Thickness and Asperity Load Formulas for Line-Contact Elastohydrodynamic Lubrication With Provision for Surface Roughness

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
M. Masjedi ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Deformation ◽  
Elastohydrodynamic Lubrication ◽  
Load Ratio ◽  
Material Surface ◽  
Line Contact ◽  
Wide Range ◽  
Minimum Film Thickness

Three formulas are derived for predicting the central and the minimum film thickness as well as the asperity load ratio in line-contact EHL with provision for surface roughness. These expressions are based on the simultaneous solution to the modified Reynolds equation and surface deformation with consideration of elastic, plastic and elasto-plastic deformation of the surface asperities. The formulas cover a wide range of input and they are of the form f(W, U, G, σ¯, V), where the parameters represented are dimensionless load, speed, material, surface roughness and hardness, respectively.

Influence of Surface Roughness and Its Orientation on Partial Elastohydrodynamic Lubrication of Rollers

1983 ◽  
Vol 105 (4) ◽  
pp. 591-597 ◽  
Author(s):  
J. Prakash ◽  
H. Czichos
Keyword(s):  
Reynolds Equation ◽  
Complete Solution ◽  
Elastohydrodynamic Lubrication ◽  
Coupled System ◽  
Line Contact ◽  
Roughness Parameters ◽  
Regime Changes ◽  
Lubrication Regime ◽  
Elasticity Equation ◽  
The Stability

In this paper, a complete solution for a rough, isothermal elastohydrodynamic line contact operating in the partial lubrication regime is presented. The semianalytical EHD line contact model developed recently [12], is used in solving the coupled system of average Reynolds equation and the elasticity equation. The effects of various operating parameters and the roughness parameters are investigated with an emphasis on the outlet behavior. The results indicate that in the partial lubrication regime changes in the outlet may play an important role on the stability of elastohydrodynamic films.

The line contact problem of elastohydrodynamic lubrication - I. Asymptotic structure for low speeds

1989 ◽  
Vol 424 (1867) ◽  
pp. 393-407 ◽  
Keyword(s):  
Asymptotic Solution ◽  
Contact Problem ◽  
Film Thickness ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Thin Layers ◽  
Line Contact ◽  
Asymptotic Regime ◽  
Lubricating Film ◽  
Pressure Spike

This paper reports the first formal asymptotic solution to the line contact problem of elastohydrodynamic lubrication (EHL), a fundamental problem describing the elastic deformation of lubricated rolling elements such as roller bearings, gear teeth and other contacts of similar geometry. The asymptotic régime considered is that of small λ , a dimensionless parameter proportional to rolling speed, viscosity and the elastic modulus. The solution is shown to possess four regions: a zone where the lubricating film is both thin and slowly narrowing and which is closely related to the contact area that occurs in the absence of lubricant, an upstream inlet zone of low pressure, and two thin layers on either side of the contact zone. The solutions in the first two just-mentioned zones are given by simple analytical expressions. The solutions in the two thin layers are obtained from two universal functions obtained by Bissett & Spence ( Proc. R. Soc. Lond . A 424, 409 (1989)). Although these two functions, related to the local film thickness, are obtained by numerical techniques by Bissett & Spence, it should be emphasized that all cases in the asymptotic régime considered are hereby solved definitively without recourse to further computation. Although some features of this structure have been suggested by other solution approaches, generally, these are numerical or ad hoc approximations. See the texts by Johnson ( Contact Mechanics , pp. 328 (1985)) and Dowson & Higginson ( Elasto-hydrodynamic lubrication (1977)), this work provides a formal mathematical basis for understanding most of the principal features of EHL. The solution provides a simple formula for minimum film thickness and displays the sharp narrowing of the lubricating film in the thin layer near the exit. In the basic asymptotic solution provided here, the dimensionless pressure-viscosity coefficient, α , is assumed to be O (1), and in this parameter régime, no pressure spike will occur. By comparing with the work of Hooke ( J. mech. Engng Sci . 19(4), 149 (1977)), we can show that an incipient pressure spike occurs when α becomes as large as O ( λ -1/5 ). However, asymptotic solutions in this latter parameter régime require new numerical solutions for each case of interest and are not pursued here.

scholarly journals Reflections on early studies of elasto-hydrodynamic lubrication

2021 ◽  
pp. 135065012110372
Author(s):  
Duncan Dowson ◽  
Gordon Robert Higginson
Keyword(s):  
Numerical Solutions ◽  
Hydrodynamic Lubrication ◽  
Elastohydrodynamic Lubrication ◽  
Theoretical Work ◽  
Early Years ◽  
Line Contact ◽  
Major Event ◽  
Late Professor ◽  
Significant Events ◽  
The University

It is almost 50 years since theoretical work on elastohydrodynamic lubrication commenced in the Department of Mechanical Engineering of The University of Leeds. Details of the development of numerical solutions to the line contact problem during the 6-year period (1956–1962) that the authors worked together on the problem will be outlined. The computing aids available during the 18-month period involved in generating the first solution consisted of two hand-operated mechanical calculating machines, with the first digital computer at Leeds being installed in 1959. The general research environment during the period will be recalled and a number of significant events recorded. It is appropriate to record at this Symposium aspect of these initial developments in a subject that has dominated research in tribology throughout the latter part of the 20th century and into the early years of the 21st century. The excitement of being involved in taking some of the first steps in a field described by the late Professor F.T. Barwell (1970) as ‘The major event in the development of lubrication science since Reynolds's own paper’, will be recalled.

