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Z.On an inconsistency in the derivation of the equations of elastohydrodynamic lubrication
 Proc. R. Soc. Lond. A
"... Reynolds’s lubrication approximation, one of the cornerstones of °uid mechanics, is constructed on the assumption that the viscosity is independent of the pressure. This assumption is reasonable at low pressures and is appropriate for a large class of applications. However, in an important instance ..."
Abstract

Cited by 8 (1 self)
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Reynolds’s lubrication approximation, one of the cornerstones of °uid mechanics, is constructed on the assumption that the viscosity is independent of the pressure. This assumption is reasonable at low pressures and is appropriate for a large class of applications. However, in an important instance that appeals to the approximation (elastohydrodynamic lubrication (EHL)), the liquid lubricant is subjected to extremely high pressures and the assumption that the viscosity is independent of the pressure no longer holds. On the contrary, pressure dependence of viscosity is severe and the viscosity can increase by several orders of magnitude due to pressure increase. Nevertheless, in the current literature the pressure dependence of viscosity in the derivation of the governing equations for EHL is only recognized a posteriori, that is, after the Reynolds equation has been stated under the assumption of constant viscosity. A consistent derivation of the equations of EHL that takes into account the pressure dependence of viscosity right from the outset leads to additional and hitherto neglected terms in the governing equations. Consequently, construction of a single pressure equation, analogous to the Reynolds equation, is no longer possible without additional, drastic, assumptions. In this study, we provide a consistent derivation of the equations of motion for EHL and, with additional, simplifying assumptions, derive a modi¯ed Reynolds equation. We then provide a comparison between the solutions to the classical equation of Reynolds’s and our modi¯ed equation. The modi¯ed equation results in slightly higher pressures, but at signi¯cantly higher viscosities, than the classical Reynolds equation.
Calculation of Friction in SteadyState and Transient EHL Simulations
"... The total friction through a lubricated contact is a physical quantity which may be measured experimentally in an EHL test rig. Numerical EHL simulations will wish to accurately reproduce the results from directly comparable simulations, and hence the friction will be one of the key variables of int ..."
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The total friction through a lubricated contact is a physical quantity which may be measured experimentally in an EHL test rig. Numerical EHL simulations will wish to accurately reproduce the results from directly comparable simulations, and hence the friction will be one of the key variables of interest. It is shown that not only are very smooth meshes needed to resolve some features of EHL calculations but also that the accuracy achieved on standard quantities of interest such as minimum film thickness varies greatly and may not correlate well to quantities such as friction. The use of adaptive mesh techniques for steady problems is considered in the same context with results presented for how well the accuracy of the friction is maintained. This is generalised to transient cases with surface roughness, hence incorporating numerous pressure spikes needing accurate resolution. 1.