Theoretical and experimental investigation of squeeze film damping in microsystems

Squeeze film damping is one of the most common phenomena that occurs in many devices that involve a surface moving normally in close proximity to another solid surface. The relative motion alternately squeezes out and draws in any fluid in between the two surfaces, which gives resistance to the motion and has a significant effect on the dynamics of the system. Squeeze film damping is often one of the largest sources of parasitic losses in Microelectromechanical systems (MEMS). Therefore an accurate evaluation of hydrodynamic forces due to squeeze film damping effect is critical in the design and optimization of MEMS. Previous studies investigating squeeze film damping in microsystems were mostly focused on devices working in a compressible fluid, such as air. However, inertia effect becomes significant when velocity or oscillation frequency of the surface is high or when the fluid is dense. This force is usually not considered in classical lubrication theory which is typically employed to predict squeeze film damping. Hence discrepancies between theoretical predictions based on classical lubrication theory and experimental results for microsystems in liquids started to emerge in literature, which motivated the studies discussed here.;In this research hydrodynamic lubrication theory at microscale was developed with the objective to better understand the origin of the discrepancies mentioned above. It was found that fluid inertia effects, nonlinearity of the system and inclination angle of the damping surface can all contribute to the discrepancies from the classic lubrication theory. In the content, first of all, a simple perturbation solution was presented for the hydrodynamic force acting on a plate vibrating in an incompressible fluid, with distinctive terms describing inertia and viscous damping to separate the two effects. Similar to the damping constant describing viscous losses, an inertia constant was developed to accurately calculate fluid inertia for small oscillation Reynolds numbers. In contrast with viscous forces which suppress the amplitude of the oscillation, it was found that fluid inertia acts as an added mass, shifting the natural frequency of the system to a lower range. In addition to the linear solution, a nonlinear model for arbitrary oscillation amplitude and Reynolds number was developed. The dynamic response of the system was solved numerically for realistic cases. It was found that system response depended strongly on the actuation frequency and system properties. The critical oscillation amplitude (i.e., the largest amplitudes at which linear model is applicable) was found for a wide range of actuation frequencies. At last, a modified tilt model was investigated for a damping system consisting nonparallel surfaces. A perturbation solution for the hydrodynamic force associated with small Reynolds numbers was obtained. It was found that the pressure distribution, fluid force and damping coefficient were significantly affected by the tilt effect even when the angle of inclination was small.;Besides theoretical investigation, experimental efforts were carried out to validate the theoretical models. Two different techniques were employed to study the squeeze film damping effect in microscale system. In the first method, experimental setup consisted of vibrating devices with micro plate anchored by cantilevers to a vibrating frame. The test specimens were fabricated via a single mask process by microfabrication techniques. The frequency response of the plate in air and five liquids was investigated and the results were compared with theoretical prediction. In the second method, an improved technique was employed from which the damping coefficient was determined directly. The setup consisted a vibrating container which was filled with liquid and a plate that was attached to a force sensor and immersed in the fluid. The damping coefficient was determined directly by measuring the force exerted on the plate and the velocity of the substrate. It was found that the experimental result agreed well with the theoretical predictions provided by the tilt model if a constant correction was added to the original gap between the damping surfaces.