具線性齒頂修整之螺旋齒輪接觸特性研究

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：10

、訪客IP：18.191.195.110

姓名

王志根(Zhi-Gen Wang) 查詢紙本館藏

畢業系所

光機電工程研究所

論文名稱

具線性齒頂修整之螺旋齒輪接觸特性研究
(Tooth Contact Analysis of A Helical Gear Set with Linear Tip Relief)

相關論文

★ 光學遮斷式晶圓定位系統與半導體製程設備之整合	★ 應用於太陽能聚光器之等光路型與金字塔型二次光學元件的分析與比較
★ 口徑550 mm反射鏡減重與撓性支撐結構最佳化設計	★ 光機整合分析應用於620mm反射鏡變形分析與八吋反射鏡彈性膠緊固設計
★ 應用投射疊紋技術於齒輪精度量測	★ 反射鏡減重與撓性支撐結構最佳化
★ 曲面反射鏡減重與背向支撐撓性機構最佳化	★ 建構拉焊機感測系統之人機介面與機器學習
★ 考量成像品質之最佳化塑膠透鏡結構設計	★ 離軸矩形反射鏡輕量化與撓性支撐結構最佳化
★ 電路板拉焊製程參數優化與烙鐵頭剩餘使用壽命預測之研究	★ ZK型雙包絡蝸桿蝸輪組接觸分析
★ 整合深度學習與立體視覺之六軸機械手臂夾取系統開發	★ 整合光源控制與深度學習辨識之平放膠體散料夾取系統開發
★ 整合視覺及力量控制之六軸機械手臂系統開發	★ 平板式太陽能菲涅爾集光透鏡與二次光學元件之設計與分析

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)

本論文旨在進行一單階螺旋齒輪減速機之特性分析。利用齒輪原理，建立具有線性齒頂修整(Linear Tip Relief)、導程修整(Lead Crowning)與轉位(Profile Shift)之螺旋齒輪齒面數學模式，進行該齒輪對之齒面接觸分析，包含傳動誤差(Transmission Error，TE)與接觸齒印(Contact Pattern)等，並探討組裝誤差對系統的影響。再利用有限元素分析軟體搭配自行撰寫的自動化網格分割程式，進行五齒對之負載下齒面接觸分析，將所得結果與機械設計分析軟體進行比對，驗證分析結果的正確性。根據齒頂修整相關規範及機械設計分析軟體建議值，提出針對齒頂修整參數之優化設計。
動態模擬部分，建立齒輪系統動態模型，將齒面接觸分析與機械設計分析軟體所得之靜態傳動誤差與嚙合剛性(Meshing Stiffness)代入，利用龍格-庫塔法(Runge-Kutta Methods)求解動態方程式，取得動態傳動誤差(Dynamic Transmission Error，DTE)與模擬振動訊號，分別透過均方根值計算(Root Mean Square，RMS)及快速傅立葉轉換(Fast Fourier Transform，FFT)探討優化前後之平均振動量與嚙合頻能量變化，模擬結果顯示，優化設計可成功降低齒輪系統的振動量。

摘要(英)

The purpose of this study is to analyze the meshing characteristics of a single-stage helical gear speed reducer. The mathematical model of a helical gear pair with linear tip relief, lead crowning and profile shift was developed based on the theory of gearing and differential geometry. The transmission errors and contact patterns were calculated by tooth contact analysis. The effects of assembly errors on the contact stress and contact patterns were also investigated and discussed. An auto-mesh-generation computer program was developed based on the mathematical model. Finite element analysis and a commercial machine design package were used in the loaded tooth contact analysis. Based on the standards of tip relief and suggestions of commercial machine design package, an improved design was attained.
In the dynamic simulation aspect, the dynamic model of a modified helical gear pair was developed. Based on the results of loaded tooth contact analysis, including the static transmission errors and meshing stiffness, the dynamic transmission errors (DTE) and vibration signals were solved by using Runge-Kutta method. Furthermore, the energy level of meshing frequencies and average energy of DTEs were evaluated by Fast Fourier Transform (FFT) and Root Mean Square (RMS) method. The results from original design and improved design were compared and discussed. The simulation results show that the improved design can reduce the amount of vibration.

關鍵字(中)

★ 組裝誤差分析
★ 齒面接觸分析
★ 嚙合剛性
★ 動態傳動誤差

關鍵字(英)

★ Assembly error analysis
★ Tooth contact analysis
★ Meshing stiffness
★ Dynamic transmission error

