Calculating inertia moment
5-4
A
ppe
ndi
x
Appe
Appe
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 reference values for specific gravity. Check the specific gravity for each
material.
Material Specific gravity
[
×
10
3
kg / m
3
]
Material
Specific gravity
[
×
10
3
kg / m
3
]
Material
Specific gravity
[
×
10
3
kg / m
3
]
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) Both centerlines of rotation and gravity are not the same:
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) Inertia moment of linear operation objects
The inertia moment, converted to output shaft, 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 motor axis [kg
･
m
2
]
m
:
mass [kg]
P
:
Linear travel per motor one revolution [m/rev]
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
×10
3
×10
3
×10
3
×10
3
2
mF
Ig
I
+
=
2
2
P
m
I
π
=
Rotary
center
axis
Gravity
center
axis
F
Содержание MMA Series
Страница 10: ...Conformance to overseas standards 8...
Страница 32: ...1 13 Cable specifications 1 21 Outlines 1 Appe...
Страница 48: ...3 3 Location and installation 3 7 Installing the motor 3 Appe...
Страница 49: ...Chapter 4 Options This chapter provides information on the options 4 1 Options 4 1...
Страница 53: ...Chapter 5 Appendix A 1 Unit conversion 5 1 A 2 Calculating inertia moment 5 3...
Страница 60: ......