The Pressure-Velocity Relation

Aircraft, automobiles, industrial machines and many appliances rely on lubricated concentrated contacts to function. A fundamental requirement of elastohydrodynamic lubrication (EHL) is a description of the viscosity of the liquid as a function of pressure. Without a piezoviscous response the liquid cannot generate a film thick enough to separate engineering surfaces. The classical film thickness formulas all require a value for a property known as a pressure-viscosity coefficient; although the many definitions of this property make it unclear as to how it may be extracted from viscosity data.

The classical field of EHL that has existed since the Fifties has employed two assumptions. First, the liquid in the inlet zone must respond in Newtonian fashion and, second, a friction versus sliding velocity curve has the same functional form as a shear stress versus shear rate curve for the liquid. The pressure-viscosity relation may take any form which reconciles these assumptions with experimental measurement of film thickness and friction. Viscometer measurements are ignored.

The first EHL film thickness analysis using viscometer data for the pressure dependence was published in 2006 for squalane[1]. The new Quantitative EHL is now predicting film thickness and friction from properties of liquids that have been measured in viscometers and the value of such data is now recognized. However, physical measurements require a physical sample of any liquid with an interesting chemical structure.

Molecular dynamics simulations have the promise of generating pressure-viscosity data for liquids which have not yet been synthesized but only if the accuracy of the method can be validated.

[1] Liu, Y., Wang, Q. J., Wang, W., Hu, Y., Zhu, D., Krupka, I., & Hartl, M. (2006) Tribology Letters, 23(1), 27-37.