Re: [FEMM] [Founded some different value of Back EMF]

[David Meeker <dmeeker@xxxxxxxxxxxxxxxxx>]

??? wrote:

> Hi, everyone.
> In my calculation results of Back EMF in slotless motor, I found some 
> difference of the value in two method. I'd like to know about the reason.
> So, I specified this in my attached files. It is pdf fie. Anyone help 
> me please?
> Best Regards,
> Kang

From the attached file:

> To verify the some result like Back EMF of slotless BLDC motor, I 
> perform the Back EMF calculation using two methods.
>
> Fisrt one is classic Faradays law. This formula is e=B*l*v*N.
> (B : Magnetic Flux Density [T], l : stack length [m], v : line 
> velocity of rotor [m/s], N : total conductor number)
>
> Second one is using magnetic vector potential and lua script. Basic 
> formula is like followings.
> e = -N*d(flux)/dt = -N*d(flux)/d(theta)*d(theta)/dt
> (N : total conductor number, : magnetic flux [Wb])

Faraday's law really just says that terminal voltage is the change in 
flux linkage with respect to time. Your first equation, e=B*l*v*N, isn't 
a general statement of Faraday's law, but rather the version that would 
apply in a very specific case. For example, your equation would apply if 
you had the ideal situation in which an N-turn coil was partially inside 
a thin gap with a uniform flux density B and it was moving 
translationally outside the gap (where the flux density was zero) at a 
speed v. Since this isn't really like your motor, the equation doesn't 
really apply very well.

For your problem, the field of the magnet is nearly perfectly 
sinusoidally distributed with this geometry, so the flux linkage (and 
therefore the voltage) varies sinusoidally. In this case, the amplitude 
of the induced voltage is:
V=omega*P
where P is the amplitude of the flux linkage in the position that you 
had drawn, and omega is the speed that the rotor spins at in radians per 
second.

You drew the motor incorrectly, so that the flux linkage is 
overpredicted. If you use the "series circuit" feature of the new 4.0 
version, you don't have to do any extra work to get the flux linkage, 
because it gets computed automatically, as long as you set up the 
geometry right--just push the "inductor" button on the postprocessor 
toolbar. I've assumed 48 turns/pole/phase, which appears to be what you 
have done.

In your case, 1000 RPM => omega = 100*Pi/3 rad/s
and the amplitude of the flux linkage P = 0.152796 Webers
so that the amplitude of the induced voltage is omega*P = 16.0 Volts.

--
David Meeker
Senior Engineer
Foster-Miller, Inc.
350 Second Avenue
Waltham, MA 02451-1196
781-684-4070
781-890-3489 (fax)
dmeeker@xxxxxxxxxxxxxxxxx 
http://femm.foster-miller.com

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