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 齒輪傳動具有運轉平穩、高效率與負載能力等優點而被廣泛應用。隨著大型風力發電已成為全球極具優勢綠色能源，而克服風力機組處於嚴峻負載運轉條件，提升傳動齒輪系性能對於機組運轉動態性能可靠度為其關鍵，機組組件中之軸承剛性、慣性矩與自重與系統間的非線性動態關聯，逐漸受到注意。因此本研究以3D離散模式進行行星齒輪系動態響應探討，計算內、外齒輪對以及行星齒輪軸承的動態嚙合力，並討論包括轉子自重、慣性矩與軸承剛性等設計參數與系統動態的關係。行星式螺旋齒輪箱動態分析是複雜多自由度系統，本研究將獲得承受各種變動負載下單級增速螺旋行星式齒輪箱之模態與動態分析方法與分析結果，也包括非線性嚙合剛度之影響探討。將分別應用非線性與時變的等效離散動態模式與有限元素之連體模式來分析單階齒輪箱之動態響應與振動模態特性。在離散模式方面，將先計算內/外螺旋齒輪對之非線性時變等效嚙合剛度、齒輪對相位關係、以及組裝與幾何關係，推導出單級螺旋行星齒輪系之離散運動方程式，並考慮軸承、輸出入軸與齒輪箱體剛度，從風場條件搜集、機組操作資料等獲得輸出入軸的變動負載，進行數值求解計算行星齒輪系統的動態特性，計算動態齒輪應力與動態軸承負載，並進行模態分析計算其自然頻率與模態。然後探討各種變動負載下行星式螺旋齒輪箱之暫態與穩態響應特性，結果顯示轉子自重、慣性矩與軸承剛性對於行星齒輪系動態響應有重要影響。
 Gear transmission has been widely used for fine operation performance of smooth running, high efficiency and high load to weight. With increasing quantity of large scale wind turbines become the most potential source of renewal energies. However, reliability increase in the harsh operation condition and performance enhancement of their geared transmission trains is the most critical topic. Recently, nonlinear dynamic effect due to the weight has been highly concerned. Thus in this study dynamic analyses are undertaken to a single-stage helical planetary gear system using a 3D discrete stiffness model. The bearing stiffness, weight, and inertia of wind rotor and generator are also incorporated. Accordingly, the dynamic responses of the planetary system are resulted after assigning at constant speed and input load operation. The dynamic contact forces between gear pairs and gear-bearing pairs are calculated, the dynamic contact force of planet gearing are discussed at kinds of weight, inertia, and bearing stiffness.Planetary helical speed increasing gearings used in large scaled wind turbines are complex and multi-degrees of freedom dynamic systems. This study focuses on modal characteristics of single stage planetary gear systems and their dynamic characteristics under variant wind types of extreme fluctuation excitations. The harmonic vibration due to non-linear mesh stiffness of gear pairs is also investigated. Both approaches which respectively use an equivalent discrete model and finite element model to calculate dynamic responses and modal characteristics are used. In the discrete approach, the equivalent time varying mesh stiffness and meshing phases among the external and internal gear pairs will be derived. The geometry and assembly constraints of the planetary gear sets are also established. Then, equations of dynamic analyses for single stage planetary helical gearings are derived. Additionally, stiffnesses of ball bearing and shafts are also incorporated. The excitations exerting on gearing input and output shafts are applied. After performing numerical calculations, the dynamic responses of gearings are obtained. Natural frequencies and modal shapes are also resulted using the modal analysis. The FE results are compared with the numerical results of the discrete model. Basing on the variant operation conditions, the dynamic contact forces between gear pairs and gear-bearing pairs are calculated, the dynamic contact force of planet gearing are discussed at kinds of weight, inertia, and bearing stiffness, The result shows weight, inertia, and bearing stiffness are extremely important for investigation for gear dynamic behavior.
