Combined effects of non-Newtonian rheology and fluid inertia forces on the non-linear transient behaviour in circular squeeze films

Abstract

On the basis of the momentum integral method and the microcontinuum theory, the combined effects of total fluid inertia forces and non-Newtonian couple stresses on the non-linear squeeze film characteristics between parallel circular discs are presented. The squeeze-film lubrication equation is derived from the Stokes couple-stress motion equation retaining total fluid inertia terms to take into account the effects of non-Newtonian couple stresses resulting from the base oil blended with various types of additives, and the effects of local fluid inertia and convective fluid inertia. The non-linear motion equation for the squeezing disc is then numerically solved by using fourth-order Runge-Kutta method. Comparing with the Newtonian-lubricant inertialess case, the combined effects of fluid inertia forces and non-Newtonian couple stresses provide a significant increment in the response time of the squeeze film. The operating life of squeeze film discs are therefore lengthened, especially for larger couple stress parameters, Reynolds numbers and body inertia parameters. A design example is provided to facilitate the engineers assessing the extent to design the non-linear squeezing film discs considering the combined effects of total fluid inertia forces and non-Newtonian couple stresses.