臺灣博碩士論文加值系統

圓柱齒輪之精加工方法有精滾、刮齒與磨齒，其中磨齒又可分為成形磨與創成磨兩類，而成形磨在磨削過程中砂輪與工件齒輪齒面為線接觸，相較於創成磨法其磨削效率較高，且易於透過砂輪修整達成齒面修形之目的，因此非常適合大尺寸大模數齒輪之磨削。長期以來國內磨齒設備皆仰賴國外進口，關鍵技術亦掌握在國外各大工具機製造廠，由於此類齒輪專用機台所有加工運動路徑皆須經過複雜數學運算，因此必須提供專門的製造軟體以自動產生修砂和磨削NC碼。本論文主要目的即在於發展成形磨齒機數學模式，首先建立圓柱齒輪端面齒形與齒形修整方法，接著根據成形磨理論和端面齒形推導砂輪軸向廓形，並提出砂輪軸向廓形修正方法，再由已知泛用成形砂輪磨齒機機械設定推導出五軸CNC成形砂輪磨齒機之機械設定，然後據此機械設定可規劃成形磨削齒輪加工運動路徑並編寫NC加工程式，最後利用Visual Basic 2008做為開發平台，發展五軸CNC成形砂輪磨齒機製造程式。

There are three methods for finishing cylindrical gears, finish hobbing, finish shaving, and finish grinding. Grinding processes can be further divided into two types: form grinding and generating grinding. In the form grinding process, it is the line contact between the grinding wheel and the gear surface. In addition, because of advances in higher efficiency and easier way to achieve the purpose of flank correction through the wheel modification, compared with the generating grinding process, the form grinding is suitable for gears with large-size and large-module. Up to now, many grinding machines in Taiwan are imported from abroad, and the key techniques are also relied on foreign manufacturers. For the gear machines, because of complicated calculation in programming NC codes, the sophisticated manufacturing software needs to be provided to generate dressing and grinding NC codes automatically. Therefore, in this thesis, we establish the mathematical model for form grinding machine. First, we develop the mathematical model of gear profile for cylindrical gear and its profile modification methods, and then the axial profile of the grinding wheel are derived based on the form grinding theory and the gear profile. Additionally, a correction method for the wheel profile is proposed. We derive the machine settings of the five-axis CNC gear profile grinding machine from the given machine settings of a universal gear profile grinding machine. According to the derived machine settings, the grinding path for form grinding process can be determined, and it can be used to program the grinding NC code. Finally, we use Visual Basic 2008 as a tool to develop the manufacturing program of five-axis CNC gear profile grinding machine.

中文摘要 I
Abstract II
誌 謝 III
目 錄 IV
符號說明 VII
圖索引 IX
表索引 XII
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 文獻回顧 2
1.3.1 砂輪軸向廓形推導 2
1.3.2 齒形修整 3
1.3.3 齒面誤差修正 3
1.3.4 NC程式編程 4
1.4 論文架構 4
第二章 圓柱齒輪端面齒形和軸向砂輪廓形推導 5
2.1 前言 5
2.2 圓柱齒輪端面齒形 5
2.2.1 漸開線齒形 5
2.2.2 齒條刀具齒形 7
2.2.3 嚙合方程式計算包絡線 10
2.3 端面齒形修整 12
2.3.1 K形修整 14
2.3.2 鼓形修整 17
2.3.3 自由曲線修整 19
2.3.4 壓力角調整 21
2.3.5 齒頂與齒根部位圓角及倒角 22
2.4 砂輪軸向廓形推導與作用線 24
2.4.1 工件齒輪齒面方程式 24
2.4.2 建立泛用型成形磨齒機坐標系統 26
2.4.3 計算作用線及推導砂輪軸向廓形數學模式 28
2.4.4 砂輪軸向廓形B-spline曲線擬合 30
2.4.5 砂輪軸向廓形修正 32
2.5 數學範例 33
2.5.1 端面齒形 33
2.5.2 砂輪軸向廓形 35
2.6 小結 36
第三章 五軸CNC成形砂輪磨齒機數學模式建立 37
3.1 前言 37
3.2 五軸CNC成形砂輪磨齒機坐標轉換 37
3.3 五軸機械設定推導 38
3.4 數學範例 39
3.5 小結 40
第四章 修砂及研磨NC路徑規劃 41
4.1 前言 41
4.2 程式原點 41
4.2.1 修砂程式原點 42
4.2.2 研磨原點 45
4.3 程式號碼規劃 46
4.4 參數表 47
4.5 舊砂輪修砂路徑規劃 48
4.5.1 舊砂輪廓形修砂點計算 48
4.5.2 舊砂輪修砂修整器倒圓中心計算 49
4.5.3 NC路徑規劃 49
4.6 新砂輪修砂路徑規劃 50
4.6.1 新砂輪修砂路徑點計算 51
4.6.2 NC路徑規劃 52
4.7 研磨路徑規劃 53
4.7.1 研磨路徑點計算 54
4.7.2 NC路徑規劃 56
4.8 NC加工碼範例 59
4.9 小結 61
第五章 成形砂輪磨齒機製造程式與NC路徑模擬 62
5.1 前言 62
5.2 成形砂輪磨齒機製造程式研發 62
5.3 修砂及研磨NC路徑模擬 67
5.3.1 新砂輪修砂NC路徑模擬 67
5.3.2 研磨NC路徑模擬 69
5.4 小結 70
第六章 結論與建議 71
6.1 結論 71
6.2 未來研究目標及發展方向 72
參考文獻 73
作者簡介 75
附錄A. 砂輪修整NC副程式 76
附錄B. 全齒研磨NC副程式 85

