Rockwell Automation 1398-DDM-xxx USE MNL/ULTRA 200 DIG.SERVO.DR - Manual (Page 287)

Publication 1398-5.0 – October 1998
Appendix F
Dynamic Braking Resistor Selection
Appendix F
This appendix provides equations to assist in sizing resistors for
dynamic braking.
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 7-6 depicts the necessary circuitry.
Winding inductance is ignored in this analysis, which allows the load
on the motor winding to be considered 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.
Table F.1: Dynamic Braking Resistor Parameters
Parameter Description Parameter Description
i(t) Phase Current R
L
Line-Neutral Dynamic Braking Resis-
tance
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 Resis-
tance t Time
Intro
ω
t
( ) ω
o
e
t –
τ ⁄
=
1
( )
where
τ
0.866
R 2R
L
+
( )
J
M
J
L
+
( )
K
E
K
T
------------------------------------------------- =
i t
( )
K
E
ω
o
e
t – τ ⁄
0.866 R 2R
L
+
( )
--------------------------------------- =
E t
( ) 1
2
--- J
L
J
M
+
( )ω 2
o e
2t –
τ ⁄
=