本論文提出弦波形態離散解析幾何模型和推導與模擬弦波鋸齒切屑負載在鋸切過程的特性方程，並探討不同單位波長切齒下的鋸切行為。影響單位波長的切屑負載因子有七項，分別為波長長度、單位波長的切齒數、鋸齒厚度、單位齒上的等效切深、每刃切齒間的重疊切削面積率、切削干涉比因子、和弦波振幅比例。模擬不同波長下n=3, 5, 7 和40的單位切齒負載分配可以發現最大切屑負載的齒刃皆為波峰相齒或波谷相齒的前一刃。切屑負載特性方程式可以藉由離散切齒函數、切齒序列窗函數和切齒間距函數捲積獲得。弦波式多刃切齒切削鋁6061所獲得移除單位體積材料的平均比切削能(n=1 到 n=7)為1580 MPa；在y (刀具側向)方向的平均比係數為0.44; 在z (刀具徑向)方向的平均比係數為0.2。切屑負載與平均切深、切齒寬度和切齒相位角相關。透過以材料移除率為目標函數，可建立最大切屑負載與切齒間干涉比之關係，比切削能和未變形切削面積之間的關係呈現超越負指數衰減曲線；弦波式多刃齒切削力模型與實驗量測的力量趨勢一致；切齒的磨耗位置與磨耗形態可以經由切齒負載特性函數預測。本研究可以達到下列目標:(I)對一般化弦波式多刃鋸齒建立切削力模型; (II)對於準靜態與高速動態切削製程發展切齒序列函數數學模型; (III)對弦波狀排列形態的切齒預測失效位置與磨耗形態; (IV)找出比切削能，切齒排列和切齒幾何間關係，同時對這參數建構理論模型; (V)從切齒拓撲、微觀切削到巨觀切削的觀點，去預測切屑負載與單位切削面積之間的關係; (VI)從統計學上分析多刃形態比切削能分布的變異誤差; (VII)使用離散捲積模型分析複雜多維度切削製程之切削特性; (VIII)對多刃切齒之摩擦效應與磨耗形態建立數學模型; (IX)以材料最大移除率獲得最佳化切齒間的排列重疊率。

In this dissertation, a sinusoidal-type discrete analytic geometry model was proposed and sinusoidal serrated chip loading characteristics equations were derived for the simulation of the hack-sawing process. The factors affecting chip loading of unit wave, namely, the length of the wavelength, the cutters numbers of unit wavelength, saw blade thickness, the equivalent cutting depth per tooth, the cutting overlap-area ratio per cutter edge, the pitch per each cutter, the cutting overlap-area factor and the proportional factor of sinusoidal amplitude in hack-sawing were investigated. The effects of sinusoidal cutter arrangement on chip loading were simulated by the chip loading equations. It is found that the maximum chip loading is always in the front of the cutters, which is at either the peak or the trough of different phase with the numbers of wavelength unit 3, 5, 7 and 40, respectively. The chip loading characteristics depends on the discrete convolution of chip loading function, the cutter order window function and the cutter interval function. The average specific energy of sinusoidal multi-cutters for workpiece of Al 6061 in different wave length (n=1 to n=7) is 1580 MPa, the average specific coefficient in y-direction is 0.44 and the average specific coefficient in z-direction is 0.20. The chip loading on each cutter is related to the average cutting depth, cutting width and cutter angle. The maximum chip loading of cutter order occurs in cutting overlap-area ratio can be obtained by optimizing the material removal rate. The specific energy with multi-undeformed cutting areas demonstrated the trend as exponent decay. The simulated results from the established cutting force model for sinusoidal multi-cutters agreed well with the experimental measurements. The wear location and failure types of cutters for in hack-sawing process could be predicted.

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