Fuji Electric FRENIC-HVAC User Manual page 113

(3) For a load running horizontally
Assume a carrier table driven by a motor as shown in Figure 3.7. If the table speed is υ (m/s) when the
motor speed is N (r/min), then an equivalent distance from the shaft is equal to 60·υ / (2π·N
M
The moment of inertia of the table and load to the shaft is calculated as follows:
60 υ
•
2
J = ( ) ( W + W )
•
0
2 π
N
•
M
[ 2 ] Calculation of the acceleration time
Figure 3.9 shows a general load model. Assume that a motor drives a load via a reduction-gear with
efficiency η . The time required to accelerate this load in stop state to a speed of N
G
calculated with the following equation:
η
+
2 π (
J J
N
•
1 2
=
G
t
•
ACC η
− 60
τ τ
M L
G
where,
J : Motor shaft moment of inertia (kg·m
1
J : Load shaft moment of inertia converted to motor shaft (kg·m
2
τ : Minimum motor output torque in driving motor (N·m)
M
τ : Maximum load torque converted to motor shaft (N·m)
L
η : Reduction-gear efficiency.
G
As clarified in the above equation, the equivalent moment of inertia becomes (J
considering the reduction-gear efficiency.
Figure 3.9 Load Model Including Reduction-gear
[ 3 ] Calculation of the deceleration time
In a load system shown in Figure 3.9, the time needed to stop the motor rotating at a speed of N
(r/min) is calculated with the following equation:
η
+
J J 2 π 0 (
−
•
•
1 2
= G
t
•
DEC τ τ η
− 60
M L •
G
where,
J : Motor shaft moment of inertia (kg·m
1
J : Load shaft moment of inertia converted to motor shaft (kg·m
2
τ : Minimum motor output torque in braking (or decelerating) motor (N·m)
M
τ : Maximum load torque converted to motor shaft (N·m)
L
η : Reduction-gear efficiency
G
In the above equation, generally output torque τM is negative and load torque τL is positive. So,
deceleration time becomes shorter.
2
( kg m )
•
− ) 0
M ( ) s
2
)
)
N
M
) s (
2
)
3-9
3.1 Selecting Motors and Inverters
(r/min) is
M
2
)
+J
1 2
2
)
) (m).
M
(3.9)
(3.10)
/η ) by
G
M
(3.11)