修整型正齒輪對動態模擬與實驗

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：39

、訪客IP：13.58.158.56

姓名

鄭凱鴻(Kai Hong Jheng) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

修整型正齒輪對動態模擬與實驗
(Dynamic Simulation and Experiment of Modified Spur Gear Pairs)

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
★ 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
★ 高轉速正齒輪之多目標最佳化與動態特性分析	★ 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)

本論文主要目的為探討正齒輪之齒頂修整與齒形誤差對動態特性之影響。首先利用有限元素軟體進行負載下接觸分析，計算其接觸應力與齒輪對之嚙合剛性。接著以等效阻尼(equivalent damping)、嚙合剛性與傳動誤差建立齒輪系統動態模型，並利用龍格庫塔法(Runge-Kutta methods)計算齒輪系統之動態傳動誤差(Dynamic Transmission Error, DTE)與加速度變化，比對不同齒頂修整參數與齒形誤差對於齒輪系統動態特性之影響。
實驗的部分則是於泛用型齒輪嚙合測試機上架設加速規，先量測機台之共振頻率，在避開共振頻率下擷取振動訊號，並運用經驗模態分解法EMD(Empirical Mode Decomposition, EMD)及快速傅立葉轉換FFT(Fast Fourier Transform, FFT)探討嚙合頻能量變化與齒形誤差之關係，並運用所建立之齒輪系統動態模擬流程互相比對，結果顯示模擬之振動訊號與實驗所得振動訊號，在嚙合頻能量變化與齒形誤差趨勢相符。

摘要(英)

The main purpose of this thesis is to analyze the dynamic characteristics of spur gear pairs with profile tip relieves or tooth profile errors. The meshing stiffness and contact stress were calculated by loaded tooth contact analysis. A dynamic model of a modified spur gear pair was developed based on the calaulated meshing stiffness, equivalent damping and transmission error. According to the derived equations of motion, the dynamic transmission errors and acceleration were solved by using the Runge-Kutta methods. The effects of various tip relieves and tooth profile errors on the gear dynamic characteristics were investigated and discussed.
In the experimental aspect, the acceleration signals were measured on an universal gear rolling tester. Then the energy levels of meshing frequencies were evaluated by using Empirical Mode Decomposition (EMD) and Fast Fourier Transform (FFT). The results from experiments and dynamic simulation were compared and discussed. Both simulation and experimental results show that the energy levels at meshing frequencies were positively correlated with the magnitudes of tooth profile errors.

關鍵字(中)

★ 嚙合剛性
★ 動態傳動誤差
★ 齒面接觸分析

關鍵字(英)

★ Meshing stiffness
★ Dynamic Transmission Error
★ Tooth contact analysis

論文目次

摘要 I
ABSTRACT II
目錄 IV
圖目錄 VII
表目錄 XIII
符號對照表 XIV
第1章緒論 1
1.1研究背景 1
1.2文獻回顧 3
1.2.1齒輪系統動態模擬 3
1.2.2齒輪動態測試 5
1.2.3經驗模態分解法 7
1.3研究目的與方法 8
1.4論文架構 9
第2章齒面數學模式 11
2.1前言 11
2.2修整型正小齒輪之假想齒條刀數學模式 11
2.3修整型正齒輪之小齒輪數學模式 18
2.4修整型大齒輪之假想齒條刀之數學模式 22
2.5修整型正齒輪之大齒輪數學模式 26
2.6 大小齒輪齒面數學模式 29
2.6.1小齒輪齒面數學模式(齒頂修整與導程修整正齒輪) 29
2.6.2大齒輪齒面數學模式(齒頂修整正齒輪) 31
2.7 正齒輪齒頂修整特徵與導程修整特徵 33
2.7.1 正齒輪之齒頂修整齒形特徵 33
2.7.2 正齒輪之導程修整齒形特徵 35
第3章負載下齒面接觸分析 37
3.1 前言 37
3.2 齒面接觸分析 39
3.2.1 傳動誤差分析 42
3.3接觸敏感區域 45
3.4接觸表面特性定義 47
3.5邊界條件設定與材料性質 48
3.6多齒對負載下接觸分析結果 49
3.7 齒根彎矩應力分析結果 64
3.8嚙合剛性計算 65
3.8.1 嚙合剛性計算原理 65
3.8.2 接觸點齒面法向變形量 67
3.8.3 嚙合剛性計算結果 68
3.9結論 70
第4章齒輪系統動態分析 71
4.1 前言 71
4.2齒輪系統動態模型 72
4.3齒輪系統動態方程式 74
4.4齒輪系統動態分析結果 76
4.4.1動態傳動誤差RMS值比較 77
4.4.2加速度訊號頻譜圖 82
4.5綜合討論 85
4.6結論 86
第5章動態測試實驗與分析 87
5.1前言 87
5.1訊號分析理論 87
5.1.1 經驗模態分解法 87
5.1.2 集成經驗模態分解法(Ensemble EMD, EEMD) 88
5.1.3集成經驗模態分解法後處理過程(Post-Processing of EEMD) 89
5.2實驗設置與流程 91
5.2.1泛用型齒輪嚙合測試機 91
5.2.2實驗設置 94
5.2.3實驗齒輪參數 96
5.3實驗流程 97
5.3.1實驗校正 98
5.4單齒腹測試結果 99
5.4.1 齒形誤差與偏擺分析結果 100
5.4.2傳動誤差數據FFT頻譜分析結果 102
5.5動態測試實驗與模擬 105
5.5.1機台自然頻率測試 105
5.5.2實驗參數之動態模擬 106
5.5.3 動態測試實驗與分析 113
5.6 實驗結果比較 137
5.7結論 142
第6章結論與未來展望 143
6.1 結論 143
6.2未來工作 145
參考文獻 146
附錄 151
附錄A CASE 1至CASE 5大齒輪齒面接觸分析結果圖 151
附錄B CASE 1至CASE 5齒根彎矩應力結果 157
附錄C 162
C-1標準齒輪檢測報表 162
C-2實驗1待測齒輪(無齒形修整)檢測報表 164
C-3實驗2待測齒輪(Rp450mm)檢測報表 169
C-4實驗3待測齒輪(Rp350mm)檢測報表 174
附錄D 179
D-1 Case 1至Case 5嚙合剛性計算結果(KISSsoft) 179
D-2實驗1至實驗3嚙合剛性計算結果(KISSsoft) 180

