Dynamic Braking Resistor Selection
D-1
Installation Manual for Models ODM-005, ODM-005i, ODM-010, ODM-010i, ODM-020 and ODM-020i
A
PPENDIX
D:
Dynamic Braking Resistor Selection
This appendix provides equations to assist in sizing resistors for dynamic braking.
Introduction
A properly sized resistive load may be required to dynamically brake the system by dissipating the energy
stored in a motor. The section “Emergency Stop Wiring” on page 7-4 depicts the necessary circuitry.
Winding inductance is ignored in this analysis, which allows the load on the motor winding to be con-
sidered as purely resistive when dynamic braking occurs. This simplifies the evaluation to a scalar analysis,
instead of a vector analysis. For simplicity, friction, damping and load torque also are ignored in the
equations.
Dynamic Braking Equations
Equations for the magnitutde of instanteous velocity, and per phase current, energy and power are derived
by solving the differential equation governing the motor velocity. The equations are shown below.
For this type of response, 98% of the energy will be dissipated in 4 time constants. Therefore the average
power for each dynamic braking event can be calculated as:
T
ABLE
D.1
Dynamic Braking Resistor Parameters
Parameter
Description
Parameter
Description
i(t)
Phase Current
R
L
Line-Neutral Dynamic Braking Resistance
E(t)
Per Phase Energy
K
E
Peak Line-to-Line Back EMF
J
m
Motor Inertia
K
T
Peak Line-to-Line Torque Constant
J
L
Load Inertia
ω
o
Initial Angular Velocity
P(t)
Per Phase Power
w
Angular Velocity
R
Motor Line-to-Line Resistance
t
Time
ω
t
( )
ω
o
e
t
–
τ
⁄
=
1
( )
where
τ
0.866
R
2
R
L
+
(
)
J
M
J
L
+
(
)
K
E
K
T
------------------------------------------------
=
i t
( )
K
E
ω
o
e
t
–
τ
⁄
0.866
R
2
R
L
+
(
)
--------------------------------------
=
E t
( )
1
2
---
J
L
J
M
+
(
)ω
2
o
e
2
t
–
τ
⁄
=
P t
( )
J
L
J
M
+
(
)ω
o
2
2
τ
------------------------------
e
2
–
t
τ
⁄
1.154
K
E
K
T
ω
2
o
R
2
R
L
+
(
)
------------------------
e
2
t
–
τ
⁄
=
=
2
( )
D
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