Differences of Neutral and Ground
To try and simplify the differences between neutral wire and ground wire.
First off they should never be used interchangeably for any machine hookup, regardless of it appearing that they both connect back to the same place.
Second the colors should never be used interchangeably either. White or Gray for neutrals only. Green or bare for ground.
They do go back to the same point in the supply system but for entirely different reasons.
The Neutral is intended for normal current flow to power the load, expected operating current from the connected device. It is always insulated from ground, because it is expected to have current flowing and therefore expected to have some voltage (shock) potential as a condition of normal operation.
The ground on the other hand is NOT intended for normal current flow. It's function is intended for current flow ONLY when there is a fault (short circuit) or an abnormal leakage of the connected device. It should never have current flowing on it as a normal condition.
The ground serves two basic functions.
First is to provide a solidly connected path back to the source to conduct large fault (short circuit) currents, in order to trip off the circuit protection as soon as possible.
Second is to reduce or eliminate the voltage difference (shock potential) from the connected device and any other nearby conductive object including the earth.
To use the ground and neutral interchangeably will defeat the intended purpose of the system and therefore decrease the overall safety of the system as well as increase the shock and electrocution hazard of the system.
In the above case given (OP), a device requiring 3Φ with a neutral and ground connection for it's supply circuit, and a RPC providing the 3Φ source. The basic RPC has no neutral connection and the only true neutral is from the 1Φ source panel supplying the RPC system.
The ground of the 1Φ supply panel and the RPC output are the same and should be solidly connected together, as well as the ground from the connected device. This comprises the safety part of the system.
The insulated neutral of the connected device should only connect to the to the true neutral bar of the 1Φ source. Since the RPC fed panel has no true neutral, it must be connected to the neutral bar of the 1Φ panel supplying the RPC.
Another (better) way of accomplishing the same thing would be to provide a true neutral bar in the 3Φ RPC output sub-panel. The 3Φ sub-panel most likely has an insulated neutral bar as standard. But it's likely being used as a ground bar instead, and bonded (solidly connected) to the enclosure and the supplying 1Φ panel system ground.
To convert it back to a true neutral bar, remove all ground (bonding) connections to the panel enclosure and any branch circuit grounds. Connect a insulated white neutral wire from the 3Φ neutral bar to the 1Φ source panel neutral bar.
Then you would add a separate ground bar to the 3Φ RPC fed panel, mounted directly to the enclosure, and bonded to the enclosure through its mounting means. The 1Φ panel system ground and the 3Φ RPC panel grounds then must be solidly bonded together. This could be done through a dedicated ground wire or metal conduit connections between the two panels. Then connect all of the previously removed branch circuit grounds to your newly installed dedicated ground bar in the 3Φ panel.
The way you received the lathe was correct in that it had a white wire for the neutral connection. But either it lacked a ground connection, used the neutral and ground interchangeably (bad) or had an approved metal conduit connection acting as the grounding connection.
So to summarize the lathe circuit requires 5 wires not the 4 that it originally came with or 4 wires and an approved (listed) metal conduit grounding connection.
SAF Ω