在粗糙表面的量測中可觀察到多重尺度的現象，亦即，山中有山，大山馱背著小山，而形成由碎形幾何所描述的隨機階級結構。在這樣的幾何結構下，當兩接觸表面負荷加大時(亦即間距縮小時)，較小尺度的峰端會因塑性流而埋沒入其下較大尺度的峰端中；換句話說，較大負荷需要較大尺度的峰端來支撐。
然而在1966年所提出的傳統GW model的解析方式只考慮到單一峰端尺度，其峰端尺度不會隨著兩接觸表面的負荷或間距而改變，是固定在單一尺度上的。在這樣的條件下，某尺度的峰端所解析出來的結果只能適用於某負荷範圍內。
本研究發展出峰端尺度可隨負荷而改變的新模型，稱之為“多重峰端尺度GW model”。首先，以Nayak峰端統計模型為基礎解析出在不同尺度及表面參數下的多重尺度峰端特性，接下來是以材料降伏理論發展出一套可求得支撐負荷的最佳峰端尺度的準則。最後藉由此準則與多重尺度峰端特性建立成多重峰端尺度GW model。
新模型與傳統模型做定性及定量上的比較，顯示出彼此本質上的差異。並探討界面接觸力學的行為如何隨表面參數及材料力學特性參數的改變而變化。最後與實驗做比較，而兩者結果極為吻合。

The observed multiscale phenomenon of rough surfaces, i.e. the smaller mountains mount on the bigger ones successively, renders the hierarchical structures which are described by the fractal geometry. In this situation, when two rough surfaces are loaded together with a higher load, the smaller asperities will undergo plastic flow and immerge into the bigger asperities below them. In other words, the higher load needs to be supported by the bigger asperities.
However, when the GW model was proposed in 1966, its analytical method considered that the length-scale of asperities is fixed, which is independent of load (or surface separation). In such condition, the analytical results for a specific asperity length-scale can only suit the situation of a certain narrow range of load.
In this research, a new model, called the multiscale GW model, has been developed, which takes into account the relationship between the load and the asperity length-scale. At first, based on the Nayak’s model the multiscale asperity properties with different surface parameters have been derived, and based on the material yielding theory a criterion for determining the optimal asperity length-scale, which functions as supporting the load, is developed. Then both of the above are integrated into the GW model to build the multiscale GW model.
The new model is compared with traditional one qualitatively and quantitatively and show their essential differences. The effects of surface parameters and material parameters are discussed in this model. Finally a comparison with the experiment is made, and reveal the good coincidence.

摘要-----------------------------------------------------Ⅰ
Abstract-------------------------------------------------Ⅱ
目錄-----------------------------------------------------Ⅲ
圖目錄---------------------------------------------------Ⅴ
符號說明-------------------------------------------------Ⅶ
第一章 緒論-----------------------------------------------1
1.1 微接觸力學的應用-------------------------------------1
1.2 文獻回顧 --------------------------------------------2
1.2.1 GW model的演進-------------------------------------------------2
1.2.2 峰端特性統計模型的演進---------------------------------------3
1.3 傳統單一峰端尺度模型的缺陷-----------------------------------------4
1.4 研究目的及論文架構-----------------------------------------------------7
第二章 隨機表面的特徵化及多重尺度峰端特性--------------------------8
2.1 隨機表面的特徵化--------------------------------------------------------8
2.1.1 表面參數的使用---------------------------------------------------8
2.1.2 垂直方向的統計特徵--標準差及平均高度------------------9
2.1.3 水平方向的統計特徵--自我相關長度------------------------9
2.1.4 小尺度空間下的自我相仿特性--碎形維度-----------------11
2.1.5 表面參數對表面形貌的影響-----------------------------------14
2.2 多重尺度峰端特性的取得----------------------------------------------19
2.2.1 Nayak峰端特性統計模型的使用-----------------------------19
2.2.2 表面參數及高頻濾波頻率 對峰端特性的影響---------22
2.3 模擬表面的峰端特性及與解析結果比較----------------------------27
第三章 多重峰端尺度GW-model-------------------------------------------29
3.1 單一峰端尺度模型的推導----------------------------------------------29
3.2支撐負荷的峰端尺度及多重尺度效應的考慮----------------------33
3.3 與傳統單一峰端尺度GW Model的比較----------------------------37
第四章 解析結果及與實驗比較---------------------------------------------40
4.1 真接觸面積與負荷的關係----------------------------------------------40
4.2 介面剛性與負荷的關係-------------------------------------------------41
4.3 峰端高度分佈與負荷的關係-------------------------------------------42
4.4 峰端尺度與負荷的關係-------------------------------------------------44
4.5 與實驗結果比較----------------------------------------------------------45
第五章 結論與未來研究方向------------------------------------------------50
附錄A：產生隨機表面的演算法---------------------------------------------52
參考文獻--------------------------------------------------------------------------55

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