中国石油大(北京)机械原理考研习题Homework2

H 13
When n1 and n3 are in the opposite direction，
2 2' H 1 3
Z 2 Z3 n1 nH i n3 nH Z1Z 2'
H 13
常见错误3： When n1 and n3 are in the same direction，
Z 2 Z3 n1 nH i n3 nH Z1Z 2'
6
Solution: This is a differential gear train.
H 1 3
2 4
5
在1,2=3,4=5,6,H组成的差动轮系中：
n1 nH Z 2 Z 4 Z 6 25 * 24 *121 605 i n6 nH Z1Z 3 Z 5 30 * 24 *18 108
m m a 45 ( Z4 Z5 ) ( Z5 Z6 ) a 56 2 2 Z6 Z4 2Z5 17
3 64
n6 n3 n6 n3 Z4 i 3 n 4 n3 n3 Z6
2'
n1
2
6 5
1
3 4
1 i16 2 6
2'
2'
1. Dividing the gear train
n1
2
6 5
1
3 4
(a) In differential gear train 1-2-2’-3-6 :
n1 n 6 Z2 Z3 4 i n3 n6 Z1Z2' 3
6 13
2'
n1
2
6 5
1
3 4
(b) In planetary gear train 4-5-6-3
H 16
∵nH=316 r/min, n1=48 ~200 r/min，
1
6 H
108 497 n6 n1 nH 605 605
268.16r / min ~ 295.29r / min
2
3
5 4
常见错误：
1、
n3 Z4 n4 Z3
6 H 1 3
2、先写出无用的错误式 子： Z Z
n3 50r / min
2 2' H 1 3
(2) When n1 and n3 are in the opposite directions.
n1 200r / min n1 5n3 200 5*50 nH 8.33r / min 6 6
H的转速为8.33r/min,方向与轮 1转向相反。
H 13
When n1 and n3 are in the opposite direction，
2 2' H 1 3
n1 nH Z 2 Z 3 i n3 nH Z1Z 2'
H 13
Z 2 Z3 n1 nH 200 nH i n3 nH 50 nH Z1Z 2'
n1
2
6 5
1
3 4
常见错误：
两个基本周转轮系的系杆是不一样的。共用同 一代号H引起混淆。
2'
n1
2
6 5
1
3 4
常见错误：
Z 2 Z3 Z 2 Z3 n1 6 i13 i13 n3 Z1Z 2' Z1Z 2'
1-2-2’-3 不是定轴 轮系！!
2'
i
6 正负号的判断！ 13
4、
1 4
7-12 In the combined gear train shown below, Z1=36, Z2=60, Z3=23, Z4=49, Z4’=69, Z5=31, Z6=131, Z7=94, Z8=36, Z9=167, n1=3549 r/min. Find both the magnitude and the direction of nH. Solution:
n1
2
6 5
1
3 4
7-14. Shown in Fig.7-24 is a differential gear train in a textile machine with Z1=30, Z2=25, Z3=Z4=24, Z5=18, Z6=121, nH=316 r/min, n1=48 ~200 r/min. n1 and nH are in the same direction. Find n6.
40 52
5
3' 2
1 50 30
4'18
3 1
20 15
2'
常见错误： 1、蜗杆蜗轮间相对转动方向错误或漏标！ 2、齿数比前不能加正负号！
40 52
5
3' 2
1 50 30
4'18
3 1
20 15
2'
7-8 Shown below is the gear 15 4 train in a clock. S, M and H 4' denote the pointers of second, 3 minute and hour, respectively. M 60 The given numbers of teeth are 3' Z1=Z2’=8, Z2=64, Z3’=12, H 12 Z4’=15. If the modules of gear 5 4 and gear 5 are equal, find the 2' numbers of teeth Z3, Z4, and Z5. 8 2
3'
12
(2)
2'
8 64
2 S
8
z 4 48
(1)(2)联立得
z5 45
1
常见错误：
4
15
nm 12 60 nH
ns 60 *12 3600 nH
4'
60
3
M H 5
3'
12
2'
8 64
2 S
8
1
7-9. Shown in Fig.7-19 is a differential gear train with Z1=15, Z2=25, Z2’=20, Z3=60, n1=200 r/min, n3=50 r/min. Find nH when （1）n1 and n3 are in the same direction; (2) n1 and n3 are in the opposite directions.
n1 n H Z2 Z4 i n4 nH Z1 Z2'
H 14
2 2' H 1 3 4
常见错误： 1、齿数比前面的正负号。
2、
Z3 n1 nH n1 i 1 1 n3 nH nH Z1
H 13
3、
2' H
n2 ' Z 4 n4 Z 2
3
2 H 2'
4
3
n1
2 1
7-13 In the combined gear train shown below, Z1= Z5= Z6=17, Z2=18, Z2’=27, Z3=34, Z4=51. n1=110 r/min. Find both the magnitude and the direction of n6. Solution:
nm ?? nH
64
S
8
1
Solution:
nS Z 2 Z 3 64 * Z 3 i13 60 nM Z1Z 2' 8*8
4 3
15
4'
60
M H 5
60 * 8 * 8 Z3 60 64
3'
12
Z 4 Z5 Z 4 Z5 nM 12 nH Z 3' Z 4' 12 *15
H
7 9 8 4' 6 5
4
1. Dividing the gear train
3
n1
2 1
Hale Waihona Puke (a) In ordinary gear train 1-2-3-4
1 Z2 Z4 i14 4 Z1Z3
H
7 9 8 4' 6 5
4
3
n1
2 1
(b) In the differential gear train 4’-5-6-7:
n1 200r / min n1 5n3 200 5*50 nH 75r / min 6 6
H的转速为75r/min,方向与轮1 转向相同。
Solution: 此轮系为一差动轮系
H 13
Z 2 Z3 n1 nH 25 * 60 i 5 n3 nH Z1Z 2' 15 * 20
Z 4 Z 5 12 *12 *15 (1)
2'
8 64
2 S
8
1
m4 m5 m3' m4 m4' m5 a3'4 a4'5 z3' z4 z4' z5
12 Z 4 15 Z 5 Z 4 Z5 3
4 3
15
4'
60
M H 5
常见错误1：
Z 2 Z3 Z 2 Z3 n1 nH i n3 nH Z1Z 2' Z1Z 2'
H 13
2 2' H 1 3
常见错误2： When n1 and n3 are in the same direction，