FujiFilm FRENIC5000G11S Series, Technical Information

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Chapter 4
1. Inverter and Motor Selection
4-7
4
The force of gravity F may become a negative force to
brake both lifting and lowering movements, depending
on the load weight. This is the same as for vertical lifting
and lowering. Required torque around the motor shaft
can be also calculated similarly. That is, when F is
positive, use expression (4.1); when it is negative, use
expression (4.2).
1.3.2 Acceleration and deceleration time calcula-
tion
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:
E = J ( 2
π
· N )
2
2 60
[J] ................................................. (4.9)
To accelerate the above rotation, kinetic energy will be
increased; to decelerate, kinetic energy must be dis-
charged.
The torque required for acceleration and deceleration can
be expressed as follows:
τ
= J · 2
π
( dN )
60 dt
[N·m] ............................................. (4.10)
In this way, the mechanical moment of inertia is an
important element in acceleration and deceleration. First,
calculation method of moment of inertia is described, then
that for acceleration and deceleration time are explained.
1. Calculation of moment of inertia
For an object that rotates around the rotation axis,
vertually divide the object into small segments and
square the distance from the rotation axis to each
segment. Then, sum the squares of the distances and
the masses of the segments to calculate the moment of
inertia.
Moment of inertia J =
∑
(Wi · ri
2
) [kg·m
2
] .................... (4.11)
q q
q q
q
Hollow cylinder and solid cylinder
The common shape of a rotating body is hollow
cylinder. The moment of inertia 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 weight is W [kg] in Fig. 4.10.
J = W · (D 1
2
+ D
2
2
)
8
[kg·m
2
] .............................. (4.12)
For a similar shape, a solid cylinder, calculate the
moment of inertia as D
2
is 0.
D
1
[m]
D
2
[m]
W [kg]
Fig. 4.10 Hollow cylinder