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# RE: [femm] SRM Inductance plot at constant current

- To: <femm@yahoogroups.com>
- Subject: RE: [femm] SRM Inductance plot at constant current
- From: "Brad Frustaglio" <fuzz@wildrail.net>
- Date: Wed, 7 May 2003 08:05:56 -0500
- Importance: Normal
- In-reply-to: <3EB7C495.8090700@ieee.org>

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@ieee.org] Sent: Tuesday, May 06, 2003 9:20 AM To: femm@yahoogroups.com 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@ieee.org` `www: http://femm.berlios.de/dmeeker` `Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service.`

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