臺灣博碩士論文加值系統

齒輪是機械構件中最常見的傳動零組件，背負著傳遞動力、改變運動速度和方向的重要任務。由於傳統的螺旋傘齒輪強度計算(美國齒輪製造協會，AGMA)中幾乎沒有考慮到齒輪材料彈性變形、動態嚙入及嚙出衝擊、及熱處理的滲碳深度對一齒輪對齒面接觸應力及等效應力的影響。本論文建立一套螺旋傘齒輪三維動態接觸/衝擊分析模組，以C++視窗程式計算出螺旋傘齒輪真實齒面藉以匯入Pro/E軟體建構三維模型，再將三維模型匯入HyperMesh前處理器進行有限元素模型網格劃分、材料性質設定、碰撞接觸模式的選擇、速度載荷設定、沙漏控制設定與輸出條件控制等，最後藉由LS-DYNA顯式動力學軟體進行分析求解運算。考慮齒輪材料為一彈性體在不同轉速、扭矩、大小齒輪各別滲碳深度及硬度等參數影響下對傳動誤差曲線之影響。分析齒輪對在動態接觸/衝擊負載下其齒面接觸應力、等效應力、暫態及穩態響應，並與AGMA計算結果作一比對，提供齒輪設計者在轉速、扭矩、硬度及其滲碳深度一建議值。

Gears are the most important components of the transmission systems that support power carrying out and motion characteristics changing. Many researchers had applied AGMA standards to evaluate the strength of spiral bevel gear, presently. However, the elastic deformation of gear materials, dynamic meshing-in and meshing-out impact, and the surface hardening depth did not considered in AGMA standard. A great portion of research efforts on spiral bevel gear transmission errors is focused on contact stress and V/H values, while only a few investigate into the relations between transmission errors and rotational speeds. In this research, an approach for 3D dynamic contact and impact analysis of spiral bevel gear drives is addressed. The HyperMesh /LS-DYNA software is utilized to calculate the transmission errors, surface contact stresses and root bending stresses of a spiral bevel gear pair. The vibration behavior of actual gear set under dynamic loading conditions has been simulated in the dynamic model. The dynamic responses of the spiral bevel gear drives are obtained under the conditions of initial speed with driver and the resistance with driven. The stiffness and elastic deformation of the gear teeth are calculated by using the finite element method with actual geometry and positions of the gears. The influences of the transmission errors, initial speed, and the surface hardening depth on impact characteristics of the meshing teeth are analyzed. After the impact analysis, the numerical results of transmission errors, contact pressure, and effective stress involve with the transient and steady states that difference AGMA standards.

中文摘要...................................................i
Abstract..................................................ii
致謝.....................................................iii
目錄......................................................iv
表目錄....................................................ix
圖目錄....................................................xi
符號說明...............................................xviii
第一章　緒論...............................................1
1.1　研究動機與目的........................................1
1.2　文獻回顧..............................................2
1.3　研究方法..............................................6
第二章　LS-DYNA基礎理論....................................7
2.1　前言..................................................7
2.2　基本控制方程(Governing Equation)......................7
2.2.1　運動方程............................................8
2.2.2　邊界條件...........................................10
2.2.3　本構方程...........................................12
2.3　空間有限元離散化.....................................13
2.4　元素性質的選擇.......................................17
2.5　材料模型的選擇.......................................18
2.6　時間積分(Time Integration)...........................19
2.7　中央差分法(The Central Difference Method)............21
2.8　局部座標系設定.......................................22
2.9　接觸面的定義.........................................23
2.10　沙漏模態控制........................................24
2.11　LS-DYNA主程式處理...................................25
2.12　LS-PREPOST後處理器..................................25
第三章　LS-DYNA接觸碰撞理論...............................26
3.1　主(Master)和從(Slave)的概念..........................26
3.2　接觸算法的介紹.......................................27
3.3　接觸界面的條件.......................................31
3.4　接觸搜索的方式.......................................32
第四章　材料機械性質的改變和拉伸試驗結果..................39
