I corrected my current value and I am
getting the results I expected. The analysis I ran assumes constant current
throughout the stroke angle. I am using this analysis as a first iteration
design check to get an idea for the magnitude of current I need to produce a
certain amount of torque. Here comes the hard part (I think).
I am attempting to simulate the best Ican,
a high speed case. The rotor will be commutated at 75,000 rpm. I do realizethe
torque profile will take on a different shape at this speed. The current needs
a finite time to build in the coil. I was wondering what is
the best way to perform a pseudo time stepping integration.
The inductance is a function of rotor
position and coil current. This becomes an interesting differential equation to
solve in my opinion. I was thinking of stepping the rotor in small finite
angles in FEEM. Each time adjusting the current in the blocks
to better simulate the “real world” case. Would it be
sufficient to just re compute the current value at each rotor position withsimple
current rise time formulas, inserting the appropriate incremental inductance value
each time? The conduction angle happens very fast when the rotor is spinning at
75,000. We are talking micro seconds in this case.
I realize I may be trying to do something
that may not be done easily in FEMM.
Many thanks,
Brad
-----Original Message-----
From: David Meeker
[mailto:dmeeker@xxxxxxxx]
Sent: Tuesday, May 06, 2003 9:20 AM
To: femm@xxxxxxxxxxxxxxx
Subject: Re: [femm] SRM Inductance
plot at constant current
Brad Frustaglio wrote:
> Hi All,
>
>
>
> I have been using FEMM for a few years now.
Many thanks to Dave,
> excellent program.
>
>
>
> I have question on evaluating the A-J
integral and then calculating
> the self inductance from the result.
>
>
>
> I am modeling a 4 phase SRM with 8 stator
poles and 6 rotor poles. I
> am attempting to extract the torque profile
and inductance profile
> with one phase excited at constant current as
the rotor moves through
> one stroke. The torque magnitude and shape
looks reasonable. However I
> am having trouble understanding how to
calculate the inductance
> correctly. The profile shape looks as
expected I am just concerned on
> the magnitude of inductance. My method is:
>
>
>
> 1. Highlight the blocks
with the current flowing ( In my case there
> are2
current blocks per pole (one on each side of the stator
> pole) for
a total of 4 current blocks per phase.
> 2. Evaluate the A-J
integral at each respective rotor position
> 3. The self inductance as
defined is int(A-J)dV /i^2) where i is
> thecoil
current
>
>
>
> I think I am running into trouble on the coil
current term. What is
> the correct coil current to use to evaluate
the inductance correctly?
>
>
>
> The value of one current block or the sum of
all current blocks. Also
> this is actually amp-turns. Not the actual
current flowing in the wire
> itself. Right?
>
>
>
> For instance: the current in one block in the
model is defined as
> 11.15 MA/m^2. The coil area is 2.6903 x10^-5
m^2. So the magnitude of
> current in the coil block is 300 A-T. Is this
the current I use for
> the evaluation of self inductance usingthe
A-J integral?
>
>
>
> Regards,
>
>
>
> Brad Frustaglio
>
The /i/ in the equation actually /is /the actual
current flowing in the
wire itself. Like in your example, saythat
your coil is made of 60
turns of wire. Since you have 300 Amp*Turns,
the current in the wire
would be 5 Amps. The 5 Amps is then the value
that you'd use as /i/ in
the equation. There's also an example that
might be relevant to you at
http://femm.berlios.de/induct1/induct1.htm
One last thought--switched reluctance motorsare typically
run in a
highly saturated condition. The quantity
that you are computing with
the A.J integral is (flux linkage/current), but it
doesn't have the same
relationship to stored energy as inductance in a
linear problem.
Furthermore, this "nonlinear inductance"
appears in a subtly different
way in any electric circuit equations that you
might write. For example,
the electric circuit equation that applies to your
case is:
D(flux linkage)/Dt + R i = v
where the Dt is meant to represent the /total/
derivative with respect
to time. If inductance, L, is not a
function of current, this
simplifies to the usual:
L di/dt + R i = v
However, if L is a function of i, we'd get:
(L(i) + i*dL/di)*di/dt + R i = v
Dave.
--
David Meeker
email: dmeeker@xxxxxxxx
www: http://femm.berlios.de/dmeeker
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