Omron R6Y Series - Page 69

3-29
CHAPTER 3 Installation
3) Moment of inertia for cylinder (part 2)
The equation for the moment of inertia for a cylinder that has a rotation
center such as shown in Fig. 3-81 is given below.
h
D
2
h
J=
ρπ D h
16g
W
4g
=
2
... (Eq. 3.3)
D
4
h
3
(
2 2
+
)
D
4
h
3
(
2 2
+
)
I=
ρπ D h
16
m
4
=
2
D
4
h
3
(
2 2
+
)
D
4
h
3
(
2 2
+
)
ρ : Density (kg/m
3
, kg/cm
3
)
g : Gravitational acceleration (cm/sec
2
)
m : Mass of cylinder (kg)
W : Weight of cylinder (kgf)
(kgf · cm · sec
2
)
(kgm
2
)
Fig. 3-30
4) Moment of inertia for prism
The equation for the moment of inertia for a prism that has a rotation center
as shown in Fig. 3-82 is given as follows.
J=
ρ abc(a +b )
12g
W(a +b )
12g
=
2
2
... (Eq. 3.4)
a
c
b
1/2a
2
2
I=
ρ abc(a +b )
12
m(a +b )
12
=
2
2
2
2
(kgf · cm · sec
2
)
(kgm
2
)
ρ : Density (kg/m
3
, kg/cm
3
)
g : Gravitational acceleration (cm/sec
2
)
m : Mass of prism (kg)
W : Weight of prism (kgf)
Fig. 3-31