
15.2 Basic Inverter Drive mechanics
1
5
-7
15.2.3 Inertial Moment and GD
2
Inertial moment is a measure of the ease of the rotation operation of the rotator. Taking the total mass
m
(kg) of the rotator, and the rotation radius
r
(m), the inertial moment
J
can be expressed using the following
formula.
J
=
mr
2
(kg
⋅
m
2
)
The relationship to the flywheel effect
GD
2
that has been used until now can be expressed using the follow-
ing formula.
J
=
GD
2
4
(kg
⋅
m
2
)
The various inertial moment shapes are summarized below. Friction and other losses, however, have not
been considered, and the efficiency is taken to be 1.
J
Cylindrical Inertial Moment
Inertial moment
J
1
during rotation along an axis centered on the mass
m
1
(kg) and radius
r
1
(m) of a cylinder
can be expressed using the following formula.
J
1
=
m
1
r
1
2
2
(kg
⋅
m
2
)
r
1
(m)
L
(m)
Mass
m
1
(kg)
Fig 1
5
.
10
Cylindrical Inertial Moment
J
Tubular Inertial Moment
Inertial moment
J
2
during rotation along an axis centered on the mass
m
2
(kg), outer radius
r
1
(m), and inner
radius
r
2
(m) of a cylinder can be expressed using the following formula.
J
2
=
m
2
(
r
1
2
+
r
2
2
)
2
(kg
⋅
m
2
)
r
1
(m)
r
2
(m)
L
(m)
Mass
m
2
(kg)
Fig 1
5
.
11
Tubular Inertial Moment
J
Load Reel Inertial Moment
Inertial moment
J
3
of a load reel, as shown in Fig. 15.12, concentrates the entire load on the contact point
between a rope and pulley, and can be expressed using the following formula.
J
3
=
m
3
r
1
2
(kg
⋅
m
2
)
Rope
Pulley
r
1
(m)
m
3
(kg)
Fig 1
5
.
12
Load Reel Inertial Moment
15