The Pressure-Viscosity Coefficient for Newtonian EHL Film Thickness With General Piezoviscous Response

There has been a long-standing need for a piezoviscous parameter $αfilm$ that, together with the ambient viscosity $μ0$⁠, will completely quantify the Newtonian rheology so that the film thickness for liquids that do not shear-thin in the inlet may be calculated as $h=h(μ0,αfilm,…)$⁠, regardless of the details of the pressure-viscosity response. It seems that Blok’s reciprocal asymptotic isoviscous pressure has certain advantages over the conventional pressure-viscosity coefficient, which is poorly suited for this purpose. The first detailed review of piezoviscous models for low pressures is provided. A simulation code that is apparently stable for all realistic pressure-viscosity response was utilized with diverse piezoviscous models and model liquids to develop a satisfactory definition of $αfilm$ that reads $αfilm=[1−exp(−3)]∕[∫03∕α*μ(0)dp∕μ(p)]$⁠; $1∕α*=∫0∞μ(0)dp∕μ(p)$⁠. In the case of $μ=μ0exp(αp),αfilm=α$ and formulas are provided for other models.