
B-65262EN/03 SPECIFICATIONS FOR THE αiS/αi SERIES 3.SELECTING A MOTOR
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3.2.3 Calculating the load inertia
Unlike the load torque, an accurate load inertia can be obtained just
by calculation.
The inertia of all objects moved by the revolution of a driving motor
forms the load inertia of the motor. It does not matter whether the
object is rotated or moved along a straight line. Calculate the inertia
values of individual moving objects separately, then add the values
together, according to a rule, to obtain the load inertia. The inertia of
almost all objects can be calculated according to the following basic
rules:
Inertia of a cylindrical object (ball screw, gear, coupling, etc.)
Lb
Db
The inertia of a cylindrical object rotating about its central axis is
calculated as follows:
SI unit
][
4
32
2
mkg
b
L
b
D
b
Jb ⋅=
πγ
J
b
: Inertia [kg⋅m
2
]
γ
b
: Weight of the object per unit volume [kg/m
3
]
D
b
: Diameter of the object [m]
L
b
: Length of the object [m]
Gravitational system of units
][
98032
24
scmkgf
b
L
b
D
b
Jb ⋅⋅
×
=
πγ
J
b
: Inertia [kgf⋅cm⋅s
2
]
γ
b
: Weight of the object per unit volume [kg/cm
3
]
D
b
: Diameter of the object [cm]
L
b
: Length of the object [cm]
Example)
When the shaft of a ball screw is made of steel
(γ=7.8×10
3
[kg/m
3
]), inertia Jb of the shaft is calculated as
follows:
When D
b
=0.040[m], L
b
=1[m],
Jb=7.8×10
3
×π÷32×0.040
4
×1=0.00196[kg⋅m
2
] (=0.0200[kgf⋅cm⋅s
2
])
)
8.9
100
1(
22
scmkgfmkg ⋅⋅=⋅