Most of the machines we see in our workshops have fixed-speed motors. Some have switchable 2-speed windings but fundamentally they are designed to work directly on-line ie from 50Hz or 60Hz mains. Some of us improve the operation by using VFDs to provide some speed variation but they are still the same motors, designed for 1500rpm (4 pole) or 3000rpm (2 pole) base speed.
"Proper" grown-up machine tools, (sorry, "machining centres"
have motors that are optimised to operate over a wide range of speeds. If you think about it, the alternative would be to use fixed speed motors and (messy) automatic or variable ratio gearboxes. Generally, as noted above, motors have a constant torque region (at speeds up to base speed) which is limited by the magnitude of the magnetic flux and electric currents; and a constant(ish) power region between base speed and some upper limit (usually mechanical eg burst speed).
Motors that are intended for driving machine spindles usually have a fairly wide range of operating speeds eg 0-10000rpm or higher, with a constant power speed range of 5 or 6 to 1. They can then drive the spindle through a fixed ratio or possibly even directly, coaxial with the spindle.
Interestingly, the operating characteristics of these machines are actually very similar to those required for vehicle traction (eg hybrid and electric vehicle drives) and of course the result of coupling an IC engine to a multi ratio gearbox actually results in a very similar overall speed-torque curve – namely constant power. So my earliest experience of electric vehicle development involved the use of spindle drive motors directly coupled to the prop shaft. We used the Indramat motors (rated at 35kW "S1" continuous duty) to develop peak power of 75kW and over 800Nm of torque (more than the Dodge Viper) in our applications in buses and vans.
"Frameless" motors are simply supplied without the housings, bearings etc that make them self-contained, stand-alone motors. But if you are integrating them into a complex machine, you can save a lot of space, mass and cost by providing those elements yourself. It just takes a bit more engineering to do it.
There's nothing magical about the direct drive machines in these Korean washing machines. However, they get rid of extra bearings, belts etc and presumably are quieter and suffer less wear as a result. I have a Samsung direct drive washing machine (with heat pump etc) that claims a 10 year warranty on the drive system. Generally speaking, if you want reliable white goods you are going to be buying either Korean or German.
Murray