高轉速正齒輪之多目標最佳化與動態特性分析

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：27

、訪客IP：18.217.220.114

姓名

劉鴻志(Hung-Chih Liu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

高轉速正齒輪之多目標最佳化與動態特性分析
(Multi-Objective Optimization and Dynamic Characteristics of A High-Speed Spur Gear Set)

相關論文

★ G10液晶玻璃基板之機械手臂牙叉結構改良與最佳化設計	★ 線性齒頂修整對正齒輪之傳動誤差與嚙合頻能量影響分析
★ 沖床齒輪分析與改善	★ 以互補型盤狀圓弧刀具創成之曲線齒齒輪有限元素應力分析
★ 修整型曲線齒輪對齒面接觸應力與負載下傳動誤差之研究	★ 衛載遙測取像儀反射鏡加工缺陷檢測與最佳光學成像品質之運動學裝配設計
★ 應用經驗模態分解法於正齒輪對之傳動誤差分析	★ 小軸交角之修整型正齒輪與凹面錐形齒輪組設計與負載下齒面接觸分析
★ 修整型正齒輪對動態模擬與實驗	★ 應用繞射光學元件之齒輪量測系統開發
★ 漸開線與切線雙圓弧齒形之諧波齒輪有限元素分析與齒形設計	★ 創成螺旋鉋齒刀之砂輪輪廓設計與最佳化
★ 動力刮削創成內正齒輪之刀具齒形輪廓最佳化設計	★ 非接觸式章動減速電機結構設計與模擬
★ Helipoid齒輪接觸特性研究與最佳化分析	★ 圓柱型齒輪之動力刮削刀具輪廓設計

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 ( 永不開放)

摘要(中)

本論文旨在進行高轉速修整型正齒輪之特性分析，並建立最佳化分析流程，探討齒頂修整對於動態特性之影響。首先，由齒輪原理，建立具導程隆齒修整(Lead Crowning)、線性齒頂修整(Linear Tip Relief)與轉位(Profile Shift)之正齒輪齒面數學模式。經由齒面接觸分析，求解靜態傳動誤差(Static Transmission Error, STE)，並由有限元素分析軟體與齒輪設計分析軟體進行負載下齒面接觸分析，並探討組裝誤差對於齒面接觸應力之影響。並依據美國齒輪製造協會(American Gear Manufacturers Association, AGMA)所訂定之齒輪相關規範，計算齒輪組之齒面、齒根等安全係數。
其次，在最佳化部分，以負載下傳動誤差之峰谷值(Peak-to-Peak Loaded Transmission Error, PPLTE)作為目標函數，並結合齒輪設計分析軟體KISSsoft與數值分析軟體Matlab，分別以全域搜索演算法(GlobalSearch Algorithm, GS)及基因演算法(Genetic Algorithm, GA)進行最佳化分析，藉以建立最佳化齒形修整參數。
最後，在動態模擬部分，建立齒輪系統動態模型，將齒面接觸分析所得之靜態傳動誤差與嚙合剛性(Meshing Stiffness)代入齒輪系統動態方程式，並利用龍格-庫塔法(Runge-Kutta)求解動態方程式，取得動態傳動誤差(Dynamic Transmission Error, DTE)與加速度振動訊號，並透過均方根值計算(Root Mean Square, RMS)及快速傅立業轉換(Fast Fourier Transform, FFT)，探討線性齒頂修整對於動態特性之影響。根據模擬結果顯示，具線性齒頂修整之優化設計，可成功改善齒輪系統之振動幅度。

摘要(英)

The purpose of this study is to analyze the characteristics of high-speed spur gear with optimum linear tip-relief. The influence of tip-relief on dynamic characteristics was also discussed. First, the mathematical model of spur gear with lead crowning, linear tip-relief, and profile shift was developed based on the theory of gearing and differential geometry. In addition, tooth contact analysis (TCA) of spur gears was carried out to solve the static transmission error (STE). Loaded tooth contact analysis (LTCA) was carried out by using finite element analysis software and gear design software, and the influence of assembly errors was discussed. The safety factors, including pitting and bending of gear set, were calculated according to the relevant specifications of American Gear Manufacturing Association (AGMA).
Besides, in the optimization aspect, the gear design analysis software KISSsoft was linked with global search algorithm (GS) and genetic algorithm (GA) respectively to determine the optimum gear design parameters.
In the dynamic simulation aspect, a dynamic model of the gear system was established based on the results of the TCA and LTCA, including the STE and meshing stiffness then the dynamic transmission error (DTE) was calculated by using Runge-Kutta method. The influence of the tip-relief on the dynamic characteristics was discussed through the Root Mean Square (RMS) and Fast Fourier Transform (FFT) methods. According to the simulation results, the optimum tip-relief design successfully reduced RMS of DTE and the vibration level.

