Eddy Current Study

[Kingfish]

Greetings –

I was in a conversation the other night and we landed on the subject of Eddy Currents. Going through the math, it was my understanding that the calculation for determining the diameter of Phase Wire Conductors inside the motor is based upon the Motor Frequency – and NOT the Controller Frequency.

For the sake of discussion I am not concerned with core laminations; this is pure theory dealing with conductors in a rotating magnetic field.

Calculate RPM & Motor Frequency
OD = Diameter of Wheel (inches)
C = Circumference (inches)
C = OD * π
V = Velocity (mph)
FPS = Feet/Sec = (V * 5280 ft/mile)/(60 sec/min* 60 min/hr)
IPS = FPS * 12
RPS = IPS/C
RPM = (IPS/C) * 60
P = Count of Poles
f = (RPS * P) or (RPM/60 * P)

Make sense?
Therefore a 46-pole motor attached to a 26” diameter wheel at 40 mph should have an rpm of 517 with a motor frequency of 396.5 Hz.

Continuing… We can calculate the Skin Effect from the following formula:
δ = 1/(√πfμσ), where
δ = Depth (m) penetration
f = frequency (Hz)
μ = Magnetic Permeability (H/m)
σ = Electrical Conductivity (S/m)

According to the source, f in this case uses erpm:
f = erpm = (RPM/60)*(P/2); for the example above this value equals 198.2 Hz.
I’m a little fuzzy here: Is it because we only care about ½ of the phase? :?

The value of μ varies on the material; Copper and Aluminum are very close together, although not the same. And the value of σ is obviously going to be quite different between these mats.

The end result suggests that the equivalent AWG conductor diameter for Copper can be up to “00”, and “0000” for Aluminum. That’s quite a large conductor, and I am uncertain. :?

Seeking clarity, KF

 

[Hugechainring]

I have to admit I could not entirely follow the math, although I did do some research to better understand what you were talking about.

Is it possible that your calculation for skin effect is based on a single conductor? I believe high count multi-strand conductors are more efficient from that point of view, which would reduce the required conductor size.

You might try looking up a good wire chart and backing out your calculation that way and see if it makes more sense.

 

[johnrobholmes]

The poles/2 is because they are using pole pairs for the equation. Since HZ is measured as one complete cycle from top to bottom (north to south, v+ to v-) and not each swing from neutral you use pole pairs.


Your calculations follow my own findings. On very high speed motors of the 30,000rpm two pole type we find a skin effect only below 17.5g or so. Four pole would be 20ish gauge, 8 pole 23ish, etc..

 

[John in CR]

JRH,
I'm glad my hubbies have only 10 pole pairs, so I'm good to substantial rpm, faster than I'd want to spin a shell that size.

 

[Miles]

this is pure theory dealing with conductors in a rotating magnetic field.

Just waking up but.... I don't see skin effect being that significant when dealing with eddy currents induced in the coils by the switching of the field?

Edit: As it was KF, I assumed a coreless motor.........

 

[Kingfish]

^ Coreless Yes! :wink: <snicker>

Thanks JRH; Pole Pairs make complete sense.

I simply wanted to know the largest conductor – not that I want to have one that big (or could employ one that big in a design). I recall from some automotive direct-drive designs seeing vary large single conductors, plus there’s that recent “who’s doing AF” thread floating around – and you can see from the stator that the conductor is not stranded – but a moderately large single conductor (maybe 12- or 10-AWG).

For my design studies, I wish to use the largest conductor possible for two reasons: low DC resistance, and simplicity (no Litz). This is for an ironless design (<-- Miles), and if I can avoid using expensive conductors – more the better.

Larger conductors do present a problem in fabrication for bending, although I’ve seen some tight turn radii possible in images which completely break convention, possibly 1- to 2-diameters with Copper (likely fully annealed).

That said, Hugechainring – I do prefer stranded wire for conducting current around the frame. With the motor though – this is a special application.

Wound up, KF

 

[Miles]

The skin effect in the phase wires is caused by the interaction between the main AC current and the currents it induces in the wire. Right?

In addition to this (for coreless motors), you have eddy currents induced in the wire by the switching magnetic field. This is why Litz wires are preferred (for coreless)....

OO AWG is over 9mm dia.

 

[Kingfish]

^ Yeah, that’s one large conductor! Can you imagine trying to wind that around a bobbin?
Think of the low resistance!

Seriously though – with AF, I am trending towards going with a solid core conductor for the prototype just to KISS.

Miles, you said it as concisely as I've ever seen it writ 8)

Parroting a long-winded version from a good source:

“Eddy Current loss is caused by electric currents induced within the ferromagnetic material under time-varying excitation. These induced eddy currents circulate within the material dissipating power (i.e. I^2R losses) due to the resistivity of the material.”

...

“In addition to eddy current losses in stator laminations, the presence of a changing magnetic field within the motor windings produces eddy currents. These currents induce a magnetic field in the winding conductors that attempts to cancel the applied magnetic field. When the applied magnetic field is due solely to current in the winding conductors, this phenomenon is called skin effect. On the other hand, if the magnetic field is due solely to a source outside the conductor, this phenomenon is called proximity effect. For motor windings buried in stator slots, both of these phenomena occur simultaneously. Each turn of the winding produces a magnetic field that interacts with it and all the other turns contained in the slot. Eddy currents created in the conductor due to the presence of a changing magnetic field forces current flowing in the conductor to crowd to the outer edges of the conductor. This outward crowding forces the conductor current through a smaller cross-sectional area and thereby increases the resistance of the conductor, which in turn increases the I^2R losses and reduces motor efficiency.”

I think we can safely presume that in a coreless design that eddy currents can originate from two sources: That of the driving current to affect reactive motion upon the rotor, and during regen wherein the magnetics are creating reverse current. I think that for reverse currents - large conductors are not going to be a problem due to the relatively low motor frequency.

However I have yet to read about how PMW currents affect the winds to create eddies. That is the salient question: Is it that Faraday's Law of induction levels change?

Curious and curiouser, KF

 

[Miles]

Lebowski is the one with practical experience of this.... What gauge did he use on his motors and what were the parasitic losses?

 

[johnrobholmes]

The simplicity of winding a single coil is sometimes overshadowed by the ease of forming the coils. There is also the question of how you are terminating them. A 1/4" or larger copper section would be easiest (for me) to silver braze onto a threaded stud for power exiting the motor. Terminating 100 little strands would be a huge pain in the ass. Wouldn't take enough heat for brazing without melting the little guys, and there would be so much insulation to deal with the only sensible choice would be a solder pot. But soldering large sections is really inconsistent in filler flow with many conductors.

 

[Kingfish]

Yeah - coil formation will be a challenge stranded or not; I was going to create a jig for that, plus solid core would hold its' shape after forming. And Termination is a good point as well: My plan is to swage the ends onto a gold-plated terminating lug of sorts.

Lebowski discusses his triple stator design here; his wire diameter is much smaller:
Re: axial flux motor question !!

Still looking for his build thread...

~KF

 

[Miles]

Lebowski discusses his triple stator design here; his wire diameter is much smaller:
Re: axial flux motor question !!

Thanks KF. Should have remembered that....

 

[LockH]

ES Search found 603 matches: +eddy +current

That guy Eddy a current topic re braking.
"If we are really serious about electric propulsion, the eddy-current braking would do the job very well."

(Discussion re airless tire-and-wheel combo
http://backfires.caranddriver.com/forums/53/posts/332875-455495