The welder is 220 volts so you don't need the nuetral at all. You need the two hots and a ground wire. Make sure these are wired up properly.
In fact if you are not sure get the help of somebody familiar with single phase 220 votls circuits. The reality is that doing this wrong can be very bad for your health. It isn't difficult either but I would not want to attempt to explain it over the internet. Maybe with pictures but I don't have the time to draw such up.
Note that the dryer outlet plugs are fairly easy to find. What isn't so easy to find is the extension receptical. It is a 6-50R device. A nice one is made by Cooper and is part number 6709N. Warning: it is not cheap and you will likely need to find an electrical distributor for it. Your welding supply house may have extension cords suitable for the welder, it might be cheaper to buy through them and just put a dryer outlet plug on the cord. Then agian it might not be cheaper, It depends on the dealer.
Dave |