A Numerical Solution of the Elastohydrodynamic Film Thickness in an Elliptical Contact

1970 ◽  
Vol 92 (1) ◽  
pp. 155-161 ◽  
Author(s):  
H. S. Cheng
Keyword(s):  
Film Thickness ◽  
Numerical Solution ◽  
Reynolds Equation ◽  
Contact Theory ◽  
Line Contact ◽  
Hertz Theory ◽  
Inlet Region ◽  
Elliptical Contact ◽  
Elastohydrodynamic Film Thickness ◽  
Circular Contact

A numerical solution of the elastohydrodynamic film thickness in an elliptical contact is developed. The two-dimensional Reynolds’ equation in the inlet region is solved by a finite-difference method. The deformation contour in the inlet region is calculated according to the classical Hertz theory for elliptical contacts. Results are presented as side leakage film reduction factors, which are defined as the ratios of the film thickness of the finite contact to that calculated by a line contact theory based on the same maximum Hertz stress. The results obtained for a b/a → ∞, which corresponds to a line contact, and for b/a = 1, which corresponds to a circular contact, agree with those obtained in [2]. Comparison with experimental data [1] indicates that this theory predicts a film thickness slightly higher than those measured by the experiment.

EHL Film Thickness Computations at Low Speeds: Risk of Artificial Trends as a Result of Poor Accuracy and Implications for Mixed Lubrication Modelling

2005 ◽  
Vol 219 (4) ◽  
pp. 285-290 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Steady State ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Validity Of Results ◽  
Erroneous Conclusion ◽  
Low Speeds ◽  
Lubrication Models ◽  
Circular Contact

When numerical and experimental results are compared to validate elasto-hydrodynamic lubrication (EHL) models, it is of utmost importance that grid-converged results are used. In particular at low speeds and high loads, solutions obtained using grids that are not sufficiently dense will exhibit an artificial trend that does not represent the behaviour of the continuous modelling equations. As it coincides with a trend observed in experiments this may lead to the erroneous conclusion that the theoretical model on which the numerical simulations are based is accurate. This risk is illustrated in detail. It is further shown that EHL models based on the Reynolds equation in a steady state circular contact predicts a positive film thickness as long as the grid used in the calculations is sufficiently dense. This has significant implications for the validity of results obtained using mixed lubrication models based on a Reynolds model and a film thickness threshold.

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.

Effect of Liquid-Solid Lubricant on Mixed Lubrication in Line Contact

2011 ◽  
Vol 148-149 ◽  
pp. 778-784
Author(s):  
Rattapasakorn Sountaree ◽  
Panichakorn Jesda ◽  
Mongkolwongrojn Mongkol
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Solid Lubricant ◽  
Reynolds Equation ◽  
Contact Region ◽  
Mixed Lubrication ◽  
Line Contact ◽  
Load Carrying ◽  
Roughness Amplitude ◽  
Raphson Method

This paper presents the performance characteristics of two surfaces in line contact under isothermal mixed lubrication with non-Newtonian liquid–solid lubricant base on Power law viscosity model. The time dependent Reynolds equation, elastic equation and viscosity equation were formulated for compressible fluid. Newton-Raphson method and multigrid technique were implemented to obtain film thickness profiles, friction coefficient and load carrying in the contact region at various roughness amplitudes, applied loads, speeds and the concentration of solid lubricant. The simulation results showed that roughness amplitude has a significant effect on the film pressure, film thickness and surface contact pressure in the contact region. The film thickness decrease but friction coefficient and asperities load rapidly increases when surface roughness amplitude increases or surface speed decreases. When the concentration of solid lubricant increased, friction coefficient and asperities load decrease but traction and film thickness increase.

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.

Transient Analysis of Surface Features in an EHL Line Contact in the Case of Sliding

1994 ◽  
Vol 116 (2) ◽  
pp. 186-193 ◽  
Author(s):  
C. H. Venner ◽  
A. A. Lubrecht
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Transient Analysis ◽  
Reynolds Equation ◽  
Line Contact ◽  
Thickness Profile ◽  
Transient Solutions ◽  
Surface Topographies ◽  
Average Film Thickness ◽  
Highly Loaded

This paper investigates in detail the influence of two different surface topographies on the pressure distribution and film thickness profile of a highly loaded (maximum Hertzian pressure 2 GPa) line contact as a function of the slide to roll ratio. To accomplish this the transient Reynolds equation is solved both in space and time. The first feature under investigation is localized, a so-called indentation, the second one is global: waviness. The observed lack of synchronism in the extremes of pressure and film thickness is explained theoretically by analyzing the Reynolds equation. The minimum and average film thickness values in case of waviness are analyzed as a function of the slide to roll ratio, amplitude, and wavelength. Depending on the slide to roll ratio, the transient solutions may differ significantly from their stationary counterparts. In such cases, therefore, a transient analysis cannot be avoided.

scholarly journals Starved Lubrication of Elliptical EHD Contacts

2004 ◽  
Vol 126 (1) ◽  
pp. 105-111 ◽  
Author(s):  
B. Damiens ◽  
C. H. Venner ◽  
P. M. E. Cann ◽  
A. A. Lubrecht
Keyword(s):  
Numerical Model ◽  
Film Thickness ◽  
Numerical Simulations ◽  
Excellent Agreement ◽  
Experimental Approach ◽  
Operating Conditions ◽  
Inlet Region ◽  
Inlet Length ◽  
Thickness Measurements ◽  
Circular Contact

This paper focuses on the lubrication behavior of starved elliptical Elasto-HydroDynamic (EHD) contacts. Starvation is governed by the amount of lubricant available in the inlet region and can result in much thinner films than occurring under fully flooded conditions. Therefore, it would be desirable to be able to predict the onset and severity of starvation and to be able to relate film reduction directly to the operating conditions and lubricant properties. The aim of this work is to explore the influence of these parameters on starvation. A combined modeling and experimental approach has been employed. The numerical model has been developed from an earlier circular contact study [1]. In this model, the amount and distribution of the lubricant in the inlet region determines the onset of starvation and predicts the film decay in the contact. Numerical simulations for a uniform layer on the surface show that a single parameter, characteristic of the inlet length of the contact in the fully flooded regime, determines the starved behavior. Film thickness measurements under starved conditions were performed to validate this theory. For a circular contact excellent agreement was found. In theory the same mechanism applies to elliptic contacts, however, the behavior is more complicated.

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.

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