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The two-stage planetary gear transmission system is shown in Fig.3 [8]. The design
variables of the problem are: the gear width of the two-stage gear(
0
≤≤
B
100
and
1
0
≤≤
B
180
2
≤≤
m
10
2
≤≤
m
10
), the module of two stage gear(
and
), the
2
1
2
14
≤≤
Z
30
14
≤≤
Z
30
tooth number of two-stage sun gear(
and
), the tooth
a
1
a
2
0
≤≤
Z
160
0
≤≤
Z
160
number of two-stage annular gear(
and
), and the
b
1
b
2
14
≤≤
Z
50
14
≤≤
Z
60
tooth number of two-stage planetary gear(
and
).
c
1
c
2
The vector of the design variables can be defined as follows:
]
T
]
T
Xxxxxxxxxxx
=
[
=
[
BBmm Z Z Z Z Z Z
123456789 0
12 12
a
1 1 1 2
b
c
a
b
2
c
2
The two objective functions are defined as follows:
Minimize the volume of the two-stage planetary gear transmission system:
VV V V V V V
=+++++
s
a
1
a
2
b
1
b
2
c
1
c
2
2
ˀ
(6)
∑
≈
Bm
2
(
Z
2
+
nZ
2
+
9
Z
−
30.2)
i
i
i
i
i
i
4
i
=
1
Maximize the efficiency of the two-stage planetary gear transmission system:
⊡
⊤⊡
⊤
p
p
b
1
b
2
H
1
H
2
ʷ
=
ʷ
ʷ
=
1
−
1
˕
1
−
2
˕
⊦
(7)
⊢
⊥⊢
⊥
aH
12
aH
11 2 2
a H
1
+
p
1
+
p
⊣
⊦⊣
1
2
where :
Z
Z
p
=
b
1
,
p
=
b
2
1
1
Z
Z
a
1
a
2
⊡
⊤
⊡
⊤
ˀ
11
ˀ
11
˕
H
=++
˕
H
˕
H
˕
H
,
˕
H
=
ʵ
f
+
,
˕
H
=
ʵ
f
−
⊢
⊥
⊢
⊥
za
zb
n
za
k
zb
k
2
Z
Z
2
Z
Z
⊣
⊦
⊣
⊦
a
c
c
b
˕
H
n
n
is the number of i -stage planetary gear,
is the bearing loss coefficient.
nn
==
3
i.e.
.
The two-stage planetary gear transmission system is subject to many constraints on
gear ratio and adjoining condition of the gears, strength and dimension of the gears,
and concentric condition for installation, etc. The lower value of volume means lower
mass of the system that leads to lower production cost. Maximizing efficiency is im-
portant because maximum efficiency leads to least power consumption for transmis-
sion and corresponding savings in the operating costs. The constraint conditions are
listed as follows:
1
2
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