分形表面模型接觸力分析的基本假設

Basic assumptions for contact force of fractal surface models

陳彥珽(Yan-Ting Chen)

指導教授 ： 盧中仁

國立臺灣大學/工學院/機械工程學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201902389

摘要

摩擦磨損普遍存在於機械工程中，影響機械和零件的壽命，若設計不當容易造成材料損耗及浪費， 工程中處處存在相接觸的表面， 而表面粗糙的形貌，是直接影響摩潤的根本原因，因此表面粗糙的接觸行為有其研究的必要性。
分形表面粗糙模型相較於傳統基於隨機分佈微凸體的統計模型具有和尺度無關的特性。然而在分析分形粗糙表面的接觸行為時，還是必須借助傳統微凸體分析的結果。明確的說，必需採用下列三種假設：（ 1）二粗糙表面接觸等價於剛性平面和等價粗糙表面接觸；（2）分形粗糙表面的接觸行為等價於一餘弦波表面（3）最後為餘弦波微凸體的接觸行為等價於近似圓球。
本論文利用有限元素法檢驗上述三種假設。我們分別比較（i）不同性質球-球模型和彈性等價球 -剛性平面模型的接觸行為；（ii）不同幾何特徵餘弦波、等價球體分別和剛性平面的接觸行為；（iii）不同波長餘弦波表面、單一波長餘弦波表面分別和剛性平面的接觸行為。除了（iii）因數值方法困難沒有明確結果外，依據（i）（ii）的結果我們提出了這兩個假設成立的判準。

關鍵字

分形 ； 碎形 ； 粗糙表面 ； 磨潤學 ； 有限元素法

並列摘要

Friction and wear, which are ubiquitous in the field of mechanical engineering, affect the life and performance of machines. An improper design would result in significance waste of material. Friction and wear exist at all contact surfaces and are directly influenced by the surface topology of the contact surfaces. As a consequence, the study of contact behavior between rough surfaces is an important topic.
Compared to traditional statistical surface model, which treats the surface as the collection of randomly distributed asperities, a fractal surface model has the merit of being scale independent. However, the analysis of contact behavior of fractal surfaces cannot be performed without using the results of traditional statistical surface model. Specifically, three basic assumptions are required as listed below: (1) The contact of two rough surfaces are equivalent to the contact of a rigid smooth surface and a rough surface. (2) The contact behavior of a fractal surface is approximately equal to a sinusoidal surface with a specified wave length. (3) The contact of a sinusoidal surface and a rigid flat surface is equivalent to the contact of a spherical asperity with a rigid flat surface.
In this thesis, we examined the above three assumptions using a commercially available FEM package. We studied the contact behavior between (i) ball-ball and ball-flat rigid surface contact pairs; (ii) single-sinusoidal-surface-rigid flat surface and multiple-sinusoidal-surface-rigid flat surface contact pairs; (iii) single-sinusoidal-surface-rigid flat surface and ball-rigid flat surface contact pairs. Due to numerical difficulties, the study of case (ii) doesn’t generate conclusive results. On the basis of (i) and (iii), we proposed conditions under which assumptions (1) and (3) hold.

並列關鍵字

fractal ； rough surface ； tribology ； finite element method

參考文獻

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