Observations on the Nonlinear Fluid Forces in Short Cylindrical Squeeze Film Dampers

Recent theoretical work by Tichy and Bou-Said (1991) and El-Shafei and Crandall (1991) has resulted in new theoretical expressions for the nonlinear inertia forces for both short and long cylindrical squeeze film dampers (SFDs). This paper provides alternative derivations for the short cylindrical SFD using as a starting point a simplified two-dimensional Navier-Stokes equation. The resulting expressions for the fluid inertia forces are similar to the Tichy and Bou-Said/El-Shafei and Crandall expressions except for differences in certain numerical constants which can be explained by the different averaging methods used within the squeeze-film thickness. The analyses give additional insight into the temporal and convective origins of the various coefficients. The theoretical results are compared with published theoretical and experimental work involving nonlinear cylindrical SFD behavior. The paper highlights the importance of convective inertia terms when cylindrical SFDs operate at large values of eccentricity ratio.