Reynolds lubrication equation

Nondimenslonal scales for the Reynolds lubrication equation are defined below ... 

The pressure and deformation calculations were begun by determining the elastic deformation due to the fluid film pressure in a linear gap. Then the new bearing gap thickness was determined. This new thickness was introduced into the Reynolds lubrication equation and the next pressure iteration was calculated. Again the elastic deformation was calculated. This process was repeated until pressure and deformation convergence was obtained. 

The analysis of nearly parallel flows originated in the study of problems of lubrication, and the approach is often called the lubrication approximation. The terminology is unfortunate from our perspective, given that this approach is at the heart of all analytical treatments of polymer processing operations - we would prefer that it be called the polymer processing approximation - but the historical name is well established. The major figure in the analysis of lubrication flows was Osborne Reynolds, and one widely used form of the resulting equations is often called the Reynolds lubrication equation. 

Equation 5.21, which is the Reynolds lubrication equation, is a linear partial differential equation for

Elliptic equations require that the dependent variable (

linear combination of both be specified everywhere on the boundary of the flow domain. It is likely that (Pwill be specified at inflow and... 

The ehl analysis Involves the simultaneous solution of the elastic deformation and lubrication equations. The following form of the Reynolds equation is assumed... 

The authors micro ehl solution technique derives from their earlier solution method for heavily-loaded spherical contacts (3) and the elongated elliptical contacts found in high conformity gears of the Wildhaber-Novlkov type (4), (5). The solution method, which utilises the inverse solution of the Reynolds equation, is as described in the above publications except that the elastic deformation calculation must take account of the deformation produced by pressures acting on adjacent asperities, as mentioned above, and in the solution of the lubrication equations the side boundary condition is one of zero transverse pressure gradient rather than zero pressure. 

Although there are some additional terms and factors due to random surface roughness and its orientation in equation (2-h), the terms occured are local mean pressure p and expectations of function of actual film thickness only. Therefore, on the meaning of statistical average the hydrodynamic lubrication according to this equation is the same as the smooth form. All the analytical and numerical methods used to evaluate the full film Reynold s equation are still applicable. 

Because we are dealing with a compressible medium, which also serves as a lubricant for the spiral groove bearings, the Reynold s equation used in the calculations must contain a 9p/3t term. This term describes the compression and expansion of the lubricant in the film. 

In 1959, Burgdorfer [39] first introduced a concept of the kinetic theory to the field of gas film lubrication. This was to derive an approximation equation, called the modified Reynolds equation, using a slip flow velocity boundary con-... 

The failure of TFL only means a loss of mobility here, but monolayers can stay on solid surfaces to separate the solid surfaces in relative motion, and subsequently sustain a feasible boundary lubrication state [10]. Because the film thickness of TFL is of the nano scale or molecular order, from a mechanical point of view, TFL is the last one of the lubrication regimes where the Reynolds equation can be applied. 

Being compared to conventional Reynolds equations, /12 can be regarded as a modification coefficient of the micropolar effects on viscosity, and its effects are shown in Fig. 8. This shows that the microstructure and microrotation will add an increase in lubricant viscosity. When the ratio hH increases, the viscosity enhancement decreases further increasing the ratio, the modiflcation approaches unit. Because I is related to the molecular size, and h is the film gap, this means that if the problem scale is much larger than the molecular dimension, microrotation and the microstructure of particles will contribute msignrhcantly to the macroscopic properties. The larger N is, the more the increase is, as also evidenced by Fig. 8. 

Singh, C., and Suiha, P., The Three-Dimensional Reynolds Equation for Micropolar-Fluid Lubricated Bearings, Wear, Vol. 76, No. 2,1982,pp. 199-209. 

Modified Reynolds Equations for Ultra-Thin Film Gas Lubrication... 

For steady state lubrication, the general modified Reynolds equation can be written as... 

The main task of head-disk gas lubrication analysis is to calculate the air pressure distributions for various known slider surface structures and given working conditions. In the following calculation examples, the modified Reynolds equation derived by Fukui and Kaneko was used, and the flow rate coefficient Qp was calculated by using the Eq (10). 

Mitsuya, Y., Modified Reynolds Equation for Ultra-thin Film Gas Lubrication Using 1.5-order Slip-Flow Model and Considering Surface Accommodation Coefficient," ASME J. Tri- [25] fcoZ.,Vol. 115,1993, pp. 289-294. 

Li, W. L. and Weng, C. I., "Modified Average Reynolds Equation for Ultra-Thin Film Gas Lubrication Considering Roughness Orientations at Arbitrary Knudsen Numbers, Wear, Vol. 209,1997,pp. 292-230. 

Instead of dividing the computation domain into lubrication regions and asperity contact areas, the mixed lubrication model proposed by the present authors assumes that the pressure distribution over the entire domain follows the Reynolds equation ... 

In this model, there will be no asperity contacts in the traditional sense, but as the film thickness between the interacting asperities decreases below a certain level, the right-hand terms in Eq (9), which represent the lubricant flow caused by pressure gradient, become so insigniheant that the pressure can be predicted by a reduced Reynolds equation [16,17] ... 

An effective viscosity rp has been introduced in the Reynolds equation to describe the non-Newtonian lubricant properties. Ignoring the variation of viscosity across the film thickness, one may evaluate the effective viscosity via the following rheological model that considers a possible shearthinning effect [19],... 

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