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And I echo the statement, undersized wire isn't helping at all.
Apparently it is not hurting either, as he put a parallel wire, with no significant difference.
Check post # 13, where the problem is shown clearly..... At the RPC, the output is 220 V on the pass-through lines when starting, but 135 V from either of them to the generated leg. The generated leg is falling a large amount.
Seriously..... When there is a problem, there is a right and a wrong way to solve it.
The wrong way is to guess that a particular issue is the problem, and then just go fix it. That can work, but is generally expensive, since if you do not guess right, you waste time and money on something that was not a problem.
The right way (if you want to actually solve your problem) is to check if that issue is a problem, and not "fix it" unless you can show it is a problem. Any possible "cause" has some effect that will result in what you see. So check if that is present.
For instance.... if the wire is too small, it would have too much resistance, and would cause a voltage drop. So see if the right voltage goes in one end, and the wrong voltage (too low) comes out.
If so, then the wire is at least part of the problem, and you are justified in fixing it. If there is no significant voltage drop in the wire, then the wire is NOT your problem, even though it could have been.
You have to look at the problem you have, check out possible causes, and fix the one(s) that are actually present.
The OP seems to have pretty well proven the wire is not an issue here.
The RPC may be too small for THIS lathe. That has not been tested, but the measurements made suggest the RPC is the problem. We do not know if it is just too small, or if it has some fault.
In this case, one simple way to determine if the RPC is the issue, is by connecting another 3 phase motor, as mentioned, to act as an additional idler. If the RPC is the cause, then the extra motor should make an improvement by supplying additional power on the generated leg, increasing the voltage.
If there is no "extra" motor, then the OP is in a pickle, because the RPC appears insufficient, yet there is no good way to test that.
There is a possible argument that the 240V dropped to 220V on start, so "the problem must be a wiring issue".
Not necessarily, though.... If the RPC were able to hold up the generated leg, then the generated leg might possibly fall to 200V at start. That would be in rough proportion to the drop of input voltage
But it actually falls to 135V. That is way out of proportion, suggesting again that the RPC is not able (for some reason) to hold up the generated leg.
Unless the RPC can be shown to have an actual fault, it appears pretty clear that it is too small to start this lathe at the high speed configuration. That is a known problem with a number of lathes.