Nonlinear Models for Long Cylindrical Squeeze Films Incorporating Elliptical Velocity Profiles

Abstract

Abstract In this paper, nonlinear models for infinitely long, cylindrical squeeze films with arbitrary inner cylinder motion have been derived using three approximation methods. Two kinds of fluid velocity profiles are employed in the derivation with the aim to see the differences caused by using the two profiles, parabolic and elliptical. Each term in the squeeze film force equations is a nonlinear function of cylinder position (or eccentricity). The only differences in the final squeeze film force equations, due to the three approximation methods and the two different velocity profiles, are in the four constant coefficients. Comparing the present nonlinear expressions with existing models shows that: (1) the viscous, unsteady inertia and convective inertia terms, acting in the normal direction, are essentially the same as in other studies; (2) the normal-direction centripetal inertia term shows similar variations with position as one published study, but very different from another study; and (3) the three tangential-direction force terms show variations with position which are very different from a previous published study.