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Oil film thickness of the oils containing non-functionalized polyalkylmethacrylate (PAMA) was determined under pure rolling condition between 0.001 and 1 m/s and a temperature of 40 • C with a glass disc-on-steel roller tester. The measurements for PAMA solutions with shortchain alkyl group (C1mix) showed a pronounced enhancement of film thickness in the low speeds, while those for long chain (C16mix) fell on the theoretical line. Adsorption test indicated that the increase in film thickness for C1mix was due to the absorbed layer formed by polymer molecule. Then, traction behaviour was studied by varying the rolling speed under a slide/roll ratio of 50 per cent with a sapphire disc-on-steel roller tester. In traction-speed curves, the measurements of all the polymer solutions fell on the base oil line in the high speeds. In the region below 0.1 m/s, as the speed was decreased, the traction for high-molecular-weight (HMw) C1mix and C16mix solutions deviated downward from the base oil line. The traction-film parameter curves suggested that the traction for C1mix and HMw-C1mix solutions was influenced by the mutual interaction of polymer molecules in the partial EHL region including thin-film lubrication, where the concentration of the polymer is high compared to bulk solution.

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)

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