11.2 Reference Information for Servomotor Capacity Selection
11.2.1 Formulas Required to Select the Servomotor Capacity
11-4
11.2
Reference Information for Servomotor Capacity Selection
11.2.1
Formulas Required to Select the Servomotor Capacity
Type of Motion
Rotary Motion
Linear Motion
Horizontal Axis
Vertical Axis
Machine Configura-
tion
N
: Load shaft speed (min
-1
)
V
: Load speed (m/min)
T
: Load torque calculated at load
shaft (N
m)
μ
: Friction coefficient
P
B
: Ball screw lead (m)
M
: Linear motion section mass
(kg)
M
c
: Counterweight mass (kg)
1/R
: Gear ratio
η
: Mechanical efficiency
T
pM
: Servomotor instantaneous
maximum torque (N
m)
Speed Diagram
Travel distance (m)
Load Shaft Speed
(min
-1
)
N
Motor Shaft Speed
(min
-1
)
N
M
=
N
R
Load Torque Calcu-
lated at Motor Shaft
(N
m)
Load Moment of Iner-
tia Calculated at
Motor Shaft (kg
m
2
)
J
L
=
J
L1
+
J
L2
+
J
L3
Linear Motion
Section
–
Rotary Motion
Section
Minimum Starting
Time (s)
Continued on next page.
1/R
Servomotor
N
R
1/R
V
R
Servomotor
Lead:
M
P
B
μ
1/R
P
B
Lead:
Servomotor
Counter-
weight
M
M
c
V
T
p
T
L
T
s
t
a
t
c
t
m
t
d
t
t
e
Motor speed
Motor speed
Vertical axis
Torque
Torque
One cycle, (S)
0
V
R
=
R...
= ( - )
= If... ,
+ +
60
2t
c
60
2
V
V
t
a
t
a
t
a
t
m
t
d
t
d
N =
P
B
V
=
R
η
T
L
T
M P
B
=
9.8
×
2
π
R
T
L
η
μ
M M
c
P
B
=
9.8
×
( - )
T
L
2
π
R
η
P
B
M
J
L1
=
( )
R
2
π
2
( + )
P
B
J
L1
=
( )
R
2
π
M M
c
2
M
k
M
k
M
k
D
=
OR
: Solid cylinder mass (kg)
: Density (kg/m
3
)...Iron
...Aluminum
Hollow Cylinder
Moment of Inertia of Rotary Motion Section Calculated at Motor Shaft
Rotary motion section at gear input shaft
Solid Cylinder
= 7.87
×
10
3
(kg/m
3
)
= 2.70
×
10
3
(kg/m
3
)
8
1
L
=
D
32
R
L (m)
L (m)
(m)
(m)
(m)
D
=
Rotary motion section at gear output shaft
=
( + )
OR
8
1
L
=
D
0
D
1
D
0
D
i
( - )
D
0
D
i
32
J
L2
J
L3
J
K
J
K
J
K
J
K
J
K
=
π
ρ
ρ
ρ
ρ
J
K
π
ρ
4
4
2
2
2
2
4
N
M
J
M
J
L
=
2
π
( + )
60 ( - )
t
am
T
PM
T
L
