Why does a single phase 220 volt motor run off two legs of a three-phase circuit?
In three-phase power, the voltages of the three power wires fluctuate up and down cyclically so that they are “120 degrees” apart. By “120 degrees” apart, I mean that each wire reaches its peak voltage at a separate time—first the X wire, then the Y wire, and then the Z wire—with the Y wire reaching its peak 1/3 of the 360 degree cycle (or 120 degrees) after the X wire and the Z wire reaching its peak 1/3 of the 360 degree cycle (or 120 degrees) after the Y wire.
The specific voltages and their relationships with ground or a possible fourth “neutral” wire depend on the exact type of transformer arrangement that supplies your home or business. In the standard “Delta” arrangement (which you can find discussed at sites dealing with power distribution), the voltage differences between any pair of the three phases is typically 240 VAC. In the standard “Wye” arrangement, the typical voltage difference between any pair of phases is 208 VAC and the voltage difference between any single phase and ground is 120 VAC. And in the “Center-Tapped Grounded Delta” arrangement, the voltage difference between any pair of phases is 240 VAC and the voltage difference between a single phase and neutral is 120, 120, and 208 VAC respectively (yes, the three phases behave differently in this third arrangement).
If you run a single-phase 220 VAC motor from two wires of a Delta arrangement power outlet, that motor will receive a little more voltage (240 VAC) than it was designed for and if you run it from two wires of a Wye arrangement outlet, it will receive a little less voltage (208 VAC) than appropriate. Still, the motor will probably run adequately and it’s unlikely that you’ll ever notice the difference.