臺灣博碩士論文加值系統

本論文研究主要針對具正輪係值之單迴路行星減速機的嚙合效率與傳動效率分析，並由唐修晨依據Stribeck Curve修正Buckingham所提出的摩擦係數經驗公式，修正並分析出內外齒輪對嚙合效率。本論文設計出減速比20之行星減速機(FPR+20)並計算其相對嚙合效率 ( )，再依據相對功理論，計算出行星減速機之嚙合效率( )，並計算軸承效率、油封效率與攪油效率，求出整體行星減速機之理論效率( )；再設計一組減速比-20之行星減速機(FPR-20)，並計算其嚙合效率( )在與(FPR+20)之嚙合效率進行比較。本研究成果如下：
1. 螺旋齒輪行星減速機(FPR+20)使用齒輪油75W90，在輸入轉速從100 rpm至3600 rpm、輸出負載從80 N-m至400N-m，理論嚙合效率為71.764％～93.401％，理論傳動效率介於66.526％～92.226％。
2. 螺旋齒輪行星減速機(FPR-20)使用齒輪油75W90，在輸入轉速從100 rpm至3600 rpm、輸出負載從80 N-m至400N-m，理論嚙合效率為57.39％～91.01％。
3. 由第五章可得知行星減速機(FPR+20)理論嚙合效率比行星減速機(FPR-20)之理論嚙合效率高出-0.2676%～14.374%。
4. 螺旋齒輪行星減速機(FPR+20)使用2號潤滑脂潤滑，在輸入轉速從100 rpm至3600 rpm、輸出負載從80 N-m至400N-m，理論嚙合效率為58.654%~88.849%之間，理論傳動效率介於51.784％～87.613％。
5. 對行星減速機(FPR+20)而言，使用2號潤滑脂的理論嚙合效率較使用75W90機油小約4.552％~13.11％，理論傳動效率則小約4.61％~14.74％。

In general, planetary gear reducers have negative gear train values, reduction ratios of single-stage planetary gear reducers Rr<10. 3K type and 2K-2H type planetary gear reducers have high reduction ratio, However, their meshing and transmission efficiencies are low. Some scholars and companies want to use N-type and NN-type involute gear drive with small teeth difference to replace the cycloid gear. However, due to involute interference and balance problems, it can’t be used in powertrain. In order to ameliorate the above problems, By referring to the NN-type involute gear drive with small teeth difference, this research proposes “single-loop planetary gear reducer with positive gear train value” to provide high reduction ratio. However, due to the reason that single-loop planetary gear reducer will not produce power circulation and the tooth surface force amplification phenomenon, it will have better theoretical meshing efficiency and transmission efficiency.
This research focuses on the transmission efficiency of planetary spur-gear reducer. In this research, the gear reducer with reduction ratio Rr=+20 (FPR+20) and the gear reducer with reduction ratio Rr=-20 (FPR-20) are synthesized. Then, the meshing efficiency equations of external and internal spur gear pairs are derived firstly. According to the “Stribeck Curve”, the empirical formula of friction coefficient proposed by Buckingham was modified and the corresponding meshing efficiencies external and internal spur gear pairs are analyzed. Based on the latent power theory, the theoretical meshing efficiencies of gear reducers (FPR+20 and FPR-20) are analyzed. Then, the efficiencies of bearings, oil seals, and oil stirring are also calculated and the corresponding theoretical transmission efficiencies are analyzed. The results are summarized as follows:
1. For the gear reducer (FPR+20) with oil 75W90, its theoretical meshing and transmission efficiencies are between 71.764％～93.401％ and 66.526％～92.226％ under input speed form 100rpm to 3600rpm and output load from 80N-m to 400N-m.
2. For the gear reducer (FPR-20) with oil 75W90, its theoretical meshing efficiencies are between 57.39％～91.01％ under input speed form 100rpm to 3600rpm and output load from 80N-m to 400N-m.
3. The theoretical meshing efficiencies of gear reducer (FPR+20) are larger than (FPR-20) by -0.2676%～14.374%.
4. For the gear reducer (FPR+20) with grease No.2, its theoretical meshing efficiencies are between 58.654%~88.849% under input speed form 100rpm to 3600rpm and output load from 80N-m to 400N-m.
5. The theoretical meshing efficiencies of gear reducer (FPR+20) with grease No.2 are less than gear reducer (FPR+20) with oil 75W90 by 4.552％~13.11％.

