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Title: | 隨機Cantor集表面模型的接觸溫度與熱阻 Contact Temperature and Thermal Contact Resistance Based on a Random Cantor Set Surface Model |
Authors: | Tsung-Hsin Lin 林宗信 |
Advisor: | 盧中仁 |
Keyword: | 碎形,Cantor集,熱阻, fractal,Cantor set,thermal resistance, |
Publication Year : | 2008 |
Degree: | 碩士 |
Abstract: | 本文探討兩種情形下的接觸溫度和熱阻:一為兩接觸面間有相對速度的滑動摩擦接觸,一為兩不同溫度接觸面間沒有相對速度的熱傳接觸。接觸力和位移的關係以及界面間的傳熱現象,除了受物體的材料特性影響外,兩接觸面間的表面型態(surface topography)亦為一重要因素。常見的描述粗糙表面的模型之一是假設接觸面是由一些隨機分佈的固定幾何形狀之凸起(asperity)所組成。但近來的研究發現,表面凸起機率分佈函數與實際測量時所選用的尺度有關,即接觸表面具有碎形(fractal)的特性。因此本文將利用Cantor 集來建立碎形表面模型以模擬粗糙表面,同時為求更真實的表面模型,將Cantor集的重要參數視為隨機變數。探討隨機Cantor集表面與光滑絕熱剛體平面相接觸的情況,推導下壓力、溫度和熱阻之期望值與標準差,最後再以蒙特卡羅法(Monte Carlo method)來驗證。 This paper studies the contact temperature and thermal resistance at the interface of two solids. Two different cases are considered: (1) sliding contact with Coulomb friction and (2) static contact while the two surfaces have different temperatures. When two surfaces are in contact, the load-displacement relationship and the interfacial heat conduction depend on the surface topography as well as the material properties of the contact solids. Most surface models treat the rough surface as a collection of asperities with a fixed shape. The heights of the asperities are distributed stochastically. However, recent studies showed that conventional geometrical parameters used to characterize the shape of the asperities depend on the resolution of the roughness-measuring instrument. This result suggests the use of fractal geometry for the characterization of surface roughness. In this thesis, we construct a random fractal surface model based on the Cantor set. We study the situation where a random Cantor surface is in contact with a rigid insulated smooth surface. Given the probability density functions of the random fractal parameters, we derive the expectations and standard deviations of the applied load, contact temperature, and thermal resistance. Finally, the Monte-Carlo simulation is employed to verify the analytical results. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/40883 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 機械工程學系 |
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ntu-97-1.pdf Restricted Access | 700.66 kB | Adobe PDF |
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