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APPENDIX
App. 5.7 Load moment of inertia equations
Typical load moment of inertia equations is indicated below.
Type
Axis of rotation is on the cylinder
center
Axis of rotation
Cylinder
Axis of rotation is on the cylinder
center
Axis of rotation D
Square block
Axis of rotation
Servo motor
Object which
moves linearly
Object that is
hung with pulley
W
N
3
J
Converted
21
load
Mechanism
D
1
D
2
R
R
b
a
b
a
V
W
N
D
Servo motor
Load B
J
J
B
31
N
Load A
J
2
22
J
A
N
1
J
11
• L
W
4
4
• (D
- D
)
J
=
=
1
2
L0
32
8
ρ: Cylinder material density [kg/cm
L: Cylinder length [cm]
D
: Cylinder outside diameter [cm]
1
D
: Cylinder inside diameter [cm]
2
W: Cylinder mass [kg]
Reference data: material density
Iron: 7.8 • 10
[kg/cm
]
-3
3
Aluminum: 2.7 • 10
[kg/cm
-3
Copper: 8.96 • 10
[kg/cm
-3
W
J
=
• (D
+ 8R
) ·································································· (5.23)
2
2
L0
8
a
2
+ b
2
J
= W •
····························································· (5.24)
2
+ R
L0
3
W: Square block mass [kg]
a, b, R: Left diagram [cm]
2
V
J
= W •
= W •
L
600 •
2 •
V: Speed of object which moves linearly [mm/min]
∆S: Travel distance of object moving linearly per servo motor revolution
[mm/rev]
W: Square block mass [kg]
2
D
J
= W •
+ J
····································································· (5.26)
L
P
2
J
: Pulley moment of inertia [× 10
P
D: Pulley diameter [cm]
W: Square block mass [kg]
N
2
J
= J
+ (J
+ J
+ J
) •
L
11
21
22
A
N
1
J
, J
: Moment of inertia of load A, B [× 10
A
B
J
to J
: Moment of inertia [× 10
11
31
N
to N
: Speed of each shaft [r/min]
1
3
App. - 21
Equation
2
2
• (D
+ D
)
······································ (5.22)
1
2
3
]
]
3
]
3
2
2
1
V
S
•
= W •
• N
10
20 •
kg•m
]
-4
2
2
2
N
3
+ (J
+ J
) •
························ (5.27)
31
B
N
1
-4
kg•m
2
]
kg•m
]
-4
2
··········· (5.25)
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