隨著數控加工技術的進步、精度要求的提升、產品的多樣化，用於加工複雜曲面及特殊模具的各種特殊迴轉刀具需求的種類與形狀越來越多。傳統由熟練工依實驗結果所完成的鉋銑刀加工，雖然有不少相關研究論文，但截至目前為止，尚無一具有整合設計模型印證之完整理論的提出。本文以微分幾何為基礎，進行刀具幾何模型的建構，並運用系統性逆包絡求解法，根據溝槽及螺旋角設計成型砂輪，可自動化地完成所需螺旋迴轉鉋銑刀具設計，提昇加工重現性。本文所提出之設計模型及加工的技術方法，主要是針對新型螺旋迴轉銑刀及特殊螺旋鉋刀。

　　在新型銑刀研究方面，本文提出以最大溝槽外徑為基準，首先設計可加工多種不同外型銑刀之磨輪共用模型，並提出軸向與法向截形兩種砂輪設計法，以加工同樣外型之銑刀。討論了三種不同的刃口曲線定義下多種不同外形銑刀的加工設計模型，並運用二軸同動NC加工方案，在一定轉速的條件下，推導出砂輪一次加工各種銑刀所需徑向及軸向之切速。為了提昇製作精度，文中也提出多種補償式迴面殘留消除法，並探討此類刀具所存在的設計建模方面的諸多問題，對於球頭及角圓所產生過切及無刃口定義的部分，也考慮了平面刃口之填補及光滑刃口曲線之改良。本文又進一步地將上述微分幾何建模方法，推廣運用到特殊螺旋迴轉鉋刀的設計模型建構上。根據等距等價原理，先行建立圓環形平面刀刃與圓柱上漸開螺旋面的等距等價模型，待求得螺旋鉋刀圓桿上的螺旋溝槽及磨製溝槽的砂輪，設計刀桿溝槽參數與刀片參數，再探討螺旋鉋刀的前角與裝配原理，進行螺旋鉋刀的設計與裝配模型研究，並以計算機模擬建立完整的模型。

　　本文依據微分幾何理論所建立之特殊鉋銑刀理論模型，經數值印證，並透過模擬所得資料，印證了本文所提之理論及建模步驟確實精確可行。

　　The continued development of high-precision NC manufacturing techniques, together with the requirement to machine an increasing variety of freeform and complex surfaces, has resulted in a demand for specialized milling and shaping cutters. While a review of the published literature reveals an abundance of material relating to the manufacture of such cutters, typically these studies assume that experienced engineers operating on a more-or-less trial-and-error basis will carry out tool fabrication. As yet, no systematic integrated modeling approach for the design of these cutters has been proposed. Accordingly, this current paper adopts a differential geometry approach to construct a geometric model of these cutters. Furthermore, a process of reverse envelope is used to design the necessary sectional profiles of the grinding wheel based upon the required helical angle and groove section of the cutter. In this way, this paper proposes a comprehensive method that can facilitate the automatic design of milling and shaping cutters with a helical cutting edge. This paper concerns itself chiefly with the machining theory and design models associated with the newly developed helical rotating milling and shaping cutters.

　　Taking the maximal outer radius of the grooved section of the cutter as its basis, this paper first develops a generic model for a grinding wheel that is capable of manufacturing many different forms of cutter. Then, taking the same maximal outer radius, two grinding methods are proposed, i.e. axial and normal section methods, to manufacture cutters of the same form. The paper discusses the design models for many different forms of cutter with reference to three different types of cutting edge curve. For a constant rotating cutter speed, it is demonstrated how a simple two-axis NC machining operation may be used to complete grinding of the cutter in a single manufacturing pass through the application of suitable axial and radial grinding wheel feeding speeds. Furthermore, this paper presents a compensatory grinding operation that remedies the problem of residual revolving surface following the initial grinding process. The problems associated with the design model of these types of cutters are investigated. The use of a supplementary planar curve cutting edge to resolve the problems of over-cutting and non-existence of the cutting edge at the upper part of ball-end and end-mill cutters is also considered, together with the smooth conjunction of this supplementary curve with the original helical cutting edge on the shank.

