
系統識別號 
U00262008201416323900 
論文名稱(中文) 
可計算彈性回復之彈塑性微接觸模型研究 
論文名稱(英文) 
Study of An Elastoplastic Microcontact Model For Evaluating Elastic Recovery 
校院名稱 
成功大學 
系所名稱(中) 
航空太空工程學系碩士在職專班 
系所名稱(英) 
Department of Aeronautics & Astronautics (on the job class) 
學年度 
102 
學期 
2 
出版年 
103 
研究生(中文) 
鄭光甫 
研究生(英文) 
KuangFu Chang 
學號 
p47001090 
學位類別 
碩士 
語文別 
中文 
論文頁數 
55頁 
口試委員 
指導教授崔兆棠 共同指導教授劉正倫 口試委員張政仁

中文關鍵字 
微接觸
斜度
峭度
粗糙峰高度分佈

英文關鍵字 
microcontact
skewness
kurtosis
asperity height distributions

學科別分類 

中文摘要 
以統計理論為基礎分析微接觸行為的研究中，一般均假設表面粗糙峰的高度分佈為高斯分佈。然而，對於加工平面而言，因為加工方式與材料特性，其粗糙峰高度分佈呈現非高斯分佈。當兩平面相互接觸時，表面原始形貌會因粗糙面承載而產生變化；而在負載卸除並經彈性回復後的最終形貌與負載時的形貌又有相當的差異。
本論文中提出一理論方法探討上述兩種接觸情況的表面形貌變化。兩平面發生接觸時，粗糙峰高度分佈之機率密度函數曲線會變得細長尖銳；試件材料的初始塑性指標較低者，表面經過彈性回復後，粗糙峰高度分佈機率密度函數的預測值與接觸前相當接近；而初始塑性指標較大者，機率密度函數的預測值則與承載時較為接近。本文另探討表面在承受不同負載時，不同初始斜度或初始塑性指標對機率密度函數的斜度及峭度造成的影響；同時也探討在不同機率密度函數的情況下，接觸總負載與總面積的變化情形。將粗糙峰高度分佈機率密度函數固定之模型與本模型比較發現，兩者接觸性質的變化情況有相當的差異。
關鍵字：微接觸，斜度，峭度，粗糙峰高度分佈。

英文摘要 
SUMMARY
Normally, in statistical contact analyses, asperity height distributions are assumed to follow a Gaussian distribution. However, engineered surfaces are frequently nonGaussian, depending upon the material and surface state being evaluated. When two surfaces experience contact deformations, the original topographies of the surfaces vary with different loads, and the deformed topographies of the surfaces after unloading and elastic recovery are different from those of two contacting surfaces under a constant load.
Keywords: microcontact, skewness, kurtosis, asperity height distributions.
INTRODUCTION
All engineered surfaces are microscopically rough, and a contact behavior between two such surfaces is related to the asperities on the surfaces. This characterization is very important to the study of interfacial phenomena, such as friction, thermal and electrical contact resistance. The study of the deformation behavior of contact asperities and accurate modeling of rough surfaces is important in order to discuss contact problems as well.
MATERIALS AND METHODS
A theoretical method is proposed in the present study to discuss the variations of the topographies of the surfaces for two contact conditions. The profile of the probability density function (PDF) of asperity height is sharp if it is obtained from the surface contacts under a normal load. If the material initial plasticity index is small, the PDF of asperity height of a contact surface after elastic recovery is close to that before contact.
RESULTS AND DISCUSSION
The probability density function of asperity heights in the nonGaussian form before the deformations is determined by the initial skewness and the initial kurtosis only. After the deformations, the skewness and the kurtosis no longer remain unchanged, but vary with the interference formed by a rigid, smooth surface in contact with a rough surface. The profile of the g(z*) function becomes steep and sharp as the d*value decreases to a sufficiently small value. When d*<0.5, the calculation of integrating g(z*) is hard to converge unless the error tolerance is enlarged. If the tolerance is loosened, the behavior of the integration of g(z*) demonstrated in the case of d*<0.5 shows a big difference in its characteristic from that demonstrated in the case of d^>0.5. Therefore, the lower bound of d* was set to be 0.5 in the present study. Apart from the initial skewness and initial kurtosis, the mean separation between two contact surfaces is also an important factor in the variations of g(z*). The topography of the rough surface will be changed when two surfaces are subjected to contact deformations. The skewness and kurtosis parameters in the nonGaussian probability density function vary with the mean separation of two contact surfaces. In the present study, these two parameters can be evaluated under the condition of either two contact surfaces under a constant load or the rough surface after elastic recovery. By fixing the contact loads of two surfaces, the negative magnitude of skewness for the surface contacts under a constant load is lowered by increasing the initial skewness of the rough surface. The behavior of kurtosis due to the change in the dimensionless contact load is exactly opposite to that demonstrated in the skewness parameter. If the initial values of skewness and kurtosis are given, the kurtosis value evaluated for the surface contacts under a constant normal load is lowered by decreasing the contact load of two contact surface. The kurtosis value evaluated at the same contact load is lowered by increasing the negative magnitude of the initial skewness. However, the effect of the initial skewness magnitude on the skewness after elastic recovery is exactly opposite to the effect on the skewness created at the contact of a constant load if they are evaluated at the dimensionless contact load. This feature is related to the magnitude of the plasticity index. A relatively high possibility of elastic recovery generally occurs at the contact surface with a small plasticity index. In addition, the degree of the elastic recovery corresponding to a surface with a small initial skewness is always higher than that exhibited in a surface with a large initial skewness. We find the effect of a small plasticity index and a surface with a small initial skewness makes the skewness (negative magnitude) after the elastic recovery be overtaken by the combined effect of the same plasticity index and a large initial skewness. The influence of different initial skewnesses on the contact load or the contact area exhibited in the present model is obviously smaller than that exhibited in the case of assuming constantskewness and constantkurtosis.
CONCLUSION
However, the PDF of asperity height of a contact surface after elastic recovery is closer to that of a contact surface under a normal load if a large initial plasticity index is assumed. How the influence of the dimensionless contact load, the initial skewness, and the initial plasticity index of the rough surface, are investigated on the basis of the topography models mentioned above. The behavior exhibited in the model of the invariant PDF is different from the present model.

論文目次 
摘要 I
Abstract II
誌謝 V
表目錄 VIII
圖目錄 IX
符號說明 XI
第一章 緒論 1
11 前言 1
12 文獻回顧 2
13 研究目的與內容 4
第二章 基本理論 7
21 應用統計理論分析微接觸行為 7
22 粗糙峰彈性接觸變形 8
23 粗糙峰完全塑性接觸變形 9
24 粗糙峰彈塑性接觸變形 9
25 粗糙峰高度機率密度分佈函數 11
26 粗糙峰接觸負載及接觸面積 15
第三章 彈性回復微接觸之統計理論模型 20
31 兩平面接觸時粗糙峰高度分佈機率密度函數的變化 20
32 粗糙峰經彈性回復後高度分佈機率密度函數的變化 24
第四章 結果與討論 29
第五章 結論 34
參考文獻 36
圖/表 41

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