多于两个齿轮组成的齿轮系统称为轮系

1、Chapter 10. Gear Trainscontent Know about the gear train and the classification can calculate the transmit ratio of different gear trains know about the mechanical efficiency of planetary gear trainthe tooth numbers of gear and number of planet The difficulties How to measure off the types of differ

2、ent gear trains correctly .How to calculate the transmit ratio ,how to design the tooth of gear in the gear trains. 10-1 Gear Train and its classification 1. What is gear train? Such a transmission system with more than a pair of gears is called a gear train 多于两个齿轮组成的齿轮系统称为轮系。多于两个齿轮组成的齿轮系统称为轮系。2. Cl

3、assification2.1 Gear train with Fixed Axes /Ordinary Gear Train (定轴轮系定轴轮系)The position of all gear axes in a gear train are fixed when it works.Gear trains with fixed parallel axesGear trains with fixed non-parallel axes2.2Epicyclic gear train(周转轮系周转轮系) At least one gear axis in a gear train rotates

4、 around the fixed axis of other gears, this kind of gear train is ca1led an epicyclic gear train.Sun gear(太阳轮）: The gears rotating around fixed axis are called sun gears.planet gear（行星轮）: In a gear train ,the planet gear rotates around the fixed axis,at the same time ,it also rotates relatively to t

5、he link H around it is own axis.Planet carrier（行星架/系杆）: The link carrying planet gears is called the planet carrier,。fundamental members :H321341234421Differential gear trains（差动轮系）（差动轮系） ： degree of freedom is 2 .planetary gear train （行星轮系）：（行星轮系）： degree of freedom is 1 .差动轮系差动轮系行星轮系行星轮系657H3421 A

6、 combined gear train is a combination of several epicyclic gear trains or a combination of at least one epicyclic gear train with at least one ordinary gear train .周转轮系周转轮系定轴轮系定轴轮系6123H145H2周转轮系周转轮系2周转轮系周转轮系12.3 Combined gear train（混合轮系）（混合轮系）Classification:1. ordinary gear train or gear train with

7、fixed axes. (定轴轮系)2. Epicyclic gear train. (周转轮系)Gear train Gear train with fixed axesEpicyclic gear trainsGear trains with fixed parallel axesGear trains with fixed non-parallel axesElementary epicyclic gear trainsCombined gear trainsPlanetary gear trainsDifferential gear trains123344510-2 Train Ra

8、tio of a Gear Train with Fixed Axes(定轴轮系定轴轮系) w w1 1The train ratio of a gear train is the ratio of the angular velocities of input and output members in the gear train. 515115nni w ww ww w5 5The train ratio here includes two factors, the magnitude and the relative rotating direction of the two memb

9、ers. 1. Train Ratio = i12 i23 i34 i45Train Ratio ：w w2w w2w w3w w3 w w4w w4 i15 =w w1w w5z2 2z1(- )(- )z3 3z2(+ )(+ )z4 4z3(- )(- )z5 5z4(- )(- )=i12 =w w1w w2 2= - -z2z1=z3z2i23 =w w2 2w w3= - -z4 4z3i34 =w w3 w w4 41233445w w1 1w w5 5= - -z5z4i45 =w w4 4 w w5，2. Calculation of Train RatioTransmiss

10、ion ration of every gear pair:Conclusion:= i12 i23 i34 i45w w2 2w w2 2w w3 3w w3 3 w w4 4w w4 4 i15 =w w1 1w w5 5z2 2z1(- )(- )z3 3z2(+ )(+ )z4 4z3(- )(- )z5 5z4(- )(- )=1233445w w1 1w w5 5iAB =(-1)n所有从动轮齿数连乘积所有从动轮齿数连乘积所有主动轮齿数连乘积所有主动轮齿数连乘积A，B 分别为主动轮和从动轮；分别为主动轮和从动轮；n 为为外啮合齿轮的对数。外啮合齿轮的对数。iAB =(-1)npro

