A New Viscosity-Pressure Formula for Calculating Viscosity from Density of Lubricating Oils

The relation between the density and viscosity of lubricating oils was studied, and a new formula for calculating the oil viscosity from the density under a certain pressure was proposed. With the Dowson-Higginson's density-pressure relation as bridge, the new formula can regress into the Barus's viscosity-pressure formula or the Doolittle's free-volume viscosity formula by simply changing one or two constants. Furthermore, the new formula can become the same form as the Roelands' viscosity-pressure formula but with different constants. Taking squalane as example, a simple way for the determination of the values of constants in the new formula was presented. It is shown that the viscosity predicted by the formula agrees well with experimental data. The isothermal elastohydrodynamic lubrication problem of elliptic contacts was solved with a multi-grid solver by using the new formula and with squalane as lubricant, and the applicability of the new formula proved to be very good.