　　This paper also develops the use of the differential geometry modeling method mentioned previously for application to the design modeling of specialized helical rotating shaping cutters. Based upon a concept of equidistance and equivalence, this paper develops models for the helical surface and the corresponding torus planar cutting edge for a cutter that comprises a helical cutting edge on a cylindrical shank surface. Having established the helical groove on the cylindrical shank of the shaping cutter, the corresponding grinding wheel profile, and the design parameters for the shank groove and the cutter, the lead angle of helical shaping cutters and the set-up principles for such cutters is discussed. Finally, the proposed models are verified numerically through a process of computer simulation.

　　The numerical results confirm the validity and accuracy of the theoretical models proposed for specialized milling and shaping cutters proposed in this current paper.

1. Akivis, M.A. and Goldberg, V.V., Conformal Differential Geometry and Its Generalizations, John Wiley & Sons, New York, 1996.

2. Aitintas, Y. and Lee, P., ”A General Mechanics and Dynamics Model for Helical End Mills,” Annals of the CIRP, Vol. 45, No. 1, pp. 59-63, 1996.

3. Aschinov, V and Alekseav, Metal Cutting Theory and Cutting Tool Design, Mir Publishers, Moscos, 1976.

4. Barsov, A., Cutting Tool Production, Moscow, Mir Publisher, pp. 179-194, 1978.

5. Bedi, S., Gravelle, S. and Chen, Y. H., “Principal Curvature Alignment Technique for Machining Complex Surfaces,” ASME Journal of Manufacturing Science and Engineering, Vol. 119, pp. 756-765, 1997.

6. Beer, P., “Anti-abrasive Coatings in a New Application-Wood Rotary Peeling Process,” Vacuum, Vol. 53, pp. 363-366, 1999.

7. Chen, C. K. and Kuo, T. Y., “The Theory of Center Offset and Its Application in Cutter Manufacture,” Journal of Materials Processing Technology, Vol. 83, pp. 217-222, 1998a.

8. Chen, C. K. and Kuo, T. Y., “A Study of The Geometrical Models of Grinding a Spheroid,” Journal of Materials Processing Technology, Vol. 83, pp. 231-233, 1998b.

9. Chen, C. K. and Lin, R. Y., “A study of manufacturing models for ball-end type rotating cutters with constant pitch helical grooves”, International Journal of Advanced Manufacturing Technology, Vol. 18, No. 3, pp. 157-167, 2001.

10. Chen, C. K., Lai, H. Y. and Tang, Y., “A manufacturing model of carbide-tipped spherical milling cutters,” Proc Inst Mechanical Engineers. Part B, Vol. 213, pp. 713-724, 1999.

11. Chen, Y. J. and Ravani, B. “Offset Surface Generation and Contouring in Computer Aided Design,” ASME J. Mechanisms, Transmissions & Automat. Des. Vol. 109, pp. 132-142, March 1987.

12. Choi, B. K. and Jun, C. S. “Ball-end cutter interference avoidance in NC machining of sculptured surfaces”, Computer-Aided Design, Vol.21, No.6, pp. 371-378, 1989.

13. Choi, B. K., Lee, C. S., Hwang, J. S. and Jun, C. S., “Compound Surface Modelling and Machining,” Computer-Aided Design, Vol. 20, No. 3, pp. 127-136, 1988.

14. Chyan, H. C. and Ehmann, K. F., “Tapered-Web Helical Groove Machining,” Proc. Instn. Mech. Engrs. , Part B, Vol. 213, pp. 779-785, 1999.

15. Doroshenko, R.V. and Bunga, G.A., “Correcting Calculation of Intricate Profiles of Super-abrasive Wood-Cutting Tools,” Sverkhtverdye Materialy, Vol. 5, pp. 29-31, 1998.

16. Ehmann, K. F., “Grinding Wheel Profile Definition for The Manufacture of Drill Flutes,” Annals of the CIRP, Vol. 39, No. 1, pp. 153-156, 1990.

17. Friedman, M. Y. and Meister, “The Profile of a Helical Slot Machined by a Form-Milling Cutter,” Annals of the CIRP, V01. 22, No. 1, pp. 157- 164, 1973.

18. Gardon, Y., Mathematics and CAD: Numerical Methods for CAD, The MIT Press, Cambridge, Massachusetts, 1986.

19. Gasparetto, A., “System Theory Approach to Mode Coupling Chatter in Machining,” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, Vol. 120, pp. 545-547, 1998.

