Determination of variable pseudo-viscosity coefficients for oils with the Rivlin - Ericksen properties

Modern oils, that lubricate the sliding friction pairs, contain more and more additives. These additives change the oil properties to the non-Newtonian. Furthermore, the friction and wear products and also the products of combustion in internal combustion engines, result in a change of the oil properties, from Newtonian to the non-Newtonian. Frequently, researchers suggest to use so-called „smart fluids”, for example, the ferro-oils as lubricants of sliding friction pairs exposed to strong magnetic fields or the absence of gravity. The ferro-oils are also characterized by the non-Newtonian properties. The viscosity characteristics of these oils are described rather well by the Rivlin-Ericksen constitutive equation. The Rivlin-Ericksen constitutive equation contains the coefficients, which are difficult to estimate or determine experimentally. One of the possibilities to determine these coefficients is the method proposed by Prof. K. Wierzcholski [12]. This method requires the experimental results of dynamic viscosity changes as a function of shear rate. The measurements of dynamic viscosity should be conducted for the widest possible range of shear rates. Then, using the viscosity curves and nonlinear system of equations, the auxiliary coefficients are determined. These coefficients generate the equations that describe the variable pseudo-viscosity coefficients. Not all oils have an intensive exponential character of viscosity changes in dependence on shear rate. In these cases it is possible to determine the constant coefficients of pseudo-viscosity [1, 3, 7, 8]. This paper presents the examples of determination of the variable pseudo-viscosity coefficients for the selected lubricating oils and ferro-oils.