上海交通大学：《Design and manufacturing（ME371、ME337）》课程教学资源（讲义）Lecture 12-II gear train

图 上酒短大峰 色a人口 LECTURE 12-I ME371/ME337 DESIGN AND MANUFACTURING Gear train Covered Cha9 in Design of Machinery SHAN 手柄 齿轮1 磁铁 齿轮2 齿轮4 线轮 ·LEDT 齿轮3 1

1 Gear train LECTURE 12-II ME371/ME337 DESIGN AND MANUFACTURING Covered Cha9 in Design of Machinery

图 上海久通大学 outline ▣Types of Gear trains Velocity ratio for fix-axis gear train Velocity ratio for epicyclic gear train 圆上泽支大学 Types of Gear trains Gear trains Gear shaft supporter Fixed Epicyclic Complex 定轴轮系 周转轮系 复合轮系 Non-reverted Simple gear Compound train gear train Reverted 2

2 outline  Types of Gear trains  Velocity ratio for fix-axis gear train  Velocity ratio for epicyclic gear train Types of Gear trains Gear trains Fixed 定轴轮系 Compound gear train Simple gear train Epicyclic 周转轮系 Complex 复合轮系 Gear shaft supporter Non-reverted Reverted

图 上游久通大学 in 圆上泽支大学 Simple Gear Trains N2 Maximum gear ratio of 1:10 based on size constraints; A N3 Useful for changing direction; Gear ratios cancel each other out; NA Also Could change direction with belt. 5 @out Nz N.NaN5m A N3 N4 Ns N6 N2Om 2N6 6 食N6 3

3 Simple Gear Trains  Maximum gear ratio of 1:10 based on size constraints;  Useful for changing direction;  Gear ratios cancel each other out;  Also Could change direction with belt. in out in ω N N ω N N N N N N N N ω 6 2 6 5 5 4 4 3 3 2  

国 上酒短大峰 Compound Gear Trains More than 1 gear on a shaft Allows for larger gear train ratios o ,Yiim"ge 的.Vi☑%， 10 明 的 5 4 ⊕ 圆上泽支大学 Compound Train Design @u 2 ) If N2=N,and N3=Ns 3 4 → → 0n= Reduction ratio 5 ou Will be used to determine the no.of stages given a reduction ratio 2 stages 4

4 Compound Gear Trains  More than 1 gear on a shaft  Allows for larger gear train ratios 2 4 3 5             out in N N ω ω N N Compound Train Design ωin ωout 2 3 4 5 2 4 3 5 in out N N ω ω N N           If N2=N4 and N3=N5 2 2 3 in out N ω ω N        2 3 2 in out ω N ω N        Reduction ratio 2 stages  Will be used to determine the no. of stages given a reduction ratio

国 上海久通大学 Compound Train Design:example Design train with gear ratio of 180:1 Two stages have ratio 180=13.4164 (too large) Three stages has ratio180=5.646 180=5.646 N, At 14 teeth actual ratio is =179.6789 Pinion Teeth *ratio Gear teeth 12 5.646 67.7546 13 5.646 73.4008 14 5.646 79.0470 15 5.646 84.6932 16 5.646 90.3395 图上涤夫廷大学 Example-1 Desired ratio:180=22x32x5 Want to keep each ratio about the same (i.e.6x6x5) wwww viziiMsiN 14t84 >14x6=84 >14x5=70 XZZZZ4ZZZZ ▣Total ratio: a (70/84)2 =180 14八14 ▣Ve could have used: 180=2x90=2x2x45=2x2x5x9=4x5x9 or4.5x6x(20/3)etc. 5

5  Design train with gear ratio of 180:1  Two stages have ratio （too large）  Three stages has ratio  At 14 teeth actual ratio is 180 13.4164 180 5.646 3  Pinion Teeth * ratio Gear teeth 12 5.646 67.7546 13 5.646 73.4008 14 5.646 79.0470 15 5.646 84.6932 16 5.646 90.3395 179.6789 14 79 3        3 3 2 180 5.646 N N         Compound Train Design：example  Desired ratio: 180=22x32x5  Want to keep each ratio about the same (i.e. 6x6x5)  14x6=84  14x5=70  Total ratio: 180 14 84 14 70 2               We could have used: 180=2x90=2x2x45=2x2x5x9=4x5x9 or 4.5x6x(20/3) etc. Example-1