摘要...i
Abstract...ii
誌謝...iv
目錄...v
表目錄...viii
圖目錄...ix
符號說明...xi
第一章 前言...1
1.1 文獻回顧...1
1.1.1齒輪摩擦...1
1.1.2滑動速度...1
1.1.3齒輪潤滑...2
1.1.4相對功理論...2
1.2 研究動機與目的...2
1.3論文架構...2
第二章 相關專利...3
2.1專利分析...3
第三章 行星減速機與理論效率...7
3.1輪系方程式與減速比...7
3.2 相對功理論...7
3.3 齒輪嚙合效率...8
3.3.1 減速比正值(Rr>1)之行星減速機...8
3.3.2 減速比負值(Rr<-1)之行星減速機...9
3.4 外齒輪為主動之內齒輪對之嚙合效率...10
3.4.1 漸近區主動齒輪的輸入功(外齒輪主動)...13
3.4.2 漸遠區主動齒輪的輸入功(外齒輪主動)...14
3.4.3 漸近區從動齒輪的輸出功(外齒輪主動)...15
3.4.4 漸遠區從動齒輪的輸出功(外齒輪主動)...16
3.4.5 外齒輪為主動之內齒輪對嚙合效率...17
3.5 內齒輪為主動之內齒輪對嚙合效率...18
3.4.1 漸近區主動齒輪的輸入功(內齒輪主動)...20
3.4.2 漸遠區主動齒輪的輸入功(內齒輪主動)...21
3.4.3 漸近區從動齒輪的輸出功(內齒輪主動)...22
3.4.4 漸遠區從動齒輪的輸出功(內齒輪主動)...23
3.4.5 內齒輪為主動之內齒輪對嚙合效率...24
3.6 內齒輪嚙合效率...25
3.5.1 螺旋齒輪嚙合效率...25
3.6.2 螺旋齒輪內嚙合效率...26
3.6 摩擦係數...27
3.6.1 摩擦係數修正...27
3.7 軸承效率...29
3.8 油封效率...32
3.9 攪油效率...32
3.10 理論傳動效率...33
第四章 減速比20行星減速機之傳動效率...34
4.1減速比20行星減速機(FPR+20)...35
4.2理論嚙合效率(協同2號油脂)...37
4.2.1摩擦修正係數...38
4.2.2內齒輪為主動之內嚙合效率...38
4.2.3外齒輪為主動之內嚙合效率...42
4.2.4滾針軸承效率...45
4.2.5行星齒輪相對嚙合效率...48
4.2.6行星減速機(FPR+20)理論嚙合效率...50
4.3理論嚙合效率(使用Mobil Synthetic Gear Oil 75W-90)...52
4.3.1摩擦修正係數...52
4.3.2內齒輪為主動之內嚙合效率...52
4.3.3外齒輪為主動之內嚙合效率...56
4.3.4滾針軸承效率...59
4.3.5行星齒輪相對嚙合效率...62
4.3.6行星減速機(FPR+20)理論嚙合效率...64
4.4 不同油品嚙合效率之比較...66
4.5理論傳動損失之效率...67
4.5.1軸承效率...67
4.5.2油封效率...77
4.5.3攪油效率...80
4.6理論傳動效率...85
4.6.1 理論傳動效率(75W90)...85
4.6.2理論傳動效率(2號油脂)...88
4.6.3不同油品傳動效率比較...91
4.6.4 理論傳動效率(損失功率相加)...92
4.6.5 損失效率相乘與相加之效率比較...95
第五章 減速比-20行星減速機之嚙合效率...96
5.1 減速比-20行星減速機(FPR-20)...96
5.2 理論嚙合效率...98
5.2.1 摩擦修正係數...98
5.2.2 內齒輪為主動之內嚙合效率...99
5.2.3 外齒輪為主動之內嚙合效率...102
5.2.4 滾針軸承效率...105
5.2.5 行星齒輪相對嚙合效率...108
5.2.6 星減速機(FPR-20)理論嚙合效率...110
5.3 (FPR+20)與(FPR-20)效率之比較...112
第六章 結論與未來展望...114
參考文獻...116
Extended Abstract...118

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