參考文獻

[1] F. L. Litvin and J. Zhang, ”Topology of modified helical gears and tooth contact analysis (TCA) program,” DTIC Document,1989.
[2] F. L. Litvin, I. Gonzalez-Perez, A. Fuentes, K. Hayasaka, and K. Yukishima, ”Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis,” Mathematical and Computer Modelling, vol. 42, pp. 1063-1078, 2005
[3] 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, vol. 44, pp. 867-874, 2001.
[4] V.-T. Tran, R.-H. Hsu, and C.-B. Tsay, ”Tooth contact analysis of double-crowned involute helical pairs shaved by a crowning mechanism with parallel shaving cutters,” Mechanism and Machine Theory, vol. 79, pp. 198-216, 9// 2014.
[5] 郭仁傑, ”「齒頂修整之正齒輪齒面受負載分析」,” 國立中央大學，碩士論文, 民國102年。
[6] Z. Chen and Y. Shao, ”Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack,” Mechanism and Machine Theory, vol. 62, pp. 63-74, 2013.
[7] N. L. Pedersen and M. F. Jørgensen, ”On gear tooth stiffness evaluation,” Computers & Structures, vol. 135, pp. 109-117, 2014.
[8] J. Wang and I. Howard, ”The torsional stiffness of involute spur gears,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 218, pp. 131-142, 2004.
[9] J. Wang and I. Howard, ”Finite element analysis of high contact ratio spur gears in mesh,” ASME, Journal of tribology, vol. 127, pp. 469-483, 2005.
[10] A. Kahraman and R. Singh, ”Non-linear dynamics of a spur gear pair,” Journal of sound and vibration, vol. 142, pp. 49-75, 1990.
[11] 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.
[12] 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.
[13] A. Kahraman, ”Effect of axial vibrations on the dynamics of a helical gear pair,” ASME,Journal of Vibration and Acoustics, vol. 115, pp. 33-39, 1993.
[14] A. Kahraman, ”Planetary gear train dynamics,” ASME,Journal of Mechanical Design, vol. 116, pp. 713-720, 1994.
[15] A. Kahraman and G. Blankenship, ”Effect of involute tip relief on dynamic response of spur gear pairs,” ASME,Journal of mechanical design, vol. 121, pp. 313-315, 1999.
[16] A. Kahraman, H. N. Ozguven, D. R. Houser, and J. J. Zakrajsek, ”Dynamic analysis of geared rotors by finite elements,” ASME, Journal of Mechanical Design, vol. 114, pp. 507-514, 1992.
[17] R. Parker, S. Vijayakar, and T. Imajo, ”Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons,” Journal of Sound and vibration, vol. 237, pp. 435-455, 2000.
[18] 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,” ASME,Journal of Mechanical Design, vol. 129, pp. 75-84, 2007.
[19] 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),” ASME,Journal of Mechanical Design, vol. 117, pp. 460-469, 1995.
[20] H. Ma, J. Yang, R. Song, S. Zhang, and B. Wen, ”Effects of tip relief on vibration responses of a geared rotor system,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, p. 0954406213500615, 2013.
[21] 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.
[22] K. Jao Huang and H. Wei Su, ”Approaches to parametric element constructions and dynamic analyses of spur/helical gears including modifications and undercutting,” Finite Elements in Analysis and Design, vol. 46, pp. 1106-1113, 2010.
[23] K. J. Huang, M. R. Wu, and J. T. Tseng, ”Dynamic analyses of gear pairs incorporating the effect of time-varying lubrication damping,” Journal of Vibration and Control, 2010.
[24] R. E. Smith, ”What single flank measurement can do for you,” AGMA Technical Paper,No.84FTM2, 1984.
[25] R. E. Smith, ”Identification of gear noise with single flank composite,” AGMA Technical Paper ,No.85FTM13, 1985.
[26] R. E. Smith, ”The relationship of measure gear noise to measured gear transmission errors,” AGMA Technical Paper, No.87FTM6, 1985.
[27] R. E. Smith, ”Noise reduction in plastic and power metal gear set through control of ”mean involute slope”,” AGMA Technical Paper, No.92FTM12, 1992.
[28] 張永源, ”修整型螺旋齒輪傳動誤差之測試與分析,” 國立交通大學，碩士論文。, 民國86年。
[29] 陳義仁, ”受負載之正齒輪對運動誤差之探討,” 國立交通大學，碩士論文。, 民國94年。
[30] A. Kahraman and G. 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.
[31] M. A. 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.