20. Gliklikh, Yu. E., Ordinary and stochastic differential geometry as a tool for mathematical physics, Kluwer Academic Publishers, Dordrecht; Boston, 1996.

21. Hidehj, A. Y., “Development of Elliptic Ball-End Mill,” Bulls. Jap. Soc. of Prec. Eng., Vol. 20, N0. 4, pp. 59-66, 1986.

22. Huang, Y. and Oliver, J. H., “Non-constant Parameter NC Tool Path Generation of Sculptured Surfaces,” International Journal of Advanced Manufacturing Technology, Vol. 9, pp. 28l-290, 1994.

23. Hwang, J. S., “Interference-free Tool-path Generation in the NC Machining Parametric Compound Surface,” Computer-Aided Design, Vol. 24, No.12, pp. 667-676, l992.

24. Hwang, J. S. and Chang, T. C., “Three-Axis Machining of Compound Surfaces Using Flat and Filleted End Mills,” Computer-Aided Design, Vol. 30, No. 3, pp. 641-647,1998.

25. Kaldor, S., Trendler, P. H. H., and Hodgson, T., “Investigation into the Clearance Geometry of End Mills,” Annals of the CIRP, Vol. 33,No. 1, pp. 133-139, 1984.

26. Kaldor, S., Trendler, P. H. H., and Hodgson, T., “Investigation and Optimization of the Clearance Geometry of End Mills,” Annals of the CIRP, Vol. 34, No.1, pp. 153-159, 1985.

27. Kaldor, S., Rafael, A. M. and Messinger, D., “On the CAD of Profiles for Cutters and Helical Flutes-Geometrical Aspects,” Annals of the CIRP, Vol.37, No.1, pp. 53-57, 1988.

28. Kang, S.K., Ehmann, K.F. and Lin., C., “A CAD Approach to Helical Groove Machining Mathematical Model and Model Solution,” International Journal of Machine Tools & Manufacture, Vol. 36, No. 1, pp.141-153, 1996.

29. Kang, S. K., Ehmann, K. F. and Lin, C., “A CAD Approach to Helical Flute Machining-I. Mathematical Model and Model Solution,” Int. J. Mach. Tools Manufact., Vol. 36, No. 1, pp. 141-153, 1996.

30. Kang, S.K., Ehmann, K.F. and Lin, C., “A CAD Approach to Helical Groove Machining: Numerical Evaluation and Sensitivity Analysis,” Int. J. Mach Tools Manufact, Vol. 37, No.l, pp. 101-117, 1997.

31. Kataev, A. V., “Computer aided Design of Tool with Complex Forming Faces,” Soviet Engineering, Vo1. 9, No.7, pp. 22-28, 1989.

32. Kato, C. T. and Bailey, J. A., “Wear Characteristics of a Woodworking Knife with a Vanadium Carbide Coating Only on the Clearance Surface (Back Surface),” Key Engineering Materials, Vol. 138, pp. 479-520, 1998.

33. Kops, L. and Vo, D. T., “Detennination of the Equivalent Diameter of an End Mill Based on its Compliance,” Annals of the CIRP, Vo1. 39, No. 1, pp. 93-96, 1990.

34. Lai, J. Y. and Wang, D. J., “A Strategy for Finish Cutting Path Generation of Compound Surfaces,” Computers in Industry, Vol. 25, pp. 189-209, l994.

35. Lee, P. and Aitintas, Y., “Prediction of Ball-end Milling Forces from Orthogonal Cutting Data,” Int. J. Mach. Tools Manufact., Vol. 36, No.9, pp. 1059-1063, 1996.

36. Lin, P. D., Lee, M. F., “NC Data Generation for 4-Axis Machine Tools Equipped with Rotary Angle Head Attachments to Produce Variable Pitch Screws,” Int. J. Mach. Tools Manufact., Vol. 37, No. 3, pp. 341-353, 1997.

37. Lin, S. W., “ Study On The 2-Axis NC Machining of A Toroid-Shaped Cutter With A Constant Angle Between The Cutting Edge and The Cutter Axis,” Journal of Materials Processing Technology, Vol. 115, pp. 338- 343, 2001a.