4.1　材料拉伸試棒規格及硬度...............................39
4.2　材料拉伸試驗結果.....................................41
第五章　螺旋傘齒輪接觸碰撞與分析..........................51
5.1　螺旋傘齒輪之分析架構.................................51
5.2 有限元模型的建立.....................................52
5.3　網格劃分.............................................54
5.4　創建集合器(Collectors)...............................57
5.5　拘束條件設定.........................................59
5.6　速度扭矩設定.........................................60
5.7　範例一：分析模擬結果與AGMA標準公式驗證...............61
5.7.1　AGMA標準公式.......................................61
5.7.2　分析模擬結果.......................................68
5.7.3　模擬與標準公式比較討論.............................72
5.8　範例二：螺旋傘齒輪對之不同轉速比較...................73
5.8.1　傳動誤差的變化情形.................................74
5.8.2　傳動誤差的結果與討論...............................77
5.8.3　齒面接觸壓應力的變化情形...........................82
5.8.4　齒面接觸壓應力的結果與討論.........................85
5.8.4　齒面接觸等效應力的結果與討論.......................88
5.9　改變機械性質後的結果與比較...........................90
5.9.1　範例三：不同滲碳層深度的比較.......................90
5.9.2　不同滲碳層深度的結果與討論.........................91
5.9.3　範例四：不同表面硬度的比較.........................94
5.9.4　不同表面硬度之應變結果與討論.......................94
5.9.5　不同表面硬度之傳動誤差結果與討論...................97
5.9.6　範例五：相同轉速不同扭矩的比較.....................98
5.9.7　相同轉速不同扭矩之傳動誤差結果與討論...............98
5.9.8　相同轉速不同扭矩之等效應力結果與討論..............100
5.9.9　範例六：相同扭矩不同轉速的比較....................102
5.9.10　相同扭矩不同轉速之傳動誤差結果與討論.............103
5.9.11　相同扭矩不同轉速之等效應力結果與討論.............105
第六章 結論與未來研究方向..............................107
6.1　結論................................................107
6.2 未來研究方向........................................109
參考文獻.................................................110
Extended Abstract
簡歷

[1]Vilmos Simon, FEM stress analysis in hypoid gears, Mechanism and Machine Theory 35 (2000) 1197-1220.
[2]Jesper Brauer, A general finite element model of involute gears, Finite Elements in Analysis and Design 40 (2004) 1857-1872.
[3]K.Mao, Gear tooth contact analysis and its application in the reduction of fatigue wear, Wear 262 (2007) 1281-1288.
[4]V. Abousleiman, P. Velex, A hybrid 3D finite element/lumped parameter modle for quasi-static and dynamic analyses of planetary/epicyclic gear sets, Mechanism and Machine Theory 41 (2006) 725-748.
[5]Yi-Cheng Chen, Chung-Biau Tsay, Stress analysis of a helical gear set with localized bearing contact, Finite Element in Analysis and Design 38 (2002) 707-723.
[6]Wallance DB, Seireg A. Computer simulation of dynamic stress deformation, and fracture of gear teeth. Journal of Engineering for Industry, 1973, 95(11):1108~1114.
[7]Vijayarangan S, Ganesan N, A study of dynamic stresses in a spur gear under a moving line load and impact load conditions by a three-dimensional finite element method, Journal of Sound and Vibration, 1993,162(1):185~188.
[8]Shuting Li,Contact problem and numeric method of a planetary drive with small teeth number different,Mechanism and Mechine Theory 43 (2008) 1065-1086.
[9]Y. Wang, W.J. Zhang, H.M.E Cheung, A finite element approach to dynamic modeling of flexible spatial compound bar-gear system, Mechanism and Machine Theory 36 (2001) 469-487.
[10]Shuting Li, Effects of machining errors, assembly errors and tooth modifications on loading capacity, load-sharing ratio and transmission error of a pair of spur gear, Mechanism and machine theory 12 (2007) 698-726.
[11]Shuting Li,Finite element analyses for contact strength and bending strength of a pair of spur gears
[12]Chia-Chang Liu, Chung-Biau Tsay, Contact characteristrics of beveloid gears, Mechanism and Machine Theory 37 (2002) 333-350.
[13]Shuting Li, Effect of addendum on contact strength, bending strength and basic performance parameters of a pair of spur gears, Mechanism and Theory 43 (2008) 1557-1584.
[14]Vilmos Simon, Influence of tooth errors and misalignments on tooth contact in spiral bevel gears, Mechanism and Machine Theory 43 (2008) 1253-1267.
