I'm just a 'multi-skilled' fitter who hasn't fired a multi-meter (at work) in years. But aren't most 3 phase motors intended for use with an inverter for work use too?
(for a multi-million £ firm, we still use a lot of 'Task Units' where now-a-days you'd use an inverter, apparently a 60's answer to variable speed control ..... no idea how they work - they just do!
or they do while they can get the obsolescent spares :-/
)
Depends what you want to do with them. In most cases, you just want them to run at constant speed, so you can just connect it to a 3 phase supply. If you need to precisely control speed and direction then yes, some sort of inverter will be used to control the motor.
In a domestic setting, 3 phase mains is not available, so you need an inverter simply to generate a 3 phase supply from an incoming single phase supply.
3 phase is a more efficient way of distributing leccy than using a single phase system, which is why most of the grid is 3 phase. Individual phases in a domestic supply are used to supply domestic properties but heavier users will have a 3 phase connection.
A 3 phase supply also allows physically smaller AC motors to supply more power. Induction motors can build up a rotating field just by having three stator windings rather than the single phase arrangement where you need a capacitor to introduce a phase shift between wstator windings. There is also a more or less constant delivery of power with a 3 phase supply whereas with a single phase supply this is not the case, and this leads to less vibration with a 3 phase motor.
Kevin