Elastohydrodynamic Theory

An elastohydrodynamic problem customarily involves the calculation of the pressure distribution in the lubricant film, allowing for the effects of pressure on the properties of the fluid and on the geometry of the interface. The shape of the lubricant film and its thickness are functionally related to the pressure distribution. The technologically important solutions are for bounding surfaces of counterformal geometry, which in most cases can be approximated satisfactorily by two opposing circular cylinders. 

For simplicity let us first consider the problem for the following conditions (a) the displacements of the boundaries are calculated for 

The first of these is the Reynolds equation in its simplest form the second equation covers the variation of viscosity as a function of pressure the third expression gives the film thickness, where R is the radius of the equivalent cylinder and i j is the combined displacement of the two solid boundaries. The equivalent cylinder treatment is a way of generalizing and simplifying the geometry of curvilinear boundaries if x is small enough relative to R, 

In order to use Eqn 3-45 in conjunction with Eqn 3-44, an explicit expression must be found for f(p). A relation frequently used is the exponential expression 

In Eqn 3-46 ijj is the combined displacement of the two bounding surfaces as calculated from elastic theory  

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Another approach to the detection of fluid film failure is the study of wear in relation to lubricant film thickness. Figure 6-18 shows observations by E. M. Landen [25] of the wear of two disks rubbing with velocities in the ratio 1 1.25. The film thicknesses were calculated from the operating parameters of the apparatus and elastohydrodynamic theory. As shown by curve D, for an oil film 65 nm thick wear ceases after a break-in period of one hour. When the oil film is only 20 nm... 

According to elastohydrodynamic theory, in high-pressure lubricated contacts, the motion of the surfaces entrains lubricant into the contact to form a film whose thickness is dependent on the mean speed, U, the dynamic viscosity, r, of the fluid in the contact inlet and the pressure viscosity coefficient, a, of this fluid according to ... 

The classical elastohydrodynamic theory assumes that the lubricant behaves as a newtonian fluid with a viscosity which increases with pressure. Although other solutions are available for... 

Das, N. C., Elastohydrodynamic Lubrication Theory of Line [39] Contacts Couple Stress Fluid Model, Tribal. Trans., Vol. 40, No.2,1997,pp.353-359. 

Experimental confirmation of the elastohydrodynamic lubrication theory has been obtained in certain selected systems using electrical capacitance, x-ray transmission, and optical interference techniques to determine film thickness and shape under dynamic conditions. Research is continuing in this area, including studies on micro-EHL or asperity lubrication mechanisms, since surfaces are never perfectly smooth. These studies may lead to a better understanding of not only lubricant film formation in high-contact-stress systems but lubricant film failure as well. 

Obviously, at very high contact pressures, the lubricating liquid between the two surfaces rapidly increases in viscosity until it must attain the consistency of a solid or wax rather than a liquid. In such a case, it is easy to see why some lubricating oils that exhibit such thickening behavior show better performance than would be predicted for classic hydrodynamic theories. It also helps explain why other materials (e.g., sihcone oils), which have less dramatic viscosity increases with pressure, do not perform as well under extreme conditions. In the viscosity range where elastohydrodynamic lubrication occurs, fluids may begin to exhibit non-Newtonian behavior leading to a more complicated relationship in terms of lubricant effectiveness. 

The paper is concerned with the problem which arises in the elastohydrodynamic lubrication (ehl) analysis of real surfaces under conditions where conventional ehl theory predicts a lubricant film thickness which is of the scune order or less them the mean height of surface roughness asperities. A simple micro ehl model for the lubrication of rough surfaces is described and theoretical results are given which demonstrate the effect of load. The results show the transition from "isolated asperity contact behaviour to a situation where significant pressures are generated in the valleys between asperities. 

The current study has provided further confirmation of the major role played by micro-elasto-hydrodynamic lubrication in synovial joints. The model adopted Is still relatively simple and It may be necessary to give further attention to lubricant rheology in order to bring theory and experiment fully Into accord In relation to joint friction. However, the Imposition of fully dynamic conditions has not impaired the essential Indications of quasl-statlc mlcro-elastohydrodynamic analysis of synovial joints reported earlier. 

To determine the oil film thickness width the sealing zone precisely practically and theoretically, however, they are assumed to exist from 0.1 to 1 m approximately. This suggests the necessity for application of the elastohydrodynamic lubrication theory of thin film considering surface roughness or for the starved lubrication theory. 

Professor T Murakami (Kyushu University, Japan). Your application of mlcro-elastohydrodynamic lubrication theory to natural synovial joints provides strong support for fluid film lubrication In natural joints under walking condition. (1) Could you show some data on the effective film parameter which Is defined as the ratio of minimum film thickness to effective roughness after deformation (2) Have you Investigated the Influence of highly concentrated gel formed on articular cartilages in the concave area on the effective film parameter under thin film conditions ... 

Raman spectroscopy is very efficient in measuring pressure inside the contact area. Mansot used it to measure the pressure in a sphere/flat contact containing a thin polymer film [90]. Pressure curves obtained are in agreement with Hertzian theory. Similar works determined the disttibution of the pressure in a contact in an elastohydrodynamic lubrication regime [91]. 

Holmes, M. J. A., Hughes, T. G., Evans, H. P. and Snidle, R. W. Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method Part 1 Theory and validation. Submitted to Proc. Instn. Mech. Eng., Part J, Journal of Engineering Tribology. 

Johnson, K. L. et al A simple theory of asperity contact in Elastohydrodynamic lubrication Wear, 19(1972)p.91-108... 

Raman microspectrometry is a powerful technique well adapted to local measurements in contacts owing to its spatial resolution of a few microns [16-17]. In a previous study, Raman microspectrometry was applied to in situ measurements of pressure in a roiling elastohydrodynamic point contact [18]. Pressure profiles and 3D-pressure maps were recorded for two model lubricants. The obtained results were in good qualitative agreement with the predictions of EHL theory. In particular, the presence of the Petrusevich pressure spike and the evolution of its position and intensity with load and speed were clearly evidenced. This study has demonstrated the ability of Raman microspectrometry to measure pressure in dynamic lubricated contacts. However, the experimental pressures have not been compared quantitatively with theoretical predictions. Furthermore, the experimental conditions (load, speed and temperature of the lubricant) were limited by the capacities of the EHL test rig. 

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