關鍵字(中)

★ 多目標最佳化
★ 齒面接觸分析
★ 動態特性
★ 動態傳動誤差

關鍵字(英)

論文目次

摘要 I
Abstract II
致謝 III
圖目錄 VIII
表目錄 XII
符號對照表 XIV
第1章緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 齒輪系統動態分析 2
1.2.2 嚙合剛性 5
1.2.3 齒輪修整最佳化 5
1.3 研究目的 6
1.4 論文架構 8
第2章修整型正齒輪齒面數學模式 10
2.1 前言 10
2.2 假想齒條刀法向剖面數學模式 11
2.3 三維假想齒條刀數學模式 -無導程隆齒修整 13
2.4 三維假想齒條刀數學模式 -具導程隆齒修整 15
2.5 修整型正齒輪數學模式 18
2.6 齒輪設計參數 22
第3章齒面接觸分析 24
3.1 傳動誤差分析 24
3.2 組裝誤差分析 25
3.3 無負載齒面接觸分析 27
3.4 結論 29
第4章負載下齒面接觸分析 30
4.1 有限元素分析 30
4.1.1 有限元素分析設定 30
4.1.2 有限元素分析結果 32
4.1.3 嚙合剛性 36
4.2 齒輪設計分析軟體 38
4.3 結論 42
第5章強度分析 43
5.1 安全係數 43
5.1.1 齒面安全係數 43
5.1.2 齒根安全係數 44
5.1.3 刮蝕機率 45
5.2 安全係數分析結果 46
5.3 結論 49
第6章齒形最佳化分析 50
6.1 最佳化演算法 50
6.1.1 最佳化概論 50
6.1.2 全域搜索演算法 52
6.2.3 基因演算法 54
6.2 最佳化參數 55
6.2.1 全域搜索演算法 57
6.2.2 基因演算法 59
6.2.3 全域搜索演算法與基因演算法之目標函數值比較 59
6.3 基因演算法之優化參數-負載下齒面接觸分析 60
6.4 基因演算法之優化參數-強度分析 68
6.5 結論 70
第7章齒輪系統動態分析 76
7.1 前言 76
7.2 嚙合剛性 76
7.3 齒輪系統動態模型 78
7.4 齒輪系統動態方程式 80
7.5 齒輪系統動態分析流程 82
7.6 齒輪系統動態分析結果 83
7.6.1動態傳動誤差分析結果 83
7.6.2加速度訊號之頻譜分析與嚙合頻能量計算 88
7.7 結論 91
第8章實務優化參數與動態分析 92
8.1 實務優化設計 92
8.1.1 實務優化參數 92
8.1.2 現有設計與實務優化參數-強度分析 93
8.2 動態特性分析(一) 96
8.2.1 齒輪設計分析軟體KISSsoft-嚙合剛性 96
8.2.2 動態傳動誤差分析結果 97
8.3 動態特性分析(二) 103
8.3.1 有限元素分析-嚙合剛性 103
8.3.2 動態傳動誤差分析結果 108
8.4 結論 114
第9章結論 115
9.1 結論 115
9.2 未來工作 117
參考文獻 118

