本論文主要利用有限元素法分析探討各尺寸參數對大型環狀螺旋齒輪(Rim Type Helical Gear)對承受扭矩負載時，其負載分配、齒對表面接觸應力、齒根彎曲應力分佈與變形之影響。文中有限元素模型採用理想彈性模式配合20O壓力角全齒(Full Depth)模式，分析其應力與變形。
文中探討的主要尺寸參數有：環厚、腹板厚、齒面寬及螺旋角(Helix Angle)，並分析研究各參數對齒面赫茲應力、齒根彎曲應力與變形之影響，同時比較分析其與實心螺旋齒輪之差異性，希望由此分析結果提供未來在進行大型螺旋齒對設計，如風機傳動系統設計，時之參考。

In this thesis, the ideal elastic finite element model is employed to evaluate the possible effects of gear parameters in large module rim type helical gear pair’s Hertz stress、root bending stress and tip deformation under power loading. The full depth helical gear shape with 20O pressure angle is employed in the analysis.
The geometrical parameters, i.e. the backup ratio(rim thickness), web plate thickness, tooth face width and helix angle, on the stress distributions and deformation of rim type helical gear pairs have been investigated and discussed. The difference between the rim type and solid helical gear pair has also been compared.
Numerical results indicate that these geometrical parameters of rim type helical gear pair may affect the stress and deformation significantly. We do hope this analysis results may helped and be a good reference for large size rim type helical gear pair design used widely in high power transmission systems, e.g. the wind power transmission system.

謝誌 i
摘要 ii
Abstract iii
目錄 iv
表目錄 vi
圖目錄 vii
符號說明 xii
第一章 緒論 1
1.1前言 1
1.2文獻回顧 5
1.3研究動機 8
1.4組織章節 10
第二章 研究相關理論 11
2.1路易斯齒根應力方程式 11
2.2 AGMA接觸應力方程式 17
2.3 AGMA彎曲應力方程式 24
第三章 螺旋環齒輪有限元素模式建立 27
3.1有限元素模型建立流程 28
3.2 CAE軟體模型建立方法 30
3.3收斂性分析 38
第四章 結果分析與討論 43
4.1螺旋環齒輪參數說明 43
4.2齒面赫茲應力分析 46
4.2.1齒面赫茲應力分佈探討 46
4.2.2齒面最大赫茲應力分析 50
4.3齒根彎曲應力分析 54
4.3.1齒根彎曲應力分佈探討 54
4.3.2齒根最大彎曲應力分析 59
4.4齒頂von Mises Stress分析 64
4.5齒輪變形分析 69
第五章 結論與未來展望 75
5.1結論 75
5.2設計成果展示 76
5.3未來展望 80
參考文獻 81

