Analyses of the dependence of lubricant viscosity on temperature and pressure, μ(T,P), have been carried out by using a modified WLF equation in which pressure effects on viscosity are given in terms of the pressure dependence of the glass transition temperature, Tg, and of thermal expansivity of free volume, αf.
where C1 and C2 are well known WLF constants, and μg is a viscosity at Tg. Tg(P) and F(P) are functions for describing the pressure dependence of Tg and αf, respectively. On the basis of the iso-viscous concept for Tg(P), μg has been assumed to have a constant value, 1 TPa•s, at any pressure (SCHEME I). SCHEME I yields a reasonable variation in Tg and αf with pressure for synthetic lubricants, while this analysis suggests a lower μg for mineral oils. In order to improve the applicability of the free volume model, a reference temperature Ts(P), at which the viscosity is 10 MPa•s, has been introduced instead of Tg(P) (SCHEME II). Analyses of dielectric transition for some lubricants and of μ(T,P) in the ASME Pressure-Viscosity Report have confirmed the excellent applicability of the present free volume model over wide ranges of temperature and pressure.
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