[32] K. Umezawa, T. Suzuki, H. Houjoh, and T. Sato, ” Vibration of power transmission helical gear -the effect of contact ratio on the vibration,” Bulletin of the JSME, vol. 28, pp. 694-700, 1985.
[33] S. Matsumura, K. Umezawa, and H. Houjoh, ”Rotational vibration of a helical gear pair having tooth surface deviation during transmission of light load (4th report, effect of tooth profile deviation),” Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C, vol. 62, pp. 4324-4331, 1996.
[34] Y. Ogawa, S. Masumura, H. Houjoh, T. Sato, and K. Umezawa, ”Rotational vibration of a spur gear pair considering tooth helix deviation (Development of simulator and verification),” JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing, vol. 43, pp. 423-431, 2000.
[35] 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 2003 ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Chicago, IL; United States, pp. 433-440, 2003.
[36] C. Ratanasumawong, S. Matsumura, and H. Houjoh, ”Inspection of tooth surface geometry by means of vibration measurement (Assessment of tooth surface undulation from synchronous averaged signal and application of frequency response function),” JSME International Journal, Series C: Mechanical Systems, Machine Elements and Manufacturing, vol. 48, pp. 704-714, 2006.
[37] 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),” ASME,Journal of Applied Mechanics, vol. 74, p. 269, 2007.
[38] 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 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, NV; United States, pp. 395-403, 2008.
[39] 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,” ASME, Journal of Mechanical Design, vol. 131, p. 101003, 2009.
[40] E. N. Mohamad, M. Komori, S. Matsumura, C. Ratanasumawong, M. Yamashita, T. Nomura, et al., ”Effect of variations in tooth flank form among teeth on gear vibration and an sensory evaluation method using potential gear noise,” JSME Journal of Advanced Mechanical Design, Systems, and Manufacturing, vol. 4, pp. 1166-1181, 2010.
[41] S. Matsumura, T. Nagumo, and H. Houjoh, ”Estimation method of mesh excitation waveform of a gear system (hybrid estimation with vibration measurement and simulation),” in ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Washington, DC; United States, pp. 433-436, 2011.
[42] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, et al., ”The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 454, pp. 903-995, 1998.
[43] Q. Gao, C. Duan, H. Fan, and Q. Meng, ”Rotating machine fault diagnosis using empirical mode decomposition,” Mechanical Systems and Signal Processing, vol. 22, pp. 1072-1081, 2008.
[44] D. Yu, J. Cheng, and Y. Yang, ”Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings,” Mechanical Systems and Signal Processing, vol. 19, pp. 259-270, 2005.
[45] Z. Wu. and N. E. Huang, “Ensemble empirical mode decomposition: a noise assisted data analysis method,” Advances in Adaptive Data Analysis, Vol. 1, No. 1, pp. 1-41, 2009.
[46] Y. Lei, Z. He, and Y. Zi, ”Application of the EEMD method to rotor fault diagnosis of rotating machinery,” Mechanical Systems and Signal Processing, vol. 23, pp. 1327-1338, 2009.
[47] L. Guan, Y. Shao, F. Gu,B. Fazenda and A. Ball, “Gearbox fault diagnosis under different operating conditions based ontime synchronous average and ensemble empirical mode decomposition,” ICROS-SICE International Joint Conference, 2009.
[48] W.-C. Tsao, Y.-F. Li, D. D. Le, and M.-C. Pan, ”An insight concept to select appropriate IMFs for envelope analysis of bearing fault diagnosis,” Measurement, vol. 45, pp. 1489-1498, 2012.
[49] M.-C. Pan and W.-C. Tsao, ”Using appropriate IMFs for envelope analysis in multiple fault diagnosis of ball bearings,” International Journal of Mechanical Sciences, vol. 69, pp. 114-124, 2013.
[50] 張銘弘, ”應用經驗模態分解法於正齒輪對之傳動誤差,” 國立中央大學，碩士論文。, 民國102年。
[51] Wu, Z. and Huang, N. E., “Ensemble Empirical Mode Decomposition: A Noise Assisted Data Analysis Method,” Advances in Adaptive Data Analysis, Vol. 1, No. 1, pp. 1-41, 2009.
[52] F. L. Litvin and A. Fuentes, Gear geometry and applied theory: Cambridge University Press, 2004.

指導教授

陳怡呈

審核日期

2014-12-3

推文