Theory of Machinery Gears and Gear Trains

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30 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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Theory of Machinery
Gears and Gear Trains
Dr. Ahmed Shaaban
Dr. Mohammed Al-Hazmi
GEAR TRAINS
Kinematics & Dynamics
A gear train consists of several gears that are
meshed together to transmit the power from
input shaft to the output one. The gear works
as reducer or accelerator.
a) Ordinary gear trains
b) Planetary or Epicyclic gear trains
c) Any combination of a and b
1-Kinematic Analysis of Gear Trains
Gear ratio, transmission ratio =i
in/out
=± ω
in

out
2-Kinematic Synthesis of Gear Trains
3-Dynamic Analysis of Gear Trains
Study the flow of power (or mainly, the torque)
through the individual shafts
Kinematic Analysis of Ordinary Gear Train
The ratio of the speed of the driver to the speed of the
follower is known as velocity ratio or speed ratio.
The reciprocal of the speed ratio (or velocity) is known
as train value
Types of gear trains
a)Simple gear train
b)Compound gear train
c)Reverted gear train
d)Epicyclic gear train
Velocity Ratio of a Simple Gear Train
2
3
3
2
.
Z
Z
N
N
ratioSpeed ==
Simple gear train in which
each shaft carries only one
gear
2
4
4
2
3
4
2
3
4
3
3
2
.
.
Z
Z
N
N
ratiospeed
Z
Z
Z
Z
N
N
N
N
ratioSpeed
==
×=×=
1
3
3
1
2
3
1
2
3
2
2
1
.
.
Z
Z
N
N
ratiospeed
Z
Z
Z
Z
N
N
N
N
ratioSpeed
==
×=×=
Problem: A simple gear train consists of three gears, each mounted on
separate shaft. Gear 1 is the driver and Gear 3 is the follower. The
gear 1 rotates CW at speed of 750 rpm and the number of teeth of
gears 1,2 and 3 are 30,45 and 75 respectively. Find,
i) Speed ratio of the gear train
ii) direction of rotation of the follower.
Given: N
1
=750 rpm, Z
1
=30
i) Speed ratio = speed of driver/ speed of follower = Z
3
/Z
1
=75/30=2.5
ii) Speed of the follower N
3
N
1
/N
3
=2.5
N
3
= 750/2.5 =300 rpm
Problem: Two parallel shafts are connected with two gears. The number of
teeth of one gear is 38 and speed of its shaft is 420 rpm. If the speed ratio
is equal to 3 and circular pitch of the gear is 25 mm. Find,
i) Number of teeth and speed of the other shaft
ii) Center distance between shafts.
Solution: Z
1
=38 , N
1
=420 rpm , speed ratio i =3 & p= 25mm
i) Speed ratio = N
1
/N
2
= Z
2
/Z
1
=3
N
2
=N
1
/3=420/3=140 rpm
Z
2
=Z
1
x3= 3x38= 114
ii) Center distance C= r
1
+r
2
=(d
1
+d2)/2
p=πxd
1
/Z
1
d
1
=Z
1
xp/π = 38x25/π=302.39 mm
Z
2
= πd
2
/p
d
2
= Z
2
xp/π=114x25/π=907.18 mm
Center distance C = (302.39+907.18)/2= 604.78 mm
GEAR TRAINS
Compound Ordinary Gear Train
4
5
3
4
2
3
5
2
44
33
4
5
3
4
2
3
5
4
4
3
3
2
′′


′′
′′
××===
=
=
××=××=
Z
Z
Z
Z
Z
Z
N
N
N
N
i
NN
NN
Z
Z
Z
Z
Z
Z
N
N
N
N
N
N
i
output
input
3
4
2
3
4
2
33
3
4
2
3
4
3
3
2




×===
=
×=×=
Z
Z
Z
Z
N
N
N
N
i
NN
Z
Z
Z
Z
N
N
N
N
i
output
input
a) Compound gear train
b) Reverted gear train
3
4
1
2
4
1
32
3
4
1
2
4
3
2
1
Z
Z
Z
Z
N
N
N
N
i
NN
Z
Z
Z
Z
N
N
N
N
i
output
input
×===
=
×=×=
Problem 10-1: Find the direction and speed of the output
shaft if the input shaft rotates with 1250 rpm.
rpm
N
N
Z
Z
Z
Z
N
N
N
N
i
output
input
.200
25.6
1250
25.6
25.6
2030
5075
1
4
3
4
1
2
4
1
===
=
×
×
=×===
Problem 10-2:Find the direction and speed of the output shaft, if the
input shaft rotates with 1125 rpm.
rpm
N
N
Z
Z
Z
Z
Z
Z
N
N
N
N
i
output
input
.60
75.18
1125
75.18
75.18
284030
7012075
1
4
5
6
3
4
1
2
6
1
===
=
××
××
=××===