摘要
A differential equation that is generally effective for squeeze film air damping of perforated plate and non perforated plate as well as in MEMS devices is developed.For perforated plate,the thickness and the dimensions of the plate are not limited.With boundary conditions,pressure distribution and the damping force on the plate can be found by solving the differential equation.Analytical expressions for damping pressure and damping force of a long strip holeplate are presented with a finite thickness and a finite width.To the extreme conditions of very thin plate and very thin hole,the results are reduced to the corresponding results of the conventional Reynolds' equation.Thus, the effectiveness of the generalized differential equation is justified.Therefore,the generalized Reynolds' equation will be a useful tool of design for damping structures in MEMS.
推导建立了一个用于微电子机械 (MEMS)器件压膜空气阻尼的一般化微分方程 .该方程很好地解决了分析有限尺寸孔板的边界和孔板的厚度对压膜阻尼的影响的困难 .结合边界条件求解该方程可以得到各种压膜阻尼结构中的阻尼压强分布和阻尼力 .以长条板为例得到了有限宽度和有限厚度孔板压膜阻尼的压强分布和阻尼力的解析解 ,在非孔板的条件下该解退化为一般传统雷诺方程的解 ,而在无限大薄孔板的极端条件下 ,该解也与传统雷诺方程在此条件下的解相一致 ,进一步证明了该方程的正确性 .因此 ,该一般化的雷诺方程为
基金
国家重点基础研究 (No.G19990 3 3 10 1)
国家自然科学基金资助项目 (批准号 :698760 0 9)~~
