Xu Xiang, Fang Weidong, Bai Jian, Chen Jiaxiao, Yao Yuan, Lu Qianbo
State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou 310027, China.
Huazhong Institute of Electro-Optics-Wuhan National Lab. for Optoelectronics, Wuhan 430074, China.
Sensors (Basel). 2022 Jan 29;22(3):1054. doi: 10.3390/s22031054.
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.
挤压薄膜空气阻尼是微机电系统（MEMS）器件设计中的一个重要因素，因为它对振动结构的动态性能有很大影响。然而，挤压薄膜空气阻尼的传统理论结果是从雷诺方程推导出来的，其中存在与真实结果的偏差，特别是在低纵横比情况下。虽然已经花费了大量精力来证明这种偏差是由于忽略了薄膜上的压力变化引起的，但定量研究仍然难以实现。本文着重研究挤压薄膜空气阻尼的有限尺寸效应，并使用一组模拟进行数值研究。从挤压薄膜空气阻尼的原始模型扩展出一个修正表达式，以适用于更低纵横比的情况。基于模拟结果的新快速计算公式能够准确再现具有有限尺寸效应的挤压薄膜空气阻尼，在无边界效应的模型中最大误差小于1%，在有边界效应的紧凑模型中为10.185%。新公式与模拟结果之间的高度一致性表明充分考虑了有限尺寸效应，这为MEMS器件提供了以前无法实现的精确阻尼设计指南。
