The rheological parameters characterizing the non-linear viscosity of lubricants having a low viscosity at a Hertzian contact were determined on an assumption of a parallel film, a Hertzian pressure distribution and the Eyring model expressing the relationship between the shear stress and the shear rate in an elliptical contact. Making a reasonable approximation and taking the variation in viscosity with pressure in the Hertzian contact into account, an approximate formula expressing the mean shear stress with shear rate was derived as a function of a viscosity±pressure coefficient and the representative stress determining the onset of non-Newtonian behaviour. Traction characteristics of two kinds of paraffinic mineral oil were determined with an elastohydrodynamic lubrication tester. Then, a regression analysis using a least-squares method with the proposed formula was applied to the traction measurements, from which the available rheological parameters and the effective pressure were obtained. The viscosity±pressure coefficients derived from traction measurements fall on the extrapolated line from the relation between the viscosity± pressure coefficient and the pressure in the pressure range from atmospheric pressure to 0.3 GPa obtained with a high-pressure viscometer. NOTATION a semi-axis of an elliptical Hertzian contact in the rolling direction (m) b semi-axis of an elliptical Hertzian contact in the transverse direction (m) G elastic shear modulus (Pa) h central film thickness (m) p pressure (Pa) P e effective pressure (Pa) P m mean Hertzian pressure (Pa) P H maximum Hertzian pressure (Pa) r dimensionless radius r à reference radius U rolling speed (m/s) ÄV sliding speed (m/s) á viscosity±pressure coefficient (Pa À1 ) á 0 viscosity±pressure coefficient in the vicinity of atmospheric pressure (Pa À1 ) _ ã shear rate (s À1 ) ç 0 viscosity at atmospheric pressure (Pa s) ç N Newtonian viscosity (Pa s) ç N mean Newtonian viscosity in the contact (Pa s) ô shear stress (Pa) ô 0 representative stress (Pa) ô m mean shear stress (Pa) ô N shear stress based on the Newtonian contribution (Pa) ô e shear stress based on the non-Newtonian contribution (Pa)
The electrohydrodynamic (EH D ) properties of polyolester (POE) in refrigerant environments were determined with a ball-on-sapphire disc-type EH D tester. The ®lm thickness and the traction were both lower for hydro¯uoroether H F E-245mc than for hydro¯uorocarbon (H F C) at an identical gas pressure. This is because of the higher refrigerant concentration (R C) for H F E-245mc than for H F C, which resulted in a lower atmospheric viscosity and a lower viscosity± pressure coef®cient of the refrigerant/POE mixture for H F E-245mc. The boundary lubrication performance was studied with a block-on-ring type tribometer. The coef®cient of frictio n in H F E245mc was lower than that in H F C, and H F E-245mc was superior to H F C in terms of antiwear performance. X-ray photoelectron spectroscopy (XPS) of the surface ®lm showed the presence of FeF 2 and iron oxide whose concentration was much higher, and the boundary ®lm thickness was much thicker for H F E-245mc than for H F C. Thus, it was inferred that H F E-245mc adsorbed on to the rubbing surface was decomposed to form an effective antiwear ®lm having a low shear resista nce which resulted in reduction in the frictio n and wear.
EHD traction of polyol ester in some refrigerants is analyzed using the non-Newtonian theory, from which available rheological parameters are determined. Then the rheological parameters are studied in elation to refrigerant concentration. As a result, the viscosity pressure coefficient of the mixtures is inversely correlated with refrigerant concentration in terms of mole per volume, while the representative stress characterizing the non-Newtonian is positively correlated. When the viscous volume relating to the unit of viscous flow is plotted as a function of molecular volume of refrigerant/POE mixture, the relation between them is well described by a single line independent of kinds of refrigerants.
Viscosity-pressure-temperature relations for paraffinic minera1 base oils at pressures up to 0.7 GPa and temperatures between 30 and 90°C were determined using a falling-ball-type viscometer. The oils used were solvent refined oils, hydrocracked oils, and a n oil produced by a wax isomerisation process. The viscosity at pressures higher than those possible I : t : i i the viscometer was then derived by applying a simplified solution to the traction curves determined using a n elastohydrodynamic disc-on-ball tester. When the measured viscosity and the calculated viscosity were plotted against pressure, for the oils with a viscosity index higher than 120 the viscosity derived from traction measurements followed the curve extrapolated to the high-pressure region using either the Yasutomi or Roelands equations (the parameters for which were obtained using the viscometer). However, the calculated viscosity for the lowerviscosity-index oils deviated upwards from the extrapolated curve.
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