[1] 經濟部，「能源產業技術白皮書」，2014。
[2] 張永源、康志堅，「2014全球風力發電市場發展趨勢與展 望」，工業技術研究院，2014。
[3] International Energy Agency, ”IEA Wind 2013 Annual Report,” 2014.
[4] The European Wind Energy Association, “Wind in Power 2014 European Statistics,” 2015.
[5] 台灣電力公司Taipower，2015。
[6] G.D. Bibel, S.K. Reddy, R.E. Handschuh and M. Savage, “Effects of Rim Thickness on Spur Gear Bending Stress,” NASA Technical Memorandum, U.S., 1991.
[7] David G. Lewicki and Roberto Ballarini, “Effect of Rim Thickness on Gear Crack Propagation Path,” NASA Technical Memorandum, U.S., 1996.
[8] David G. Lewicki and Roberto Ballarini, “Rim Thickness Effects on Gear Crack Propagation Life,” International Journal of Fracture, 87, pp. 59–86, 1997.
[9] David G. Lewicki, “Gear Crack Propagation Path Studies_ Guidelines for Ultra-Safe Design,” The 57th Annual Forum and Technology Display sponsored by the American Helicopter Society, Washington, DC, 2001.
[10] Yi-Cheng Chen and Chung-Biau Tsay, “Stress Analysis of A Helical Gear Set with Localized Bearing Contact,” Finite Elements in Analysis and Design, 38, pp. 707–723, 2002.
[11] J. Kramberger, I. Potrc and J. Flašker, “Prediction of 3-D Crack Growth in Thin Rim-Gears,” International Design Conference, 2002.
[12] 洪榮德、連聰賢、曾莉雅、林新智、林昆明，「SAE 8620合金鋼熱處理效應之研究」，2006。
[13] Yesh P. Singh and Ravichandra Patchigolla, “Effect of Rim Thickness on Bending Stresses in Low Addendum Large Spur Gears,” 2006.
[14] Andrzej Kawalec, Jerzy Wiktor and Dariusz Ceglarek, “Comparative Analysis of Tooth-Root Strength Using ISO and AGMA Standards in Spur and Helical Gears With FEM-based Verification,” Journal of Mechanical Design, 128, pp. 1141-1158, 2006.
[15] 劉柏村，「空間漸開線齒面之合成與接觸分析」，國立成功大學機械工程學系碩士論文，台南，2006。
[16] Gordana Marunić, “Maximum Web Stress of Thin-Rimmed Gear,” 12th International Research/Expert Conference-Trends in the Development of Machinery and Associated Technology, Istanbul, Turkey, pp. 1001-1004, 2008.
[17] Gerhard G. Antony, “How to Determine the MTBF of Gearboxes,” pp. 32-37, 2008.
[18] G. Mallesh, V B Math, Ravitej, Krishna Prasad Bhat P and Paramesh Kumar M K, “Effect of Rim Thickness on Symmetric and Asymmetric Spur Gear Tooth Bending Stress,” 14th National Conference on Machines and Mechanisms, Durgapur, India, pp. 113-118, 2009.
[19] Gonzalo González Rey, “Factor por espesor de llanta para evaluar resistencia a la fractura en ruedas dentadas,” Revista Cubana de Ingeniería, 2(2), pp. 35-41, 2011.
[20] Milan Opalić, Krešimir Vučković and Milan Kljajin, “Effect of Web Arrangement on Thin-Rim Gear Tooth Contact Stress,” 15th International Research/Expert Conference-Trends in the Development of Machinery and Associated Technology, Prague, Czech Republic, pp. 545-548, 2011.
[21] D. A. Patel and P. A. Vaghela, “Improvement of Load Caring Capacity of Spur Gear by Asymmetric Teeth,” 5th International Conference on Advances in Mechanical Engineering, Gujarat, India, pp. 898-902, 2011.
[22] 李鳳、芮曉明，「基於彈性理論的齒圈輪緣應力變形特性
分析」，華北電力大學能源動力與機械工程學院，2011。
[23] Abiy Tessema, Doug Walton and David Weale, “Effect of Web and Flange Thickness on Nonmetallic Gear Performance,” pp. 30-35, 2011.
[24] 翁士茗、李岡晏，「溫度與負載對轉位塑膠齒強度的影響」，國立中山大學機械與機電工程學系，第十五屆全國機構與機器設計學術研討會，台南，pp. 299-306，2012。
[25] E.E. Taskinoglu, V.Y. Öztürk and Y. Paça, “Gear Web and Rim Thickness Optimization to Improve Vibration and Fatigue Reliability of A Rotary UAV Gearbox,” Dynamics of Rotating Machinery, pp. 1361-1372, 2012.
[26] Andrew Wright, “A Comparison of The AGMA Gear Design Stresses, The Lewis Bending Stress, and The Stresses Calculated by The Finite Element Method for Spur Gears,” 2013.
[27] Jaya.S.Kailuke and Y. L. Yenarkar, “Investigation of Stresses in The Thin Rimmed Spur Gear Tooth Using FEM,” International Journal of Research in Engineering and Technology, 02(11), pp. 437-441, 2013.
[28] J M Prajapati and P A Vaghela, “Objective Function to Optimize Bending Stress at Critical Section of Asymmetric Spur Gear,” Journal of Mechanical and Civil Engineering, 10(1), pp. 58-65, 2013.
[29] 石田 武、日高照晃、王 宏猷、山田 浩與橋本正孝, “Bending Stress and Tooth Contact Stress of Cycloid Gear with Thin Rims,” The Japan Society of Mechanical Engineers, 62(593), pp. 291-297, 2013.
[30] 秦慧斌、吕明、佘銀柱、王時英、李向鵬, “Modeling and Solving for Transverse Vibration of Gear with Variational Thickness,” J. Cent. South Univ., 20, pp. 2124-2133, 2013.
[31] Victor Roda-Casanova, Francisco T. Sanchez-Marin, Ignacio Gonzalez-Perez, Jose L. Iserte and Alfonso Fuentes, “Determination of The ISO Face Load Factor in Spur Gear Drives by The Finite Element Modeling of Gears and Shafts,” Mechanism and Machine Theory, 65, pp. 1-13, 2013.
[32] F. Curà, A. Mura and C. Rosso, “Investigation about Crack Propagation Paths in Thin Rim Gears,” Frattura ed Integrità Strutturale, 30, pp. 446-453, 2014.
[33] Wu Jia Hang, “Maximum Torque of Combination Threats for Spur Gear based on AGMA and JGMA Standards,” University Tun Hussein Onn, Malaysia, 2014.
[34] Richard G. Budynas and J. Keith Nisbett, Shigley’s Mechanical Engineering Design, 8th Edition, McGraw-Hill, 2008.
[35] American Gear Manufacturers Association, “Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth,” ANSI/AGMA 2001-D04, 2004.
[36] Ahmad Mujahidin, Sekedar Curhat Pribadi, Kamis, 2014.
[37] ANSYS Company, ANSYS 14.0 Help.
[38] Mack Aldener, Magnus and Mårten Olsson, "Interior Fatigue Fracture of Gear Teeth," Fatigue and Fracture of Engineering Materials and Structures, 23(18), pp. 283–292, 2000.
[39] KISSsoft AG Company, “Gear Calc User’s Manual,” 2006.