You don't need a neutral to utilize the 220, in fact doing so negates it from _being_ 220v. This is 180 degree out of phase AC, not DC. All you need is a voltage potential and somewhere for it to travel, for current to flow. This is provided by the two 120v out-of-phase legs of your typical residential service. Hopefully you do not become part of the conduction path, and is the primary reason that most woodworking equipment requires a ground. It is not designed to be a current carrying conductor.
Great confusion exists among novices as concerns Grounds and Neutrals, especially when it involves outbuildings. Protection against electrocution and lightning are two of the main reasons that the current grounding guidelines/codes exist.
The ground on most 220vac equipment is for safety grounding only. It is a ground, not a neutral, although they do eventually connect together in your main panel, but never in an in-house subpanel.
Older stoves and cloths dryers sometimes used a common ground/neutral to provide 120v for lamps and timer motors, but the new code and all new appliances require a 4 conductor plug and wiring. Two hots, a neutral, and a ground. It's a safety thing...
Get a copy of the NEC if you want to read up on how to wire things safely, and to code. Otherwise, please, call an electrician. Mistakes can be deadly and cause great property loss.
FWIW