多軸切削加工技術廣泛應用於模具及航太零件加工。對於複雜的雕刻曲面，為了避免干涉的發生，多軸切削是唯一的解決刀具干涉的對策。然而切削力會因刀具姿態的不同而改變，因此工件表面的特徵也會隨之變化。

本論文的主要目的在於討論多軸切削中，刀具姿態對於工件表面粗糙度的影響。理論方面探討在不同刀具傾斜角時刀具與工件間的包絡情形，並以此推導出不同刀具傾斜角與其切屑的平均厚度的變化關係。為了觀測切屑平均厚度變化與工件表面粗糙度的關聯，論文中以鋁合金進行切削實驗。在切削深度及切削寬度固定情形下，以不同的主軸轉速及變動刀具軸傾斜角度，並量測加工件表面粗糙度變化情形。由實驗結果得知，對應於特定的刀具軸傾斜角，工件表面粗糙度會產生一峰值。實驗結果所呈現的趨勢與理論推導的切屑厚度與刀具傾斜角的關係大致相符，因此理論的推導結果將可做為選定刀具軸傾斜角的依據。

The technology of multi-axis machining has been applied extensively to the manufacturing of dies, molds, and various aerospace components. For machining mechanical parts with complex, sculptured surfaces, the use of multi-axis machine tools is probably the only one solution for avoiding tool-part collision during machining. Since cutting force will be changed by cutter attitudes, the machined surface characteristic can also be affected by cutter attitudes.

In this thesis, the major concern is focused on investigating the effect of the cutter attitude on machined surface roughness. Based on the relationship between the cutter incline angle and the enveloped condition in cutting, the correlation of the mean chip thickness and the cutter incline angle is observed. To identify the relationship between the cutter attitude and the workpiece surface roughness, experimental verification is performed by milling aluminum alloy material. By fixing the cutting depths and the width of tool paths, different spindle rotational speeds and cutter incline angles are taken to machine the workpieces. And then, the machined surfaces are measured for their surface roughness. Form the experimental results, it shows that the surface roughness will reach a peak value at a special cutter incline angle. The tendency between the surface roughness and the incline angle agrees with that between the mean chip thickness and the cutter attitude approximately.

摘要……………………………………………………………………..Ⅰ
目錄…………………………………………………………………….. Ⅲ
圖目錄…………………………………………………………………..Ⅳ
表目錄………………………………………………………………….. Ⅵ

第一章 緒論
1.1簡介…………………………………………………………1
1.2研究動機……………………………………………………2
1.3文獻回顧……………………………………………………3
1.4研究目的與研究方法………………………………………5
1.5論文架構……………………………………………………5

第二章 多軸加工之相關切削幾何參數
2.1多軸切削的定義……………………………………………7
2.2球銑刀相關幾何定義之說明………………………………10
2.2.1球銑刀球頭幾何關係之建立…………………………10
2.2.2刀具軸傾斜角之定義………………………………….13
2.2.3切屑厚度的定義……………………………………….14
2.2.4刀刃切削點位置……………………………………….17
2.2.5刀具埋入情形……….………………………………….18

第三章 實驗規劃與預測分析
3.1實驗規劃…….……………………………………………20
3.2實驗設備…..……………………………………………..23
3.3實驗結果預測….………………………………………..26

第四章 實驗結果與討論
4.1實驗結果………………..………………………………..36
4.2實驗結果討論…………………………………………..52

第五章 結論……………………………………………………………58

參考文獻………………………………………………………………..60

[1] Stute G., Storr A. and Sielaff W., 1979, “NC Programming of Ruled Surfaces for Five-Axis-Machining,” Annals of the CIRP, Vol. 28/1/1979, pp. 267-271.

[2] Tönshoff H. K. and Camacho H., 1989, “Die Manufacturing by 5- and 3- Axes Milling,” Journal of Mechanical Working Technology, Vol. 20, pp. 105-119.

[3] Yang M. and Park H., 1991, “The Prediction of Cutting Force in Ball-End Milling,” International Journal of Machine Tools and Manufacture ,Vol. 31, No. 1, pp. 45-54

[4] Ng E. G., Lee D. W., Sharman A. R. C., Dewes R. C. and Aspinwall D. K., 2000, “High Speed Ball Nose End Milling of Inconel 718,” Annals of the CIRP, Vol. 49/1/2000, pp. 41-46.

[5] Yucesan G., And Altintas Y., 1996, “Prediction of Ball End Milling Forces,” ASME Journal of Engineering for Industry, Vol. 118, February, pp. 95-103.

[6] Lazoglu I., and Liang S. Y., 2000, “Modeling of Ball-End Milling Forces With Cutter Axis Inclination,” ASME Journal of Manufacturing Science and Engineering, Vol. 122, February, pp. 3-11.

[7] Spence, A. and Altintas, Y., 1994, “A Solid Model Based Milling Process Simulation and Planning System,” ASME Journal of Engineering for Industry, Vol. 116, February, pp. 61-69.

[8] Radzevich S. P. and Goodman D. D., 2002, “Computation of Optimal Workpiece Orientation for Multi-axis NC Machining of Sculptured Part Surfaces,” ASME Journal of Mechanical Design, June, Vol. 124, pp. 201-212.

