Modified Reynolds equation

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-... 

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

In spite of the different assumptions adopted in derivation, all of the modified Reynolds equations presented in the literature up to now has the same form as below... 

Among these models, the Fukui-Kaneko model is regarded as the most accurate one because it is derived from the linearized Boltzmaim equation. However, the flow rate coefficient, Qp, in the Fukui-Kaneko model, is not a unified expression, as defined in Eqs (6)-(8). This would cause some inconveniences in a practical numerical solution of the modified Reynolds equation. Recently, Huang and Hu [17] proposed a representation of Qp, as shown in Eq (10), for the whole range of D from 0.01 to 100, by a data-fitting method, to replace the segmented expressions of the Fukui-Kaneko model... 

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). 

In order to analyze the dynamic behavior of a magnetic head, time-dependent pressure should be calculated. This can be attained by solving the modified Reynolds equation including a squeezing term, i.e.. 

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. 

Huang, P., Niu, R. J., and Hu, H. H., A New Numerical Method to Solve Modified Reynolds Equation for Magnetic [31] Head/Disk Working in Ultra Thin Gas Films, Sci. China,... 

R. M. Crone, M. S. Jhon, T. E. Karis, and B. Bhushan, The behavior of a magnetic sliders over a rigid-disk surface A comparison of several approximations of the modified Reynolds equations, Adv. Inform. Storage Syst. 4, 105-121 (1992). 

Film thinning is modeled using a modified Reynolds equation [41] for the flow between two circular parallel disks, which gives the rate of film thinning as ... 

The inertia effect in hydrodynamic thrust bearings are considered here with finite width stepped oil film profiles. In the analysis, the momentum and continuity equations are integrated across the oil film thickness, and combined to produce the modified Reynolds equation. The oil film pressure are obtained from the Reynolds equation by the finite element method, and corrected by a finite difference scheme. 

The third method employs Galerkin s method in a finite element formulation to solve the single modified Reynolds equation, which is obtained by introducing explicit expressions of, V into the continuity equation (2,5). An appeal of the finite element method is its ease of implementing varying grid size close to the step. Similar technique is adopted in... 

The authers (1) presented the equivalent flow model for an analysis of journal bearings with cavitation. The modified Reynolds equation is applied to the oil film region and the cavitation region in common. This model is based on the extreme difference of the fluidity between the oil and the gas in the cavity, and considers the oil mass conservation throughout the bearing clearance. 

This contact between the eye and the eyelid through the liquid lachrymal as the third body leads to a tribological approach to this phenomenon. This contact between three bodies is coupled. It takes into account the contact of the eyelid on the lachrymal fluid as well as that of the lachrymal fluid on the cornea and the lens. The intrinsic performances of every element are determined using basic equations. Thus, the equation governing the behavior of the lachrymal fluid is that of a modified Reynolds equation [13], assuming the following hypotheses ... 

Coupled with the modified Reynolds equation, the equation of the motion of the thin fluid film with regard to the porous cornea or lens requires [7,8] the resolution of the Darcy s equation which reads ... 

The oil profile is imposed in the inlet of the contact. The position of the boundary (meniscus) between the two sub-domains is found by solving simultaneously the system of equations composed by the load equation (8), the modified Reynolds equation (6), the complementarity equation (5)... 

---