鑽頭在鑽孔加工上是相當有效率的工具，且近年多利用自動化工具機大量生產鑽頭，鑽頭之設計及其在工具機研磨的NC程式，實是鑽頭生產的重要課題。本文將對鑽頭設計與五軸工具機進行研究，分為四個主題:
(1)利用 齊次矩陣對BCXYZ類型的五軸工具機進行建模，透過正向運動學求出該工具機之功能矩陣，再透過逆向運動學推導該工具機各軸變數，以計算出該工具機之NC程式。並透過線上量測，計算出會影響切削精度的工具機主動參數。
(2)建立研磨輪在空間中之切線與法線向量，再用共軛法推導鑽槽之切線與法線向量。再設計切削鑽槽時研磨輪相對於素材之位姿矩陣，並令其與工具機功能矩陣相等，即可得切削鑽槽時之NC程式，再利用相同方法計算出加工鑽頭間隙之NC程式。
(3)利用錐形體研磨鑽腹，使鑽腹外型由四個參數控制，再由鑽腹以及鑽槽的數學式推導出鑿刃角以及間隙角之數學式，並探討該四個參數對於鑿刃角以及間隙角之影響。最後利用夾持器使刀具相對於素材在空間中形成虛擬錐形體，再計算出加工鑽腹之NC程式。
(4)利用切削軟體Vericut搭建出BCXYZ類型五軸工具機，並將計算出之NC程式碼進行切削模擬，觀察加工過程以及成品，藉此驗證數學模型之正確性。

Drills are highly efficient tools for hole drilling, and in recent years, they have been mass-produced using automated machine tools. The designs of drills and the NC programs for grinding them on machine tools are crucial topics in drill production. This paper will study the design of drill and five-axis machine tools, divided into four main topics:(1) Using homogeneous matrices, we model a BCXYZ-type five-axis machine tool. The forward kinematics are used to derive the functional matrix of the machine tool, and the inverse kinematics are applied to deduce the variables for each axis of the machine tool, thus calculating its NC program. Through online measurement, we determine the active parameters of the machine tool that affect cutting accuracy.(2) Establish the tangent and normal vectors of the grinding wheel in space, and then use the conjugate method to derive the tangent and normal vectors of the flute. Design the position matrix of the grinding wheel relative to the workpiece during flute cutting and equate it to the functional matrix of the machine tool to obtain the NC program for cutting the flutes. Using the same method, calculate the NC program for machining the drill clearance.(3) Use a conical shape to grind the chisel edge, with its geometry controlled by four parameters. Derive the mathematical expressions for the chisel edge angle and clearance angle from the equations of the chisel edge and flute, and analyze the influence of these four parameters on the chisel edge and clearance angles. Finally, employ a fixture to position the tool relative to the workpiece to form a virtual conical shape in space, and calculate the NC program for machining the chisel edge.(4) Use the cutting software Vericut to build a BCXYZ-type five-axis machine tool and run the calculated NC program code for cutting simulation. Observe the machining process and the final product to verify the accuracy of the mathematical model.

[1] Tsai, W. D. and Wu, S. M.,"A Mathematical Model for Drill Point Design and Grinding," Trans. ASME, J. of Eng. for Ind., Vol.101 Aug. pp. 333-340, 1979
[2] K. F. Ehmann, "Grinding Wheel Profile Definition for the Manufacture of Drill Flutes",CIRP Annals,Volume 39,Pages 153-156, 1990
[3] M.A. Fugelso, "Conical flank twist drill points",International Journal of Machine Tools and Manufacture, Pages 291-295, 1990
[4] Viktor P. Astakhov, " Modern machining technology ", Woodhead Publishing, Pages 79-212, 2011
[5] Kaichun Ren and Jun Ni, "Analyses of Drill Flute and Cutting Angles", Int J Adv Manuf Technol, pp.546-553,1999
[6] Anish Paul、Shiv G. Kapoor and Richard E. DeVor, "Chisel edge and cutting lip shape optimization for improved twist drill point design",International Journal of Machine Tools & Manufacture,pp. 421–431, 2005
[7] Tsai, W. D. and Wu, S. M., "Computer Analysis of Drill Point Geometry" ,Int. J. Mach. Tool. Des. Res. Vol. 19, pp. 95-108,1979
[8] M. A. FUGELSO, "CONICAL FLANK TWIST DRILL POINTS",Int. J. Mach. Tools Manufact. Vol. 30, No. 2, pp. 291-295, 1990
[9] NITHIN KRISHNA N,PRATHEEKA T P,SHAMSWAROOP M S,SHIVARAJ K,K A VENUGOPAL and PRATHAP M S, "DESIGN AND FABRICATION OF MULTI – PURPOSE 3-AXIS VISE FOR RE-SHARPENING OF TWIST DRILL AND LIGHT MILLING WORK",International Journal of Mechanical and Production Engineering,pp.64-67,2019
[10] Raiminor Ramzi, Elmi Abu Bakar and M. F. Mahmod, "Drill Bit Flank Wear Monitoring System in Composite Drilling Process Using Image Processing",pp.551-557,2019
[11] Haiqing Bai, Fei Gao, Yu Shen, Chao Zhu and Pan Wang, " Forming method and experimental research on wire cutting of twist drill cone flank",The International Journal of Advanced Manufacturing Technology,pp. 4815-4823,2019
[12] S.M.Wu and J. M. Shen, "Mathematical Model for Multifacet Drills", ASME Journal of Engineering for Industry, Vol.105, pp.173-182 , 1983.
[13] Tsai, W. D. and Wu, S. M., "MEASUREMENT AND CONTROL OF THE DRILL POINT GRINDING PROCESS",Int. J. Mach. Tool Des. Res. Vol. 19, pp. 109-120.,1979
[14] P.D.Lin, "Advanced Geometrical Optics",Springer Science,pp.5-28,2017
[15] Jung-Fa Hsieh, "Mathematical model for helical drill point",International Journal of Machine Tools & Manufacture,pp.967-977,2005
[16] Jung-Fa Hsieh and P.D.Lin , "Drill point geometry of multi-flute drills", Int J Adv Manuf Technol, pp. 466-476, 2005
[18] Lin, P. D. and Hsieh, Jung-Fa, "Dimension Inspection of Spatial Cams by CNC Coordinate Measuring Machines," Transactions of the ASME Journal of Manufacturing Science and Engineering Vol.122, pp.149-157,2000
[19] Lin, P. D. and Lee, M. F., "Applications of D-H Notation in Machining and On-Line Measurement of Roller-Gear Cams on 5-Axis Machine Tools," Transactions of the ASME Journal of Manufacturing Science and Engineering Vol.119, pp.393-401, 1997
[20] 沈邦正，"多面鑽的幾何設計"，碩士論文，國立成功大學機械研究所，2012
[21] 曾乾生，"薄刃鑽頭之刀具路徑設計與加工"，博士論文，國立成功大學機械研究所，2008
[22] 謝榮發，"多槽鑽頭設計與研磨"，博士論文，國立成功大學機械研究所，2003
[23] 曾乾生，"Ewag 六軸CNC工具磨床之研究"，碩士論文，國立成功大學機械研究所，2003
[24] 殷碩鴻，"多面鑽頭之幾何設計與研磨"，碩士論文，國立成功大學機械研究所，2000
[25] 郭禮安，"Development of Automated Universal Postprocessor for Non-Orthogonal Multi- Axes Machine Tools with Modified D-H Notation"，碩士論文，國立成功大學機械研究所，2008