2.2 Selecting Servomotors
2-5
2
Selecting Products
2.2.2
Selection Calculations
This section describes how to make the calculations and select a servomotor for the following machine speci-
fications.
(1) Speed Diagram
(2) Rotation Speed
(3) Load Torque
(4) Load Moment of Inertia
(5) Load Moving Power
(6) Load Acceleration Power
• Load speed:
υ
L
= 15 m/min
• Linear motion section mass:
m
= 250 kg
• Ball screw length:
l
B
= 1.0 m
• Ball screw diameter:
d
B
= 0.02 m
• Ball screw lead:
P
B
= 0.01 m
• Ball screw material density
:
ρ
= 7.87
×
10
3
kg/m
3
• Gear ratio : 1/2 (R = 2)
• Gear + coupling moment of inertia:
J
G
= 0.40
×
10
-4
kg
m
2
• Feeding times:
n
= 40 times/min
• Feeding distance:
l
= 0.275 m
• Feeding time:
tm
= 1.2 s max.
• Friction coefficient:
μ
= 0.2
• Mechanical efficiency:
η
= 0.9 (90%)
Servomotor
Coupling
Ball screw
Gear
Linear motion
Mechanical Specifications
L
υ
tc
ta
td
(m/min)
Speed
Time (s)
tm
t
L
15
υ
t
=
=
=
1.5
㧔
s
㧕
where ta = td
ta
=
tm
−
=
1.2
− =
1.2
−
1.1
=
0.1
㧔
s
㧕
tc
=
1.2
−
0.1
×
2
=
1.0
㧔
s
㧕
60
n
60
40
60
×
0.275
15
60ℓ
L
υ
Load axis rotation speed
n
L
=
=
=
1500
㧔
min
-1
㧕
P
B
15
0.01
L
υ
Motor shaft rotation speed
Gear ratio 1/R = 1/2 (R=2)
Therefore,
n
M
=
n
L
R
=
1500
×
2
=
3000
㧔
min
-1
㧕
T
L
=
=
=
0.43
（
N
･
m
）
2
R
・
9.8
・
m
・
P
B
2
2
0.9
9.8
0.2
250
0.01
μ
η
Linear motion section
J
L1
=
m
=
250
×
=
1.58
×
10
-4
㧔
kg
㨯
m
2
㧕
2
2
π
R
P
B
2
2
π
×
2
0.01
Ball screw
J
B
=
ℓ
B
d
B
4
=
×
7.87
×
10
3
×
1.0
×
㧔
0.02
㧕
4
=
0.31
×
10
-4
㧔
kg
㨯
m
2
㧕
R
2
1
32
π
2
2
1
32
π
ρ
Coupling
J
G
=
0.40
×
10
-4
㧔
kg
m
2
㧕
Load moment of
inertia at motor shaft
J
L
=
J
L1
+
J
B
+
J
G
=
㧔
1.58
+
0.31
+
0.40
㧕
×
10
-4
=
2.29
×
10
-4
㧔
kg
m
2
㧕
P
O
=
=
=
135
（
W
）
60
2
n
M
・
T
L
60
2
3000
0.43
Pa
=
=
=
226
（
W
）
n
M
2
60
2
ta
J
L
3000
2
60
2
0.1
2.29
10
-4