38. Lin, S. W. and Lai, H. Y, “A Mathematical Model for Manufacturing Ball-End Cutter Using A Two-Axis NC Machine,” The International Journal of Advanced Manufacturing Technology, Vol. 17, pp. 881-888, 2001b.

39. Lin, Y. L. and Lee, T. S., ”An Adaptive Tool Path Generation Algorithm for Precision Surface Machining,” Computer-Aided Design, Vol. 31, pp. 237-247, l999.

40. Ling, F. Q. and Hewitt, W. T., “Expressing Coons-Gordon Surface as NURBS,” Computer-Aided Design, Vol. 26, No. 2, pp. 145-155, 1994.

41. Li, S. X. and Jerard, R. B., “5-Axis Machining of Sculptured Surfaces with a Flat-end Cutter,” Computer-Aided Design, Vol. 26, No. 3, pp. 377-386, March 1994.

42. Liu, X. W., “Five-axis NC Cylindrical Milling of Sculptured Surfaces,” Computer-Aided Design, Vol. 27, No.1, pp. 887-894, 1995.

43. Loney, G. C. and Ozsoy, T. M. “NC Machining of Free Form Surfaces,” Computer-Aided Design, Vol. 19, No.2, pp. 85-90, 1987.

44. Lychagin, V. V., The interplay between differential geometry and differential equations, American Mathematical Society, Providence, R.I., 1995.

45. Madore, J., An introduction to noncommutative differential geometry and its physical applications, Cambridge University Press, New York, 1995.

46. Mannan, M. A. and Lindstrom B., “Performance for End Mills Made of Different Tool Materials with Regards to Tool Life and Stability,” Annals of the CIRP, Vol. 35, No. 1, pp. 37-44, 1986.

47. Ma, W. and Kruth, J. P., “NURBS Curve and Surface Fitting for Reverse Engineering,” Int. J. Adv. Manuf. Technol. , Vol. 14, pp. 918-927, 1998.

48. Marshall, S. and Griffiths, J. G., “A New Cutter-Path Topology for Milling Machines,” Computer-Aided Design, Vol. 26, No. 3, pp. 204-214, March 1994.

49. Nutbourne, A. W. and Martin, R. R., Differential geometry applied to curve and surface design, Halsted Press, New York, 1988.

50. Ren, B. Y., Tang, Y. Y. and Chen, C. K., “The general geometrical models of the design and 2-axis NC machining of a helical end-mill with constant pitch,” Journal of Materials Processing Technology, Vol. 115, No. 3, pp. 265-270, 2001.

51. Ryosnke, H. S. and Jugelso, M. A., “A five Axis Computer controlled Twist Drill Grinder,” Machine Tool Design and Research, Vo1.24, No.4, pp. 101-110, 1984.

52. Sarma, R. and Dutta, D., “The Geometry and Generation of NC Tool Paths,” Tran. of the ASME., Journal of Mechanical Design, Vol. 119, No. 2, pp. 96-103, l997.

53. Sarma, R. and Dutta, D., “Tool Path Generation for NC Grinding,” Mach. Tools Manufacturing, Vol. 38, No. 3, pp. 177-195, 1998.

54. Sheth, D.S., CAD Software for Geometry and Process Analysis of Helical Machining, MS Thesis. University of Massachusetts. 1988, September.

55. Sheth, D.S. and Malkin, S.,"CAD/CAM for Geometry and Process Analysis of Helical Groove Machining," Annals of the CIRP, Vo1.39, No.1, pp. 129-132, 1991.

56. Suh, Y. S. and Lee, K., “NC Milling Tool Path Generation for Arbitrary Pockets Defined by Sculptured Surfaces,” Computer-Aided Design, Vol. 22, No. 5, pp. 273-284, June 1990.

57. Tai, C. C. and Fuh, K. H., “Model for Cutting Forces Prediction in Ball-end Milling,” Int. J. Mach. Tools Manufact., Vol. 35, No. 4, pp. 511-524, 1995.

58. Takench, T. I., “5-axis Control Machining and Grinding Based on Solid Model,” Annals of the CIRP, Vol. 40, No. 1, pp. 455-458, 1991。

59. Tsai, Y. C. and Hsieh, J. M., “A study of a design and NC manufacturing model of ball-end cutters,” Journal of Materials Processing Technology, Vol. 117, pp. 183-192, 2001.