[9] Fussel B. K., Jeard R. B. And Altintas Y., 2003, “Modeling of cutting geometry and forces for 5-axis sculpture surface machining,” Computer-Aided Design, Vol. 35, 2003, pp. 333-346.

[10] You S. J. and Eman K. F., 1989, “Scallop Removal in Die Milling by Tertiary Cutter Montion,” ASME Journal of Engineering for Industry, Vol. 111,pp. 213-219.

[11] You S. J. and Ehmann K. F., 1991, “Synthesis and Generation of Surfaces Milled by Ball Nose End Mills Under Tertiary Cutter Montion,” ASME Journal of Engineering for Industry, Vol. 113,pp. 17-24.

[12] 趙曉明、堤 正臣、是田規之、葛東方和陳亮, 1996, “5軸制御加工におけるボールエソドミルの最適傾斜角決定方法－仕上げ面粗さを基準にした決定方法とニューラルネットワの應用”, 精密工學會誌, Vol. 62, No. 7, pp. 1019-1023.

[13] 趙曉明、堤 正臣、是田規之和葛東方, 1997, “5軸制御加工におけるボールエソドミルの最適傾斜角決定方法－仕上げ面粗さを基準にした球面の場合”, 精密工學會誌, Vol. 63, No. 7, pp. 992-996.

[14] Lo C. C., 2002, “A Tool-path Control Scheme for Five-axis Machine tools,” International Journal of Machine Tools and Manufacture, Vol. 42, No. 1, pp. 79-88.

[15] Metalworking Products-Rotating Tools, 1999, Scandvik Coromant, Denmark.

[16] Eng L. M. B., 1992, Surface Texture Analysis-The handbook, Hommelwerke GmbH, West Germany.

[17] Smith S., and Tlusty J., 1991, “An Overview of Modeling and Simulation of the Milling Process,” ASME Journal of Engineering for Industry, May, Vol. 113, pp. 169-175.
[18] Choi B. K., and Jerard R. B., 1998, Sculptured Surface Machining - Theory and Applications, Kluwer Acdemin, Inc.

[19] Zhu, R., Kapoor S. G., and DeVor R. E., 2001, “Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces,” ASME Journal of Manufacturing Science and Engineering, Vol. 123, August, pp. 369-379.

[20] Mizugaki Y., Hao M., and Kikkawa K., 2001, “Geometric Generating Mechanism of Machined Surface by Ball-Nosed End Milling,” Annals of the CIRP, Vol. 50/1/2001, pp. 69-72.

[21] Schulz H. and Hock St., 1995, “High-speed Milling of Dies and Moulds - Cutting Conditions and Technology,” Annals of the CIRP, Vol. 44/1/1995, pp. 35-38.

[22] Altintas Y., and Engin S., 2001, “Generalized Modeling of Mechanics and Dynamics of Milling Cutters,” Annals of the CIRP, Vol. 50/1/2001, pp. 25-30.

[23] Lacalle L. N. L. D., Lamikiz A., Sanchez J. A., and Sanchez. L. , 2002, “Improving the Surface Finish in High Speed Milling of Stamping Dies,” Journal of Materials Processing Technology, Vol. 123, pp. 293-302.

[24] Vickers G. W. and Guan K. W., 1989, “Ball-Mills Versus End-Mills for Curved Surface Machining,” Transactions of ASME, Vol. 111,pp. 22-26.

[25] Wang X. C., and Yu Y., 2002, “An Approach to Tnterference-free Cutter Position for Five-axis Free-form Surface Side Finish Milling,” Journal of Material Processing Technology, Vol. 123, pp. 191-196.

[26] Altintas Y., and Lee P., 1998, “Mechanics and Dynamics of Ball End Milling,” ASME Journal of Manufacturing Science and Engineering, November, Vol. 120, pp. 684-692.
[27] Lim E. M.., Feng H. Y., Menq C. H., and Lin Z. H., 1995, “The Prediction of Dimensional Error for Sculptured Surface Productions Using the Ball-End Milling Process. Part 1: Chip Geometry Analysis and Cutting Force Prediction,” International Journal of Machine Tools and Manufacture, Vol. 35, No. 8, pp. 1149-1169.

[28] Lee P. and Altintas Y., 1996, “Prediction of Ball-End Milling Forces from Orthogonal Cutting Data,” International Journal of Machine Tools and Manufacture, Vol. 36, No. 9, pp. 1059-1072.

[29] Tlusty, J. and Macneil, P., 1975, “Dynamics of Cutting Forces in End Milling,” Annals of the CIRP, Vol. 24/1/75, pp. 433-436.

[30] Montgomery D. and Altintas Y., 1991, “Mechanism of Cutting Force and Surface Generation in Dynamic Milling,” ASME Journal of Engineering for Industry, Vol. 113, pp. 160-168.

[31] Sutherland J. W. and DeVor R. E., 1986, “An Improved Method for Cutting Force and Surface Error Prediction in Flexible End Milling Systems,” ASME Journal of Engineering for Industry, Vol. 108, pp. 269-279.

[32] Marciniak K., 1987, “Influence of Surface Shape on Adminnible Tool Positions in 5-axis Face Milling,” Computer-Aided Design, Vol. 19, No. 5, pp.233-236.