利用有限元素法模擬分析來解決工程問題之技術已發展甚久，且有許多非常成熟的套裝軟體供使用者使用，如ANSYS、MSC.Marc等等，但在使用中往往都會有材料性質無法完全找齊之問題，特別是與溫度相關之性質，使模擬結果無法更加貼近真實情況。本研究主要目的為透過LAMMPS分子動力學模擬軟體來模擬摩擦實驗，藉此模擬得到高溫之動摩擦係數。本研究不僅成功建立起一套完整之指令供使用者使用，且可以依使用者所需求改變金屬類別以及模擬溫度，即可計算出任意兩金屬在任意溫度下之摩擦係數。經比較模擬與文獻提供之常溫摩擦實驗結果所示，單晶模型之誤差為7.66 %、多晶模型之誤差為8.33 %。而本研究又以銅對銅之摩擦為例進行各種不同探針速度、刮痕深度以及模擬溫度對於摩擦特性影響之探討，其中不僅以單晶結構做為討論，還建立了往年鮮少數人討論的多晶結構模擬來加以描述實際材料之結構。
研究結果顯示，在刮痕深度為2.50 nm、模擬溫度為293.0 K以及探針速度從100.0 m/s增加至400.0 m/s時，單晶銅結構之摩擦係數由2.30下降至1.24；多晶銅結構之摩擦係數由1.86下降至1.44。在探針速度為100.0 m/s、模擬溫度為293.0 K以及刮痕深度從1.00 nm增加至2.50 nm時，單晶銅結構之摩擦係數由4.30下降至2.30；多晶銅結構之摩擦係數由2.25下降至1.86。在探針速度為100.0 m/s、刮痕深度為2.50 nm以及模擬溫度從293.0 K增加至1000.0 K時，單晶銅結構之摩擦係數由2.30下降至1.38；多晶銅結構之摩擦係數維持在1.77與1.90之間。

The use of solving simulations using the finite element method has been developed over a long time, and mature software , such as ANSYS, MSC, Marc, and other packages, is available. Some of the software does not include enough material properties, and especially too few properties that are relate to temperature. Accordingly the results of simulations not close to the reality. The study uses the LAMMPS, which is software for simulating molecular dynamics, to simulate the experiments on the friction. The coefficient of the kinetic friction at high temperature is thus obtained. This work successfully developed a complete calculating package of coefficient of the kinetic friction. The user can change the metal and the temperature. Comparing experimental at room temperature in the literature with the results of the simulation yields a, single crystalline model error of 7.66% and a polycrystalline model error of 8.33%. This investigation discusses the effects of the frictional properties by copper on copper at various friction velocities, depth of ploughing and temperatures. In recent years, a few people have studied the polycrystalline model. In this work, not only a single crystalline model but also polycrystalline model is developed and utilized to describe the real structure of a material.
The results obtained herein yield a depth of ploughing of 2.50 nm, a simulated temperature of 293.0 K and an increase in tip velocity from 100.0 m/s to 400.0 m/s. The coefficient of kinetic friction of the single crystalline structure decreased from 2.30 to 1.24 and that of the polycrystalline structure decreased from 1.86 to 1.44. When the tip velocity is 100 m/s, temperature is 293.0 K and the depth of ploughing increased from 1.00 nm to 2.50 nm. The coefficient of kinetic friction of the single crystal structure decreased from 4.30 to 2.30 and that of the polycrystalline structure is decreased from 2.25 to 1.86. Finally, when the tip velocity is 100 m/s, the depth of ploughing is 2.50 nm and temperature increased from 293.0 K to 1000.0 K. The single crystal structure decreased from 2.30 to 1.38 and that of the polycrystalline structure is maintained between 1.77 to 1.90.

論文審定書 i
致謝 ii
摘要 iii
Abstract iv
目錄 vi
表目錄 ix
圖目錄 xi
第一章 緒論 1
1.1 研究目的 1
1.2 文獻回顧 2
1.2.1 摩擦歷史回顧 2
1.2.2 分子動力學歷史回顧 3
1.2.3 摩擦係數實驗歷史回顧 4
1.2.4 摩擦係數模擬歷史回顧 5
1.3 全文架構 7
第二章 基本理論 16
2.1 分子動力學之基本理論 16
2.1.1 勢能函數(Potential Energy Function) 16
2.1.2 系綜種類(Ensemble) 19
2.1.3 積分法 20
2.1.4 溫度修正之積分法 22
2.1.5 鄰近範圍 23
2.1.6 邊界條件 24
2.1.7 軟體介紹 25
2.2 摩擦係數之計算理論 29
2.3 隨機多晶結構製造理論 31
2.4 中心對稱軸參數 32
2.5 田口法(Taguchi Methods)介紹 32
第三章 指令使用方法與研究流程 45
3.1 基本假設 45
3.2 模擬流程 46
3.3 模擬設定 47
3.4 參數設定與收斂分析 50
第四章 結果與討論 62
4.1 模擬之驗證 62
4.2 摩擦係數與模擬溫度之關係討論 65
4.3 單晶結構之摩擦特性討論 66
4.3.1 單晶結構於不同摩擦速度下之摩擦特性影響 68
4.3.2 單晶結構於不同刮痕深度下之摩擦特性影響 71
4.3.3 單晶結構於不同模擬溫度下之摩擦特性影響 73
4.4 多晶結構之摩擦特性討論 76
4.4.1多晶結構於不同摩擦速度下之摩擦特性影響 79
4.4.2多晶結構於不同刮痕深度下之摩擦特性影響 81
4.4.3多晶結構於不同模擬溫度下之摩擦特性影響 83
第五章 結論與未來展望 122
5.1 結論 122
5.2 未來展望 123
參考文獻 125
附錄A 133
附錄B 135
附錄C 137
附錄D 139

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