利用多槽鑽頭修整內孔，其表面粗糙度，偏心度及直度都比雙槽鑽頭的工件表面優異，對鑽削精密孔是一個有效率的工具，但目前缺乏這類數學模式。本文提出一個簡單且嚴謹的方法來設計多槽鑽頭，所提出的模式具有三個特點：

(1)利用幾何迴轉曲面來建立軸向刀具或碟式研磨輪，因此鑽槽及鑽腹的法線、切線可用顯函數表示，因此鑿刃及切刃的前角與後角可根據ISO標準求得。

(2)吾人結合鑽槽與鑽腹的數學模式，所以鑿刃與切刃以及它們的特徵角的變化可利用數值方法求得，最後平面法向量的觀念，提出一個簡易且廣泛的方法，以求得前角及後角。本文以三槽錐形鑽頭、雙曲線形鑽頭、橢圓形鑽頭為例，利用數值計算方法模擬三種鑽頭，並依據國際標準ISO規範建議求鑽頂角、鑿刃角、刀具主偏角、法前角、法後角。

(3)本研究並且用萬能工具研磨機及CNC六軸工具研磨機，研磨出三槽鑽頭，以驗證理論之正確性。為達此目的，首先使用4×4 齊次座標轉換矩陣對該六軸CNC研磨機建模，以推導該機器的功能函數矩陣，再依研磨輪相對於素材的位置與方向，推導鑽槽與鑽腹的研磨輪方位矩陣， NC程式即可由機器的功能函數矩陣與研磨輪方位矩陣的相等而獲得。本文不僅將探討多槽鑽頭機器的設定，同時本文更提出了虛擬研磨輪與虛擬修整器的觀念，改變了鑽腹須置於成型研磨輪內凹面的限制，使得單一研磨輪可同時切削鑽槽及鑽腹，以避免原點多次設定的缺點，並可提高加工精度，且可以使多軸CNC工具研磨機製造多槽鑽頭的程序更具彈性化。

　　Multi-flute drilling is an efficient means of making high accuracy holes without reaming. Because of the current lack of a comprehensive mathematical model for this kind drilling, this paper presents a complete and simple method for designing multi-flute drills. There are three special features of the proposed model.

　　The first is that rotational axial-type cutting tools and disk-type abrasive wheels are modeled by revolution geometry, so that the normal and tangent vectors of flute and flank surfaces can be obtained explicitly. Consequently, rake and clearance angles of cutting and chisel edges can be investigated according recommended ISO standards.

　　The second feature is that we integrate the mathematical models of flute and flank surfaces, so that cutting and chisel edges and their various characteristic angles can be obtained by numerical calculation. A simple way to determine the rake angles and wedge angles and clearance angles is presented by using the unit normal of the ISO-recommended reference planes. This model is comprehensive, simple, easy to use, and is capable of describing a wide range of drill design features. This paper analyzes three types of drill geometries for conical, hyperboloidal and ellipsoidal drills. Presents a model to determine and express drill geometries and characteristics (semi-point angle, tool cutting edge inclination, chisel angle, normal rake angle and normal clearance angle) according to all current international standards.

　　Finally, This paper presents a kinematic model to produce multi-flute drills on a 6-axis CNC tool-grinding machine. The ability matrix of a 6-axis CNC tool-grinding machine is established by Denavit-Hartenberg notation. Moreover, due to manufacturing difficulty reasons, most grinding wheel are solid without any inner concave surface to cast drill flanks into convex surfaces to provide clearance angles in drill. Therefore, a concept of virtual hollow grinding wheel and virtual solid dresser is invented to overcome that difficulty. Eventually, we generate the desired configuration matrices to express the positions and orientations of the grinding wheel during the machining of the flutes and flanks. NC data equations are obtained by equating the corresponding elements of the ability matrix and the configuration matrices of grinding wheel. To verify the validity of the proposed methodology, a designed three-flute drill was machined on an Ewag 6-axis CNC tool-grinding machine. This paper combines the activities of drill design and manufacturing, thus making the production process more flexible, automatic, cost efficient and controllable.

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