11、duct of teeth numbers of all the driven gears product of teeth numbers of all the driving gears A-input gear; B -output gear；n -number of external gear pair223.The rotating direction of the first and last gear1 1) determined by“，” External gear： “” ；适用于平面定轴轮系（轴线平行，适用于平面定轴轮系（轴线平行，两轮转向不是相同就是相反）。两轮转向不是

12、相同就是相反）。1 12 2Internal gear： “”2 21pvp转向相反转向相反转向相同转向相同1 11vpp iAB =(-1)nproduct of teeth numbers of all the driven gears product of teeth numbers of all the driving gears A-input gear; B -output gear；n -number of external gear pair123122)2) determined by arrows External meshing ：I n t e r n a l mesh

13、ing ：Attention: the rotating directions of gears in gear trains with fixed non-parallel axes can only be determined by drawing arrows. in the opposite direction 头头相对或尾尾相对。头头相对或尾尾相对。in the same direction两箭头同向。两箭头同向。u bevel gear 12Arrow indicates that of the periphera1 velocity of the gear on the visi

14、ble side. u worm and worm gear左左旋旋蜗蜗杆杆12伸出左手伸出左手伸出右手伸出右手右右旋旋蜗蜗杆杆211233445Example 1:Known: direction of gear 1Determine: direction of worm gear 5Z1Z3Z4Z4Z5Z2Z3Known: the number of each gear in the gear trainDetermine: train ratio i15 Idler (惰轮惰轮):):齿轮齿轮2 2对传动比没有影响，但能改变从动轮的转向，称为过轮对传动比没有影响，但能改变从动轮的转向，称

15、为过轮( (惰轮惰轮) )或或中介轮。中介轮。2. ratioresolution：1.direction惰轮惰轮z z1 1 zz3 3 zz4 4 z z3 3 z z4 4 z z5 5 =z z1 1 z z2 2 zz3 3 zz4 4 z z2 2 z z3 3 z z4 4 z z5 5 =i15 = 1 /5Example 2:known：n1=1500r/min，z1=32， z2=64， z3=38， z4=56， z5=22， z6=66， z7=17， z8=16。Determine: n3。y34126578xn1n3解：解：1. 离合器啮合离合器啮合n3 = n1

16、= 1500r/min2. 齿轮齿轮1与与2、3与与4啮合啮合 i13= n1 / n3 = (- z2 / z1 ) (- z4 / z3 ) =56/19所以：所以： n3 =19* n1 /56=509 r/min3. 齿轮齿轮1与与2、5与与6啮合啮合 i13= n1 / n3 = (- z2 / z1 ) (- z6 / z5 ) =6所以：所以： n3 =n1 /6=250 r/min 4. 齿轮齿轮1与与2、7与与8 、8与与8啮合啮合 i13= n1 / n3 = (- z2 / z1 ) (- z8 / z7 ) (- z8 / z8 ) =-132/17所以：所以： n3

17、=-17n1 /132=-193 r/minExample 3:8中心轮中心轮Sun gearplanet gearPlanet carrier特点：特点： 有一个轴线不固定的有一个轴线不固定的齿轮；齿轮； 两个太阳轮与系杆共轴线；两个太阳轮与系杆共轴线； 一个太阳轮固定为行星轮系；一个太阳轮固定为行星轮系；太阳轮都运动为差动轮系。太阳轮都运动为差动轮系。 213H123H00011-3 Train Ratio of a Epicyclic Gear Train (周转轮系周转轮系) 给整个周转轮系加一个与系杆给整个周转轮系加一个与系杆H的角速度的角速度大小相等、方向相反的公共角速度大小相等、

18、方向相反的公共角速度 HwwH3w w221H123H00w w1w wHw w3213H123H00w wH1w wH2w wH3 converted train 转转化化轮轮系系差差动动轮轮系系link in the real train in the converted train w wH HH H = =w wH H - - w wH H = =0 0注意注意：转化机构转化机构: :w wH H1 1 = =w w1 1- - w wH Hw wH H2 2 = =w w2 2- - w wH Hw ww w1 1w w2 2w w3 3w wH H3 3 = =w w3 3- -