60. Vickers, G. W. and Quan, K. W., “Ball-Mills Versus End-Mills for Curved Surface Machining,” Transactions of the ASME, Journal of Engineering for Industry, Vol. 111, No. 2, pp. 22-26, Nov. 1989.

61. Wu, C. T. and Chen, C. K., “Manufacturing models for the design and NC grinding of a revolving tool with a circular arc generatrix,” Journal of Materials Processing Technology, Vol. 116, No. 2-3, pp. 114-123, Oct 24, 2001a.

62. Wu, C. T. and Chen, C. K., “Study on rotating cutters with different definitions of helical angle,” International Journal of Advanced Manufacturing Technology, Vol. 17, No. 9, pp. 627-638, 2001b.

63. Wu, C. T., Chen, C. K. and Tang, Y. Y., ”Modeling and computer simulation of grinding of the ball end type rotating cutter with a constant helical angle,” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol. 215, pp. 1-14, 2001c.

64. Yang, M. Y. and Park, H. D., “The Prediction of Cutting Force in Ball-end Milling,” Int. J. Mach. Tools Manufact., Vol. 31, No. l, pp.45-54, 1991.

65. Yang, D. C. H. and Han, Z., “Interference Detection and Optimal Tool Selection in 3-axis NC Machining of Free-form Surfaces,” Computer-Aided Design, Vol. 31, No. 10, pp. 303-315, 1999.

66. Yan, H. S. and Lin, J.Y., “Geometric Design and Machining of Variable Pitch Lead Screws with Cylindrical Meshing Elements,” Tran. of the ASME: J. of Mech. Des., Vol.115, pp. 490-495, 1993.

67. Yu, D. Y. and Deng, J. C. et al. “Generation of Gouge-free Cutter Location Paths on Free-form Surfaces for Non-spherical Cutters,” Computers in Industry, Vol. 28, No. 2, pp. 81-94, 1996.

68. Yucesan, G. and Altintas, Y., “Prediction of ball end milling forces,” Journal of Engineering for Industry, Vol. 118, No. 2, pp. 95-103, 1996.

69. Zhou, J., Zhou, Y. H. and Zhan Y., “Enveloping Theory Based Method for the Determination of Path Internal and Tool Path Optimization for Surface Machining,” Chinese Journal of Mechanical Engineering, Vol. 12, No. 2, pp. 21-25, 1999.

70. Zhu, C., “Tool-Path Generation in Manufacturing Sculptured Surfaces with a Cylindrical End-Milling Cutter,” Computers in Industry, Vol. 17, pp. 385-389, l991.

