ABSTRACT
Modern lubricating oils are formulated with a variety of additives designed to (1) provide beneficial rheological characteristics to lubricants, (2) to stabilize their physical and chemical properties, and (3) to protect lubricated equipment against wear, fatigue, and corrosion. Under the influence of chemical and mechanical stresses and elevated temperatures lubricants tend to undergo certain reversible and irreversible changes. The reversible changes are caused by temporary alignment of polymeric additives in the direction of flow, resulting in an apparent drop in viscosity. When the liquid returns to a state of rest, the viscosity returns to its initial value. This is known as non-Newtonian rheology. The irreversible changes are due to a number of ongoing processes such as stress-induced scission of polymeric additives, oxidation, contamination, etc. The latter detrimental processes limit the useful life of lubricants and can lead to costly repairs and down time if a lubricated system is not properly maintained. In this chapter we focus on the combined effects of the lubricants’ non-Newtonian rheology and stress-induced polymer molecule scission and on changes in lubricant contact parameters. It is established experimentally that many lubricants exhibit some reversible
non-Newtonian rheological properties (see, for example, Bair and Winer [2] and Hoglund and Jacobson [3]). Some rheological models of lubricant behavior are given in Bair and Winer [2] and in Eyring [4]. Also, there exist a number of theoretical studies of the effect of non-Newtonian behavior on various parameters of lubricated contacts such as lubrication film thickness, frictional stress, etc. Examples include studies by Houpert and Hamrock [5] and Kudish [6]. Several experimental studies of non-reversible stress-induced degradation
of lubricants are presented in [7, 9] - [12] while the theoretical studies of lubricant degradation with few exceptions such as [13, 14] dealt only with the processes of homogeneous degradation caused by temperature [15] - [18] and radiation [19] effects. A semi-deterministic attempt of a theoretical study of
for Line and Point
stress-induced degradation was made by Kudish and Ben-Amotz in [20]. In later papers [21] - [23] and in monograph [1] a kinetic probabilistic approach to stress-induced degradation was developed. The approach is based on the derivation and usage of a probabilistic kinetic equation(s) describing the process of stress-induced polymer scission. These kinetic equations have been successfully applied to practical cases. In particular, the numerically simulated data are in excellent agreement with experimental data as it is shown in [1]. In this chapter we consider the application of the developed kinetics ap-
proach to the phenomenon of elastohydrodynamic lubrication of surfaces lubricated with non-Newtonian fluids that undergo some changes caused by lubricant degradation. The problem is reduced to a coupled system of the generalized Reynolds equation for non-Newtonian lubricant flow, the equation for the gap between the surfaces of the elastic solids, the equations for the lubricant flow streamlines, the kinetic equation describing the changes in the polymer molecular weight distribution, and the equations for the lubricant viscosity. The generalized isothermal EHL equations are coupled with the kinetic equation through the lubricant viscosity, which depends not only on lubricant pressure but also on the concentration of polymer molecules and the distribution of their chain lengths. The solution of the problem is obtained using numerical methods similar to the ones described by Kudish and Airapetyan in [24] and [25]. The kinetic equation is solved along the lubricant flow streamlines. The solution of the kinetic equation predicts the density of the probabilistic distribution of the polymer molecule chain lengths. The shear stress and the changes in the distribution of polymer molecular weight caused by lubricant degradation affect local lubricant properties. In particular, the lubricant viscosity experiences reversible and irreversible losses and, in general, is a discontinuous function of spacial variables. The changes in the lubricant viscosity alter virtually all parameters of the lubricated contact such as film thickness, friction stresses, pressure, and gap. Several comparisons of lubricants with Newtonian and non-Newtonian rheologies with and without lubricant degradation are considered. The material presented in this chapter is mainly based on papers [24] - [27].
Let us consider a plane EHL problem. Suppose two infinite parallel cylinders steadily move with linear surface speeds u1 and u2. The cylinders have radii R1 and R2 and are made of elastic materials with Young’s moduli E1 and
