Abstract
Squeeze film air damping is a significant factor in the design of MEMS devices owing to its great impact on the dynamic performance of vibrating structures. However, the traditional theoretical results of squeeze film air damping are derived from the Reynolds equation, wherein there exists a deviation from the true results, especially in low aspect ratios. While expensive efforts have been undertaken to prove that this deviation is caused by the neglect of pressure change across the film, a quantitative study has remained elusive. This paper focuses on the investigation of the finite size effect of squeeze film air damping and conducts numerical research using a set of simulations. A modified expression is extended to lower aspect ratio conditions from the original model of squeeze film air damping. The new quick-calculating formulas based on the simulation results reproduce the squeeze film air damping with a finite size effect accurately with a maximum error of less than 1% in the model without a border effect and 10.185% in the compact model with a border effect. The high consistency between the new formulas and simulation results shows that the finite size effect was adequately considered, which offers a previously unattainable precise damping design guide for MEMS devices.
Highlights
The squeeze film air damping effect occurs when a plate is pushed towards a rigid surface with a fluid film in between
The damping coefficient is a significant parameter in the design of MEMS devices, which motivates the need to modify the theory to improve the overall accuracy of the calculation
We have a quantitative investigation of the finite size effect of squeeze film air damping through a series of simulations
Summary
The squeeze film air damping effect occurs when a plate is pushed towards a rigid surface with a fluid film in between. The Reynolds equation was introduced by Tipei half a century ago [12] It is a good approximation of Navier–Stokes equations under the conditions of a small Reynolds number and sufficiently large ratios of structure dimension to fluid film thickness in general cases. This simplification tends to bring notable errors for the microsystem components [13,14], whose ratio of the plate width to film thickness is small In such cases, the damping effect derived from the Reynolds equation tends to be underestimated owing to the neglect of the border effect and finite size effect. As the new formulas are based on simulations of scalable parameters, they will be a fast and strong guide in the damping-related analysis and corresponding MEMS design
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