臺灣博碩士論文加值系統

本文提出一雙主軸銑削加工穩定性之簡化模型。此模型藉由旋轉矩陣將兩主軸之局部座標旋轉至機器座標系，再合併兩主軸之方向係數矩陣(Directional Coefficient Matrix, DCM)以求得工件所受之總銑削力，此方法可將雙主軸複雜的四次特徵方程式簡化為二維特徵方程式。再藉由工件為對稱結構之假設，可運用特徵分解(Eigendecomposition)將此特徵方程式簡化為兩個非耦合的一維特徵方程式並可推導出特徵值與特徵向量之解析式，藉由解析式可以掌握在各加工參數對於穩定性之影響。本論文自定義銑削組態編碼，有系統地的考慮雙主軸銑削加工的組合並探討各種銑削情形之穩定性，建立一套繪製兩主軸於各種加工方式下銑削穩定圖之流程。本文也探討當工件為非對稱結構時的雙主軸銑削穩定性。在不同銑削組合的分析中發現，若其中一主軸為逆向旋轉時，其穩定性有隨徑向切深比增加而增加，此特性可大幅增加雙主軸銑削加工之優勢，提高加工的效率。最後以時域模擬與實驗驗證本論文銑削穩定圖之準確性。

This thesis provided a simple model of parallel milling. The model transformed the local coordinates of two spindles to the global coordinate with rotation matrix, combined the directional coefficient matrix (DCM) of two spindles to obtain the total milling force of the milling system. With the assumption of axis-symmetric structure and some equal cutting parameters, the combined directional coefficient matrix could be decoupled to reduce the 2D milling system to 1D eigenvalue problems. The method could simplify the fourth order characteristic equation of the parallel milling system and derivative the analytic of eigenvalue and eigenvector. The analytic is useful to understand the effect of different parameters in milling stability. In order to consider the different combinations of the stability in parallel milling systematically, the code of parallel milling combination is defined and the procedure of the stability lobe diagram in parallel milling is established. The results of analysis shows that if two spindles have different direction of rotation, the parallel milling system will be more and more stable as immersion angle increased. The study also investigated the stability in asymmetric structure and the critical axial depth of cut in different feed direction is different. The model is validated by time-domain numerical simulation and milling experiment in the fourth chapter.

摘要 I
Abstract II
誌謝 X
總目錄 XI
表目錄 XIV
圖目錄 XVI
符號表 XX
第一章 緒論 1
1.1 動機與目的 1
1.2 文獻回顧 2
1.2.1 切削顫振之文獻回顧 2
1.2.2 雙主軸加工之文獻回顧 3
1.3 研究架構 5
第二章 雙主軸銑削穩定性模型建立 7
2.1 銑削力模型 7
2.2 順逆銑與方向係數矩陣之關係 12
2.3 單主軸銑削穩定模型 15
2.4 雙主軸銑削動態模型 19
2.4.1 雙主軸模型座標系 19
2.4.2 雙主軸模型建立 20
2.4.3 系統座標旋轉 22
2.4.4 雙主軸簡化模型 24
2.4.5 雙主軸簡化模型解析 25
第三章 考慮不同組合之銑削穩定性分析 29
3.1 定義雙軸銑削加工組合指標 29
3.2 繪製穩定圖流程 33
3.3 同向進給(兩主軸皆順時針旋轉)：[1, 1, 2, 2] 36
3.4 對向進給(兩主軸皆順時針旋轉)：[1, 0, 0/1, 2] 39
3.5 同向進給(一主軸逆轉)：[1, 1, 0/1, 1] 42
3.6 對向進給(一主軸逆時針旋轉)：[1, 0, 2, 1] 47
3.7 非平行銑削 48
3.8 非對稱結構 52
第四章 時域模擬及實驗驗證 57
4.1 時域模擬驗證 57
4.2 同向進給驗證 60
4.3 對向進給驗證 63
4.4 同向進給(一軸反轉)驗證 66
4.5 對向進給(一軸反轉)驗證 68
4.6 垂直進給驗證 71
4.7 非對稱結構驗證 73
4.8 時域模擬小結 76
4.9 驗證實驗 77
4.9.1 實驗配置及設備 77
4.9.2 結構敲擊實驗 79
4.9.3 切削顫振實驗 81
第五章 結論與建議 86
5.1 結論 86
5.2 建議 87
參考文獻 88

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