本文發展出準穩態分子靜力學奈米級正交單晶矽切削模式，其除可計算切削力、等效應力與等效應變外，亦可計算被切削工件所提升之溫度；進而可進行被切削工件的溫度分佈分析。本文假設奈米級正交切削時被切削工件溫度的提升是由塑性變形熱與摩擦熱兩種熱源產生。本文發展單晶矽之等效應力與等效應變的計算方法為使用三維準穩態奈米靜力學奈米切削模式模擬計算。本文應用力平衡之概念，並以Hooke-Jeeves搜尋法來求解力平衡方程式求出被切削工件每個原子新的位移位置，再推算出切削時切屑的形狀及切削力之大小。求出原子變形位移的位置之後，配合本文有限元素的形狀函數概念，本文發展出對單晶矽材料進行分割，將原子視為節點，晶格視為元素，將單晶矽中各節點進行編碼，並對晶格進行分割，本文建立將晶格分割成36個等應變四面體，並對分割出之晶格進行編碼，即可求得切削工件之三維等效應變，再配合的奈米級薄膜拉伸數值實驗之應力-應變曲線經回歸處理後所得之塑流應力-應變(flow stress – strain)關係式，利用塑流曲線來計算元素之等效應變下所產生之等效應力。本文所發展之塑性變形熱可由被切削工件單晶矽之等效應力與等效應變計算出，進而發展由塑性變形熱產生的提升被切削工件溫度之計算方法。又本文另發展出針對奈米正交切削單晶矽刀面上的工件原子產生摩擦熱的方法及計算刀面上的工件原子的溫度提升之方法。其方法為將莫氏力分解成刀面上之摩擦力，再計算摩擦力做的功所產生的熱量。再將此熱量再分配給刀面上之工件原子及分配給刀具原子，進而計算刀面上的工件原子的溫度提升之數值。本文再將兩種熱源所產生之溫度提升加總計算後，得到被切削單晶矽工件各原子提升之總溫度，再進行溫度場分析。此外本文亦進一步將前述所得被切削單晶矽工件各原子提升之總溫度帶入三維有限差分熱傳方程式，進行熱量傳遞，亦即為將每一步階產生之總溫度數值帶入熱傳方程式計算所得之工件溫度即為下一步階之工件初始溫度，利用此方法計算出每一步階奈米級正交切削之被切削單晶矽工件溫度場，再進行分析。最後並與前述未考慮有限差分熱傳遞所計算的被切削單晶矽工件各原子之溫度提升之數值做比較。

The quasi-steady molecular statics orthogonal nanocutting model of single-crystal silicon developed by the paper not only can calculate the cutting force, equivalent stress and equivalent strain, but also can calculate the temperature rise of the cut workpiece, and furthermore, can analyze the temperature distribution of the cut workpiece. The paper supposes that the temperature rise of the cut workpiece during orthogonal nanocutting is produced by two heat sources, namely plastic deformation heat and friction heat. The calculation method of equivalent stress and equivalent strain of single-crystal silicon developed by the paper is the use of three-dimensional quasi-steady nanostatics nanocutting model to simulation calculation. The paper applies the concept of force balance, and Hooke-Jeeves search method to solve the force balance equation, solve the newly displaced position of each atom of the cut workpiece, and then calculate the shape of chips and size of cutting force during cutting. After the position where the atoms are deformed and displaced is acquired, and employing the paper’s finite-element shape function concept, the paper develops cutting of single-crystal silicon material. Atoms are regarded as nodes, and lattices are regarded as elements. The paper conducts numbering of each node in the single-crystal silicon, and carries out cutting of lattices. The paper cuts lattices into 36 constant -strain tetrahedron, and conducts numbering of each of the cut lattices. Then the three-dimensional equivalent strain of the cut workpiece can be obtained. Using the flow stress-strain relational equation acquired after regression treatment of stress-strain curve in nanoscale thin-film tensile numerical experiment, the paper uses flow curve to calculate the equivalent stress produced under equivalent strain of elements. The flow deformation heat developed by the paper can be calculated by the equivalent stress and equivalent strain of the single-crystal silicon workpiece being cut. Furthermore, the paper develops the calculation method for temperature rise of the cut workpiece produced by flow deformation heat. Besides, the paper additionally develops the method of friction heat produced by workpiece atoms on the tool flank performing orthogonal nanocutting of single-crystal silicon, and the calculation method of temperature rise of workpiece atoms on tool flank. Regarding these methods, Morse force is decomposed to be friction force on tool flank, and the heat produced from the power of friction force is calculated. Such heat is then distributed to workpiece atoms on tool flank and to atoms of cutting tool. Furthermore, the numerical value of temperature rise of workpiece atoms on tool flank is calculated. The temperature rise produced from those two heat sources are added up, and the total temperature rise of the various atoms of the cut single-silicon workpiece can be obtained for making analysis of temperature field. Besides, the paper also further substitutes the total temperature rise of the various atoms of the cut single-crystal silicon workpiece in the three-dimensional finite-difference heat transfer equation in order to perform heat transmission. It refers that the workpiece temperature, calculated by substituting the numerical value of total temperature produced at each step in the heat transfer equation, is just the initial temperature of workpiece at the next step. This method is used to calculate the temperature field of the single-crystal silicon workpiece having undergone orthogonal nanocutting at each step, and further analysis is made. Finally, comparison is made with the numerical values of temperature rise of the various atoms of the cut single-crystal silicon workpiece being calculated above without consideration of finite-difference heat transfer.

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