上海交通大学：《Design and Manufacturing》课程教学资源（讲义）Lecture11 gear train

冠 上海充通大￥ t-f+口 LECTURE 11 Gear train 轮系与传动比 5t1 手柄 2 ·LD灯 5花

1 Gear train 轮系与传动比 LECTURE 11

上海充通大 outline JNO TONG LN A pair of Gears ©Types of Gear trains More about Velocity ratio Velocity ratio for fix-axis gear train Velocity ratio for epicyclic gear train ME357 Design Manufacturing ll 上海充通大粤 A pair of Gears Pn1=Pn2 Pn1>pn2 Pn1<pn2 nl=Pn2

2 ME357 Design & Manufacturing II outline A pair of Gears Types of Gear trains More about Velocity ratio Velocity ratio for fix-axis gear train Velocity ratio for epicyclic gear train Pn1＝ Pn2 Pn1>pn2 Pn1<pn2 A pair of Gears

For a pair of engaging gears, A pair of Gears 01 m1=m2,Pal Pd2,1=d2 Conulton iol engaying. Pat =Pn2 then: P1=P2 πdh= nd dp d a2 02 =p cos a =πm·COS O: π cos a Pa 上游文通大 A pair of Gears Contact Ratio(重合度) 0 口Contact line:NN2 Common normal of Ks:N N2 Common tangent of base circles:N N2 Contact forces'direction:N,N2 4 lines in 1 02

3 O1 O2 1 2 N2 N1 B2 B1 K ra2 ra1 rb1 rb2 O1 O2 N2 N1 B1 P i i j Condition for engaging: Pn1  Pn 2 Pb1  Pb 2 then: d d N d N d P b b b      p c  cos   m  cos      cos pd 1 2 d1 d2 1 2 m m , p p , For a pair of engaging gears,      A pair of Gears Contact Ratio(重合度) rb2 O2 1 2 N2 O1 rb1 P N1 K K’ 4 lines in 1  Contact line: N1N2  Common normal of Ks：N1N2  Common tangent of base circles： N1N2  Contact forces’ direction：N1N2 A pair of Gears

上海充通大学 A pair of Gears 01 Segment of action:N,N2 When engaging begins Driver:root→top 口 driven:top→root 口 Engaging begins at:point B2 Engaging ends at:point B Real segment of action:B,B2 「a2 02 02 Real arc of action of the gears 上海充通大粤 A pair of Gears In order to transmit motion smoothly:one tooth is leaving contact after the next engaged. 口condition:B,B2>Pb Contact Ratio: 8=B,B21P6 皿p=Z/P6 in p281 of design of machinery 01 where, Z=+ap)-(rcos)++ag)2-(rgcos)2-C sin in p272

4  Segment of action:N1N2  When engaging begins  Driver：roottop  driven：toproot  Engaging begins at：point B2  Engaging ends at： point B1  Real segment of action： B1B2  Real arc of action of the gears rb2 O2 1 2 N2 O1 rb 1 P N1 ra1 ra2 B1 B2 A pair of Gears  In order to transmit motion smoothly:one tooth is leaving contact after the next engaged.  condition: B1B2 > pb  Contact Ratio: O1 O2 1 2 N2 N1 B2 B1 K ra2 ra1 rb1 rb2 O1 O2 N2 N1 B1 B2 P B B pb /  1 2  in p272 Z (r a ) (r os ) (r a ) (r os ) sin where, / in p281 of 2 g 2 g g 2 p 2 p p c  c  C  m p Z p b design of machinery         A pair of Gears

上海充通大学 A pair of Gears 1.3P。 The larger the Pb Pb contact ratio,the 0.3P6 0.7Pb0.3Pb more tooth meshed simultaneously 口if:8。=1.3 N1 B1 N2 Single pair Two pairs are engaging 上游充通大 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

5  The larger the contact ratio, the more tooth meshed simultaneously  if:  = 1.3 N2 P N1 B1 B2 Pb Pb 1.3Pb 0.3Pb 0.7Pb 0.3Pb D C Single pair Two pairs are engaging A pair of Gears 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