For axial air gap machines the current capacity will be nearly the sum of the individual wire capacities. ( don't try [paralleling coils wound with dissimilarly-sized wire] on motor conversions with wires more than one gauge apart as the current is determined by the reluctance rather than the resistance and you will fry the thin wires).
Flux: We started this discussion before (and I bought some stuff to do a test but haven't gotten around to it yet.) Now that I see this post I think we were talking about apples and pears.
When the paralleled coils wound with dissimilarly-sized wire are on different poles the reactance dominates and the thinner winding will fry (me: Unless the one wound with thinner wire is wound n-in-hand to bring the total cross-section up to the same as the heavier-wire coil it's paralleled with).
IMHO if two gauges of wire are wound in-hand on the same pole and paralleled, the mutual inductance will be essentially the total reactance and the relative resistances will dominate the division of current. However, skin effect will still try to push current toward the smaller wire a (very little at these frequencies) bit because the thinner wire is a higher-proportion of "skin" and the current penetrates it faster percentage-of-cross-section-wise. (And this same difference in skin effect might, similarly, very slightly bias the current toward the thin wires in the previous case of thick-vs.-N-in-hand on different poles.) Do you agree?
Only just seen this one, sorry for the delay in replying.
I am inclined to think you are right but leakage reactance is a bit of a difficult concept to get to grips with. I see where you are coming from, if the turns are tightly coupled by mutual inductance it would be similar to having a series inductor and sharing the current between the strand resistances just as in an air gap machine. The leakage inductance is caused by flux that is not linking everything so the strands will not be accurately mutually coupled but the flux that failed to link one strand would probably fail to link the others in general.
Yep. Giant common inductor representing the mutual inductance, in series with tiny individual inductors representing the individual inductance from the leakage flux and individual resistors representing the DC resistance of the strands. If the differential of leakage flux is small the resistance dominates the division of current and the in-hand windings share current in proportion to their cross-section.
You could represent skin effect with an additional per-wire series element: The lumped-constant version would be an inductor paralleled by a large resistor. (Maybe multiple taps with multiple resistors for a closer approximation to the continuous case.) The resistor represents the extra resistance of the wire when only some amount of skin is conducting (and the eddy-current losses from the penetration of the circular field as it expands and contracts), the inductance represents the stored energy of the circular flux inside the metal of the wire. Thicker wires have more inductance and the "skin" resistance, though lower than for thin wires, is higher in proportion to the wire's own DC resistance. So current in thicker wires lags that in thinner, and the thinner wire gets a disproportionately high I-squared-R loss due to the more even current distribution, out of proportion to the cross-section resistance, that results from this phase-shift.
We tend to think of skin effect as being something associated with high frequencies but i suspect the effect is still there at low frequencies in this case.
We also tend to think of "high frequencies" as very high - megahertz and more powers of ten. But what people like Tesla and Westinghouse thought of as "high frequencies" are more like what we think of as ultrasound. This is a linear circuit so the effects are directly in proportion to frequency and thus don't disappear until you get to DC. And we're dealing with a lot of inductance combined with low resistance so they should be nontrivial even at audio and subaudio frequencies.
I may be off course here but I believe the current is forced to the outside at high frequencies by the magnetic field directly associated with the current in the wire. This would be too small to be of much consequence for small wires at low frequency but I have a suspicion that the actual field causing the flux linkage in an alternator does the same thing and concentrates the current flow to the outside of the wires. If this is correct it ties in with your idea.
As you see above in the lumped-constant model I propose we're on the same page here.
There are things with the axial alternators that are difficult to explain. I have found that for the small size machines we play with the effective resistance seems to be about 1.3 times the dc resistance. I have some data from something playing with a much bigger alternator implying that the factor gets significantly worse. This skin effect idea seems the most likely explanation. Others seem to blame reactance but I find the leakage reactance of this type of alternator to be lower than the resistance and things don't have much effect until the reactance at least becomes equal to the resistance.
Complete agreement. And that extra 30% sounds like the effect is significant even at these frequencies. IMHO if going to n-in-hand reduces the extra effective resistance it says the eddy current losses were broken up by "laminating" the wire. And how do eddy current losses map to increased resistance in the wire? How about by forcing the current into a path that isn't evenly distributed in the copper as the current changes? That sure sounds like some variant on the skin effect, doesn't it?
For successful operation of large air gap alternators eddy loss in the copper has to be dealt with by laminating the copper bars a transposition is also necessary to equalise the voltages even then to prevent currents within the strands. I feel certain that if the eddy current problem hadn't forced the early pioneers to do this then they would have found it necessary from the point of view of this reduction of effective area.
And the workaround sounds a lot like the design of litz wire - which brings us full circle. B-)
Normally with slotted core machines problems don't arise until the size becomes very large so most of this goes unnoticed.
Probably because there isn't much room for leakage flux. Virtually all the flux goes through all the wires in the slot equally, as the lines snap through the low-permeability slot into the high-permeability core. And even when there is leakage flux it would tend to cut both the thick and thin wire of an in-hand winding.
A single conductor is normally adequate and if more than one strand is used they are normally the same size. I know that Zubbly found that a small strand in the bunch does in fact overheat.
With little to drive the leakage flux to prefer crossing the thin to the thick wire except extra retardation in the thick one caused by extra eddy currents - corresponding approximately or exactly to the skin effect - I'd say that's a strong argument for skin-effect phenomena at these frequencies, too.
What i don't know is how the ac resistance of a slotted core alternator compares with its dc resistance, the limitations on output current are determined by the leakage reactance so resistance is less important in the characteristic but it must still figure into the efficiency calculations.
Also, the eddy currents in the metal core, and the resistance they see, are transformer-coupled back to the windings, appearing as extra resistance there. Cores make it more complicated.
I am not sure if this rambling has got us anywhere but things are far from simple when you get into the finer points of these things.
Flux
Seems very productive to me.