論文目次

摘要 I
Abstract II
致謝 III
目錄 IV
圖目錄 VII
表目錄 X
符號對照表 XI
第1章緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.2.1 齒輪系統動態模擬與實驗 2
1.2.2 嚙合剛性計算方法 8
1.2.3 齒頂修整相關規範 10
1.3 研究目的 11
1.4 論文架構 12
第2章螺旋齒輪齒面數學模式 13
2.1 前言 13
2.2 創成修整型小齒輪之假想齒條刀數學模式 13
2.3 修整型螺旋齒輪之小齒輪數學模式 19
2.4 創成修整型大齒輪之假想齒條刀數學模式 22
2.5 修整型螺旋齒輪之大齒輪數學模式 27
2.6 大小齒輪齒面數學模式 30
2.6.1 小齒輪齒面數學模式 - 具轉位、線性齒頂修整及導程修整 30
2.6.2 大齒輪齒面數學模式 - 具轉位及線性齒頂修整 32
2.7 齒輪設計參數與修整方式 34
第3章齒面接觸分析 36
3.1 前言 36
3.2 傳動誤差分析 36
3.3 組裝誤差分析 37
3.4 接觸齒印 41
3.5 邊緣接觸 44
3.6 齒面接觸分析結果 46
3.7 結論 52
第4章負載下齒面接觸分析 53
4.1 前言 53
4.2 有限元素分析 54
4.2.1 自動化網格分割程式 54
4.2.2 有限元素分析設定 56
4.2.3 有限元素分析結果 57
4.2.4 有限元素法之接觸齒印 58
4.2.5 嚙合剛性計算原理 59
4.3 機械設計分析軟體 62
4.3.1 齒面接觸應力 62
4.3.2 組裝誤差之探討 63
4.3.3 嚙合剛性 69
4.4 齒輪對優化設計分析 70
4.4.1 前言 70
4.4.2 齒頂修整量與修整長度 70
4.4.3 齒頂修整方式 70
4.5 結論 72
第5章齒輪系統動態分析 75
5.1 前言 75
5.2 齒輪系統動態模型 76
5.3 齒輪系統動態方程式 79
5.4 齒輪系統動態分析流程 81
5.5 齒輪系統動態分析結果 82
5.5.1 動態傳動誤差之均方根值比較 82
5.5.2 加速度訊號之頻譜分析與嚙合頻能量計算 83
5.6 結論 86
第6章結論 87
6.1 前言 87
6.2 結論 87
6.3 未來工作 89
參考文獻 90

參考文獻

[1] J.D. Smith, “Gear Noise and Vibration (Second Edition),” New York: Marcel Dekker, 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, Second Edition,” Cambridge University Press, New York, 2004.
[4] F. L. Litvin and J. Zhang, “Topology of modified helical gears and tooth contact analysis (TCA) program,” DTIC Document, 1989.
[5] 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.
[6] C. B. Tsay, “Helical Gears with Involute Shaped Teeth: Geometry, Computer Simulation, Tooth Contact Analysis, and Stress Analysis,” Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 110, pp. 482-491, 1988.
[7] S. L. Chang, C. B. Tsay and C. H. Tseng, “Kinematic Optimization of A Modified Helical Gear Train,” Journal of Mechanical Design, Transactions of the ASME, Vol. 119, pp. 307-314, 1997.
[8] 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.
[9] 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.
[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] 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.
[13] 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.
[14] 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.
[15] 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
[16] 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.
[17] 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.
[18] 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.
[19] 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.
[20] 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.
[21] 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.
[22] 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.
[23] 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.
[24] 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,” ASME,Journal of Advanced Mechanical Design, Systems, and Manufacturing, vol. 4, pp. 1166-1181, 2010.
[25] 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.
[26] D. C. H. Yang and J. Y. Lin, “Hertzian Damping, Tooth Friction and Bending Elasticity in Gear Impact Dynamics,” J. Mech., Trans., and Automation, vol. 109, pp. 189-196, 1987.
[27] P. Sainsot and P. Velex, “Contribution of Gear Body to Tooth Deflections - A New Bidimensional Analytical Formula,” ASME, Journal of Mechanical Design, vol. 126, pp. 748-752, 2004.
[28] X. Zhou, Y. Shao, Y. Lei and M. Zuo, “Time-Varying Meshing Stiffness Calculation and Vibration Analysis for a 16DOF Dynamic Model With Linear Crack Growth in a Pinion,” ASME, Journal of Vibration and Acoustics, vol. 134, 2012.
[29] Z. Chen and Y. Shao, “Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth,” Engineering Failure Analysis, vol. 18, pp. 2149-2164, 2011.
[30] 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.
[31] F. Chaari, W. Baccar, M. S. Abbes and M. Haddar, “Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission,” European Journal of Mechanics A/Solids, vol. 27, pp. 691-705, 2008.
[32] F. Chaari, T. Fakhfakh and M. Haddar, “Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness,” European Journal of Mechanics A/Solids, vol. 28, pp. 461-468, 2009.
[33] H. Ma, R. Song, Xu. Pang and B. Wen, “Time-varying mesh stiffness calaulation of cracked spur gears,” Engineering Failure Analysis, vol. 44, pp. 179-194, 2014.
[34] H. Ma, R. Song, X. Pang and B. Wen, “Fault Feature Analysis of a Cracked Gear Coupled Rotor System,” Hindawi Publishing Corporation Mathematical Problems in Engineering, Volume 2014.
[35] X. Liang and M. J. Zuo, “Analytically evaluating the influence of crack on the mesh stiffness of a planetary gear set,” Mechanism and Machine Theory, vol. 76, pp. 20-38, 2014.
[36] I. Howard, S. Jia and J. Wang, “The dynamic modeling of a spur gear in mesh including friction and a crack,” Mechanical Systems and Signal Processing, vol. 15, pp. 831-853, 2001.
[37] J. Wang and I. Howard, “The torsional stiffness of involute spur gears,” Proc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, vol. 218, pp. 131-142, 2004.
[38] 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.
[39] Chun Hung Lee, “Non-Linear Contact Analysis of Meshing Gears,” M.S. thesis, San Luis Obispo: The Faculty of California Polytechnic State University, 2009.
[40] BS 436-2:1970, “Specification for spur and helical gears. Part2. Basic rack form, modules and accuracy,” British Standards Institution, London.
[41] ISO 6336:2006, Parts 1-3, Organization for International Standardizations, Belgium.
[42] Hans Sigg, “Profile and longitudinal corrections on involute gears,” AGMA 109.16, 1965.

指導教授

陳怡呈(Yi-Cheng Chen)

審核日期

2016-7-28

推文