On the elastohydrodynamic analysis of shear-thinning fluids

2007 ◽  
Vol 463 (2088) ◽  
pp. 3271-3290 ◽  
Author(s):  
J.Y Jang ◽  
M.M Khonsari ◽  
S Bair
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Shear Thinning ◽  
Line Contact ◽  
Carreau Model ◽  
Shear Thinning Fluids ◽  
Realistic Prediction ◽  
Comparison With Experiments ◽  
Ehl Contact

Realistic prediction of the characteristics of the elastohydrodynamic lubrication (EHL) contact requires consideration of the appropriate constitutive equation for the lubricant. In many applications, the lubricant exhibits a shear-thinning behaviour which significantly affects the film thickness. In this paper, we present a generalized formulation that can efficiently treat shear-thinning fluids with provision for compressibility in the EHL line contact. Specifically, the Carreau model and the sinh-law model are investigated. An extensive set of numerical solutions and comparison with experiments reveal that the Carreau equation properly captures the film thickness behaviour under both rolling and sliding conditions.

On the Theory of Thermal Elastohydrodynamic Lubrication at High Slide-Roll Ratios—Line Contact Solution

2000 ◽  
Vol 123 (1) ◽  
pp. 36-41 ◽  
Author(s):  
Peiran Yang ◽  
Shiyue Qu ◽  
Qiuying Chang ◽  
Feng Guo
Keyword(s):  
Steady State ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Contact Surfaces

Complete numerical solutions are obtained for the steady-state line contact thermal elastohydrodynamic lubrication (TEHL) problems. The contact surfaces are arranged to run in opposite directions. The slide-roll ratios are allowed to be as high as infinity. The new theory reveals that the characteristics of the high slide-roll contacts are significantly different from those of the low slide-roll contacts. The unusual zero-entrainment films discovered by Dyson and Wilson and the abnormal surface-dimple phenomena observed by Kaneta et al. are explained.

Elastohydrodynamic Lubrication of Rough Surfaces Under Oscillatory Line Contact With Non-Newtonian Lubricant

2007 ◽  
Author(s):  
Mongkol Mongkolwongrojn ◽  
Khanittha Wongseedakaew ◽  
Francis E. Kennedy
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Power Law ◽  
Reynolds Equation ◽  
Initial Conditions ◽  
Rough Surfaces ◽  
Elastohydrodynamic Lubrication ◽  
Oscillatory Motion ◽  
Line Contact ◽  
Minimum Film Thickness

This paper presents the analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with non-Newtonian fluids under oscillatory motion. The effects of transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using multi-grid multi-level method with full approximation technique. Film thickness and pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally. For an increase in the applied load on the cylinders, the minimum film thickness calculated numerically becomes smaller. The predicted film thickness is slightly higher than the film thickness obtained experimentally, owing to cavitation that occurred in the experiments. For both hard and soft EHL contacts, the minimum film thickness under oscillatory motion is very thin near the trailing edge of the contact, especially for stiffer surfaces. The surface roughness and power law index of the non-Newtonian lubricant both have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.

Elastohydrodynamic Line-Contact of Compressible Shear Thinning Fluids With Consideration of the Surface Roughness

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Total Pressure ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Shear Thinning ◽  
Line Contact ◽  
Lubricating Film ◽  
Shear Thinning Fluids ◽  
Modified Reynolds Equation

Applications involving highly loaded elastohydrodynamic lubrication (EHL), particularly when the lubricant experiences shear thinning, operating with small film thicknesses may necessitate consideration of surface asperities. A modified Reynolds equation with provision for surface roughness and shear thinning is treated to predict the pressure and surface asperity effect in an EHL line-contact. The unknown in the Reynolds equation is the hydrodynamic pressure instead of the total pressure to ensure that the pressure boundary condition at the outlet is properly posed. The Carreau viscosity model is used for characterizing the shear thinning behavior, Patir and Cheng flow factors for taking into the influence of roughness on the lubricating film, and Greenwood–Trip for determination of pressure at the asperity level. The modified Reynolds equation is solved for the hydrodynamic pressure instead of the total pressure with appropriately defined boundary conditions.

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