On Squeeze Film Damping in Microsystems

Abstract

Classical hydrodynamic lubrication theory has been one of the most successful and widely used theories in all of engineering and applied science. This theory predicts that the force resisting the squeezing of a fluid between two parallel plates is inversely proportional to the cube of the fluid thickness. However, recent reports on liquid squeeze film damping in microsystems appear to indicate that experimentally measured damping force is proportional to the inverse of the fluid thickness to the first power—a large fundamental discrepancy from classical theory. This paper investigates potential limitations of lubrication theory in microsystems by theoretical and computational methods. The governing equations for a Newtonian incompressible fluid are solved subject to two-dimensional, parallel surface squeezing by an open-source computational fluid dynamics program called parallel hierarchic adaptive stabilized transient analysis (PHASTA), and by a classical similarity solution technique. At low convective Reynolds numbers, the damping force is determined as a function of the ratio of a reference film thickness H to a reference direction B along the film. Good agreement with classical lubrication theory is found for aspect ratios H/B as high as 1 despite the fact that lubrication theory requires that this ratio be “small.” A similarity analysis shows that when instantaneous convective Reynolds number is of order 10–100 (a range present in experiment), calculated damping deviates significantly from lubrication theory. This suggests that nonlinearity associated with high Reynolds numbers could explain the experimentally observed discrepancy in damping force. Dynamic analysis of beams undergoing small vibrations in the presence of a liquid medium further supports this finding.

Unsteady squeezing flow of a magnetized nano-lubricant between parallel disks with Robin boundary conditions

“…1). The The conservation equations in an axisymmetric coordinate system (r, z) are (following Hayat et al 25 and Hashmi et al 43 ) 0, u u w r r r 1 ,…”

“…The transient squeezing hydrodynamics of fluids in the gap between two parallel disks is finding increasing applications in liquid-metal lubrication bearing support systems for machines and roller coasters, 1 polymeric injection modeling, 2 automotive shock absorbers, 3 prosthetic bio tribiology, 4 and damping devices in power transmission. 5 The term “squeezing transition” is habitually used in practical situations to define a fluid transition within a shrinking domain of a prearranged length.…”

Tilt effects on experimental measurement of squeeze film damping in microsystems

“…These findings are of critical importance to the accurate determination of hydrodynamic lubrication forces and design of dynamic MEMS subjected to squeeze film damping. previous papers from this group (Marrero et al 2010;Huang et al 2011, the effect of fluid inertia and system nonlinearity on the accurate evaluation of squeeze film damping forces for parallel microscale surfaces was investigated extensively.…”