B-65302EN/01 SPECIFICATIONS FOR THE βiS SERIES 3.SELECTING A MOTOR
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Inertia of a heavy object moving along a straight line (table, workpiece, etc.)
SI unit
][
2
2
2
mkg
l
W
w
J ⋅×=
÷
ø
ö
ç
è
æ
π
W : Weight of the object moving along a straight line [kg]
l : Traveling distance along a straight line per revolution of the
motor [m]
Gravitational system of units
][
2980
2
2
scmkgf
lW
w
J ⋅⋅×=
÷
ø
ö
ç
è
æ
π
W : Weight of the object moving along a straight line [kgf]
l : Traveling distance along a straight line per revolution of the
motor [cm]
Example)
When W is 300 [kg] and l is 20 [mm], J
w
of a table and
workpiece is calculated as follows:
J
w
=300×(0.020÷2÷π)
2
=0.00304 [kg⋅m
2
] = 0.0310 [kgf⋅cm⋅s
2
]
Inertia of an object whose speed is increased above or decreased below the
speed of the motor shaft
The inertia applied to the motor shaft by inertia J
0
is calculated as
follows:
0
2
0
2
1
2
1
J
Z
orJ
Z
Z
J ××=
÷
ø
ö
ç
è
æ
÷
÷
ø
ö
ç
ç
è
æ
J
0
: Inertia before the speed is changed
Z
1
,Z
2
: Number of teeth when the gear connection
1/Z : Deceleration ratio