The rotor, the spinning part is a bar magnet. It has a north pole and a south pole. Sometimes it goes NSNS, we call that a four pole. You can have more (even numbers) of poles too. They just make the motor spin slower.
The stator is the outside part that doesn’t move. This is where the coils of wire are. Passing an electric current through a coil of wire makes it an electromagnet, with a north and south pole.
So as you can imagine, passing a DC current through the stator makes the rotor lineup with it. North of the rotor magnet will match south of the stator electromagnet. Now, if you flip the DC current, the electromagnet will flip poles. The rotor will now rotate 180° to lineup again.
Now, if you fed the stator AC current, the current is always flipping. In North America, AC is 60 Hz. So the stator electromagnet will swap directions and back 60 times per second. This means a 2-pole rotor magnet will spin in a circle 60 timers per second (3600 RPM). The mechanical spinning frequency and the electrical AC frequency match, they are synchronous. It’s just two magnets chasing each other. One is flipping because of electricity, the other flips mechanically.
If you had a 4-pole motor, it would only spin at 30 Hz / 1800 RPM. This is because a full electromagnet flip only makes the rotor flip halfway, aligning the second north pole back to the position the first north pole started at. Needs two electrical cycles to get the first north pole back or its same starting position. This is still called synchronous, as it’s a nice whole factor of the electrical frequency.
Now, what I described is a permanent magnet synchronous motor. A lot are not a permanent magnet, but another DC fed electromagnet on the rotor. Works the same. DC electromagnet does the same thing a permanent bar magnet does.
The real complicated motor to understand is the asynchronous induction motor. If the electrical frequency is 60 Hz, they might spin at 58 Hz. That means the two magnets are still chasing, but they are slipping aparte every now and then. The rotor also has no permanent magnet or DC fed electromagnet, but is just some metal. It’s basically a spinning transformer, making it more complicated.
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