The EHL theory based on the Reynolds equation, which had been proposed by Dowson et al. in 1959, has made it possible to determine the oil film thickness and pressure distribution at the Hertz contact surfaces for bearings, gears and traction drives. The EHL theory is related to the high-pressure density of lubricant. Therefore, in this study, the two-variable quadratic multinomial regression density equation was derived using a statistical analysis, and was applied to estimate the high-pressure density of lubricant. Additionally, the obtained results were compared with five known density equations. Consequently, it was found that this equation could be automatically calculated via the regression analysis; moreover, this equation had derivability and estimability. Furthermore, the errors (%) for the standard deviation were the smallest, underlying the effectiveness of this method for statistical analysis. Notably, both deductively and inductively, this equation is equivalent to the five known equations. Therefore, this equation simply examines physical properties such as density from a different viewpoint. However, because statistical analysis is used in this equation, it has no physical meaning. Additionally, as found in this study, the density data were included in this equation, similar to the theoretical equations.

Dilute concentration as 0.1 mass% of oleic acid in PAO as a base oil was detected successfully by micro-SEIRAS (surface enhanced infra-red absorption spectroscopy) which is newly developed with a micro-Fourier transform infrared spectroscopy (FTIR) and a hemispherical silicon prism coated with a thin layer of Au for SEIRAS. In situ observation of lubricant film by micro-SEIRAS was carried out under lubricating conditions. When lubricant oil between the prism and the steel ball was sheared by rotating ball, the absorbance of carboxyl group increased gradually and the absorbance was maintained even after the termination of shearing. The result suggests that oleic acid was concentrated in a thin layer on the prism from lubricant oil by shearing. According to the observation, it was found that the concentrated layer of oleic acid was formed by shearing of lubricant oil and the layer was stable under a static condition. Since monomer of carboxyl group as well dimer was observed under shearing,even adsorbed oleic acid on the prism surface can be detected by SEIRAS.