參考文獻

[1] J. D. Smith, Gear noise and vibration: CRC Press, 2003.
[2] F. L. Litvin, "Theory of gearing,"NASA Reference Publication 1212,Washinton D. C.,1989.
[3] F. L. Litvin and A. Fuentes, Gear geometry and applied theory: Cambridge University Press, 2004.
[4] F. L. Litvin and J. Zhang, "Spur gears: Optimal geometry, methods for generation and Tooth Contact Analysis (TCA) program," DTIC Document,1988.
[5] F. Litvin and D. Kim, "Computerized design, generation and simulation of meshing of modified involute spur gears with localized bearing contact and reduced level of transmission errors," Journal of Mechanical Design, vol. 119, pp. 96-100, 1997.
[6] S.-L. Chang, C.-B. Tsay, and C.-H. Tseng, "Kinematic optimization of a modified helical gear train," Journal of Mechanical Design, vol. 119, pp. 307-314, 1997.
[7] Y.-C. Chen and C.-B. Tsay, "Contact ratios and transmission errors of a helical gear set with involute-teeth pinion and modified-circular-arc-teeth gear," JSME International Journal Series C Mechanical Systems, Machine Elements and Manufacturing, vol. 44, pp. 867-874, 2001.
[8] Y.-C. Chen and C.-B. Tsay, "Stress analysis of a helical gear set with localized bearing contact," Finite Elements in Analysis and Design, vol. 38, pp. 707-723, 2002.
[9] Y. Ogawa, S. Matsumura, H. Houjoh, and T. Sato, "Rotational Vibration of a Spur Gear Pair Having Tooth Helix Deviation: Effect of Lead Modifications," in ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2003, pp. 433-440.
[10] H. Houjoh, C. Ratanasumawong, and S. Matsumura, "Utilization of synchronous averaging for inspection of tooth surface undulations on gears (Localization of nonmesh harmonic components to individual gear)," Journal of applied mechanics, vol. 74, pp. 269-278, 2007.
[11] C. Ratanasumawong, S. Matsumura, and H. Houjoh, "An Alternative Method for Evaluating Gear Tooth Surface Geometry Based on Synchronous Average of Vibration of a Gear Pair," in ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2007, pp. 395-403.
[12] C. Ratanasumawong, S. Matsumura, T. Tatsuno, and H. Houjoh, "Estimating gear tooth surface geometry by means of the vibration measurement: Distinction of the vibration characteristics of gears with tooth surface form error," Journal of Mechanical Design, vol. 131, p. 101003, 2009.
[13] C. Ratanasumawong, P. Asawapichayachot, S. Phongsupasamit, H. Houjoh, and S. Matsumura, "Estimation of sliding loss in a parallel-axis gear pair," Journal of Advanced Mechanical Design, Systems, and Manufacturing, vol. 6, pp. 88-103, 2012.
[14] K. Kawasaki, I. Tsuji, H. Gunbara, and H. Houjoh, "Method for remanufacturing large-sized skew bevel gears using CNC machining center," Mechanism and Machine Theory, vol. 92, pp. 213-229, 2015.
[15] S. Mo, Z. Feng, G. Jin, T. Zhang, S. Ma, X. Shang, et al., "Research on tribological characteristics of bevel gear after shot blasting based on 85-pellets model," Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, p. 1350650118823095, 2019.
[16] A. Kahraman and R. Singh, "Non-linear dynamics of a spur gear pair," Journal of sound and vibration, vol. 142, pp. 49-75, 1990.
[17] A. Kahraman and R. Singh, "Non-linear dynamics of a geared rotor-bearing system with multiple clearances," Journal of sound and vibration, vol. 144, pp. 469-506, 1991.
[18] A. Kahraman and R. Singh, "Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system," Journal of Sound and Vibration, vol. 146, pp. 135-156, 1991.
[19] A. Kahraman, H. N. Ozguven, D. R. Houser, and J. J. Zakrajsek, "Dynamic analysis of geared rotors by finite elements," Journal of Mechanical Design, vol. 114, pp. 507-514, 1992.
[20] A. Kahraman, "Dynamic analysis of a multi-mesh helical gear train," Journal of Mechanical Design, vol. 116, pp. 706-712, 1994.
[21] A. Kahraman, "Planetary gear train dynamics," Journal of Mechanical design, vol. 116, pp. 713-720, 1994.
[22] A. Kahraman and G. W. Blankenship, "Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters," Journal of Applied Mechanics, vol. 64, pp. 217-226, 1997.
