First of all, put your drill away. Adding a ground rod is a worthless and dangerous way to solve a wiring problem for any appliance. Driven ground rods typically give a resistance of 25 ohms or more.
Second, did you buy this machine new or used? You can"t necessarily trust wire colors on a used machine, as the previous owner may have provided the cable, and not the manufacturer.
Third, take a picture of the back of your machine. Does the switch/circuit breaker have three poles or only two?
According to longevity"s website, these IGBT based inverter machines can be supplied with three phase or single phase. The manuals on the website only shows single phase models with three wire connections, but the text elsewhere describes the possibility of use on three phase, which would use a four (or five) wire connection.
If you bought a used three phase machine it may work find on single phase, perhaps at a reduced capacity. This would be like VFDS (variable frequency drives) which have very similar IGBT based technology.
Chances are very good that the white wire will go unused in your situation. The machine almost certainly does not need the neutral. You"ll want your green wire to be connected to the ground prong on your connector (NEVER EVER try to run a green wire from an appliance to a driven ground rod).
I would expect that you need to cut the stripped end off the white wire, insulate it with tape, and wire the red, black, and green wires to a NEMA 5-50P plug bought from the likes of Home Depot. That way it will plug into the same receptacles as the rest of your equipment.
A less likely possibility is that the machine needs three phase and will not work on single phase.
The only way to resolve this is to get more information from you and/or the manufacturer.