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研究生:曹韻國
研究生(外文):Yun-KuoTsao
論文名稱:兩粗糙表面間接觸模型研究-彎月液面力效應
論文名稱(外文):Effects of meniscus force on modeling the contact between two rough surfaces
指導教授:李旺龍李旺龍引用關係
指導教授(外文):Wang-Long Li
學位類別:碩士
校院名稱:國立成功大學
系所名稱:奈米科技暨微系統工程研究所
學門:工程學門
學類:材料工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:86
中文關鍵詞:接觸力學彎月液面力黏著力表面粗糙度
外文關鍵詞:Contact mechanicsMeniscus forceAdhesion forceSurface roughness
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自從人類的科技進入了微奈米的領域後,微奈米力學研究就變得十分興盛,不論是在半導體電子產業、生物醫學、化工、精密機械與微機電等,都有各種不同的應用。在微/奈米級的尺度下,兩界面互相接觸時的接觸行為,如:摩擦、潤滑與黏著等性質,會與巨觀之下的接觸理論十分不同。彎月液面毛細力在微奈米力學研究中,是有很大影響的。特別是在一些生物力學的研究上,彈性物體間的彎月液面毛細力影響特別大,且有關彈性物體間彎月液面毛細力模型的研究不如硬物體間的彎月液面力模型來的完善。所以本研究特別建立一種可應用在彈性物體間的彎月液面力模型,與其在粗糙表面接觸時的應用。
在本文中,我們建立剛體球體與彈性平板間,不同接觸程度的彎月液面毛細力模型。藉由這種模型,我們可以得知每一種接觸程度所產生的彎月液面毛細力大小,特別是球體與平板接觸且產生彈性變形的情形。我們可以計算球體與平板間的黏著力,影響黏著力的因素有很多,包括球體的曲率半徑與平板的楊氏模數,或是液膜的表面張力與球體和平板的接觸角等。球體曲率半徑越高時,黏著力越明顯;平板楊氏模數則相反,楊氏模數越低,黏著力越明顯,且變形量越大。液膜的表面張力越大,黏著力越大;球體的接觸角增加時,黏著力會稍微增加。但平板的接觸角增加時,黏著力卻會稍微減少。有了這些關係式,就可以將不同接觸程度的彎月液面力模型應用在粗糙度的統計中。進而用Greenwood-Williamson模型來計算兩粗糙表面間,彎月液面毛細力產生的黏著力大小與影響因素。我們發現,在兩粗糙表面間距小於10nm時,兩者間的黏著現象是較為明顯的,但兩粗糙表面間距大於10nm以上,兩者間的黏著力就會快速的降低。
Since our technology get into the field of micro/nano scale. The research of micro/nano mechanics has become very prosperous. Especially in the semiconductor industries, biomedical, chemical engineering, precision machinery and microelectromechanical systems(MEMS), micro/nano mechanics have a variety of applications in these fields. In micro/nano scale, the behavior of two surfaces during contact, such as: friction, lubrication and adhesion properties, under the macroscopic contact theory will be different. Meniscus force in micro/nano mechanics is very much affected. Paticularly in some of the biomechanics of the meniscus surface capillary force between elastic objects were particularly large, and the relevant elastic objects meniscus surface capillary force model as hard objects between the meniscus surface force model perfect. Therefore, this study has established an application in the meniscus surface force model between elastic objects, and its rough surface contact.
In this thesis, we establish a meniscus surface capillary force model a rigid sphere and the elastic plate with the different contact situation. By this model, we can see that the value of the meniscus force between two surfaces, in particular the sphere and plate contact and the elastic deformation of the case. We can calculate the adhesion force between the sphere and plate, there are many factors that affect adhesion, including the Young's modulus of the curvature radius of the sphere and plate, or the liquid film surface tension and the contact angles of ball and plate. When sphere radius of curvature increase, the adhesion force becomes more obvious. Plate’s Young's modulus of the opposite, the lower the Young's modulus, adhesion force, the more obvious, and the greater the amount of deformation. The greater the surface tension of the liquid film, the greater the adhesive force; contact angle of the sphere increases, the adhesion force will increase slightly. Flat contact angle increases, the adhesion force but it will slightly reduced. With these relationships, we can model application of different degree of exposure of the meniscus surface force in the roughness statistics. And then of Greenwood-Williamson model to calculate the size and influence factors of the meniscus surface generated by the capillary force between two rough surface adhesion. We found that the adhesion phenomenon between two rough surfaces separated by less than 10nm, the more obvious, but the rough surface spacing is greater than 10nm, adhesion force between the two plate will reduce.
中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
符號總表 X
第一章 緒論
1-1 緒論 1
1-2 文獻回顧 3
1-3 研究動機與目的 6
1-4本文內容與架構 7
第二章 接觸力學理論與彎月液面力模型
2-1 接觸力學模型 12
2-1-1 接觸理論Hertz 模型 12
2-1-2 黏著接觸理論Johnson, Kendall and Robert,
JKR 模型 16
2-1-3 黏著接觸理論Derjagin, Muller and Toropov,
DMT 模型 20
2-2 毛細冷凝現象與彎月液面力學模型 21
2-2-1 凱爾文方程式 (Kelvin equation) 22
2-2-2 拉普拉斯方程式 (Laplace equation) 23
2-2-3 彎月液面毛細力 (meniscus force) 23
2-3 彎月液面毛細力與接觸反作用力 27
第三章 表面粗糙度模型
3-1表面粗糙度介紹 40
3-2表面粗糙度影響磨潤學的原因 41
3-3表面粗糙度的特性描述 42
3-4表面粗糙度的碎形特性 42
3-5高斯機率分佈 44
3-6格林伍德-威廉姆森模型
(Greenwood-Williamson model, GW model) 44
3-7粗糙表面的彎月液面毛細力統計 45
第四章 結果與討論
4-1 彎月液面毛細力與平板變形量 57
4-1-1 楊氏模數的影響 59
4-1-2 球體曲率半徑的影響 63
4-1-3 球體接觸角的影響 64
4-1-4 液體表面張力的影響 66
4-1-5 平板的接觸角影響 67
4-1-6 物體的表面能影響 69
4-2 兩粗糙表面間的黏著力 70

第五章 結論 76

參考文獻 79

附錄 84

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