A Further Investigation on the Viscosity-Density Relation of Lubricant and a Quantitative Numerical Analysis for the Generalized Newtonian Thermal EHL Problem

The new formula proposed by the authors recently for calculating the oil viscosity from the density under isothermal conditions was extended to thermal conditions based on a hypothesis of "the same density, the same viscosity for the same lubricant", and a deeper investigation was made theoretically. By introducing a concept of generalized viscosity to deal with the Eyring shear-thinning model, a number of numerical solutions of thermal elastohydrodynamic lubrication (EHL) for point contacts with squalane as lubricant under various Hertzian pressures and entraining velocities were achieved in a wide range of slide-roll ratio. It is shown that the numerical results of friction coefficient agreed well with experimental data, implying that the new viscosity-density formula was still correct under thermal conditions and the hypothesis between viscosity and density was hold reasonably. A new method to get viscosity without a viscosity-temperature coefficient was put forward when comparing the simulated results of the new viscosity formula and those of the Barus, Roelands and Doolittle formulae. Reasonable solutions were obtained with this method.