Elastohydrodynamic Lubrication—Improvements in Analytic Solutions

Abstract

The paper develops a statement of film shape within an elastohydrodynamic conjunction and shows that the Grubin (parallel conjunction, high elastic modulus) and the Baglin and Archard (tilting pad conjunction, low elastic modulus) models are its asymptotes. A film thickness equation is presented for low values of the parameter N₃ = αE′(η₀/E′R)^1/4. The relationship between inlet pressure and maximum Hertzian pressure p₀ is explored and it is shown that /p₀ is primarily a function of N₃. Evaluation of the modified inlet condition, = (1/α)(1 − e^−α), allows a limit to be placed on the validity of the Grubin model and provides a physical explanation for the differences between the Grubin and the Dowson and Higginson formulae for film thickness. In this way it is shown that, although film thickness may be evaluated to within a few per cent by the condition = 1/α, it does not follow that the conjuction is parallel or that = ∞. The model thus provides a link between the simpler analytic theories of elastohydrodynamic lubrication and those based on computer analyses.