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MITSUBISHI CNC
7 Selection
7-1-4 Expressions for load inertia calculation
The calculation method for a representative load inertia is shown.
Type
Rotary shaft is cylinder center
Cylinder
When rotary shaft and cylinder
shaft are deviated
Rotary shaft
Column
Rotary shaft
Object that moves
linearly
Servo
motor
Suspended object
J
Servo
Converted load
motor
7 - 12
Mechanism
D
1.
D
2.
Rotary shaft
R
D
R
b
a
b
a
N
V
W
D
W
Load B
N
J
J
3
B
31
21
J
22
N
2
Load A
N
1
J
A
N
1
J
11
Calculation expression
4
4
. (D
. (D
J
=
-D
) =
L
1
2
2
T
:Load inertia(kg•cm
)
L
ρ: Density of cylinder material(kg/cm
L:Length of cylinder(cm)
D
:Outer diameter of cylinder(cm)
1
D
:Inner diameter of cylinder(cm)
2
W:Mass of cylinder(kg)
<Reference data(Material densities)>
-3
3
Iron:7.80×10
(kg/cm
)
Aluminum:2.70×10
-3
3
Copper:8.96×10
(kg/cm
)
W
2
2
. (D
J
=
+8R
)
L
8
2
J
:Load inertia(kg•cm
)
L
W:Mass of cylinder(kg)
D:Outer diameter of cylinder(cm)
R:Distance between rotary axis and cylinder axis(cm)
2
2
a
+b
2
J
= W(
+R
)
L
2
J
: Load inertia(kg•cm
)
L
W:Mass of cylinder(kg)
a,b,R:Left diagram(cm)
ΔS
1
V
2
2
.
J
= W(
)
= W(
)
L
20π
2πN
10
2
J
:Load inertia(kg•cm
)
L
W:Mass of object that moves linearly(kg)
N:Motor speed(r/min)
V:Speed of object that moves linearly(mm/min)
ΔS:Object movement amount per motor rotation(mm)
D
2
J
= W(
)
+J
L
p
2
2
J
:Load inertia(kg•cm
)
L
W:Object mass(kg)
D:Diameter of pulley(cm)
2
Jp:Inertia of pulley(kg•cm
)
N
2
2
.
J
= J
+(J
+J
+J
)
(
)
+
(J +J
L
11
21
22
A
N
1
2
J
:Load inertia(kg•cm
)
L
2
J
,J
:Inertia of load A, B(kg•cm
A
B
2
J
~J
:Inertia(kg•cm
)
11
31
N
~N
:Each shaft's speed(r/min)
1
3
2
2
D
)
1
2
＋
3
)
-3
3
(kg/cm
)
N
2
3
.
)
(
)
B
N
1
)
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