本文針對一般螺旋端銑刀在頻域中建立一套通用的解析銑削力學模式，並探討此模式在銑削加工上之幾種應用。這個模式清楚地分開考慮剪切作用與犁切作用對於銑削力的影響，在模式的建立過程中以微分幾何作為分析切削幾何的依據，並且提供本文建立局部銑削力模式的基礎。本文緊接著在時域中利用兩次捲積程序依序建立單刃銑削力模式以及總銑削力模式，利用捲積定理以及傅立葉分析，本文將銑削力表示成傅立葉級數，經由傅立葉係數的推導，本文建立了銑削力的頻域模式。由於刀具幾何以及各項銑削程序參數在傅立葉係數的表示中都有清楚的定義，因此本文的模式可以適用於任何可以用數學定義幾何關係的刀具外形及程序參數。由於本文的解析特性，首先應用在比切削係數以及銑刀偏心幾何的線上判認。本文提出了兩個方法應用於線上判認比切削常數，其中一個方法僅利用第一個諧波頻率的銑削力分量；另一個則同時利用平均力以及第一個諧波頻率的銑削力分量。由於比切削常數可以線上判認，因此銑刀偏心幾何也可以在線上經由轉速頻率的銑削力分量來判認。本文的銑削力模式同時也被應用於預測銑削系統的穩定性，本文所提出的預測模式可以清楚地包含螺旋角的影響，同時也可以擴展到三個自由度。經由數值模擬以及實驗結果都驗證了本文所提之銑削力模式及其應用的有效性。

This paper presents a frequency domain force model for a general helical end mill including edge ploughing as well as chip shearing mechanisms. The differential local cutting forces are first formulated through differential geometry for a general helical cutting edge. The single flute and the multi-flute milling forces in the angular domain are subsequently composed through convolution integration and analyzed by Fourier analysis. In this frequency domain model, cutter geometry and the parameters of a general milling process are integrated into a unified framework with their roles clearly defined such that the Fourier coefficients of the total milling force can be obtained for any analytically definable helical cutter. From the Fourier analysis, it is shown in particular that in slot milling either the dynamic shearing force or the dynamic ploughing force components might vanish for any type of helical cutter depending on its flute number. By virtue of the analytical nature of the milling force model in the frequency domain, frequency domain force model can be further explored for the applications including the identification of specific cutting constants and cutter offset. Two on-line methods are presented to identify specific cutting constants. The first method uses only the first harmonic component of the milling forces and the second method utilizes the average forces as well as the first harmonic forces. Furthermore, the force model is applied for the prediction of chatter in milling. A 3D model is developed that includes the effect of helix angle. Numerical simulation and experimental results are presented to validate the presented force model and its applications.

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