19、w wH H Planet carrierSun gearSun gear 3Planet gear 2apply a public angular velocity H to the converted gear train to make it rotate around the fixed axes of the planet carrier H. wwH3w w221H123H00w w1w wHw w3213H123H00w wH1w wH2w wH3converted train系杆系杆H机架机架周转轮系周转轮系定轴轮系定轴轮系Train ratio of converted ge

20、ar train(gear train with fixed axes )：213H123H00w wH1w wH2w wH3Converted trainiH =13w w1Hw w3Hw w3 w wH=w w1 w wHz2 2z1(- )(- )z3 3z2(+ )(+ )=z3 3z1(- )(- )=formula ：iH =ABw wAHw wBHw wB w wH=w wA w wHf( (z) )=转化轮系中传动比转化轮系中传动比f(z)： Train ratio of converted gear train：it is confirmed by the turning r

21、elation of the A and B in the converted gear train. (在转化轮系中, 轮A和轮B的方向关系)213H123H00w wH1w wH2w wH3转化轮系转化轮系iH =ABw wAHw wBHw wB w wH=w wA w wH f( (z) )=对于差动轮系，若已知两个原动件值，则可求出另一构对于差动轮系，若已知两个原动件值，则可求出另一构件值；若已知一原动件值，可求出另两构件的传动比值；件值；若已知一原动件值，可求出另两构件的传动比值；213H123H00w wH1w wH2w wH3转化轮系转化轮系iH =ABw wAHw wBHw w

22、B w wH=w wA w wH(-(-1 1) )n f( (z z) )=对于行星轮系，因其中必有一中心轮固定，假设中心对于行星轮系，因其中必有一中心轮固定，假设中心轮轮3固定，固定，于是有：于是有：iH =13w w1Hw w3H 0 w 0 wH=w w1 w wHz3 3z1(- )(- )= 0 w 0 wH / / w wH w w1 / / w wH w wH / / w wH z3 3z1(- )(- )= 1 1i1H 1 1z3 3z1(- )(- )= iH13i1H =11iH13Example 1.known: z110, z220, z350, gear 3 is

23、 fixed.Determine: i1H 2H13HHHi3113) 1wwHHwww0111Hi5 i1H=6 HHwwww312132zzzz105013zz11Hi5Resolution:Z1Z3Example 2:known:z144，z240,z242, z342determine: iH1 resolution： iH13(1-H)/(0-H )4042/4442 i1H1-iH13Z2 Z2H= 1-i1H(-1)2 z2z3 /z1 z210/11 iH11/i1H=11 1-10/111/11 If Z1=100, z2=101, z2=100, z3100，结论：系杆转结

24、论：系杆转100100圈时，轮圈时，轮1 1反向转反向转1 1圈。圈。此例说明行星轮系中输出轴的转向，不仅与输入轴的转向有关，而且与各轮的齿数有关。本例中只将轮3增加了一个齿，轮1就反向旋转，且传动比发生巨大变化，这是行星轮系与定轴轮系不同的地方i1H1-iH1H1-101/100iH1-100 1/100, 1/100, Z2 Z2HZ1Z3if Z1=100, z2=101, z2=100, z3=99i1H1-iH131-10199/100100结论：系杆转结论：系杆转1000010000圈时，轮圈时，轮1 1同向转同向转1 1圈。圈。iH110000 1/10000,1/10000,z

25、1z2z3HHHiwwww1221上式表明轮上式表明轮3的绝对角速度为的绝对角速度为0，但相对角速度不为，但相对角速度不为0。HHHiwwww1331HHwww0221zz1HHwww0332212) 1(zzzz13022Hz z1 1z z3 3z z3 3z z1 1HHHHz2z2Example 3：potato digger known: z1z2z3 ，determine 2， 3 HExample 4known:z133，z212, z233, Determine i3H Resolution:HHHiwwww1331成立否？HHHiwwww1221HHwww0313Hi31zz

