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11.SELECTION
11-7 Load inertia moment equations
Typical load inertia moment equations are indicated below:
Load Inertia Moment Equations
Type
Mechanism
Axis of rotation is on the cylinder
center
Cylinder
Axis of rotation
Axis of rotation is off the cylinder
center
Axis of rotation
R
a
Square
block
Axis of rotation
Servo motor
Object which
moves linearly
N
D
Object that is
hung with
pulley
W
J
B
N
3
J
Converted
21
load
J
22
N
1
J
11
J
=
LO
ρ
: Cylinder material density [kg/cm
øD
1
L
: Cylinder length [cm]
øD
2
D
: Cylinder outside diameter [cm]
1
D
: Cylinder inside diameter [cm]
2
W : Cylinder weight [kg]
Reference data: material density
Iron
Aluminum : 2.7
Copper
R
W
J
=
LO
8
D
J
=
LO
W •
b
a
b
W
a, b, R : Left diagram [cm]
W •
J
=
L
V
V
: Speed of object moving linearly [mm/min]
∆S : Moving distance of object moving linearly per servo
W
motor revolution [mm/rev]
W : Object weight [kg]
J
=
W •
L
J
: Pulley inertia moment [kg • cm
P
Servo motor
D : Pulley diameter [cm]
W : Object weight [kg]
J
31
=
=
J
J
L
11
J
, J
A
B
N
Load A
2
J
to J
11
J
A
N
to N
1
11– 9
Equation
π • ρ • L
4
4
• (D - D )
=
1
2
32
-3
: 7.8
x 10
[kg/cm
-3
x 10
[kg/cm
-3
: 8.96 x 10
[kg/cm
2
2
............................................
+
• (D
8R )
2
2
a
+ b
.........................................
2
+ R
3
: Square block weight [kg]
V
1
=
W •
•
600 • ω
2 • π • N
2
D
...................................................
+ J
P
2
2
N
2
+
+
•
+
+
(J
J
J
)
(J
21
22
A
31
N
1
: Inertia moments of loads A, B [kg • cm
: Inertia moments [kg • cm
31
: Speed of each shaft [r/min]
3
W
2
2
......
(11-22)
• (D + D )
1
2
8
3
]
3
]
3
]
3
]
(11-23)
(11-24)
∆S
2
2
V
=
W •
20 • π
10
........................(11-25)
(11-26)
]
2
2
N
3
•
J
)
.................
(11-27)
B
N
1
2
]
2
]
11
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