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.

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.

Elastohydrodynamic Lubrication of Involute Gears

1973 ◽  
Vol 95 (4) ◽  
pp. 1164-1170 ◽  
Author(s):  
A. Gu
Keyword(s):  
Steady State ◽  
Temperature Rise ◽  
Elastohydrodynamic Lubrication ◽  
Quasi Steady State ◽  
Line Contact ◽  
Viscosity Method ◽  
Temperature Calculation ◽  
Involute Gears ◽  
State Assumption ◽  
Zone Temperature

A criterion is suggested for the application of the steady state elastohydrodynamic theories to the analysis of involute gear contacts. The criterion is based on a comparison of two physical time scales characterizing the system. It is found that for heavily loaded gears the unsteadiness effect may be important. A mean-viscosity method using a composite pressure-viscosity model for the lubricant is introduced for contact zone temperature calculation. An example of involute gears is given for the computation of elastohydrodynamic contact variables based on quasi-steady state assumption. It is found that the surface temperature rise in the tooth tip contact is much higher than that in the pitch line contact.

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.

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.

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.

The line contact problem of elastohydrodynamic lubrication - II. Numerical solutions of the integrodifferential equations in the transition and exit layers

1989 ◽  
Vol 424 (1867) ◽  
pp. 409-429 ◽  
Keyword(s):  
Contact Problem ◽  
Film Thickness ◽  
Transition Layer ◽  
Numerical Solutions ◽  
Rapid Change ◽  
Surface Displacement ◽  
Elastohydrodynamic Lubrication ◽  
Infinite Interval ◽  
Cauchy Kernel ◽  
Line Contact

The solution of the line contact problem of elastohydrodynamic lubrication in the asymptotic régime developed by Bissett ( Proc . R . Soc . Lond . A 424, 393–407 (1989)) exhibits two regions of rapid change: a transition layer between the inlet and contact zones, and a downstream exit layer. In these regions the governing Reynolds equation of lubrication theory is essentially nonlinear, although pressure and surface displacement continue to be linearly related by the singular integral equation of plane elasticity. In combination, the system in each region reduces to a nonlinear singular integrodifferential equation with Cauchy kernel for the surface displacement, to be satisfied on either an infinite interval (transition layer) or a semi-infinite interval (exit layer). A method is developed along lines used by Spence & Sharp ( Proc . R . Soc . Lond . A400, 289 (1985), Proc . R . Soc . Lond . A422, 173 (1989)) and Spence et al . ( J . Fluid Mech . 174, 135 (1987)) for approximating the solution in either case by a finite number of trigonometric terms (up to 900). Rapid convergence is achieved by judicious allowance for end point behaviours as deduced by asymptotic analysis of the governing equations. The equations contain an eigenvalue, representing the scaled exit film thickness, which also characterizes the film thickness in the contact zone. This eigenvalue is found with high accuracy in the course of solving the transition layer problem. Close agreement with certain results of Hooke & O’Donoghue ( J . mech . Engng Sci . 14 (1), 34 (1972)) is exhibited.

Two-Dimensional Elastohydrodynamic Lubrication Part 2: Solution of the Line Contact Problem

1988 ◽  
Vol 202 (5) ◽  
pp. 354-360 ◽  
Author(s):  
R W Hall ◽  
M D Savage
Keyword(s):  
Contact Problem ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Iterative Scheme ◽  
Elastohydrodynamic Lubrication ◽  
Parameter Range ◽  
Line Contact ◽  
Two Dimensional ◽  
Lubrication Equation ◽  
Lubricated Contact

Following Part 1, this paper describes a method for solving the line contact problem in elastohydrodynamic lubrication. Using results derived in Part 1 together with the Reynolds lubrication equation and boundary conditions, an iterative scheme is designed so as to yield pressures, displacements and film thicknesses within a parabolic, lubricated contact. Converged numerical solutions are readily obtained over a parameter range which includes both isoviscous and weakly piezoviscous contacts.

Formation Mechanism of Steady Multi-Dimples in Thermal EHL Point Contacts

2003 ◽  
Vol 125 (2) ◽  
pp. 241-251 ◽  
Author(s):  
M. Kaneta ◽  
P. Yang
Keyword(s):  
Steady State ◽  
Flow Model ◽  
Numerical Solutions ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Newtonian Flow ◽  
Pure Rolling ◽  
Pressure Spike ◽  
Thermal Ehl

With optical interferometry technique, an interesting multi-dimple phenomenon has been discovered under pure-sliding conditions in the point contact between a glass disk and a 3-inch diameter steel ball. At low sliding speeds, two or three stable dimples can be generated in the contact, but at higher sliding speeds, such multi-dimples become unstable. At even higher sliding speeds, however, dimples become stable again, but two dimples become single dimple, or three become two. Numerical solutions of the steady-state thermal elastohydrodynamic lubrication (EHL) theory based on the Newtonian flow model can simulate the stable multi-dimples very well. By changing the slide-roll conditions from pure-rolling to pure-sliding, the theoretical analysis shows clearly that the stable multi-dimples are produced by the thermal effect through the familiar EHL pressure spike.

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