Fuji Electric FRENIC-Ace series, User Manual

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10.3 Equations for Selections
10-13
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LE
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IM
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Chap 1
0
10.3.3 Heat energy calculation of braking resistor
If the inverter brakes the motor, the kinetic energy of mechanical load is converted to electric energy to be
regenerated into the inverter circuit. This regenerative energy is often consumed in so-called braking resistors as
heat. The following explains the braking resistor rating.
[ 1 ] Calculation of regenerative energy
In the inverter operation, one of the regenerative energy sources is the kinetic energy that is generated when an
object with moment of inertia J is rotating.
(1) Kinetic energy of a moving object
When an object with moment of inertia J (kg·m
2
) rotates at a speed N
2
(r/min), its kinetic energy is as follows:
) Ws J (
60
N 2
2
J
E
2
2
) ( =
π
=
•
•
(Equation 10.3-21)
) J (
N
J
4 . 182
1
2
2
• •
≈
(Equation 10.3-21’)
When this object is decelerated to a speed N
1
(r/min), the output energy is as follows:
) J (
60
N 2
60
N 2
2
J
E
2
1
2
2













 π
− 




 π
=
• •
•
(Equation 10.3-22)
) J ( )
N
-
N
J
4 . 182
1
2
1
2
2
(
• •
≈
(Equation 10.3-22’)
The energy regenerated to the inverter as shown in Figure 10.3-5 is calculated from the reduction-gear efficiency
η
G
and motor efficiency η
M
as follows:
( )
( )
) J (
N N J J
4 . 182
1
E 2
1
2
2
M
G
2 1
−
η η
+ ≈
• • • •
(Equation 10.3-23)
(2) Potential energy of a lift
When an object whose mass is W (kg) falls from the height h
2
(m) to the height h
1
(m), the output energy is as
follows:
( )
) Ws (J h h g W F
1 2
= − =
• •
(Equation 10.3-24)
) s / m ( 8065 . 9 g 2 ≈
The energy regenerated to the inverter is calculated from the reduction-gear efficiency η
G
and motor efficiency η
M
as follows:
( )
(J) h h g W F
M G
1 2
η η − =
• • • •
(Equation 10.3-25)