[15]M. H. Refaat, S. A. Meguid, On the contact stress analysis of spur gears using variational inequalities, Computer & Structures Vol. 57, No. 5, pp, 871-882, 1995.
[16]Ying-Chien Tsai, Weu-Yi Hsu, The study on the design of spiral bevel gear sets with circular-arc contact paths and tooth profiles, Mechanism and Machine Theory 43 (2008) 1158-1174.
[17]Osman Asi, Fatigue failure of a helical gear in a gearbox, Engineering Gailure Analysis 12 (2006) 1116-1125.
[18]J. Kramberger, M. Sraml, S. Glodez, J. Flasker, I. Potrc, Computational modle for the analysis of bemding fatigue in gears, Computers and Structures 82 (2004) 2261-2269.
[19]An1 Ural, Gerd Heber, paul A. Wawrzynek, Snthony R. Ingraffea, David G. Lewicki ,Joaquim B.C. Neto, Three-dimensional, Parallel, finite element simulation of fatigue crack growth in a spiral bevel pinion gear, Engineering Fracture Mechanics 72 (2005) 1148-1170.
[20]Spievak LE, Wawrzynek PA, Ingraffea AR, Lewicki DG. Simulating fatigue crack growth in spiral bevel gears. Engng Fract Mech 2001; 68(1):53-76.
[21]Erogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear. J Basic Engng 1963; 85(4):519-27.
[22]Masatoshi Kuroda, Siu Lun Fok, Barry J. Marsden, S. Olutunde Oyadi ji, Analyses of the multiple cracking behavior of brittle hollow cylinders under internal pressure. International of Impact Engineering Article in Press 2004.
[23]G.P. Cavallaro, T.P. Wilks, C. Subramanian, K.N. Strafford, P. French, J.E. Allison, Bending fatigue and contact fatigue characteristics of carburized gears, Surface and Coatings Technology 71 (1995) 182-192.
[24]Ahmed M. M. El-Bahloul, Surface capacity of gears of circular-arc tooth-profile, Wear 193 (1996) 146-154.
[25]J.L. Woods, S.R. Daniewicz, R. Nellum, Increasing the bending fatigue strength of carburized spur gear teeth by presetting, International Journal of Fatigue 21 (1999) 549-556.
[26]M. Izciler, M. Tabur, Abrasive wear behavior of different case depth gas carburized AISI 8620 gear steel, Wear 260 (2006) 90-98.
[27]白金澤，LS-DYNA3D 理論基礎與實例分析，科學出版社，北京，2005
[28]蔡易修，雙層巴士翻覆之數值與分析，大葉大學機械工程研究所，2005
[29]賈宇，機車車體耐碰撞設計與碰撞仿真研究，大陸西南交通大學，2005
[30]John O. Hallquist, LS-DYNA THEORETIVAL MANUAL, Livermore software technology corporation, 1998.
[31]Version 971, LS-DYNA KEYWORD USER’S MANUAL, Livermore software technology corporation, 2007.
[32]林智群，車輛碰撞之動態反應分析，大葉大學車輛工程學系碩士班，2003
[33]陳朝漟，高爾夫桿頭形狀變化之碰撞分析，國立中山大學機械與機電工程學系，2003
[34]趙海鷗，LS-DYNA動力分析指南，兵器工業出版社，北京，2003
[35]黃淳權，材料力學第六版，滄海書局，2005
[36]AGMA Standard 2003-B97, Rating the Pitting Resistance and Bending Strength of Generated Straight Bevel, Zerol Bevel and Spiral Bevel Gear Teeth, the American Gear Manufactures Association, 1500 King Stress, Suite 201, Alexandria. VA 22314, Reedited copy, June 1988.
[37]Rochester, Calculating Instructions Generated Hypoid Gears, GLEASON WORKS, Copyright 1949, 1954.
[38]吳嘉祥，機械元件設計，高立圖書有限公司，2006
[39]Daehyun Park, Development of Surface Wear and Lapping Simulation models for Hypoid Gears, Mechanical Engineering of Ohio State University, 2009.
[40]http://www.matweb.com/
[41]Faydor L. Litvin, Gear Geometry and Applied Theory, PTR Prentice Hall, 1994.