Fuji Electric FRENIC-Ace series - Acceleration and Deceleration Time Calculation; 1 ] Calculation of Moment of Inertia

10.3 Equations for Selections
10-8
10.3.2 Acceleration and deceleration time calculation
When an object whose moment of inertia is J (kg·m
2
) rotates at the speed N (r/min), it has the following kinetic
energy:
)J(
)
60
N2
(
2
J
E
2
•π
=
•
(Equation 10.3-9)
To accelerate the above rotational object, the kinetic energy will be increased; to decelerate the object, the kinetic
energy must be discharged. The torque required for acceleration and deceleration can be expressed as follows:
)mN()
dt
dN
(
60
2
J
••
π
=τ
(Equation 10.3-10)
This way, the mechanical moment of inertia is an important element in the acceleration and deceleration. First,
calculation method of moment of inertia is described, after the calculation methods for the acceleration and
deceleration times are explained.
[ 1 ] Calculation of moment of inertia
For an object that rotates around the shaft, virtually divide the object into small segments and square the distance
from the shaft to each segment. Then, sum the squares of the distances and the masses of the segments to
calculate the moment of inertia.
)mkg()
r
W(J
2
2
i
i
••
=
∑
(Equation 10.3-11
)
The following describes equations to calculate moment of inertia having different shaped loads or load systems.
(1) Hollow cylinder and solid cylinder
The common shape of a rotating body is hollow cylinder. The moment of inertia J (kg⋅m
2
) around the hollow cylinder
center axis can be calculated as follows, where the outer and inner diameters are D
1
and D
2
[m] and total mass is
W [kg] in Figure 10.3-4.
)mkg(
8
)
DD
(W
J
2
2
2
2
1
•
•
+
=
(Equation 10.3-12)
For a similar shape, a solid cylinder, calculate the moment of inertia as D
2
is 0.
Figure 10.3-4 Hollow Cylinder