Lubrication theory terms

In the past, various resin flow models have been proposed [2,15-19], Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al. [2], Loos and Springer [15], Williams et al. [16], and Gutowski [17] assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber network permeability is a function of fiber diameter, the porosity or void ratio of the porous medium, and the shape factor of the fibers. Viscosity of the resin is essentially a function of the extent of reaction and temperature. The second major approach is that of Lindt et al. [18] who use lubrication theory approximations to calculate the components of squeezing flow created by compaction of the plies. The first approach predicts consolidation of the plies from the top (bleeder surface) down, but the second assumes a plane of symmetry at the horizontal midplane of the laminate. Experimental evidence thus far [19] seems to support the Darcy s Law approach. 

The viscous dissipation term is normally not important. Its significance has been considered in connection with lubrication theory (VI), flow through tubes (B20), extrusion of plastics melts (BIO), and viscometry in rotating-cylinder systems (W6). There is also an additional contribution to the energy flux vector describing energy transport by radiation. See discussion in connection with Eq. (29). 

Apart from the trivial inclusion of the gravitational body-force terms in (6-2) and (6-3), the governing equations, and the analysis leading to them, are identical to the governing equations for the lubrication theory of the previous chapter. The primary difference in the formulation is in the boundary conditions, and the related changes in the physics of the thin-film flows, that arise because the upper surface is now a fluid interface rather than solid surface of known shape. The boundary conditions at the lower bounding surface are ... 

Some normalisation factors in the surface transport equation for G that ordinarily would become unity in lubrication theory at leading order have also been retained. While we do not rigorously apply matched asymptotic expansions in this work, the equations contain all of the terms necessary to match the film onto a static meniscus (for the bath surface) and it has been shown that the terms neglected are small for 8 1 [65]. 

Using (88) into (87) verifies that por = 0 which implies that po s po(z, t) as would be expected from a lubrication theory. The leading order pressure throughout the jet can therefore be determined by evaluating it at the interface through the leading order terms of the normal stress balance equation (30). We find... 

The differences in antiwear properties of disulfides are related to their ability to be physisorbed about 100 to 1000 times faster than monosulfide on metal surfaces. The differences can be explained in terms of the lower energy needed for the formation of the same number of RS" ions from disulfides (Kajdas,1994). The exposed metal surface is extremely reactive to lubricant components, especially antiwear and extreme-pressure additives resulting the formation of a film on the contact surface. The reaction of emitted electrons of low energy (1 to 4 eV) with molecules of oil additives adsorbed on the friction surface may lead to formation of negative ions and negative ion radicals. The investigator (Kajdas, 1994 and 1985) pointed out the indispensability of the metal oxide film on the rubbing surface from the viewpoint of the theory of sulfide film formation. 

Polymer processing flows are always laminar and generally creeping type flows. A creeping flow is one in which viscous forces predominate over forces of inertia and acceleration. Classic examples of such flows include those treated by the hydrodynamic theory of lubrication. For these types of flows, the second term on the left-hand side of Eq. 2.5-18 vanishes, and the Equation of motion reduces to ... 

Thus each solid face makes a definite quantitative contribution to the friction, irrespective of what the other solid face may be, or what lubricant is present. At one time Hardy attempted to explain this on the theory that the influence of the attraction of the solid face extended for long distances, but more recent analysis of the occurrences during sliding indicates that the process is very complex, and that the coefficient of friction is not, as a rule, a quantity capable of simple interpretation in terms of the properties of continuous surface films, and of the underlying solid. 

The physicochemical differentiation of the liquid state from the gaseous and the solid states requires elaborate and formal treatment. But characterization of the liquid state in a fashion useful for lubrication problems can be made much simpler than is required by exact theory. It will suffice for our purposes to begin with the treatment of liquid viscosity in descriptive terms. Then those constitutive and structural aspects of liquids and the liquid state which influence viscosity will be discussed. Similar treatment will be applied to the density and compressibility of liquids. 

The conditions in which slow reactions of relative simplicity become accessible to precise measurement are not normally obvious, and have to be discovered. Even when they have been found, the phenomena which become apparent would be, in the eyes of many, little more than curiosities. Nevertheless, the development of any phenomenon in time has a fascination of its own, and the laws which it follows have an attraction to those interested in the quantitative aspect of things. The application of the so-called law of mass action led to the idea of reaction order, and provided a basis for a rational classification of slow chemical changes. Examples of reactions of different orders were sought and found, and indeed the existence of this convenient system of grouping not infrequently led to the oversimplification of the real relations. But the obvious molecular explanation of the order in terms of collision probability did not fail to arouse interest in the statistical theory of reaction rates. Even so, an unconscious tendency to compare chemical changes with phenomena of viscous flow or movement under friction persisted, terms such as chemical resistance were endowed with a fictitious significance, and catalysts were likened to lubricants. 

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. 

MILNE, A.A. a contribution to the theory of hydrodynamic lubrication, A solution in terms of the stream function for a wedge shaped oil film WEAR 1, 32-39,1957. 

It has been explained that the lubrication conditions within the sealing zone are subect mainly to fluid film lubrication. From the results measured for the friction coefficient, Hlrano and Ishlwata (1) found that the friction coefficient f was proportional to the characteristic term (ri U/Pi) which is equivalent to the bearing modulus. Furthermore, they verified this theoretically applying foil bearing theory by Blok et.al (2). On the other hand, dagger and Walker (3) defined that the friction... 

This work is a continuation of the Tichy and Bou-Said s theory, which considers convective inertia terms and surface accelerations, and in which shear thinning is also taken into account. The lubricant is described as a power law fluid. One of the main assumptions concerns the use of the velocity... 

Historically, the bulk lubricant has been studied by dielectric spectroscopy and interpreted according to the Debye relaxation theory [3,4]. In impedance terms the system can also be represented according to a theory of colloidal dispersions or polycrystalline media composed of spheres of vastly different conductivities, where the contaminants become a more conductive phase suspended inside the less conductive additive/base oil matrix [6, 34]. Alternatively, when the contaminants are absent, the polar additives can be considered as a conductive discontinuous phase suspended inside insulating continuous base oil. Initially the description of the impedance representation of the fresh, uncontaminated oil will be provided, and then the effects of oxidative degradation and contaminants will be discussed. 

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