[23] A. Kahraman and G. Blankenship, "Effect of involute tip relief on dynamic response of spur gear pairs," Journal of mechanical design, vol. 121, pp. 313-315, 1999.
[24] V. K. Tamminana, A. Kahraman, and S. Vijayakar, "A study of the relationship between the dynamic factors and the dynamic transmission error of spur gear pairs," Journal of Mechanical Design, vol. 129, pp. 75-84, 2007.
[25] M. Hotait and A. Kahraman, "Experiments on the relationship between the dynamic transmission error and the dynamic stress factor of spur gear pairs," Mechanism and Machine Theory, vol. 70, pp. 116-128, 2013.
[26] B. Boguski and A. Kahraman, "An experimental study on the motion transmission error of planetary gear sets," in ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2015, pp. V010T11A044-V010T11A044.
[27] Y. Hu, D. Talbot, and A. Kahraman, "A Load Distribution Model for Planetary Gear Sets," Journal of Mechanical Design, vol. 140, p. 053302, 2018.
[28] Y. Hu, L. Ryali, D. Talbot, and A. Kahraman, "A theoretical study of the overall transmission error in planetary gear sets," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, p. 0954406219830436, 2019.
[29] 鄭凱鴻, "修整型正齒輪對動態模擬與實驗," 碩士論文, 機械工程學系, 國立中央大學, 桃園市, 2014.
[30] 王志根, "具線性齒頂修整之螺旋齒輪接觸特性研究," 碩士論文, 光機電工程研究所, 國立中央大學, 桃園市, 2016.
[31] D. Yang and J. Lin, "Hertzian damping, tooth friction and bending elasticity in gear impact dynamics," Journal of mechanisms, transmissions, and automation in design, vol. 109, pp. 189-196, 1987.
[32] H. Ma, R. Song, X. Pang, and B. Wen, "Time-varying mesh stiffness calculation of cracked spur gears," Engineering Failure Analysis, vol. 44, pp. 179-194, 2014.
[33] H. Ma, R. Song, X. Pang, and B. Wen, "Fault feature analysis of a cracked gear coupled rotor system," Mathematical Problems in Engineering, vol. 2014, 2014.
[34] A. Saxena, A. Parey, and M. Chouksey, "Effect of shaft misalignment and friction force on time varying mesh stiffness of spur gear pair," Engineering Failure Analysis, vol. 49, pp. 79-91, 2015.
[35] K. Chen, Y. Huangfu, H. Ma, Z. Xu, X. Li, and B. Wen, "Calculation of mesh stiffness of spur gears considering complex foundation types and crack propagation paths," Mechanical Systems and Signal Processing, vol. 130, pp. 273-292, 2019.
[36] Y. Pandya and A. Parey, "Simulation of crack propagation in spur gear tooth for different gear parameter and its influence on mesh stiffness," Engineering Failure Analysis, vol. 30, pp. 124-137, 2013.
[37] N. K. Raghuwanshi and A. Parey, "Effect of back-side contact on mesh stiffness of spur gear pair by finite element method," Procedia engineering, vol. 173, pp. 1538-1543, 2017.
[38] A. Brindle, "Genetic algorithms for function optimization," 1980.
[39] G. Bonori, M. Barbieri, and F. Pellicano, "Optimum profile modifications of spur gears by means of genetic algorithms," Journal of sound and vibration, vol. 313, pp. 603-616, 2008.
[40] M. Faggioni, F. S. Samani, G. Bertacchi, and F. Pellicano, "Dynamic optimization of spur gears," Mechanism and machine theory, vol. 46, pp. 544-557, 2011.
[41] V. Simon, "Multi-Objective Optimization of Hypoid Gears to Improve Operating Characteristics," in IFToMM World Congress on Mechanism and Machine Science, 2019, pp. 905-914.
[42] ANSI/AGMA 2101-D04, "Fundamental Rating Factors and Calculation Methods for Involute Spur and Helical Gear Teeth," ed, 2016.
[43] ANSI/AGMA 925-A03, "Effect of Lubrication on Gear Surface Distress," ed, 2013.
[44] H. Blok, "Measurement of temperature flashes on gear teeth under extreme presure conditins," Proc. of the general discussion on lubrication & lubricants 1937, vol. 2, p. 14, 1937.
[45] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning: Addison-Wesley Longman Publishing Co., Inc., 1989.
[46] Y. Cai, "Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon (a new stiffness function of helical involute tooth pair)," Journal of Mechanical Design, vol. 117, pp. 460-469, 1995.

指導教授

陳怡呈

審核日期

2019-11-22

推文