本文旨在建立一預測多道次奈米切削加工深度之理論模式，藉以探討在奈米級藍寶石V型溝槽切削下，欲達到所需切削深度的下壓力與加工道次之關係。同時並應用分子靜力學奈米級切削溫度模擬模式，計算被加工工件所產生之溫度提升結果。
本文應用原子力顯微鏡(AFM)鑽石探針為刀具，進行多道次奈米切削藍寶石基板表面V型溝槽之實驗及分析，並創新提出以比下壓能之觀念進行藍寶石基板奈米V型溝槽的加工深度預測之理論模式。本文提出相同材質之比下壓約能為一定值，並用實驗驗證加工藍寶石基板的比下壓能數值，進而發展出在固定下壓力及固定探針形狀下，以原子力顯微鏡探針進行多道次切削藍寶石基板之切削深度預測方法。
而於奈米切削加工過程，在預達到所需加工深度之奈米溝槽結構下，為避免探針刀具之懸臂及探針頭因施予過大的作用力於工件而造成設備的損壞，往往需以較小的作用力來進行多道次加工以達到所需深度。本文並以所提出之比下壓能理論，再提出一能夠預估最少切削加工道次的估算方法，使在實際加工過程中，探針刀具能以適當的下壓作用力及最少加工道次來達到所需加工深度，並將估算結果與實際實驗結果作一驗證。
本文進一步假設在奈米級切削過程中，其主要熱源的產生是由工件原子間的變形而產生類似塑性變形所產生的塑性變形熱，及工件原子與刀具原子之間所產生的摩擦熱之兩種熱源產生。並應用所發展之三維準穩態分子靜力學奈米級模擬切削模式，計算所得到之等效應力及等效應變的乘積，此即可得到類似塑性變形功之塑性熱源產生熱。又本文應用準穩態分子靜力學奈米級切削模式之計算奈米級切削力之方法，其所得到莫氏力的力平衡及工件原子在瞬間的位移增量，再用力平衡概念，將與刀具面上較接近之各工件原子所受之莫氏力分解成在刀面上之正向分力與切線分力，而此切線分力即類似切削工件產生之摩擦力。而原子所受摩擦力與沿刀具切面之原子位移量的乘積即可視為工件原子在刀面上產生類似摩擦產生的摩擦熱。本文再由計算所得到塑性變形和摩擦二者所產生的熱源，利用有限差分熱傳方程式得到經過熱傳後工件和切屑的溫度分佈的結果，並進行比較分析。本文先以單晶銅工件之奈米級正交切削溫度分佈模擬之結果與分子動力學方式之文獻模擬所得到之溫度分佈結果進行比對驗證，進一步應用本論文所發展的分子靜力學奈米級切削溫度模擬模式模擬計算用AFM探針加工藍寶石基板V型溝槽之切削力、等效應變、等效應力及藍寶石切削工件溫度場分佈分析。

This thesis aims to establish a theoretical model for prediction of fabrication depth of multi-pass nanoscale cutting V-shaped groove on sapphire, attempting to explore the relationship between the down force of the expected cutting depth and cutting pass under nanocutting. Meanwhile, this thesis applies simulation of molecular statics to calculate the result of temperature rise produced from the fabricated workpiece.
This thesis applies an atomic force microscopy (AFM) diamond probe as a cutting tool, which carries out the experiment of multi-pass nanocutting of V-shaped grooves on the surface of sapphire substrate. This thesis innovatively proposes the concept of specific down force energy (SDFE) to develop the theoretical model for prediction of fabrication depth of V-shaped grooves on sapphire substrate. This thesis suggests that the SDFE of the same material is a fixed value. Through conducting the experiment, it verified the numerical value of SDFE in cutting of sapphire substrate, and further develops the prediction method of the cutting depth of sapphire substrate during multi-pass cutting by AFM probe under a fixed down force and a fixed probe shape.
When a cutting depth of the nanoscale groove structure is expected to be reached in the nanocutting process, the cantilever and the tip of probe of the cutting tool have to avoid applying excessive action force on the workpiece which makes any damage of equipment should be created. Therefore, smaller action force is always needed when carrying out multi-pass cutting so as to achieve the required cutting depth. Besides, in order to decrease the number of cutting passes and save the fabrication time, this thesis uses its proposed SDFE theory to develop an estimation method for the fewest cutting passes. In the process of actual cutting, the cutting tool of probe is able to apply a suitable down force and the least number of fabrication passes to achieve the required cutting depth. Based on the actual experimental result, the thesis verified the correctness of the estimated result.
Furthermore, this thesis supposes that in the nanocutting process, the temperature rise during nanoscale cutting the workpiece is mainly produced from two heat sources, the one is plastic deformation heat produced from quasi-plastic deformation, which is caused by deformation between atoms of workpiece, and the other is friction heat produced between workpiece atoms and tool atoms. This thesis applies the developed three-dimensional quasi-steady molecular statics nanocutting simulation model to calculate the product of multiplication of the obtained equivalent stress and equivalent strain. During this time, the thesis can acquire the heat produced from plastic heat source of quasi- plastic deformation. Besides, this thesis also applies the calculation method of nanocutting force by quasi-steady molecular statics nanocutting model, to obtain Morse force balance and displacement increment of workpiece atoms in a moment. After that, employing the concept of force balance, this thesis decomposes the Morse force borne by different workpiece atoms being closer together on the tool face, to be normal force on the face of tool and tangential force . Such a tangential force is similar to the friction force produced from cutting workpiece. And the product of multiplication of the friction force borne by atoms and the displacement of atoms on the cutting section of cutting tool could be regarded as the friction heat produced from similar kind of friction created by workpiece atoms on the face of tooling. After the increased temperature produced by these two heat sources are added up, the acquired total temperature rise at each atom of the workpiece is substituted in heat transfer finite difference equation to carry out heat transfer and the results also be carried on comparison and analysis. This thesis firstly uses the result of nano orthogonal cutting simulation of single-crystal copper workpiece to make comparative verification with the temperature distribution result obtained from the past literature’s simulation by the way of molecular dynamics. Furthermore, this thesis uses the developed molecular statics temperature field simulation model of nanoscale cutting to calculate the cutting force, equivalent strain, equivalent stress and temperature field distribution of sapphire workpiece during fabrication of V-shaped groove on sapphire substrate by AFM probe.

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