Li Pu, Fang Yuming
School of Mechanical Engineering, Southeast University, Jiangning, Nanjing 211189, China.
Nanjing University of Posts and Telecommunications, Nanjing 210003, China.
Sensors (Basel). 2015 Mar 25;15(4):7388-411. doi: 10.3390/s150407388.
Squeeze-film damping plays a significant role in the performance of micro-resonators because it determines their quality factors. Perforations in microstructures are often used to control the squeeze-film damping in micro-resonators. To model the perforation effects on the squeeze-film damping, many analytical models have been proposed, however, most of the previous models have been concerned with the squeeze-film damping due to the normal motion between the perforated vibrating plate and a fixed substrate, while there is a lack of works that model the squeeze-film damping of perforated torsion microplates, which are also widely used in MEMS devices. This paper presents an analytical model for the squeeze-film damping of perforated torsion microplates. The derivation in this paper is based on a modified Reynolds equation that includes compressibility and rarefaction effects. The pressure distribution under the vibrating plate is obtained using the double sine series. Closed-form expressions for the stiffness and the damping coefficients of the squeeze-film are derived. The accuracy of the model is verified by comparing its results with the finite element method (FEM) results and the experimental results available in the literature. The regime of validity and limitations of the present model are assessed.
挤压薄膜阻尼在微谐振器的性能中起着重要作用，因为它决定了微谐振器的品质因数。微结构中的穿孔常被用于控制微谐振器中的挤压薄膜阻尼。为了对穿孔对挤压薄膜阻尼的影响进行建模，已经提出了许多解析模型，然而，之前的大多数模型都关注穿孔振动板与固定基板之间的法向运动所引起的挤压薄膜阻尼，而缺乏对穿孔扭转微板挤压薄膜阻尼进行建模的研究，穿孔扭转微板在微机电系统（MEMS）器件中也有广泛应用。本文提出了一种穿孔扭转微板挤压薄膜阻尼的解析模型。本文的推导基于一个包含可压缩性和稀薄效应的修正雷诺方程。利用双正弦级数得到振动板下方的压力分布。推导了挤压薄膜刚度和阻尼系数的闭式表达式。通过将模型结果与有限元方法（FEM）结果以及文献中的实验结果进行比较，验证了模型的准确性。评估了本模型的有效性范围和局限性。
