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研究生:張晉翔
研究生(外文):Jin-Hsiang Jang
論文名稱:微結構空氣阻尼之開孔效應
論文名稱(外文):Air Damping on Perforated Microstructures
指導教授:薛文証黃維信黃維信引用關係
指導教授(外文):Wen- Jeng HsuehWei- Shien Hwang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:工程科學及海洋工程學研究所
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:76
中文關鍵詞:加速度計開孔效應微結構空氣阻尼
外文關鍵詞:air dampingsqueeze flimaccelerometermicrostructures
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本論文主要是研究空氣阻尼作用對於微結構所造成的影響,並以史托克方程式作為出發點,經由假設之後,將簡化後的方程式作為控制方程式,此方程式即為可壓縮雷諾方程式。在控制方程式確定之後,針對不同幾何形狀之薄板以及不同的邊界條件作其空氣阻尼的分析,探討不同條件下的空氣作用力與頻率的關係為何?且進一步模擬具有開孔洞之幾何形狀的空氣阻尼作用。
最後,利用所得到的分析結果,實際應用於微加速規之上,探討微結構受空氣阻力後,其品質因素的變化為何?並利用具有同心圓的分析資料,以面積近似法去降低空氣的效應,觀察微結構在何種條件下,可得到最佳的品質因素。
This paper investigates effects of squeeze film for microstructures that oscillates in the normal direction. The governing equation uses the Navior-Stokes equation and makes several assumptions. We not only consider the thin plate of different geometric shape but also consider the thin plate with different kinds of boundary condition. Furthermore, utilizing the analytic results of the circular plate to simulate the perforated microstructures.
Finally, we use the analytic results to apply on a capacitive micro-accelerometer and discuss variant performance while different numbers and sizes of perforations.
目錄 I
圖目錄 III
符號表 V


第一章 緒論 1
1-1 前言 1
1-2 研究動機 2
1-3 文獻回顧 4

第二章 平板之擠壓薄膜效應 8
2-1 雷諾方程式之應用 8
2-2 無限長平板之擠壓薄膜效應 11
2-3 矩形平板之擠壓薄膜效應 13
2-3-1 四邊開放式矩形平板之擠壓薄膜阻尼分析 14
2-3-2 一邊封閉矩形平板之擠壓薄膜阻尼分析 17
2-3-3對邊封閉矩形平板之擠壓薄膜阻尼分析 19
2-3-4兩相鄰邊封閉矩形平板之擠壓薄膜阻尼分析 20
2-3-5 三邊封閉矩形平板之擠壓薄膜阻尼分析 21
2-3-6四邊封閉矩形平板之擠壓薄膜阻尼分析 22

第三章 圓形平板之擠壓薄膜阻尼 25
3-1 週邊開放圓形平板之擠壓薄膜阻尼 26
3-2 內外側開放之具開孔圓板之擠壓薄膜阻尼 27
3-3 外封內開之具開孔圓板之擠壓薄膜阻尼 29

第四章 數值分析例 31
4-1 加速規之致動原理與模型 31
4-2 加速規之設計法則 33
4-3 微加速規之分析與設計 37
4-3-1 不同開孔數目、邊長之加速規設計 38
4-3-2 開孔面積保持定值之加速規設計 49

第五章 結論與未來展望 53
5-1 結論 53
5-2 未來展望 54

參考文獻 74
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[3] J. R. Lin, “squeeze film characteristics between a sphere and a flat plate:couple stress fluid model”, Computers and Structures, Vol. 75 , 1995, pp. 73-80.

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[8] J. X. Zhang, “Fluid inertia effects on the performance of short and long squeeze film dampers executing perioic vibration”, Journal of Tribology, Vol. 119, 1997, pp. 306-314.

[9] W. E. Langlois, “Isothermal squeeze films”, Quarterly of Applied Mathematics, Vol. 20, 1961, pp. 131-150.

[10] J. J. Blech, “On Isothermal squeeze films”, Journal of Lubrication Technology, Vol. 105, 1983, pp. 615-620.

[11] W. S. Griffin, “A Study of Fluid Squeeze-Film damping”, Journal of Basic Engineering, 1966, pp. 451-456.

[12] R. B. Darling, “Compact Analytical Modeling of squeeze film damping with Arbitrary Venting Conditions Using a Green’s Function Approach”, Sensors and Actuators, A105, 1998, pp. 32-41.

[13] J. B. Starr, “Squeeze-Film damping in Solid-State Accelerometers”, Solid-State Sensor and Actuator Workshop, 1990, pp. 44-47.

[14] T. Veijola, “Equivalent-Circuit Model of the Squeezed Gas Film in a Silicon Accelerometer”, Sensors and Actuators, A48, 1995, pp. 239-248.

[15] T. Veijola, “Compact damping Models for Laterally Moving Microstructures with Gas-Rarefaction Effects”, Journal of Microelectromechanical Systems, Vol. 10, 2001, pp. 263-273.

[16] T. Veijola, “Compact Model for the Squeezed-Film damping Including the Open Border Effects”, Proc. MSM2001, pp. 76-79.

[17] E. S. Hung, “Low Order Models for Fast Dynamical Simulation of MEMS Microstructures”, Proc. Solid-State Sensor and Actuator Workshop, Vol. 2, 1997, pp. 1101-1104.

[18] K. Minami, “Simple Modeling and Simulation of the squeeze film Effect and transient response of the MEMS device”, Conference of Micro Electro Mechanical Systems, 1999, pp. 338-343.

[19] M. Turowski, “High-Fidelity and Behavioral Simulation of Air damping in MEMS”, Conference of Modeling and Simulation of Microsystems, 1999, pp. 241-244.

[20] G. Schrag, “Physically based modeling of squeeze film damping by mixed-level system simulation”, Sensors and Actuators, A97-98, 2002, pp. 193-200.

[21] Yao-Joe Yang, “Numerical Simulation Of Compressible squeezed Film damping”, Solid-State Sensor and Actuator Workshop, 1996, pp. 76-79.

[22] S. Vemuri, “Low-Order squeeze film Model for Simulation of MEMS Devices”, Proc. MSM2000, pp. 205-208.

[23] J. Mehner, “Simulation of Gas damping in Microstructures With Nontrivial Geometries” , .Conference of MEMS , 1998 , pp. 172-177

[24] C. C. Cheng, “Tuning the Quality Factor of Bulk Micromachined Structures Using the squeeze film damping”, Proc. Solid-State Sensor and Actuator Workshop, 2003, pp. 1590-1593.

[25] M. Bao, “Modified Reynolds'' equation and analytical analysis of squeeze-film air damping of perforated structures”, Journal of Micromechanics and Microengineering, Vol. 13, 2003, pp. 795-800.

[26] C. Bourgeois, “Analytical Modeling of Squeeze-Film damping in Accelerometers”, Proc. Solid-State Sensor and Actuator Workshop, Vol. 2, 1997, pp. 1117-1120.

[27] M. Bao, “Squeeze-film air damping of thick hole-plate”, Sensors and Actuators, A108, 2003, pp. 212-217.

[28] E.S. Kim, “Effect of holes and edges on the squeeze film damping of perforated micromechanical structures”, Micro Electro Mechanical Systems, MEMS''99. Twelfth IEEE International Conference on, 1999, pp. 296-301.

[29] S. D. Senturia, “Microsystem Design”, Kluwer Academic Publishers, 2001, pp. 332-339.
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