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研究生:莊家慶
研究生(外文):Chuang Chia-Chin
論文名稱:碎形表面模型的接觸溫度與熱阻
論文名稱(外文):Contact Temperature and Thermal Contact Resistance Based on a Fractal Surface Model
指導教授:盧中仁
指導教授(外文):Chung-Jen Lu
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:56
中文關鍵詞:碎形
外文關鍵詞:fractal
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當兩平面相互接觸時,兩平面之間可以分為有相對速度的滑動摩擦接觸;與沒有相對速度的兩不同溫度平面的熱傳接觸。對於這兩種傳熱現象的影響除了接觸平面本身的材料特性外,兩接觸面間的表面型態(surface topography),也是一個相當重要的因素。早期描述粗糙表面的模型多是假設接觸面是由一些隨機分佈的固定幾何形狀的突起所組成。近來的研究發現這些機率分佈函數和量測時所用的尺度有關,亦即接觸面的幾何型態具有碎形(fractal)的特性。所以本文引進Cantor set碎形表面模型來模擬粗糙表面,並分成兩大部分來討論。(1)Cantor set表面模型和光滑熱絕緣剛體間有相對速度時:討論兩面相互摩擦時Cantor表面模型的溫度變化。(2) 溫度不同的Cantor set表面模型和光滑熱絕緣剛體間無相對速度,相互接觸受力時:討論兩平面間的受力大小和熱阻間的關係。

On the interface between two apparently conforming solids, only some asperities are really in contact. The real contact area is much less than the apparent contact area. Most of the heat or energy can only pass through these small contact areas. This distortion of the heat flow causes an increase in thermal resistance that is known as the thermal contact resistance. To date, the influence of surface roughness on the contact resistance and temperature has not been clearly identified. Existing theories on contact temperature and resistance have two major shortcomings: the first one is that they employed non-fractal surface models; the other one is that they neglected the effects of thermal deformation. Use of non-fractal models makes it difficult to unambiguously identify the parameters of surface models. Because of the neglect of thermal deformation, existing models can not simulate the directional effect of contact resistance. In this thesis, we study the thermal contact resistance by employing a fractal surface model and considering the effects of thermal deformation. First, we determine the relationship between the contact temperature, deformation and contact pressure of a single asperity. Then the force equilibrium and compatibility conditions are employed to find the contact force, the total heat passing through the interface, and the associated contact resistance. At last, we study quantitatively the effects of material properties, fractal dimensions, contact pressure, temperature and the direction of heat flow on the contact temperature and resistance.

第一章 導論………………………………………………….1
1 — 1 研究動機……………………………………………….1
1 — 2 文獻回顧……………………………………………….2
1 — 3 研究方法……………………………………………….4
第二章 碎形幾何…………………………………………….6
2 — 1 碎形的起源…………………………………………….6
2 — 2 Cantor 表面模型………………………………………6
2 — 3 碎形維數(Fractal Dimention)………………………….8
第三章理論分析…………………………………………...12
3 — 1 滑動摩擦模型…………………………………………12
3 - 1 — 1 單一柱體滑動摩擦分析………..……………….12
3 - 1 — 2 兩獨立柱體滑動摩擦分析……………………...14
3 - 1 — 3 無因次化………………………………………...18
3 - 1 — 4 Cantor 模型的滑動摩擦分析…………………..20
3 — 2 接觸熱阻模型…………………………………………29
3 - 2 — 1 單一柱體熱傳與熱阻分析……………………...29
3 - 2 — 2 兩獨立柱體熱傳與熱阻分析…………………...33
3 - 2 — 3 Cantor 模型熱傳與熱阻分析…………………..35
第四章分析結果……………………………………………36
4 — 1 滑動摩擦分析結果……………………………………36
4 — 2 接觸熱阻分析結果……………………………………44
第五章 結果與討論…………………………………………51
參考文獻…………………………………………………………..53

參考文獻
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