The unresolved definition of the pressure-viscosity coefficient

Scott Bair

doi:10.1038/s41598-022-07470-3

Abstract

In the classical approach to elastohydrodynamic lubrication (EHL) a single parameter, the pressure-viscosity coefficient, quantifies the isothermal pressure dependence of the viscosity for use in prediction of film thickness. Many definitions are in current use. Progress toward a successful definition of this property has been hampered by the refusal of those working in classical EHL to acknowledge the existence of accurate measurements of the piezoviscous effect that have existed for nearly a century. The Hamrock and Dowson pressure-viscosity coefficient at high temperature requires knowledge of the piezoviscous response at pressures which exceed the inlet pressure and may exceed the Hertz pressure. The definition of pressure-viscosity coefficient and the assumed equation of state must limit the use of the classical formulas, including Hamrock and Dowson, to liquids with high Newtonian limit and to low temperature. Given that this problem has existed for at least fifty years without resolution, it is reasonable to conclude that there is no definition of pressure-viscosity coefficient that will quantify the piezoviscous response for an analytical calculation of EHL film thickness at temperatures above ambient.

Highlights

In the classical approach to elastohydrodynamic lubrication (EHL) a single parameter, the pressureviscosity coefficient, quantifies the isothermal pressure dependence of the viscosity for use in prediction of film thickness
The classical approach to EHL has not employed an accurate description of the pressure dependence of the viscosity of the lubricant, a comprehensive report on the piezoviscous effect for lubricating oils has been available since 1 9531 and the methodology for viscosity measurement to 1.2 GPa has existed for nearly a c entury[2]
Work in EHL employed a fictional narrative invoking an 1893 a rticle[3] by a geologist, Carl Barus, on the effective viscosity of extruding solids. His pressure-viscosity formula was linear and he rejected the exponential form, stating “marked violence is done to the observations”, the relationship given his name in EHL is the exponential form

Summary

Introduction

In the classical approach to elastohydrodynamic lubrication (EHL) a single parameter, the pressureviscosity coefficient, quantifies the isothermal pressure dependence of the viscosity for use in prediction of film thickness. The definition of pressure-viscosity coefficient and the assumed equation of state must limit the use of the classical formulas, including Hamrock and Dowson, to liquids with high Newtonian limit and to low temperature. Given that this problem has existed for at least fifty years without resolution, it is reasonable to conclude that there is no definition of pressure-viscosity coefficient that will quantify the piezoviscous response for an analytical calculation of EHL film thickness at temperatures above ambient.

Findings

Discussion

Conclusion