Derivation of basic rheological parameters from experimental elastohydrodynamic lubrication traction curves of low-viscosity lubricants

Abstract

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)

Polyethylene as an Additive for Mineral Oils — Part II: EHL Traction Behavior

“…4, are in agreement with those reported by Muraki and Dong (1999) for a maximum Hertzian pressure varying from 0.5 to 0.7 GPa. Dalmaz (1978) used a pure mineral oil and obtained the traction coefficient of approx.…”

On the concentrated contact as a viscometer

“…A pressure± viscosity curve is then constructed from the viscosity calculated from the assumed exponential relation evaluated at each average contact pressure. Examples of this approach from the literature [9,10] are shown in Figs 4 and 5 as dashed curves. Direct viscometer measurements are plotted as data points.…”

“…Figure 4 represents the viscosity of a phthalic ester, dioctyl phthalate (DOP) [9], and Fig. 5 represents the viscosity of a solvent-refined mineral oil, SR [10]. Paraffinic mineral oils such as SR precipitate a solid fraction under pressure.…”

An experimental characterization of the friction coefficient of a wind turbine gearbox lubricant

“…This is particularly true because at the Hertzian zone of an EHD contact, the central thickness of the lubricant film determines the shear rate, a parameter that must be known to accurately calculate friction. Therefore, without a correct description of the pressure dependence of viscosity, the predicted friction values would not fit the measured data unless viscosity is adjusted . The lubricant viscosity and pressure‐viscosity coefficients needed for such a quantitative EHD prediction of friction for wind turbine lubricants are now unavailable in the literature .…”

“…Therefore, without a correct description of the pressure dependence of viscosity, the predicted friction values would not fit the measured data unless viscosity is adjusted. [7][8][9][10] The lubricant viscosity and pressure-viscosity coefficients needed for such a quantitative EHD prediction of friction for wind turbine lubricants are now unavailable in the literature. 11,12 The database for lubricants contained in the American Gear Manufacturers Association (AGMA) Information Sheet AGMA 925-A03 is a remarkable source for determining viscosity and pressure-viscosity coefficients.…”