ABSTRACT
The estimation or prediction of EHL film thickness requires knowledge of the lubricant properties. Today, in many instances, the properties have been obtained from a measurement of the central film thickness in an optical EHL point contact simulator and the assumption of a classical Newtonian film thickness formula. This technique has the practical advantage of using an effective pressure viscosity coefficient that compensates for shear-thinning. It is shown below that the practice of extrapolating from a laboratory scale measurement of film thickness to the film thickness of an operating contact within a real machine may substantially overestimate the film thickness in the real machine if the machine scale is smaller and the lubricant is shear-thinning within the inlet zone. The film thickness in EHL concentrated contacts has implications for fric-
tion and for the wear and fatigue life of the rollers. The estimation or prediction of EHL film thickness requires knowledge of the lubricant properties. If the lubricant is Newtonian within the pressure-boosting inlet zone, the film thickness may be calculated from a classical film thickness equation such as that offered by Dowson and Higginson [1]. The required liquid properties are the ambient low-shear viscosity μ0 and the pressure viscosity coefficient α. The pressure viscosity coefficients that are reported in handbooks and jour-
nals come from two sources. Originally, the pressure viscosity coefficient was calculated from measurements of viscosity as a function of pressure at fixed temperature using various definitions of the pressure viscosity coefficient [2]. These are viscosity-derived pressure viscosity coefficients α. Today, in many instances, the reported coefficient has been obtained from a measurement of the central film thickness hc by an optical EHL point contact simulator and the assumption of a classical Newtonian film thickness formula. Typically, the Newtonian Hamrock and Dowson formula [3] is solved for the value of α which will give the measured hc. These are film-derived effective pressure viscosity coefficients αe. Not surprisingly, it is often found that αe < α [4] because of the Newtonian
assumption implicit in the αe calculation [5]. The practical advantage of using an effective coefficient that compensates for shear-thinning is obvious. The
for Line and Point
film-thickness under the same conditions may then be estimated easily using the classical Newtonian formula. The disadvantage stems from the fact that the shear-thinning behavior will change the response of the film thickness to variations in rolling velocity [6], sliding velocity [6], and perhaps to geometry and other material properties. The material of this chapter sounds a warning regarding the extrapolation of
measurements of film thickness using Newtonian formulas in order to estimate the film thickness between machine elements of a different scale (and perhaps elastic modulus) from the original measurement. Significant over-estimations may result at smaller scales. In a departure from convention, the maximum Hertzian pressure pH will be used to quantify the contact loading rather than the normal force P since the pressure of an actual machine element contact would be more closely simulated in an experimental measurement than the normal force and, of course, the rheology is dependent on pressure, not normal force. The generalized Newtonian constitutive equation utilized for shear-thinning will be the single-Newtonian Carreau-Yasuda form, which accurately describes the shear dependence of the viscosity that is measured for base oils in viscosimeters [2, 5] - [8]. We will consider the results of an analytical (asymptotic) treatment of the
problem, which covers two limiting cases of relatively small and large shear stresses [9]. Then we proceed to a numerical solution, which, in turn, is well suited to covering the intermediate case of moderate shear stresses. A line contact is assumed for simplicity. Extension to the point contact that is usually used in EHL measurements can be accomplished and should not substantially change the conclusions.
