How DC motors (universal motors) work
There are two main types of motors used in most applications: DC (or universal) motors and induction motors. DC motors are much easier to understand, so I will start with those.
Universal motors are used in most hand held power tools, such as drills, routers, jigsaws and sanders.
I opened up one of my drills to show the insides and take out the rotor to demonstrate it.
These windings and contacts are arranged in such a way that if current is applied to the contacts of the commutator on opposite ends, the rotor forms an electromagnet, with north and south lined up with the contacts where current is applied.
Here I'm applying a current, using thin telephone wires pushed against the commutators and checking the magnetic field with a compass. If I change where I'm applying the current (to different commutators) them magnetic field also rotates to line up with the commutators I'm applying current to.
The way a DC motor works is that the rotor acts as an electromagnet, which is typically about 90 degrees out of alignment with the poles surrounding it (the stator). North and south poles of magnets attract each other. So magnetic attraction wants to turn the rotor to align it with the stator.
If the rotor and stator of our motor were permanent magnets it would only turn 1/4 turn and then stop.
But the rotor is an electromagnet and, as it rotates, current is applied to different contacts on the commutator. Here with telephone wires, but in a motor with pieces of carbon (which don't wear out as quickly). I'm only applying current from a 1.5 volt battery here, and holding a magnet next to the rotor. This is actually enough to make it turn, slowly.
The above demonstration does not make for a very good motor. Holding magnets next to the rotor is not the best way to subject it to a magnetic field. The "flux" of the magnetic field needs to form a loop, but the magnetic flux doesn't pass very well through air. Iron is about a thousand times more magnetically permeable than air (that's why the motor uses iron in the rotor). I bent a 2 mm thick piece of iron into a C-shape, and stuck some rare earth magnets to the inside of it. I also made some blocks to hold the bearings. Now, applying 1.5 volts, it turns much better, though still not very fast.
Part of the problem is that the motor also acts as a generator. Here, I'm spinning up the rotor manually, and I get voltage readings as high as 0.6 volts, just from this arrangement. As the motor spins, the changing magnetic fields induce a reverse-voltage in the coils, and that limits the speed the motor will spin at for a given voltage.
Next I applied 30 volts to the rotor, and that got it spinning scary fast, considering it's just sitting loosely in this arrangement. But universal motors, in real operation, usually run at about 100 to 200 turns per second.
My improved way of holding the magnets is still not optimal compared to an actual motor. In a real motor the stator is made of a lot of iron, which gives lots of room for the magnetic flux to form a loop, so the rotor is subject to much more magnetism.
The stator also closely follows the curvature of the rotor, so that the magnetic flux needs to travel through an air gap less than 1 mm thick.
In a real motor, the current is applied to the commutator with carbon "brushes". I imagine the "brushes" in the first electric motors really were like brushes, but pieces of carbon are always used today. The carbon slides with relatively little wear on the commutator. But it does wear, so the brushes always have springs behind them to keep pushing them closer to the commutator as they wear away. Eventually, the brushes get too worn away to make effective contact. So this type of motor is fine to use for hand held tools where, if it stops working, it won't cause major problems. But for applications where a motor has to run unattended for long times (such as in a refrigerator, heating furnace, sump pump, or bathroom fan) induction motors are used instead.
There is also a detailed Wikipedia article on commutators, which goes into much more detail on this type of motor.
Other common types of motors:Brushless DC motors
In recent years, brushless DC motors have also appeared in some high end cordless tools. A brushless DC motor, is similar in concept to a DC motor, but instead of brushes, transistors are used to switch the windings. This makes for a more efficient, quieter and longer lasting motor. However, to make it easier to get current to the windings, in these, the rotor is a permanent magnet and the stator has the windings that change the field. Power electronics are also needed to control the windings. The simplest brushless motor you will encounter is any fan used in a PC in the last 20 years. Hard drives also use brushless DC motors. Brushless DC motors can be very efficient and long lasting, so they are also used in some higher end cordless tools, as well as hybrid and electric cars.
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