I've never personally touched one. More common are the gasoline engine powered version. Still, I've never been fortunate enough to use one. The DC engine welder I did use was Westinghouse & bigger. I'm older now, would love to try one again. If I understand, continuous DC, (somebody here described as flat line) could best (then) be produced from a generator. Therefore, a motor powered a generator.
Three phase motors are simpler than some think. All have three magnetic coils. In some those three coils are split. Each coil will have two ends. Occasionally, in this country there will be 12 leads to connect, more commonly, there are 9. Single voltage motors rarely have 6, more commonly, 3 leads.
The coils are connected WYE or DELTA.
WYE will usually have one end of three coils connected internally. Those coils other end will be numbered 7,8,9. Other half of these coils will be 1-4, 2-5, 3-6. For higher voltage you connect the half coils in series. Lower voltage gets parallel.
To my knowledge, phase converters make three phase from single phase by a few systems.
One, a single phase motor drives a three phase alternator.
Another, both motor & alternator are combined in the same frame.
others use only capacitors to make a third "corner" by altering the timing.
A recent comer in the world is the VFD(Variable Frequency Drive) or inverter drive. This makes single phase DC from whatever source it is designed to make it from. It then converts DC into AC 3 phase of whatever voltage & frequency it is programmed to make.
I don't know if some brilliant motor mechanic could rewind a single phase motor for three phase, I'm pretty sure it isn't practical.