Omron R6Y Series, Руководство пользователя

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3-30
CHAPTER 3 Installation
5) When the object's center line is offset from the rotation center.
The equation for the moment of inertia, when the center of the cylinder is
offset by the distance "x" from the rotation center as shown in Fig. 3-83, is
given as follows.
D
h
J=
ρπ
D h
32g
WD
8g
=
4
2
... (Eq. 3.5)
x
+
ρπ
D hx
4g
2
+ Wx
g
2
Center line
Rotation center
2
I=
ρπ
D h
32
4
+
ρπ
D hx
4
2 2
mD
8
=
2
mx 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. 3-32
In the same manner, the moment of inertia of a cylinder as shown in Fig.
3-84 is given by
W
4g
=
... (Eq. 3.6)
D
4
h
3
(
2 2
+
)
h
D
x
Cneter line
J=
ρπ
D h
16g
+
2
D
4
h
3
(
2 2
+ )
ρπ
D h x
4g
2 2
+ Wx
g
2
I=
ρπ
D h
16
+
2
D
4
h
3
(
2 2
+ )
ρπ
D h x
4
2 2
m
4
=
D
4
h
3
(
2 2
+ ) + mx 2
(kgf · cm · sec
2
)
(kgm 2 )
Fig. 3-33
In the same manner, the moment of inertia of a prism as shown in Fig. 3-85
is given by
J=
ρ
abc(a + b )
12g
W(a + b )
12g
=
2
2
... (Eq. 3.7)
2
2
+
ρ
abcx
g
Wx
g
+
2
2
a
c
b
x
Center line
I=
ρ
abc(a + b )
12
2 2
+
ρ
abcx 2 = m(a +b )
12
2 2
+ mx 2
m : Mass of prism (kg)
W : Weight of prism (kgf)
(kgf · cm · sec
2
)
(kgm
2
)
Fig. 3-34