Commander SE Advanced User Guide
133
Issue Number: 4
5.1 Sizing a braking resistor
The size and rating of the resistor are calculated with respect to the energy to be absorbed, the rate at which the power is
delivered and the time between successive decelerations.
Kinetic energy of the motor and the driven machine = 0.5 J
ω
²
Where:
ω
= angular velocity in radians s
-1
Where: n = motor speed in RPM
J = total moment of inertia (kg m²) of the motor and driven machine. If there is gearing between the motor
and the machine, J is the value reflected at the motor shaft.
As energy is proportional to the square of the angular velocity, most of the energy is concentrated at the higher operating
speeds. If the motor is operated above base speed, the power delivered to the resistor is constant until the speed falls below
base speed.
Example
The information required to calculate the size of the braking resistor is as below:
Inertia
J
2kg m²
Braking cycle
10 seconds in every 60 seconds
Time required to decelerate to stop t
b
10 seconds
Motor size
4kW
Drive size
4kW
Motor nominal torque
26Nm
Motor rated speed
n
1450RPM
Braking transistor operating voltage V 780VDC
The first stage is to determine the maximum braking torque (M) available.
M
= 150% x nominal motor torque
= 1.5 x 26
= 39Nm
Now calculate the minimum deceleration time possible to ensure that the time required is within specification.
Where:
α
= angular acceleration (rad / s²)
J
= moment of inertia (kg m²)
Where:
ω
= angular velocity (rad / s)
t
b
= minimum deceleration time (s)
n = motor speed RPM
The minimum time for deceleration is 7.8 seconds. The required deceleration time is 10 seconds and is therefore within the
specification for the drive.
ω
2
π
n
×
60
-----------------
=
M
J
α
×
=
α
ω
t
b
----
=
J
ω
t
b
----
×
=
ω
2
π
×
n
×
60
----------------------
=
J
π
×
n
×
30 t
b
×
----------------------
=
2
π
×
1450
×
30 t
b
×
--------------------------------
=
39
2
π
×
1450
×
30 t
b
×
--------------------------------
=
t
b
2
π
×
1450
×
30 39
×
--------------------------------
=
t
b
7.8
onds
sec
=
Содержание COMMANDER SE
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Страница 142: ...142 Commander SE Advanced User Guide Issue Number 4 Figure 6 9 Input line reactor 4400 0241 All dimensions in mm...
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