Extending the Validity of Squeeze Film Damping Models with Lower Aspect Ratios

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.