本文主要探討銑削製程系統之特徵值與暫態響應，釐清穩定葉瓣圖上各區域之系統響應特徵。首先以平均力模式，針對對稱結構獲得系統特徵方程。進一步建立包含動態力之銑削系統模型，並以辛普森法獲得對應主軸轉速與軸向切深平面的離散特徵值，獲得z平面特徵值與s平面特徵值之映射關係式，進而建立轉速軸深平面之穩定裕度圖及顫振頻率之關係圖。經分析發現顫振頻率隨軸向切深增加而增加。同一軸向切深下，高轉速區之穩定性較低轉速區差，且高轉速區的穩定裕度對軸向切深變化較敏感。於葉瓣交集區的左右兩側其特徵值主要為各自葉瓣之貢獻，交集區相鄰葉瓣貢獻之特徵值都於單位圓外，故會有兩組顫振頻率。另外每一葉瓣內，從低頻區至高頻區系統特徵值實部由小變大再變小，呈現一山丘狀之變化。觀察z平面系統特徵值之運動軌跡，當固定主軸轉速逐漸增加軸向切深時，於穩定葉瓣圖上之半島區時，系統特徵值經過實軸(-1,0)離開單位圓稱為Flip分叉，其它離開單位圓方式則為二階Hopf分叉。最後以時域數值模擬獲得系統暫態響應，從顫振頻率以及振幅驗證本文建立之特徵值分析結果之正確性。

This study investigates the characteristics values and the transient response of the milling system to clarify the relationship between the vibration frequency, stability index (SI), spindle speeds and depth of cuts. With the assumption of axis-symmetric dynamics, zero-order-analysis (ZOA) is applied to obtain the characteristic equation of the milling system. Further, the dynamic milling model considering the dynamics forces is constructed and a discretization method based on Simpson method is proposed to calculate the characteristics values in z-domain. The formula for mapping the characteristic values from z-domain to s-domain is proposed. Stability lobe diagrams of SI are then utilized to discuss the relationship between vibration frequency, depth of cut, and spindle speed. It is shown that the vibration frequency arises as the depth of cut increases. At the same depth of cut, the stability margin at lower spindle speed is better than at higher spindle speed. The stability of the system is much sensitive to the changes of the depth of cut at higher spindle speed. The both sides of the intersection of the adjacent lobes, their own lobes contribute to the dominant characteristic values. However, in the intersection area, both the characteristic values due to the contribution of the adjacent lobes are outside of the unit circle, so there are two vibration frequencies. In addition, in each lobe, the contour of spindle speed, depth of cut, and SI is convex. Two distinct types of instabilities are illustrated by the characteristic values trajectories: (1) flip bifurcation occurs in the flip lobes for which the characteristic values passes through (-1, 0) while leaving the unit circle; and (2) a secondary Hopf bifurcation. Finally, the presented model for prediction characteristic values is verified by the time domain simulation.

摘要 i
Abstract ii
誌謝 xxi
目錄 xxii
表目錄 xxiv
圖目錄 xxv
符號表 xxx
1 第一章 緒論 1
1.1 動機與目的 1
1.2 文獻回顧 3
1.2.1 穩定性分析 3
1.2.2 特徵值分析 5
1.3 研究範疇與論文架構 5
2 第二章 平均力模式穩定性分析與特徵值分析 7
2.1 銑削力模型 7
2.2 基本切削函數 8
2.3 屑寬密度函數 9
2.4 刀刃序列函數 10
2.5 總銑削力 11
2.6 平均力模式之銑削系統模型 12
2.7 中性穩定之銑削穩定性分析 13
2.8 考慮穩定裕度之銑削穩定性分析 17
2.9 系統特徵值與銑削穩定裕度圖 21
2.9.1 顫振區系統特徵值與銑削穩定裕度圖 21
2.9.2 穩定區系統特徵值與銑削穩定裕度圖 27
3 第三章 考慮動態力之穩定性分析與特徵值分析 32
3.1 局部銑削力 32
3.2 考慮動態力之總銑削力 34
3.3 考慮動態力之銑削系統模型 34
3.4 銑削穩定性分析 35
3.4.1 Floquet 穩定性理論 35
3.4.2 辛普森法 36
3.4.3 系統特徵值與銑削穩定裕度圖 38
3.4.4 系統特徵值之運動軌跡 52
3.4.4.1 相同穩定裕度下之系統特徵值之運動軌跡 52
3.4.5 分叉突變 61
4 第四章 系統暫態響應之時域數值模擬 68
4.1 系統響應 68
4.2 銑削時域數值模擬 70
4.2.1 銑削範圍定義 70
4.2.2 切屑厚度定義 71
4.2.3 數值積分銑削力模式 72
4.2.4 數值銑削系統模型 72
4.2.5 利用時域數值模擬驗證辛普森法所求得之系統特徵值 75
5 第五章 結論與建議 109
5.1 結論 109
5.2 建議 111
6 參考文獻 112

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