微机械槽板结构空气压膜阻尼的修正雷诺方程

推导出了一个适用于槽板结构压膜空气阻尼的微分方程.该方程与传统雷诺方程的区别是在雷诺方程的左边增加了一个用以表示气体从槽流出所引起的阻尼效应的修正项,并考虑了槽中有限气流通道长度的端头修正.在适当的边界条件下,利用此方程可以求解槽板压膜阻尼的压强分布、阻尼力和阻尼力系数.该槽板结构压膜空气阻尼的微分方程对槽板的厚度和横向尺度没有限制,为分析有限尺寸和有限厚度槽板的压膜空气阻尼提供了一个有用的方法.

Modified Reynolds Equation for Squeeze-Film Air Damping of Slotted Plates in MEMS Devices

A differential equation for calculating squeeze-film air damping in slotted plates is developed by modifying the Reynolds equation. A term is added to account for the effect of airflow through the slots on the air damping of the plate. The end effect of the airflow in the slots is also treated by substituting an effective channel length for the geometric channel length (i. e. the thickness of the plate). The damping pressure distribution, damping force, and damping force coefficient of the slotted plates can be found by solving the equation under appropriate boundary conditions. With restrictions on the thickness and the lateral dimensions of the slotted plate removed,the equation provides a useful tool for analysing the squeeze-film air damping effect of slotted plates with finite thickness and finite lateral dimensions. For a typical slotted plate structure, the damping force coefficient obtained by this equation agrees well with that generated by ANSYS.