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.

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