A modified viscosity approach for shear thinning lubricants

Abstract

Lubrication is essential to minimize wear and friction between contacting surfaces in relative motion. Oil based lubricants are often enhanced via polymer additives to minimize self-degradation due to the shear thinning effect. Therefore, an accurate estimate of the load carrying capacity of the thin lubricating film requires careful modeling of shear thinning. Available models such as the generalized Reynolds equation (GR) and the approximate shear distribution have drawbacks such as large computational time and poor accuracy, respectively. In this work, we present a new approach, i.e., the modified viscosity (MV) model, based on calculating the strain rate only in one point along the vertical direction. We investigate, for both MV and GR, the load, the maximum pressure, and the computational time for (i) sliding (non-cavitating) contacts, (ii) cavitating, and (iii) squeezing contacts. We observe that the computational time is reduced (i) considerably for non-cavitating sliding and rolling contacts and (ii) by several orders of magnitudes for cavitating and squeezing contacts. Furthermore, the accuracy of MV is comparable with the GR model within an appreciable range of bearing numbers. Finally, for each type of boundary motion, we have determined the optimal vertical location to calculate the shear strain rate for MV; while this optimal value is close to half the height of the contact for sliding configurations, for rolling dominated and squeezing contacts it is around one quarter (or three quarter) of their height. We finally provide an analysis to a priori estimate the optimal location of the strain rate.