71. 王志平主編，機床數控技術應用，高等教育出版社，北京，1998。

72. 王永剛，倪紅松，斜刃特種回轉面刀具的計算機仿真，重慶大學學報，第17卷，第2期，第131-135頁，1994。

73. 王清輝，廖文和，劉狀等，五坐標數控加工刀位軌跡及其干涉檢查的算法研究，航空學報，第18卷，第3期，第330-335頁，1997。

74. 任秉銀， 劉華明，自由曲面五坐標數控加工中幾個關鍵問題的研究，組合機床與自動化加工技術，第8卷，第 33-36頁，1998。

75. 任秉銀，複雜曲面多座標數控加工優化編程技術研究，哈爾濱工業大學博士學位論文，1998。

76. 任秉銀,唐余勇，劉華明，球頭螺旋銑刀刃口曲線的求解及螺旋溝槽的二軸聯動數控加工，工具技術，第33卷，第12期，第 11-14頁，1999。

77. 任秉銀，唐余勇，數控加工中的幾何建模理論及其應用，哈爾濱工業大學出版社，2000。

78. 牟欣， 劉曉雲，自由曲面數控粗加工的一種新方法，華中理工大學學報，第23卷，第6期，第 27-41頁，1995。

79. 呂廣明，唐余勇，一種新諧型波傳動的CAD研究，高校應用數學學報，第4卷，第3期，第356-362頁，1989。

80. 李阿卻，切削刀具學，台北，全華科技圖書股份有限公司，1999。

81. 李瓊硯，陸際聯，平頭銑刀加工曲面的無干涉路徑規劃，機械工程學報，第34卷，第1期，第75-81頁，1998。

82. 吳大任，微分幾何講義，北京，高等教育出版社，第 138-144頁，1985。

83. 何耀雄， 周艷紅， 周濟， 用砂輪稜邊數控磨削回轉刀具前刀面，中國機械工程，第8卷，第8期，第7-9頁，1998。

84. 周長秀， 樂兌謙， 吳序堂，平面型前刀面的特種回轉面刀具的成型原理， 工具技術，第25卷，第5期，第 17-21頁，1991。

85. 周長秀，複合型刀刃的特種迴轉面刀具齒槽的成形原理，工具技術，第29卷，第3期，第 24-27頁，1995。

86. 周長秀，沈謙，王氓，異形回轉銑刀數控加工數學模型一前刀面成形方法，東南大學學報，第25卷，第2期，第 25-29頁，1995。

87. 孟道驥，梁科，微分幾何，北京，科學出版社，1999。

88. 洪良德，切削刀具學，台北，全華科技圖書股份有限公司，2000。

89. 喻道遠，段正澄，球面刀在數控加工中的存在問題及改進方法，機械工業自動化，第16卷，第1期，第 21-24頁，1994。

90. 喻道遠，段正澄，鐘建琳等，空間自由曲面平頭立銑刀數控編程中過切干涉的處理及算法，機械，第24卷，第3期，第 22-24頁，1997。

91. 段正澄，喻道遠，空間自由曲面非球面刀加工軌跡自動生成的新原理和計算方法，機械工程學報，第30卷，第6期，第 21-27頁，1994 。

92. 時培林，王偉，唐余勇，球面銑刀制造中的數學模型研究。機械工程學報，第30卷，第5期，第 55-59頁，1994。

93. 袁哲俊，劉雄偉，劉華明，五座標軸端銑數控加工計算理論分析，機械工程學報，第29卷，第1期，第 31-37頁，1993。

94. 孫春華，迴轉體溝槽曲面數控加工理論的研究，哈爾濱工業大學博士論文，2000。

95. 孫春華，唐余勇，吳昌祚，劉華明，關於螺旋銑刀刃口設計問題，黑龍江大學自然科學學報，第1卷，第 28-29,38頁，2000。

96. 奚威， 設計螺旋槽成形銑刀的CAD方法，工具技術，第29卷，第12期，第 11-13頁，1995。

97. 陳朝光， 唐余勇，吳鴻業， 微分幾何及其在機械工程中的應用． 哈爾濱爾濱工業大學出版社，第 28-30，89-91頁，1998。

98. 唐余勇，機械工程中常用的幾何模型．國防工業出版社，北京，1989a年6月。

99. 唐余勇，新型螺旋木工刨刀設計製造裝配中有關問題之研究，齊齊哈爾濱工學院學報，第2卷，第 47-51頁，1989b。

100. 唐余勇，幾類螺旋面逆包絡問題的求解模型，宇航學報，第四期，第64-68頁，1990a。

101. 唐余勇，有關漸開線螺旋面工件製造模型研究，齊齊哈爾濱工學院學報，第2卷，第 57-60頁，1990b。

102. 唐余勇，新型螺旋木工刨刀設計方面一註記，齊齊哈爾濱工學院學報，第1卷，第 38-42頁，1990c。

103. 唐余勇，金建濤，呂廣明，硬質合金插齒刀設計製造的幾何模型研究，機械工程學報，第31卷，第5期，第 46-31頁，1995。

