Discussion: “Modeling of Film Thickness and Traction in a Variable Ratio Traction Drive Rig,” (Sharif, K. J., Evans, H. P., Snidle, R. W., and Newall, J. P., 2004, ASME J. of Tribology, 126(1), pp. 92–104)

Abstract

Ordinary shear-thinning affects EHL film thickness by reducing the central thickness from the theoretical Newtonian value 1 and ordinary shear-thinning affects traction in point contacts by shifting the logarithmic traction gradient to higher rates 2 in a manner indistinguishable from a reduction in pressure dependence of low shear viscosity at high pressure 2. The models selected by the authors for shear-thinning are not recognizable as ordinary shear-thinning. The authors’ Eq. (10) was Eyring’s sinh law model for thixotropy 3. Thixotropy should not be an issue here since the traction fluid is not known to contain wax and in any event the waxy structures studied by Eyring were quite weak with approximately τo=0.01 MPa3. Eyring made very clear his opinion that the sinh law, Eq. (10), is not an accurate description of shear-thinning 4. The authors’ Eq. (11) is not constitutive as it results from inhomogeneous shear 5. The viscosity extrapolation rule selected by the authors also has no physical basis. Two years ago, at the request of one of the authors for an accurate extrapolation, one of the discussers (S.B.) provided the authors with the parameters of the Tait-Doolittle free volume formulation for the same early version of Santotrac 50 6. This free volume formulation has been used by physical chemists to extrapolate viscosity to the glass transition pressure 7 in order to calculate pressure fragility. We have found it to be accurate for pressure extrapolations for another traction fluid 8. The authors neglected this formulation in favor of exponential extrapolation and thus discount the greater-than-exponential response that is known to be a feature of glass forming liquids and that the authors acknowledge to be important. Numerical simulations should ideally provide traction and film thickness predictions from the best available viscosity-temperature-pressure correlation, but these simulations should include shear-thinning. For example the fluid studied in this paper, Santotrac 50, is known to contain a high molecular weight additive. Then even a central film thickness calculation must include shear-thinning to accurately predict the film thickness. To illustrate, the film thickness of the subject traction fluid was measured in rolling point contact at INSA Lyon and the data points are plotted in Fig. 1. The Newtonian solution of Hamrock and Dowson 9 using rheological properties obtained at INSA from the same sample is plotted as a straight curve which can be see to overestimate the film thickness. The same film-thinning effect was reported by Makala et al. 10 for the same traction fluid. Shear-thinning of the ordinary power-law type is required to explain this film-thinning 11 that increases with sliding. The sinh law is inadequate for this purpose as the effect of sliding becomes drastic 11. Also, in Fig. 4 of the original paper, the viscosity of a glass is calculated with a free volume model that assumes a liquid equation of state. Free volume models are useful for their accuracy and for the fact that many of the parameters such as the glass transition temperature have physical meaning and may be obtained by other measurements.