- 期刊
Mode Shapes of Directional Matrix and Chatter in Milling
銑削製程方向矩陣之模態分析與顫振振型
摘要
方向係數矩陣在銑削製程動態模式中將振動產生之動態進給轉換成銑削力，其在系統穩定性分析中扮演關鍵角色。本文透過零階方向矩陣的模態分析，推導出針對順、逆與對稱銑削型態各別模態振型之代數表示式。並以物理觀點解釋方向矩陣特徵向量之模態振型的幾何特徵。發現在小徑向切深時會有兩個實數的特徵值，其兩個模態振型皆呈線性。而在大徑向切深時會有複數共軛的特徵值而其振型呈橢圓狀。在槽銑條件下的模態振型會呈一個圓形。相同的徑向切深條件下，在逆銑和順銑製程中模態振型分別指向刀具進給方向的右側和左側，而兩個模態相差的角度等於徑向浸入角。此外，也證明方向矩陣的主要模態振型，也是具對稱結構動態系統之再生顫振的模態振型。對於所有具橢圓形的顫振模態振型，其振動軌跡皆沿著逆時針方向繞行。這些模態振型的預測經由切削實驗得到驗證。
關鍵字
無資料並列摘要
The directional matrix transforms the dynamic feed vector to the dynamic milling forces, and plays a central role in the milling chatter analysis. Through modal analysis of the zero-order directional matrix (DM), this paper presents algebraic expressions for the mode shapes of DM in up, down and symmetric milling configurations. Analysis on the eigenvectors of DM reveals physical insights into the geometrical features of its characteristic mode shapes. The two mode shapes are demonstrated to be linear for a lower radial immersion with real eigenvalues, and are elliptical for a higher immersion with complex eigenvalues, and become a circle at full immersion. The up and down-milling processes at the same immersion have their mode shapes pointing to the right and left side of the feed direction, respectively, with their modal angles differing by the radial immersion angle. The dominant mode shape of DM is also shown to be the mode shape of regenerative chatter for milling with a symmetrical structural dynamics. For all types of elliptical chatter mode shapes, their vibration trajectories are shown to move in a counterclockwise direction. These mode shape predictions are verified by experiments.