Servo braking resistor in series with motor armature

Your opinions please. The following was posted on the UHU servo amp
board discussing the need for braking resistors on certain motors to
protect the drives in case of hard deceleration and crashes.

I'm not an EE so I'm not in a position to say if any of this makes
sense or not. My inclination is toward disbelief although I recall a
lot of discussion about this with Rutex.

Roger

++++++++++++++++++++++++++++++++++++++++++++++++++
... regarding the if, when, why and how to use an extra resistor
(sometimes called a braking resistor) in series with the motor
armature in order to limit the high currents that apparently can occur
during hard deceleration, E-stop condition or a crash.

The issue is discussed in the Mystique2.pdf document published by
Rutex regarding their drives. According to Kreutz the same issues
applies to the HP-UHU and this is something that future users needs to
be aware of.

Despite Kreutz's (thank you Kretuz) endless attempts trying to explain
exactly how and why this is a problem I can't say I understand it
fully but if he says it needs to be considered then I'm positive
that's true. So I will just try my best to show you what I've grasped
from the discussion with Kreutz and if anyone sees anything wrong I
appreciate if you jump in.

Here we go…..

To determine if you need a series resistor you need to know the motors
armature resistance, the voltage constant of the motor, the max speed
you intend to use and the power supply voltage. Here, I will use my
motors as an example:

Motor voltage constant: 0.47Vs/Rad
Armature resistance: 0.24ohm
Max speed: 2000rpm
Max cont. current: 19A

So my motors max speed is 2000 rpm and I definitely want to be able to
use that. The back EMF (BEMF) at that speed is calculated as 2 * Pi *
VoltConst * MaxRPM / 60 which in my case is 2 * Pi * 0.47 * 2000 / 60
= 98.5V. The continuous current rating of the motor is 19A and the
armature resistance is 0.24ohm so utilizing full cont. torque will
result in a voltage drop across the armature resistance of 4.6V. On
top of that the max PWM duty-cycle of the UHU chip is 87% so in order
for me to actually GET 2000rpm from the motor (at full torque) my
power supply would need to be at least around 120V. 120V * 0.87 – 4.6
= 99.8V that's close enough.


[Sidenote]
Kreutz says that Power Supply Voltage * 0.87 + BEMF should be kept
below 200, I haven't understood exactly why since that will render the
HP-UHU unable to fully utilize a motor with a voltage rating above
100V, or wouldn't it?
[/Sidenote]


What determines the need of a series resistor is the current rating of
the diode inside each MOSFET. (The Rutex document says to calculate
with the continuous rating of the diode but Kretuz says that the
pulsed rating will be fine). The HP-UHU apparently uses the IRFP264N
and its diode's pulsed rating is 170A. A safety margin of 20% should
be used so the number to use for our calculation is 136A.

Now, the total resistance, as "seen" by the drive, should be at least
BEMF + 0.87 * PowerSupplyVoltage / 136 or in my case 98.5 + 0.87 * 120
/ 136 = 1.5ohm. The motor armature itself is 0.24ohm and let's say the
wiring is another 0.26ohm. Then I'd need a 1ohm resistor in series
with the motor. 1ohm may not seem much but considering I want to (be
able to) pull 19A thru it, it will have to be a pretty a big one since
it will produce 360W of heat. On top of that I will loose a bit "on
the corner" of the speed/torque curve as described in the
Mystique2.pdf document.


This is getting very long now but let's take another quick example.
HomeShopCNC sells a pretty nice Servo motor. The specs on the site are
a bit "messed up" but I believe this should be right:

Terminal Voltage: 72V
Max Cont Current: 8.2A
Voltage constant: 15.71V/1000rpm
Armature resistance: 0.85ohm
Max Speed: 4200rpm.

Here, the manufacturer already provides us with the terminal voltage
so we don't need to calculate it. ( I did anyway and got 73V, that's
close enough). Since the max PWM dutycycle is 87% we need a power
supply voltage of around 85V.

The total resistance should then be 85 * 0.87 + 72 / 136 = 1.07ohm.
The datasheet says that the armature resistance is 0.85ohm and on top
of that we have the wiring, connectors etc so we would probably be
fine without any extra resistor. But this "smallish" motor seems to be
the limit of what can be driven without any form of extra protection.

As I said at the beginning: I don't fully understand how the
regenerative current can be so large so that it destroys the diodes in
the MOSFETS but the expertise says that is a fact. So my only hope now
is that someone jumps in and tells me my understanding of the issue is
all wrong.