本文所建立的三維準穩態分子靜力學奈米級正交切削模式建立與分析，其先以正交切削為例，且是以計算每個原子的運動軌跡方法來直接求解每個原子移動一小距離時，莫氏力在X方向、Y方向和Z方向的平衡方程式，來定出原子的新運動位置。由於本文的平衡方程式具有三個需要求解的未知數x、y、z位置座標，藉由虎克 吉夫斯(Hooke-Jeeves)搜尋法求出新的運動位置，並確認此新位置達到整個系統的最小能量位置，以確認系統達到平衡。本文建立三維準穩態分子靜力學奈米級正交切削模式建立與分析，有關哪些被切削工件之原子要優先計算其平衡力，本文提出以第一次進刀的刀具原子與被切削工件原子的距離長短小於rc值內的距離優先次序，作為被模擬原子的優先次序。在第二次進刀的時候的依據第一次進刀方式的優先次序去計算莫氏力與準穩態平衡的最佳化位置。當切屑往上移動的時候已經超過rc值，鑽石刀具的刀尖原子與被切削工件原子間，計算原子平衡力之原子優先次序，還是依照第一次進刀時的計算優先次序方式相同。而後將所求的原子位移，配合有限元素法裡的形狀函數的概念來計算出節點與元素的等效應變，再由塑流應力-應變曲線(flow stress-strain)的關係式，導出工件的等效應變與等效應力的分布趨勢，進而並推導出計算各方向應變與應力之公式。
本文為了驗證切削力，增加做了一個後斜角10度且具圓角(5Å)的鑽石刀具對完美晶格的銅材料切削的模擬，以模擬所得的切削力數值來跟Ikawa【20】的數值來比較，說明本文的三維準穩態分子靜力學奈米級正交切削模擬模式為可接受的。本文並探討後斜角-10度及後斜角40度的鑽石刀具對完美晶格的銅材料，來進行奈米級的正交切削，且分析其切削行為、切削力、等效應變 、等效應力 、X軸向應變 與X軸向應力 的分析，並加以比較。在切屑形狀方面發現後斜角10度與後斜角40度之鑽石刀具，其切屑的形狀差異不大，而以後斜角-10度之鑽石刀具來切削，會造成切屑容易堆積在刀尖前面。再探討後斜角-10度具圓角及後斜角10度具有圓角的鑽石刀具對完美晶格的銅材料，來進行奈米級的正交切削。後斜角-10度具圓角(5Å)的鑽石刀具切削的有較大切削力，而後斜角10度具圓角(10Å)的鑽石刀具切削的有較大的推向力。

The study undergoes the establishment and analysis of the nano-scale orthogonal cutting model of three-dimensional quasi-steady molecular statics. First of all, taking orthogonal cutting for example, the study calculates the movement track of each atom to directly acquire the equilibrium equation of Morse force in X, Y and Z directions when each atom moves a small distance, and then determines the new movement positions of atoms. Since there are three unknown coordinates of x, y and z positions to be solved in the equilibrium equation of this study, the searching method of Hooke-Jeeves is employed to acquire the new movement positions. This new positions are confirmed to have reached the minimum energy position of the entire system, so as to confirm that the system has reached the equilibrium. As to which of the cutted workpiece’s atoms should perform prioritized calculation of their equilibrium forces, the study proposes the priority that the cutted workpiece’s atoms which has smaller distance between the cut workpiece’s atom and the cutter atom of the cutting for the first cutting step is first calculated and this distance is smaller than rc. This priority serves as the priority of the simulated atoms. During cutting for the second cutting step, according to the priority order of the cutting way for the first cutting step, the Morse force and the optimized position of quasi-steady equilibrium are calculated. When the chips move upwards, it has already exceeded rc value. The study calculates the priority order of the atoms of atomic equilibrium force between the tip atom of diamond cutting tool and the atom of cut workpiece. The calculation of the priority order of the atoms of atomic equilibrium force is still in accordance with the priority order of calculation during the cutting for the first cutting step. The subsequently acquired atomic displacement is matched with the concept of shape function in the finite element method to calculate the equivalent strain of nodes and elements. Through the relational equation of flow stress-strain curve, the distribution trend for the equivalent strain and equivalent stress of workpiece is induced. Furthermore, the formulas of strain and stress in different directions can be derived and calculated.
In order to prove the cutting force, this study additionally makes a diamond cutting tool with a rake angle of 10 degrees and a round angle (5Å) to simulate the cutting of the copper material of perfect lattice. The numerical value of cutting force acquired from simulation is compared with the numerical value of Ikawa [20], proving that the nanoscale orthogonal cutting simulation model of three-dimensional quasi-steady molecular statics is acceptable. This study also investigates the nanoscale orthogonal cutting of the copper material of perfect lattice by the diamond cutting tool with a rake angle of -10 degrees and a rake angle of 40 degrees, analyzes its cutting behavior, cutting force, equivalent strain , equivalent stress , X-axis strain and X-axis stress , and then makes comparison. As to the chip shape, it is found that between the cutting by diamond cutting tool with a rake angle of 10 degrees and the cutting by diamond cutting tool with a rake angle of 40 degrees, the difference of chip shape is not great. The cutting by diamond cutting tool with a rakel angle of -10 degrees would easily make the chips accumulated at the front tip of cutter. After that, the study investigates the nano-scale orthogonal cutting of the copper material of perfect lattice by the diamond cutting tool with a rake angle of -10 degrees and a round angle as well as a rake angle of 10 degrees and a round angle. The diamond cutting tool with a rake angle of -10 degrees and a round angle (5Å) has a greater cutting force, whereas the diamond cutting tool with a rake angle of 10 degrees and a round angle (10Å) has a greater pushing force.

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