Selection of Servo Motor Output
(Rotary Motors)
4. Provisional selection of servo motor output
Provisionally, select motors that satisfy the following 2 condi-
tions.
• The load moment of inertia (J
L
) calculated in step 2 is 10
times or below the motor's rotor moment of inertia (J
M
×
10)
J
L
≤ J
M
×
10
• The load torque (T
L
) calculated in step 3 is 80% or below the
rated torque (T
R
×
0.8) of the motor
T
L
≤ T
R
×
0.8
5. Calculate the acceleration/deceleration torque
The acceleration/deceleration torque is the torque required to
accelerate or decelerate the motor and load.
■
How to calculate acceleration torque (T
a
)
［
kg
∙
m
2
］
［
kg
∙
m
2
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
J
L1
＝
J
L2
＝
W
1
2
G
×
32
π×ρ×
D
4
×
L
（
）
1
2
G
×
×
×
×
×
9.8
（
）
P
2
2
π
T
L
＝
T
a
＝
P
2
π
1
G
（
F
＋μ
W
）
η
＋
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
ta
T
b
＝
Trms
＝
E
M
＝
Ehb
＝ ×
N
×
3
×
Keø
× ×
tb
－
×
3
×
Rø
×
tb
－
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
tb
（
T
a
2
×
ta
）
＋
（
T
L
2
×
tr
）
＋
（
T
b
2
×
tb
）
t
（
）
1
2
T
b
KT
T
b
KT
2
N
2
: Servo motor rotating speed after acceleration [min
-1
]
N
1
: Servo motor rotating speed before acceleration [min
-1
]
J
L
: Load moment of inertia about the motor axis [kg
・
m
2
]
J
M
: Servo motor rotor moment of inertia [kg
・
m
2
]
T
L
: Axial load torque [N·m]
t
a
= Acceleration time [s]
■
Deriving deceleration torque (T
b
)
［
kg
∙
m
2
］
［
kg
∙
m
2
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
J
L1
＝
J
L2
＝
W
1
2
G
×
32
π×ρ×
D
4
×
L
（
）
1
2
G
×
×
×
×
×
9.8
（
）
P
2
2
π
T
L
＝
T
a
＝
P
2
π
1
G
（
F
＋μ
W
）
η
＋
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
ta
T
b
＝
Trms
＝
E
M
＝
Ehb
＝ ×
N
×
3
×
Keø
× ×
tb
－
×
3
×
Rø
×
tb
－
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
tb
（
T
a
2
×
ta
）
＋
（
T
L
2
×
tr
）
＋
（
T
b
2
×
tb
）
t
（
）
1
2
T
b
KT
T
b
KT
2
N
2
: Servo motor rotating speed before acceleration [min
-1
]
N
1
: Servo motor rotating speed after acceleration [min
-1
]
J
L
: Load moment of inertia about the motor axis [kg
・
m
2
]
J
M
: Servo motor rotor moment of inertia [kg
・
m
2
]
T
L
: Axial load torque [N·m]
t
b
= Deceleration time [s]
6. Calculate actual torque
The actual torque is a root mean square of the load torque, ac-
celeration torque, and deceleration torque.
［
kg
∙
m
2
］
［
kg
∙
m
2
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
J
L1
＝
J
L2
＝
W
1
2
G
×
32
π×ρ×
D
4
×
L
（
）
1
2
G
×
×
×
×
×
9.8
（
）
P
2
2
π
T
L
＝
T
a
＝
P
2
π
1
G
（
F
＋μ
W
）
η
＋
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
ta
T
b
＝
Trms
＝
E
M
＝
Ehb
＝ ×
N
×
3
×
Keø
× ×
tb
－
×
3
×
Rø
×
tb
－
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
tb
（
T
a
2
×
ta
）
＋
（
T
L
2
×
tr
）
＋
（
T
b
2
×
tb
）
t
（
）
1
2
T
b
KT
T
b
KT
2
7. Assessment
We use the following conditions for assessment.
• Load torque: T
L
≤ T
R
×
0.8
(Load torque ≤ 80% of the rated torque)
• Acceleration torque: T
a
≤ T
P
×
0.8
(Acceleration torque ≤ 80% of the peak torque at stall)
T
P
: Peak torque at stall
• Deceleration torque: T
b
≤ T
P
×
0.8
(Deceleration torque ≤ 80% of the peak torque at stall)
T
P
: Peak torque at stall
• Actual torque: T
rms
≤ T
R
×
0.8
(Actual torque ≤ 80% of the rated torque)
• Inertia moment ratio J
L
≤ J
M
×
10
(Load moment of inertial ≥ 10 times or below the motor ro-
tor moment of inertial)
Furthermore, the rising temperature of the motor can be in-
hibited by securing a large margin for torque load ratios. The
moment of inertia ratio can be more than 10 times, for exam-
ple, for mechanisms that slowly rotate a table. Testing with an
actual machine is recommended.
8. Calculate the regenerative power
Calculate the regenerative power (P
M
) to determine the type
of suitable regenerative resistor. The result of this calculation
determines if a built-in regenerative resistor can be used or an
external one is required.
■
How to calculate the regenerative power (P
M
) of horizontal
shaft drive
First, calculate the regenerative energy.
［
kg
∙
m
2
］
［
kg
∙
m
2
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
［
N
∙
m
］
J
L1
＝
J
L2
＝
W
1
2
G
×
32
π×ρ×
D
4
×
L
（
）
1
2
G
×
×
×
×
×
9.8
（
）
P
2
2
π
T
L
＝
T
a
＝
P
2
π
1
G
（
F
＋μ
W
）
η
＋
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
ta
T
b
＝
Trms
＝
E
M
＝
Ehb
＝ ×
N
×
3
×
Keø
× ×
tb
－
×
3
×
Rø
×
tb
－
T
L
2
π（
N
2
－
N
1
）×（
J
L
＋
J
M
）
60
×
tb
（
T
a
2
×
ta
）
＋
（
T
L
2
×
tr
）
＋
（
T
b
2
×
tb
）
t
（
）
1
2
T
b
KT
T
b
KT
2
E
M
: Regenerative energy during horizontal driving [J]
E
hb
: Regenerative energy during deceleration [J]
K
eø
: Phase voltage constant [V
rms
/min
-1
] (motor constant)
K
T:
Torque constant [N·m/A
rms
] (motor constant)
N: Motor speed [min
-1
]
R
ø
: Phase resistance [
Ω
] (motor constant)
t
b
: Deceleration time [s]
T
b
: Torque from deceleration [N·m]
Calculate the regenerative power from regenerative energy.
P
M
=
E
M
t
P
M
: Regenerative power [W]
E
M
: Regenerative energy [J]
t: Cycle time [s]
■
Selection of regenerative resistor
Select a regenerative resistor that satisfies the following con-
ditions.
• Servo amplifier's built-in regenerative resistor
Required regenerative power [P
M
] < Maximum regenerative power
that can be handled by a built-in regenerative resistor [P
R
]
• External regenerative resistor
Required regenerative power [P
M
] < Maximum regenerative power
that can be handled by an external regenerative resistor [P
RO
]
Note and be careful when making selections, since model
numbers for servo amplifiers include those that have built-in
regenerative resistor for absorbing regenerative power and
those that do not.
122
Selection Guide