[1]J T. Black, Ronald A. Kohser, 2008, DeGarmo’s Materials and Processes in Manufacturing, tenth ed., J. Wiley, New York.
[2]Litvin, F. L., and Fuentes, A., 2004, Gear Geometry and Applied Theory, 2nd edition, Cambridge University Press, NJ.
[3]Kobayashi Youichi, Nishida Noriteru, Ougiya Yasuhiko and Nagata Hiroshi, 1995, “Tooth trace modification processing of helix gear by form grinding method, Transactions of the Japan Society of Mechanical Engineers, Part C, 61(590), pp.4088-4093.
[4]Gorla, C. and Rosa, F. 2003, Form Grinding of Helical Gears: Effects of Disk Shaped Tools Plunging, Proceedings of the ASME Design Engineering Technical Conference, 4B, pp.731-739.
[5]Faydor L. Litvin, Alfonso Fuentes, Ignacio Gonzalez-Perez, Luca Carnevali, and Thomas M. Sep, 2002, New Version of Novikov-Wildhaber Helical Gears: Computerized Design, Simulation of Meshing and Stress Analysis, Comput. Methods Appl. Mech. Engrg. 191, 5707-5740.
[6]Faydor L. Litvin, Alfonso Fuentes, Ignacio Gonzalez-Perez, Luca Carvenali, Kazumasa Kawasaki and Robert F. Handschuh, 2003, Modified Involute Helical Gears: Computerized Design, Simulation of Meshing and Stress Analysis, Comput. Methods Appl. Mech. Engrg., 192(33-34), pp.3619-3655.
[7]HOFLER, HOFLER RAPID 4000 Operating Instructions.
[8]NILES, NILES ZE 800 Instruction Manual.
[9]H. Yoshino, K. Ikeno, 1991, Error compensation for form grinding of gears, Trans. Japan Soc. Mech. Engrs. Part C 57(543) 3652-3655.
[10]Shih, Y-P., and Fong, Z-H., 2008, Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Gear Generator, ASME J. Mech. Des., 130(6), pp. 1-11.
[11]Fan, Q., Dafoe, R.S., Swanger, and J.W., 2008, Higher-Order Tooth Flank Form Error Correction for Face-Milled Spiral Bevel and Hypoid Gears, ASME, J. Mech. Des., 130(7), pp.1-7
[12]D.F. Rogers, J.A. Adams, 1990, Mathematical Elements for computer Graphics, second ed., McGraw-Hill, New York.
[13]Vera B. Anand, 1993, Computer Graphics and Geometric Modeling for Engineers, J. Wiley, New York.
[14]FANUC Series 16i/160i/160is-MB, FANUC Series 18i/180i/180is-MB5, FANUC Series 18i/180i/180is-MB Operator’s Manual.
[15]ANSI/AGMA913-A98, 1998, Method for Specifying the Geometry of Spur and Helical Gears, Alexandria VA.
[16]ANSI/AGMA2000-A88, 1988, Gear Classification and Inspection Handbook, Alexandria VA.
[17]Steven C. Chapra, 2008, Applied Numerical Methods with MATLAB, second ed., McGraw-Hill, New York.
[18]Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T., 1992, Numerical Recipes in C, 2nd Edition, Cambridge University Press., New York, NY.
[19]張永爵，1998，齒輪的設計和製造(上)，徐式基金會出版，台北。
[20]張欽宇，2011，五軸CNC成形砂輪磨齒機NC路徑模擬與碰撞檢測，國立台灣科技大學碩士論文。