### Monday, 11 October 2004 - 3:30 PM

### This presentation is part of : Rajagopal Symposium

### Elastohydrodynamic Lubrication and the Reynolds Thin Film Approximation

**Andras Z. Szeri**, University of Delaware, University of Delaware, Department of Mechanical Engineering, Newark, DE 19716-3140
The Reynolds lubrication approximation is constructed on the assumption of constant viscosity, in particular, that the viscosity is independent of pressure. This assumption is valid at low pressures and isothermal operation, and holds in a large number of applications, with one notable exception, elastohydrodynamic lubrication (EHL). In elastohydrodynamic lubrication, the lubricant is subjected to enormous pressures, there is considerable local heating, and the assumption of constant viscosity no longer holds up. Notwithstanding, in current derivation of the governing equations for elastohydrodynamic lubrication, the pressure and temperature dependence of viscosity is recognized only a posteriori, that is, after the thin film approximation has been made under the assumption of constant viscosity. This process neglects individual contributions form pressure and temperature dependence of viscosity. Individually these effects may be small, but they non-linearly reinforce one another, leading to pressure-temperature corrections that can be considerable. A consistent application of a Reynolds type thin-film approximation for variable viscosity lubricant, where the viscosity is function of both pressure and temperature, yield terms in addition to those contained in the classical Reynolds analysis. In fact, due to the presence of such terms, it is no longer possible to derive a Reynolds type approximation unless added, and severe, assumptions are made. By recognizing pressure and temperature dependence of the lubricant, this talk provides a consistent derivation of the equations that govern elastohydrodynamic lubrication and, with additional, simplifying assumptions, derives a Reynolds type equation.

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