Sizing A Braking Resistor - Control Techniques Commander SE Advanced User's Manual

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 ω²
Where:
ω = angular velocity in radians s
×
2π n
ω ---------------- -
=
60
Where: n = motor speed in RPM
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
Braking cycle
Time required to decelerate to stop t
Motor size
Drive size
Motor nominal torque
Motor rated speed
Braking transistor operating voltage V
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.
× α
M = J
Where:
α = angular acceleration (rad / s²)
J = moment of inertia (kg m²)
α
=
ω
×
----
= J
t
b
Where:
ω = angular velocity (rad / s)
t
b
ω
n = motor speed RPM
× π ×
J
----------------------
=
×
30 t
× π ×
2
------------------------------- -
=
×
30
2 π × ×
------------------------------- -
39 =
×
30
× π ×
2
t = ------------------------------- -
b
×
30
t = 7.8 sec
b
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.
Commander SE Advanced User Guide
Issue Number: 4
-1
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.
J 2kg m²
10 seconds in every 60 seconds
10 seconds
b
4kW
4kW
26Nm
n 1450RPM
780VDC
ω
----
t
b
= minimum deceleration time (s)
× π ×
2 n
----------------------
=
60
n
b
1450
t
b
1450
t
b
1450
39
onds
133