Calculating moment of inertia
104
1
2
3
4
Apx
6
7
8
9
10
11
付
A
ppe
ndi
x
Object form
Mass, inertia, gravity center
Object form
Mass, inertia, gravity center
Rhombus pillar
Hexagonal pillar
Isosceles triangle
pillar
Right triangle pillar
Example of specific gravity
The following tables show references of specific gravity. Confirm the specific gravity for the material of
the drive load.
Material
Specific
gravity
Material
Specific
gravity
Material
Specific
gravity
SUS304
7.93
Aluminum
2.70
Epoxy resin
1.90
S45C
7.86
Duralumin
2.80
ABS
1.10
SS400
7.85
Silicon
2.30
Silicon resin
1.80
Cast iron
7.19
Quartz glass
2.20
Polyurethane rubber
1.25
Copper
8.92
Teflon
2.20
Brass
8.50
Fluorocarbon resin
2.20
(2)
For cases where the center of gravity is not coincident with the axis of rotation:
The following formula calculates the inertia moment when the rotary center is different from the gravity center.
I
:
Inertia moment when the gravity center axis does not
match the rotational axis (kg
･
m
2
)
I
g
:
Inertia moment when the gravity center axis matches
the rotational axis (kg
･
m
2
)
Calculate according to the shape by using formula (1).
m
:
mass (kg)
F
:
Distance between rotary center and gravity center (m)
(3) Moment of inertia of an object in linear motion
The inertia moment, converted to actuator axis, of a linear motion object driven by a screw, etc., is
calculated using the formula below.
I
:
Inertia moment of a linear operation object converted to actuator axis (kg
･
m
2
)
m
:
mass (kg)
P
:
Linear travel per actuator one revolution (m/rev)
Rotary
center
Gravity
center
F
ρ
ABC
2
1
m
=
+
=
2
2
C
3
2
2
B
m
12
1
Ix
+
=
2
2
C
3
2
A
m
12
1
Iy
+
=
2
B
A
m
12
1
Iz
2
2
3
C
G
=
G
z
x
y
B
A
C
G
1
z
x
y
B
A
G
2
C
ABC
ρ
2
1
m
=
(
)
2
2
C
B
m
36
1
Ix
+
=
+
=
2
2
C
3
2
A
m
12
1
Iy
3
C
G
1
=
+
=
2
2
B
3
2
A
m
12
1
Iz
3
B
G
2
=
z
x
y
C
A
B
ρ
ABC
2
1
m
=
(
)
2
2
C
B
m
24
1
Ix
+
=
(
)
2
2
2A
C
m
24
1
Iy
+
=
(
)
2
2
2A
B
m
24
1
Iz
+
=
z
x
y
B
B
√
3
A
2
B
m
12
5
Ix
=
+
=
2
2
B
2
5
A
m
12
1
Iy
+
=
2
2
B
2
5
A
m
12
1
Iz
ρ
AB
2
3
3
2
=
m
2
mF
Ig
I
+
=
2
2
P
m
I
π
=
