There are many GE 20" inch 3 speed box fans between the mid 1950's and early 1970's that fit what you have described. If your fan doesn't have a model number or other identifiers, a couple photos might help folks know what you're looking for.
angus, can you describe the fan? , is it gray with bowed sides? is it aqua or beige with straight sides and sharp corners? does yours have metal blades or the 5 element plastic blade? later motors didnt have the oiling wicks in them and had a "hat" over the windings while the earlier ones did not . Plus there were a series of aqua fans with the motor mounted directly to the rear grille not to the center bar frame, they had "fins"
what is wrong with your motor?