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Motor selection
Inertia
How to calculate moment of inertia
• Disk
J (Inertia calculation)
1
• Shape
J =
WD
(kg·cm
2
2
8
D
W : Mass (kg)
D : Outer diameter (cm)
• Hollow circular cylinder
J (Inertia calculation)
1
• Shape
d
J =
W (D
+ d
) (kg·cm
2
2
8
W : Mass (kg)
D : Outer diameter (cm)
D
d : Inner diameter (cm)
• Sphere
J (Inertia calculation)
1
• Shape
J =
WD
(kg·cm
2
2
10
D
W : Mass (kg)
D : Diameter (cm)
• Cube
J (Inertia calculation)
1
• Shape
J =
W (a
+ b
) (kg·cm
2
2
12
W : Mass (kg)
c
a.b : Length of side (cm)
a
b
• Slender round bar
J (Inertia calculation)
3D
+ 4L
2
2
• Shape
J = W
(kg·cm
48
W : Mass (kg)
D : Outer diameter (cm)
D
L/ 2
L : Length (cm)
L/ 2
Panasonic Corporation Electromechanical Control Business Division
industrial.panasonic.com/ac/e/
GD
2
(Flywheel effect calculation)
1
)
GD
=
WD
(kgf·cm
)
2
2
2
2
W : Weight (kgf)
D : Outer diameter (cm)
GD
2
(Flywheel effect calculation)
1
)
GD
=
W (D
+ d
) (kgf·cm
2
2
2
2
2
W : Weight (kgf)
D : Outer diameter (cm)
d : Inner diameter (cm)
GD
2
(Flywheel effect calculation)
2
)
GD
=
WD
(kgf·cm
)
2
2
2
5
W : Weight (kgf)
D : Diameter (cm)
GD
(Flywheel effect calculation)
2
1
)
GD
=
W (a
+ b
) (kgf·cm
2
2
2
2
3
W : Weight (kgf)
a.b : Length of side (cm)
GD
2
(Flywheel effect calculation)
3D
+ 4L
2
2
)
GD
= W
(kgf·cm
2
2
12
W : Weight (kgf)
D : Outer diameter (cm)
L : Length (cm)
– A-54 –
© Panasonic Corporation 2018
AQCTB02E 201806-E
• Straight bar
• Shape
L
• Discrete shaft
• Shape
)
2
S
• Horizontal linear motion
• Shape
W
D
• Ball screw
• Shape
)
2
W
P
• Reducer
• Shape
)
2
a
J1 (GD
)
n
2 1
1
n
J2 (GD
2
b
Panasonic Corporation Electromechanical Control Business Division
industrial.panasonic.com/ac/e/
J (Inertia calculation)
1
J =
WL
(kg·cm
)
2
2
3
W : Mass (kg)
L : Length (cm)
J (Inertia calculation)
1
J =
WD
+ WS
(kg·cm
)
2
2
2
8
W : Mass (kg)
D : Diameter (cm)
S : Turning radius (cm)
D
J (Inertia calculation)
WD
2
J =
(kg·cm
)
2
4
W : Mass on the conveyor (kg)
D : Drum diameter (cm)
* Inertia of drum not included
J(Inertia calculation)
W·P
2
J = JA +
(kg·cm
)
2
4π
2
W : Mass (kg)
P : Lead of feed screw (cm)
JA : Inertia of feed screw (kg·cm
2
)
J (Inertia calculation)
Equivalent all inertia on axis "a"
( )
n
2
2
J = J1 +
J2 (kg·cm
)
2
n
1
n
: Speed of axis "a" (r/min)
1
2 2
)
n
: Speed of axis "b" (r/min)
2
J1 : J of axis "a" (kg·cm
)
2
J2 : J of axis "b" (kg·cm
2
)
– A-55 –
GD
2
(Flywheel effect calculation)
4
GD
=
WL
(kgf·cm
)
2
2
2
3
W : Weight (kgf)
L : Length (cm)
GD
2
(Flywheel effect calculation)
1
GD
=
WD
+ 4WS
(kgf·cm
)
2
2
2
2
2
W : Weight (kgf)
D : Diameter (cm)
S : Turning radius (cm)
GD
2
(Flywheel effect calculation)
GD
= WD
(kgf·cm
)
2
2
2
W : Weight on the conveyor (kgf)
D : Drum diameter (cm)
* Flywheel effect of drum not included
GD
(Flywheel effect calculation)
2
W·P
2
GD
= GD
+
(kgf·cm
)
2
2 A
2
π
2
W
: Weight (kgf)
P
: Lead of feed screw (cm)
GD
2 A
: Flywheel effect of feed screw (kgf·cm
2
)
GD
2
(Flywheel effect calculation)
Equivalent all flywheel effect on axis "a"
( )
n
2
2
GD
= GD
+
GD
(kgf·cm
)
2
2 1
2 2
2
n
1
n
: Speed of axis "a" (r/min)
1
n
: Speed of axis "b" (r/min)
2
GD
of axis "a" (kgf·cm
)
2 1
2
: GD
2
GD
2 2
of axis "b" (kgf·cm
2
)
: GD
2
© Panasonic Corporation 2018
AQCTB02E 201806-E
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