104. 唐余勇，刀具製造中的幾何理論及其應用，哈爾濱，哈爾濱工業大學出版社，1995。

105. 唐余勇，陳朝光，王松，等螺旋角銑刀二軸聯動數控加工方案及其幾何模，型哈爾濱工業大學學報，第28卷，第5期，第5-7頁，1996。

106. 唐余勇，任秉銀，二軸聯動加工迴轉刀具的幾個問題，河北科技大學學報，第21卷，第2期，第13-16頁，2000。

107. 焦建斌，多坐標側銑數控加工的誤差理論以及刀位驗證研究，哈爾濱工業大學博士學位論文，1995。

108. 游新農，陳幼平，周祖德，段正澄，數控加工的走刀模式及其評估方法，華中理工大學學報，第24卷，第9期，第 5-8頁，1996。

109. 張利波，林奕鴻，複雜曲面的五軸聯動加工，中國機械工程，第4卷，增刊，第187-189頁，1993。

110. 張利波，牟欣等． 組合曲面加工無干涉刀具路徑的產生， 華中理工大學學報，第24卷，第9期，第 15-17頁，1996。

111. 張輝，姚南珣等，等螺旋角迴轉刀具刀刃曲線的通用算法 ，大連理工大學學報，第37卷，第1期，第 63-67頁，1997。

112. 張瑞乾，王小椿，吳序堂，用密切曲率法加工自由曲面及其刀位軌跡的排列，西安交通大學學報，第31卷，第12期，第55-60頁，1997。

113. 張瑞乾，沈兵，王小樁，吳序堂，用二階密切曲率法加工自由曲面，機械工程學報，第34卷，第2期，第87-92頁，1998。

114. 楊波，吳明華，周濟，壓氣機葉輪葉片四坐標側銑加工干涉誤差的分析與計算，組合機床與自動化加工技術，第12卷2，第12-142頁，1994。

115. 趙良才，吳春才，空間直紋和準直紋曲面加工刀具軌跡生成及五軸後置軟件研製，機械工業自動化，第16卷，第3期，第43-46頁， 1994。

116. 劉井玉，劉華明，圓錐形球頭銑刀螺旋槽的數學建模，工具技術，第4卷，第 3-6頁，1997。

117. 劉井玉，特種迴轉面刀具幾何建模及數控磨削加工原理研究，哈爾濱工業大學博士論文，1998。

118. 劉世霞，唐余勇，孫家慶，球面銑刀修磨幾何模型研究，計算機輔助設計與圖形學學報，第3卷，第195-199頁，2000。

119. 劉華明， 李吉平， 任秉銀，NC驗證中通用銑刀掃描體生成方法，製造技術與機床，第9卷，第43-45頁，1999。

120. 劉雄偉，袁哲俊，五坐標側銑數控加工計算方法，組合機床與自動化加工技術，第12卷，第2-5頁，1992。

121. 劉雄偉，王增強，張定華等，葉輪五坐標數控加工及其計算機輔助編程，組合機床與自動化加工技術，第10卷，第16-19頁，1993。

122. 劉鵠然，特種迴轉刀具上的刀刃曲線 ，工具技術 ，第2卷，第10-12頁，1993。

123. 劉鵠然， 等法向前角異形刀具的生成原理與數控加工，刃具研究，第140卷，第1期，第7-16頁，1994。

124. 劉鵠然，旋轉銼加工的干涉檢驗，刃具研究，第1卷，第22-24頁，1996。

125. 劉懷蘭，周艷紅等，自由曲面NC加工無干涉刀位軌跡生成，中國機械工程, 第7卷，第3期，第47-49頁，1996。

126. 廖文和，劉狀，周儒榮，裁剪曲面的三軸銑削加工刀具軌跡的干涉處理，南京航空航天大學學報，第28卷，第6期，第818-824頁，1996。

127. 蘇步青、華宣積、忻元龍，實用微分幾何引論，科學出版社，1998。

128. 譚廣宇，袁哲俊，姚英學，加工過程碰撞干涉的矢量法檢驗，中國機械工程，第10卷，第5期，第513-515頁，1999。

129. 魏源遷，葉片型面刀位計算方法分析，航空學報，第15卷，第5期，第634-640頁，1994。

130. 鐘建琳，鄧建春等，凸曲面平頭銑刀刀位軌跡的自動生成，華中理工大學學報，第23卷，第2期，第15-17頁，1995。

131. 鐘建琳，米思南，喻道遠等，曲面加工中避免全局刀具干涉的方法， 華中理工大學學報, 第26卷，第12期，第19-21頁，1998。

132. 鐘建琳，米思南，喻道遠等，曲面平頭刀加工無干涉刀位軌跡自動生成的算法研究，機械工程學報，第35卷，第6期，第94-976頁，1999。

133. 蘭鳳崇，陳吉清，盧金火，基於NURBS方法的車身表面造型系統的研究與應用，中國機械工程，第7卷，第5期，第86-89頁，1996。