Contact elliptical

Fig. 1. The map of lubrication regimes for the non-conformal fluid-film contact (ellipticity parametCT k= 1) and the location of the tribo-contacts employed in this work (O for PDMS in load-dependence and for PDMS in speed-dependence measurements, and 0 for PP and A for PA-6,6 in load-dependence measurements). IR, VR, IE, and VE stand for isoviscous-rigid, piezoviscous-rigid, isoviscous-elastic, piezoviscous-elastic, respectively.

Fig. 8 All MTM ( ) and pin-on-disk ( ) data at different concentrations of aqueous glycerol mixtures, plotted on a lubrication-tegime map, obtained from the Esfahanian-Hamrock-Dowson equations [28] for a circular contact (ellipticity parameter k = 1). The four different regimes in the dimensionless viscosity (gv) versus elastic (gD parameter plot are iso-viscous rigid (IR), iso-viscous elastic (IE), piezo-viscous rigid (VR), and piezo-viscous elastic (VE). All the values reported in this study lie in the iso-viscous elastic regime. It should be noted that while the equations in [28] apply to rolling contact, the model can also be used for sliding geometries at the low speeds used in our pin-on-disk experiments [35]...

At a constant load there is a critical speed, below which the EHL film cannot be established and severe surface contact may take place. This critical speed appears to be a function of load and contact ellipticity. The heavier the load, the higher the critical speed. 

He = hc/R dimensionless central film thickness k = b/a, contact ellipticity p = pressure... 

The author doubts if the comparison by making the dimensionless load parameter equal is better. He believes that the contact pressure better represents the real physics, which is more closely correlated with lubricant rheology, lubrication mechanism, material performance and efficiency evaluation as well as possible failures. If the dimensionless load parameter is kept constant, for example, but the contact ellipticity changes from 1/8 to 8, the contact pressure would be reduced down to about 11.7%, at which the contact and lubrication mechanisms may be completely different. On the contrary, when keeping the contact pressure and Rx the same, for the same ellipticity change the dimensionless load needs to be increased more than 620 times. Even for the same ellipticity, we believe that the contact pressure is better correlated with the physics and the failures. Also, comparison by making the dimensionless load equal only yields a small quantitative difference. 

The results on contact problems for plates without cracks can be found in (Caffarelli, Friedman, 1979 Caffarelli et al., 1982). Properties of solutions to elliptic problems with thin obstacles were analysed in (Frehse, 1975 Schild, 1984 Necas, 1975 Kovtunenko, 1994a). Problems with boundary conditions of equality type at the crack faces are investigated in (Friedman, Lin, 1996). 

Hertz [27] solved the problem of the contact between two elastic elliptical bodies by modeling each body as an infinite half plane which is loaded over a contact area that is small in comparison to the body itself. The requirement of small areas of contact further allowed Hertz to use a parabola to represent the shape of the profile of the ellipses. In essence. Hertz modeled the interaction of elliptical asperities in contact. Fundamental in his solution is the assumption that, when two elliptical objects are compressed against one another, the shape of the deformed mating surface lies between the shape of the two undeformed surfaces but more closely resembles the shape of the surface with the higher elastic modulus. This means the deformed shape after two spheres are pressed against one another is a spherical shape. 

In Figure 6.16, the region originally occupied by the gas cloud is shaded, and the position and shape of the shock wave and the contact surface at different times following the explosion are shown as solid and dashed curves. The shape of the shock wave is almost elliptical, with ellipticity decaying to sphericity as the shock gradually degenerates into an acoustic wave. 

The film shape for the elliptoid contact region with an ellipticity parameter k = 2.9 is shown in Fig. 11 [45], which gives all characteristic features of medium loaded point... 

E Complete elliptic integral of the te Contact time duration... 

In a series of works, Tokura and coworkers have systematically studied the CD induced in a number of carboxylic acids through their association with optically active amines [14-17]. Salts of 1 1 stoichiometry were formed as contact ion pairs, with limiting values normally being obtained for the observed ellipticities at equivalent molar amounts. The degree of salt formation could be related to the polarity of the solvent medium, as has been summarized in Table 1. The data in the table illustrate that, as the degree of solvent polarity increases, the limiting ellipticity induced in the carboxylate carbonyl band decreases. 

The so-called partial slip condition, where the contact area is divided into a central stuck zone and a surrounding annulus where some microslip is occurring during the course of the loading cycle. When the tangential load is plotted as a function of the relative displacement in a Iissajous representation, elliptical loops are obtained. 

Fig. 5 Schematic description of the contact conditions encountered under small amplitude cyclic lateral micro-motions (fretting). S is the applied lateral displacement, Q is the lateral force and P is the applied constant normal load. The elliptic and trapezoidal Q(S) loops correspond to partial slip and gross slip condition respectively...

Nyburg, S. C and Faerman, C. H. (1985) Acta Crystal. B41,274-279 Shapes of many atomic surfaces are elliptical. The major radius a applies to sideways contacts and the minor radius b to "polar" contacts along a covalent bond axis. Distances are for atoms singly bonded to C and may differ slightly if bonds are to other atoms. 

The interfacial tension is obviously an important property of a liquid because it gives a direct indication of the magnitude of intermolecular forces. As a result of interfacial tension a liquid which is not in contact with another condensed phase, such as a water droplet in air, assumes the shape which has minimum area. It turns out that this shape is a sphere. As a result, there are no elliptical or square water droplets By maintaining a spherical shape, the area-to-volume ratio, and the number of molecules at the surface are their lowest possible values. One is not surprised by this fact on the basis of experience. 

In solving the elastohydrodynamic problem for "point" contact, the Reynolds equation is coupled with the expressions for the elastic deformation of the bounding surfaces and for the influence of pressure and temperature on the viscosity of the lubricant, as in the solution for "line" contact. However, a single traverse across the contact zone does not suffice as the integration path in the case of "point" contact, where the contact area is elliptical or circular instead of rectangular. This brings into play the ellipticity parameter, which is simply... 

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