完整的二維銑削加工動態方程包含了剪切及犁切效應之時變方向矩陣。但一般系統穩定性分析只包含剪切及犁切方向矩陣零階項之影響。之前研究發現在高轉速區需考慮高階剪切力之影響，在低轉速區則需考慮動態犁切力對加工穩定性之影響。本文先只考慮零階犁切力矩陣之影響，經由模態分析可將二維方程簡化為一維方程，在只考慮犁切力零階方向矩陣之實部特徵值下，可推導出只含徑向犁切製程阻尼力之臨界穩定切深解析式，獲得其臨界切深隨轉速降低而增加之結果。進一步再考慮零階犁切力零階方向矩陣之複數特徵值後，因犁切力方向矩陣之虛部特徵值引發犁切剛性使系統剛性隨軸深增加而提高，故於較大軸深處系統反而轉向穩定，極限切深隨轉速增加而增加呈現L型之穩定圖。但可能剛性增加也降低犁切阻尼之等效阻尼比，因而高切深處開始呈現不穩定，使得系統呈現Z形之加工穩定圖。接著探討高階剪切力及高階犁切力對於銑削穩定性的影響。發現同時考慮高階剪切力以及高階犁切力時因兩者高階力間之調變效應增加了對零階犁切阻尼力之貢獻，故於低轉速區因動態力相對於平均力較為顯著，因而增加了之前未曾發現之Z形局部加工穩定區，使得整體穩定圖除呈現原巨觀Z形外亦於低軸深區出現一較淺之z字形穩定區。最後以實驗驗證此Zz形穩定圖之預測。

Complete dynamic equation of two dimensional milling includes shearing and ploughing time-variant direction matrix. However, in general, system stability analyses only consider zero order term of shearing and ploughing direction coefficient matrix (SDCM and PDCM). Based on past research, high order shearing force impact in high spindle speed region while dynamic ploughing force effect the stability in low spindle speed region. The study, first, takes zero order PDCM into account and simplify 2D equation into 1D equation via modal analysis. Considering real part of eigenvalue of zero order PDCM, the study derives analytical expression of critical axial depth of cut that includes radial ploughing process damping force and finds that critical axial depth of cut raises as spindle speed decreases. Moreover, imaginary part of eigenvalue of zero order PDCM causes ploughing stiffness to enhance system stiffness as axial depth of cut increases, which makes system stable. Critical axial depth of cut increases with spindle speed increasing, and stability diagram shows a “L” profile. Yet enhancement of stiffness might reduce equivalent damping ratio of ploughing damping, leading instability in high axial depth of cut and then stability diagram presents a “Z” contour. Second, the study investigates the influence of high order shearing force and ploughing force to milling stability and finds that modulation between shearing force and ploughing force contributes to zero order ploughing damping force. Therefore, compared to average force, dynamic force is more significant in low spindle speed region, which adds a new small stable area with “z” profile on stability diagram. In conclusion, stability diagram has a “Z” and a “z” in low axial depth of cut. Verify experimentally the prediction of “Zz” stability diagram.

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