 中文摘要 i英文摘要 ii致謝 iv目錄 v表目錄 viii圖目錄 ix符號表 xii第一章 序論 11.1 研究背景 11.2 研究動機與目的 31.3 文獻回顧 41.4 大綱 5第二章 行星齒輪幾何與分析 62.1 行星齒輪系統架構 62.2 行星齒輪系統幾何關係 72.2.1外嚙合齒對之等效剛度 72.2.2齒輪對相位差 82.2.3外齒輪對與內齒輪對嚙合相位差 112.2.4外齒輪對與內齒輪對相互間之相位差 142.2.5行星齒輪系接觸率之推導 172.2.6轉速比 192.3 螺旋角方向與齒輪旋轉方向 202.3.1太陽齒輪對-行星齒輪對 202.3.2行星齒輪對-環齒輪對 222.4 齒輪誤差 232.5 設計技術與整合分析 28第三章 行星齒輪系運動方程式推導 293.1 行星齒輪系離散模式之運動方程式 293.2 離散模式之動態分析 343.3 軸與軸承剛度 363.4 激振條件 373.5 動態響應結果 41第四章 結果與討論 434.1螺旋齒輪對剛度 434.1.1齒寬與齒輪剛度 434.1.2螺旋角與齒輪對剛度 444.1.3齒數與齒輪對剛度 454.2 自然頻率與模態分析 464.3 動態分析 514.3.1 暫態響應位移 514.4 暫態響應與慣性矩之關係 544.4.1 太陽齒輪慣性矩對於動態之影響 544.4.1.1 對於自然頻率之影響 54 4.4.1.2 對於動態響應之影響 564.4.2 行星架傳動軸慣性矩對於動態之影響 584.4.2.1 對於自然頻率之影響 584.4.2.2 對於動態響應之影響 604.4.3 改變輸入軸與輸出軸輪慣性矩對於動態之影響 624.5 軸承剛性對於動態之影響 624.5.1 對於自然頻率之影響 624.5.2 對於動態響應之影響 644.6 自重對於動態之影響 664.6.1 葉輪轉子自重對於動態之影響 664.6.2 發電機轉子自重對於動態之影響 70第五章 結論與未來展望 745.1 結論 745.2 未來展望 75參考文獻 76
 1. http://wind.itri.org.tw/Thousand/ThIndex.aspx.2. L. L. Wind Energy Conversion Systems, 1990, UK: Prentice Hall.3. T. J. Chang, Y. T. Wu, H. Y. Hsu, C. R. Chu, and C. M. Liao, 2003, “Assessment of Wind Characteristic and Wind Turbine Characteristic in Taiwan,” Renewable Energy, Vol. 28, pp. 851-871.4. U. Giger, K. Arnaudov, 2011, “Redesign of a Gearbox for 5MW Wind Turbines,” ASME IDETC/CIE 2011, Washington, DC, USA.5. P. Prueter, R. Parker, and F. Cunliffe, 2011, “A Study of Gear Root Strains in a Multi-stage Planetary Wind Turbine Gear Train Using a Three Dimensional Finite Element/Contact Mechanics Model and Experiments,” Proceedings of the ASME 2011 IDETC/CIE 2011, Washington, DC, USA.6. U. Giger, K. Arnaudov, 2011, “Redesign of a Gearbox for 5MW Wind Turbines,” ASME IDETC/CIE 2011, Washington.7. Industrial Wind Action Home page Homepage: http://www.windaction.org.8. Word Wind Energy Association (WWEA) Homepage: http://www.wwindea.org.9. General Electric Homepage: http://www.ge-energy.com.10. Maag Homepage: http://www.maag-gear.com.11. R. Errichello, J. Muller, and M. Townsend, 2011, “Gearbox Reliability Collaborative Gearbox 1 Failure Analysis Report,” NREL/SR-5000-53062.12. M. Botman, 1976, “Epicyclic gear vibrations,” ASME Journal of Engineering for Industry, pp. 811-815.13. D. L. Seager, 1975, “Conditions for the Neutralization of Excitation by the Teeth in Epicyclic Gearing,” Journal of Mechanical Engineering Science, Vol. 17, pp. 293-298.14. A. Kahraman, 2001, “Free torsional Vibration Characteristics of Compound Planetary Gear Sets,” Mechanism and Machine Theory, Vol.36, pp. 953-971.15. P. Velex and L. Flamand, 1996, “Dynamic response of planetary gear trains to mesh parametric excitations,” ASME Journal of Mechanical Design, Vol. 118, pp. 7-14.16. A. Kahraman, 1994, “Planetary Gear Train Dynamics,” ASME Journal of Mechanical Design, Vol. 116, pp. 713-720.17. R. August and