图 上酒短大峰 Reverted Compound Train I Input and output shafts are aligned ▣Gear ratio is: ou=N2 N @in N3 Ns For reverted gear trains: D2+D=Da+Ds N2+Ng=N4+N5 2☑ 图上涤夫廷大学 Example-2 Design a reverted compound gear train for a gear ratio of 18:1 口Solution: 18=3x6→N3=6N2,N5=3N4 N2+N3=N4+Ns=constant N2+6N2=N4+3N4=C 7N2=4N4=C >Take C=28,then N2=4,N3=7 >This is too small for a gear! Choose C=28x4=112(say) ·N2=16,N3=96, ·N4=28.N3=84 6

6 Reverted Compound Train  Input and output shafts are aligned  Gear ratio is:  For reverted gear trains: D2+D3=D4+D5 N2+N3=N4+N5 5 4 3 2 N N N N ω ω in out  3 5 2 4 18 N N N N            Design a reverted compound gear train for a gear ratio of 18:1  Solution: 18=3x6 N3=6N2, N5=3N4 N2+N3=N4+N5=constant N2+6N2=N4+3N4=C 7N2=4N4=C  Take C=28, then N2=4, N4=7  This is too small for a gear!  Choose C=28x4=112 (say) • N2=16, N3=96, • N4=28, N5=84 3 2 6 N N        5 4 3 N N        Example-2

图 上海久通大学 Planetary or Epicyclic Gears planetary train(行星轮系) differential train(差动轮系) DOF? b) 国 上酒充通大学 Planetary or Epicyclic Gears ◇ Conventional gearset has one DOF If you remove the ground at gear 3,it has two DOF Output 0am=0 Input #1 Input #1 3 2 ou! out Am.1⑤ Output Planet gear Input #2 Pinion Gear Sun gear (o)Conventional gearset (b)Planetary or epicyclic gearset 7

7 planetary train(行星轮系) differential train(差动轮系) Planetary or Epicyclic Gears DOF? Planetary or Epicyclic Gears  Conventional gearset has one DOF  If you remove the ground at gear 3, it has two DOF

国 上酒短大峰 Planetary or Epicyclic Gears 0 ring Ring gear Output 80t Ring gear 4 Sun gear Arm 2 Am ® 02 Input Input 2 图上涤夫廷大学 Complex Gear Trains 57 3 Fixd Epicyclic 8

8 Planetary or Epicyclic Gears Complex Gear Trains Fixd Epicyclic ?

图 上海久通大学 Outline ▣Types of Gear trains Velocity ratio for fix-axis gear train Velocity ratio for epicyclic gear train Gear trains Gear shaft supporter Fixed Epicyclic Complex 定轴轮系 周转轮系 复合轮系 Non-reverted Simple gear Compound train gear train Reverted 圆上泽支大学 Velocity ratio for fix-axis gear train Input ⊕ v=@r @inin=ouou A Output (b)Internal set =() =(±) =(±) dp 9

9 Outline  Types of Gear trains  Velocity ratio for fix-axis gear train  Velocity ratio for epicyclic gear train Gear trains Fixed 定轴轮系 Compound gear train Simple gear train Epicyclic 周转轮系 Complex 复合轮系 Gear shaft supporter Non-reverted Reverted v  ωr ωin in out out r  ω r Input Output P G P G P G GP N N d d ω ω i  ()  ()  () Velocity ratio for fix-axis gear train

国 上海久通大学 Velocity ratio for fix-axis gear train 3 5= 0=? 05 M 3 3= N3 2 02 N 03 4 = 7 04 Ny = 05 N 1223i34i45= 0.02..-=is 0203040505 = N2NNNs 05 NNzNN 圆上泽支大学 Velocity ratio for fix-axis gear train Product of all b's Tooth Numbers Product of all a's Tooth Numbers i= N-N3NNs 3 NN2NsN. 4 Direction！ 10

10 1 2' 3' 4 2 3 4 5 5 1 15 N N N N N N N N i     15 5 1 5 4 4 3 3 2 2 1 12 2'3 3 4 45 i i i i       i            ? 5 1 15     i 1 2 2 1 12 N N i     34 45 3 4 45 43 54 N N i i N N         2' 3 3 2 2'3 N N i     Velocity ratio for fix-axis gear train Product of all Tooth Numbers Product of all Tooth Numbers a' s b' s iab  1 2' 3' 4 2 3 4 5 5 1 15 N N N N N N N N i     Direction！ Velocity ratio for fix-axis gear train