Harmonic Drive KDU Series, Manual

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Inertia moment calculation
Appendix
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App
13-2 Inertia moment calculation
1. Formula of mass and inertia moment
(1) Both centerlines of rotation and gravity are the same:
The following table includes formulas to calculate mass and moment of inertia.
m
：
mass (kg), Ix, Iy, Iz: inertia moments which rotates around x-, y-, z-axes respectively (kg
･
m
2
)
G
：
distance from end face of gravity center (m)
ρ
：
Specific gravity
Units Length: m, Mass: kg, inertia moment: kg
･
m
2
Object form
Mass, inertia, gravity
center
Object form
Mass, inertia, gravity
center
Cylinder Circular pipe
Slanted cylinder Ball
Ellipsoidal cylinder Cone
Rectangular pillar Square pipe
ρ L R m
2
π =
ρ L BC m
4
1
=
( )
2 2
C B m
16
1
Ix
+ =








+ =
3
L
4
C
m
4
1
Iy
2 2








+ =
3
L
4
B
m
4
1
Iz
2 2
ρ π
1
L R
3
m 2
=
( )
{ }
2 2
D D - B m
3
1
Ix
+ =
( )






+ + = 2
2
2
D D - B
A
m
6
1
Iy
2
R
L
z
x
y
2
R m
2
1
Ix
=








+ =
3
L
R m
4
1
Iy
2
2








+ =
3
L
R m
4
1
Iz
2
2
( )
ρ π
L R R m
2
2
2
1
− =
( )








+ + =
3
L
R R m
4
1
Iy
2
2
2
2
1
( )
2
2
2
1
R R m
2
1
Ix + =
( )








+ + =
3
L
R R m
4
1
Iz
2
2
2
2
1
ρ L R m
2
π =
( ) { }
θ θ
2 2 2 2
sin L cos 1 3R
m
12
1
I
+ + ×
=
θ
R
L
θ
R
ρ π
3
R
3
4
m =
2
R m
5
2
I
=
B
L
z
x
y
C
R
L
z
x
y
G
2
R m
10
3
Ix
=
( )
2 2
L 4R m
80
3
Iy + =
(
)
2 2
L 4R m
80
3
Iz + =
4
L
G =
z
x
y
C
B
A
ρ A
BC m
=
( )
2 2
C B m
12
1
Ix + =
( )
2 2
A C m
12
1
Iy + =
( )
2 2
B A m
12
1
Iz + =
D
B
A
z
x
y
( )
ρ D - B 4AD =
m
( )






+ + =
2
2
2
D D - B
A
m
6
1
Iz
2
R
1
L
R
2
z
x
y
R
1
: Outer diameter,
R
2
: Inner diameter
Appendix