10.3 Equations for Selections
10-11
SELECTING OPTIMAL MOTOR AND INVERTER CAPACITIES
[ 3 ] Calculation of the deceleration time
In a load system shown in Fig. 10.3-5, the time needed to stop the motor rotating at a speed of N
M
(r/min) is
calculated with the following equation (Equation 10.3-16):
where,
J
1
: Motor shaft moment of inertia (kg·m
2
)
J
2
: Load shaft moment of inertia converted to motor shaft (kg·m
2
)
M
: Minimum motor output torque in braking (or decelerating) motor (N·m)
L
: Maximum load torque converted to motor shaft (N·m)
G
: Reduction-gear efficiency
In the above equation, generally output torque
M
is negative and load torque
L
is positive. So, deceleration time
becomes shorter.
For lift applications, calculate the deceleration time using the negative value of
L
(maximum load torque
converted to motor shaft).
[ 4 ] Calculating non-linear acceleration/deceleration time
In applications requiring frequent acceleration/deceleration, the inverter can accelerate/decelerate the motor in
the shortest time utilizing the maximum torque capability. The inverter in vector control mode can easily perform
this type of operation.
Fig. 10.3-6 Example of driving characteristics with a constant output range
In this case, the acceleration/deceleration vs. speed curve will form a non-linear figure, and the acceleration /
deceleration time cannot be calculated by a single expression. Generally, the acceleration/deceleration time is
obtained by calculating the acceleration/deceleration time of N that is a difference of speed N broken into small
parts, and then integrating it to obtain the total acceleration/deceleration time from start to end. Because the
smaller N provides higher accuracy, this numerical calculation needs an aid of a computer program.
The following is a guide for the numerical calculation method using a computer program. Fig. 10.3-6 illustrates an
example of driving characteristics with a constant output range. In the figure, the range under N
0
is of constant
torque characteristics, and the range between N
0
and N
1
is of a constant output with the non-linear
acceleration/deceleration characteristics.
The expression (Equation 10.3-17) gives an acceleration time Δt
ACC
within a ΔN speed increment.
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