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"Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856
I doubt you are referring to actual 2 phase power. Two wave forms the second trailing the first by a 90 degree phase angle. ie hot to neutral 120V, hot to hot 141V.
It is an archaic system used around the turn of the 20th century.
I assume that you are referring to single phase wired hot to hot 240V ie USA or hot to hot 3 phase 380V (400V?) the rest of the world.
As to the type of power generator you have, I have no guesses.
Most welding machines are a single phase application. I have never seen a three phase one but I haven't seen everything either...
Welding machines produce impulse loads of low power factor. They are unbalanced when using single phase supply. The current also contains large amount of noise both in the standard harmonics range (120-2000Hz) and the high frequency range.
If the welding machine is more than 10% of the generator capacity, it will produce line voltage fluctuations, and increased heating. Depending on who else uses the generator, it might not be acceptable.
There are special filters that can be added to a welding machine to minimize this effect. Contact me for more details.
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Experienced is earned, common sense is taught, both are rare essentials of life.
"Most welding machines are a single phase application. I have never seen a three phase one but I haven't seen everything either..."
While in light welding, that is the case. We have quite a few 3 phase machines here at work.
Granted these are all 400 to 600 amp MIG and TIG units. I'll admit that most users don't see buzz boxes of this size. But, in an industrial setting they are rather common.