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研究生:吳基碩
研究生(外文):Ji-Shuo Wu
論文名稱:考慮剛性與慣性矩之行星齒輪系動態影響分析
論文名稱(外文):Dynamic Response Analyses of Planetary Gear System Including Stiffness and Inertia Effect
指導教授:黃國饒
指導教授(外文):Kuo-Jao Huang
學位類別:碩士
校院名稱:中華大學
系所名稱:機械工程學系碩士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:78
中文關鍵詞:行星齒輪系統動態風力機自重軸承剛度
外文關鍵詞:Planetary gear systemDynamicsWind turbineInertiaBearing stiffness
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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 1
1.1 研究背景 1
1.2 研究動機與目的 3
1.3 文獻回顧 4
1.4 大綱 5

第二章 行星齒輪幾何與分析 6
2.1 行星齒輪系統架構 6
2.2 行星齒輪系統幾何關係 7
2.2.1外嚙合齒對之等效剛度 7
2.2.2齒輪對相位差 8
2.2.3外齒輪對與內齒輪對嚙合相位差 11
2.2.4外齒輪對與內齒輪對相互間之相位差 14
2.2.5行星齒輪系接觸率之推導 17
2.2.6轉速比 19

2.3 螺旋角方向與齒輪旋轉方向 20
2.3.1太陽齒輪對-行星齒輪對 20
2.3.2行星齒輪對-環齒輪對 22

2.4 齒輪誤差 23
2.5 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 29
3.1 行星齒輪系離散模式之運動方程式 29
3.2 離散模式之動態分析 34
3.3 軸與軸承剛度 36
3.4 激振條件 37
3.5 動態響應結果 41

第四章 結果與討論 43
4.1螺旋齒輪對剛度 43
4.1.1齒寬與齒輪剛度 43
4.1.2螺旋角與齒輪對剛度 44
4.1.3齒數與齒輪對剛度 45

4.2 自然頻率與模態分析 46

4.3 動態分析 51
4.3.1 暫態響應位移 51
4.4 暫態響應與慣性矩之關係 54
4.4.1 太陽齒輪慣性矩對於動態之影響 54
4.4.1.1 對於自然頻率之影響 54
4.4.1.2 對於動態響應之影響 56
4.4.2 行星架傳動軸慣性矩對於動態之影響 58
4.4.2.1 對於自然頻率之影響 58
4.4.2.2 對於動態響應之影響 60
4.4.3 改變輸入軸與輸出軸輪慣性矩對於動態之影響 62
4.5 軸承剛性對於動態之影響 62
4.5.1 對於自然頻率之影響 62
4.5.2 對於動態響應之影響 64
4.6 自重對於動態之影響 66
4.6.1 葉輪轉子自重對於動態之影響 66
4.6.2 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 74
5.1 結論 74
5.2 未來展望 75

參考文獻 76

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