R. Kasuba, 1986, “Torsional Vibrations and Dynamic Loads in a Basic Planetary Gear System,” ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 108, pp. 348-352.18. R. B. Parker, 2000, “A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration,” Journal of Sound and Vibration, Vol. 236, pp. 561-573.19. H. Ligata, A. Kahraman, and A. Singh, 2008, “An Experimental Study of the Influence of Manufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing,” ASME Journal of Mechanical Design, Vol. 130, pp. 041701.1-041701.20. A. Bajer and L. Demkowicz, 2002, “Dynamic Contact/impact Problems, Energy Conservation, Planetary Gar Trains,” Computer Methods in Applied Mechanics and Engineering, Vol. 191, pp. 4159-4191.21. T. Sun and H.Y. Hu “Nonlinear Dynamics of a Planetary Gear System with Multiple Clearances,” Mechanism and Machine Theory, Vol. 38, pp. 1371-1390.22. M. Inalpolat and A. Kahraman, 2008, “Dynamic modelling of planetary gears of automatic transmissions,” Proceedings of the Institution of Mechanical Engineering, Part K: Journal of Multi-body Dynamics, Vol. 222, pp. 229-242.23. D. R. Kiracote and R. B. Parker, 2007, “Structured Vibration Modes of General compound Planetary Gear Systems,” ASME Journal of Vibration and Acoustics, Vol. 129, pp. 1-16.24. J. Helsena et al, 2001, “Insights in wind turbine drive train dynamics gathered by validating advanced models on a newly developed 13.2 MW dynamically controlled test-rig,” Mechatronics, Vol. 21, pp. 737–752.25. J. Helsen, F. Vanhollebeke, B Marrant, and D Vandepitte, 2011, “Multibody modelling of varying complexity for modal behaviour analysis of wind turbine gearboxes,” Renewable Energy, Vol. 36, pp. 3098-3113.26. R. B. Parker and J. Lin, 2004, “Mesh Phasing Relationships in Planetary and Epicyclic Gears,” ASME Journal of Mechanical Design, Vol. 126, pp. 365-370.27. 張守仁, 2009, “應用有限元素方法探討風機用螺旋行星齒輪系之結構模態與動態特性以修整技術實現高速螺旋齒輪對最佳動態特性之研究” , 中華大學碩士論文.28. 陳頌文, 2012, “應用非線性模式之大型風力機用增速行星齒輪箱之動態響應分析” , 中華大學碩士論文.29. 王如鈺, 1995, “齒輪原理概要”30. J. L. Chen and C. H. Tseng, 2001, “Assembly Considerations for Planet Gear Sets in Planetary Gear Trains, ” Journal of the Chinese Society of Mechanical Engineers, Vol. 22, No.3, pp. 235-239.
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 1 應用有限元素方法探討風機用螺旋行星齒輪系之結構模態與動態特性 2 應用非線性模式之大型風力機用增速行星齒輪箱之動態響應分析 3 大型風力發電機用單級行星齒輪箱之動態響應分析

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 1 獲得螺旋齒輪對於各種條件下之等效剛性分析 2 以有限元素之行星齒輪系模態特性分析 3 大型風力發電機用單級行星齒輪箱之動態響應分析 4 應用非線性模式之大型風力機用增速行星齒輪箱之動態響應分析 5 行星齒輪系統動態分析 6 大型風力機用多階齒輪傳動系統之特性分析 7 應用有限元素方法探討風機用螺旋行星齒輪系之結構模態與動態特性 8 應用機器視覺於小齒輪檢測高速平台之研究 9 正齒輪對之動態分析 10 正/螺旋行星齒輪系統動態特性之研究 11 齒輪修整與誤差對於螺旋齒輪動態影響之研究 12 螺旋齒輪對之動態分析 13 齒輪泵浦分析與電腦輔助設計 14 包含洩漏與應力分析之齒輪泵浦最佳化設計與實驗 15 以修整技術實現高速螺旋齒輪對最佳動態特性之研究

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