26、z z1 1z z3 3 i3H =2=1不成立！不成立！Why? 因两者轴线不平行H H2 2 2 2H HH H2 2H H特别注意：转化轮系中两齿轮轴线不平行时，不能直接计算！特别注意：转化轮系中两齿轮轴线不平行时，不能直接计算！z z2 2op三、混合轮系的传动比三、混合轮系的传动比 在图在图( (b) )中，因为一般情况下，中，因为一般情况下，w wH1 w wH2 ，所以不任给，所以不任给系统一个系统一个( ( w wH1) )或或( ( w wH2) )都无法同时使两系杆禁止。都无法同时使两系杆禁止。 把这种由定轴轮系和周转轮系或者由两个以上的周转轮把这种由定轴轮系和周转轮系或者

27、由两个以上的周转轮系组成的，不能直接用反转法转化为定轴轮系的轮系，称为系组成的，不能直接用反转法转化为定轴轮系的轮系，称为混合轮系。混合轮系。435H2( (a) )1w wH w wHH6123H145H2( (b) )例例1：在图示混合轮系中，已知各轮的齿数。求：在图示混合轮系中，已知各轮的齿数。求i14 。 解：因为解：因为435H21w w2 = w wH i14 =w w1w w4=w w1w w2w wHw w4而而 = i12 iH4 所以问题转化为分别求解定轴轮系和周所以问题转化为分别求解定轴轮系和周转轮系。转轮系。 对于定轴轮系有：对于定轴轮系有： i4H = 1- - i4

28、5 i12 = - -z2z1对于周转轮系有：对于周转轮系有： iH4 =w wHw w4=w wHw w41 i4H=1而而= 1- - (- - )z5z4=z4 + z5z4所以所以 i14 =z2z1 z4- -(z4 + z5)例例2：在图示周转轮系中，各轮齿数为：在图示周转轮系中，各轮齿数为z1 =80，z2 =25，z2 =35， z3=20，若已知，若已知n1 =50r/min，n3=200r/min，方向相反。求，方向相反。求iH 的的大小与方向。大小与方向。 解：解：2 2 2 2称为双联行星轮。称为双联行星轮。设设n1为正，则为正，则n3为负。为负。H2123n3 - n

29、Hn1 - nH i13 =H =z2 z3z1 z2-(-200) - nH50 - nH=25208035 -=285所以：所以：nH =12.12r/minnH 为正，说明系杆与轮为正，说明系杆与轮1转向相同，与轮转向相同，与轮3转向相反。转向相反。例例3：在图示轮系中，已知各轮齿数：在图示轮系中，已知各轮齿数： z1 =100，z2 =101，z2=100，z3 =99， 求求i1H。解：解： i13 n3 nH=n1 nH Hz1 z2= z2 z3即：即： iH1 10000 10000 双联行星轮另：若另：若 z3 = 100因为因为: :=101 99100 100=99991

30、0000 1 1 i13 H=110000另解另解: : i13 n3 nH=n1 nH Hz1 z2= z2 z3=101100100 100i1H 1 1 i13 H= - -1100=101100i1H 34122H例例4：图示为一卷扬机减速器的轮系中，已知：图示为一卷扬机减速器的轮系中，已知： z1 =24，z2 =48，z2=30，z3 =90， z3 =20，z4 =30，z4 =80，n1 =1450r/min。求卷同的转速。求卷同的转速n5的大小与方向的大小与方向 。 解解：(1) (1) 轮系组成分析轮系组成分析 该轮系由差动轮系该轮系由差动轮系1 1 2 2 2 2 3 3 ( (5 5) )和定轴轮系和定轴轮系3 3 4 4 5 5形形成一个封闭的复合轮系。成一个封闭的复合