I seem to recall, from a power electronics course I once took (and passed) sometime in the 1970s that induction motors work on the principle of a spatially rotating magnetic field, produced by excitation of poles on the stator, interacting with the poles of a magnetic field in the rotor. From there it gets a little complicated, what with computing magnetic flux paths, induced voltages and currents, phasors, torque and whatnot. I think it was the whatnot that made me realize I should stick with integrated circuit electronics and leave motor design to more capable hands.
However, one takeaway I got from the course was a graphical explanation of a rotating magnetic field, presented to me by my instructor, a really old codger who had in a previous life, before becoming a university professor, practiced electrical power engineering. This guy really "knew" motors... all kinds of motors... but his math skills appeared to me to be a little rusty. So, a lot of his teaching involved
graphics instead of
mathics (if that is even a word). This was quite a contrast to my other EE courses that emphasized using calculus, differential equations and Laplace transforms for circuit analysis. I was taking these course on a part-time basis, over a period of ten years, so it was quite refreshing to find a course that didn't expect me to acquire and use additional math skills..
One day my instructor made me sit down with pencil and paper and plot three sine waves, one above the other, with identical frequency and amplitude but separated in time from each other by one hundred twenty degrees. Then he told me to add them together, using a pair of dividers to add and subtract amplitudes algebraically at arbitrary increments in phase from zero to three hundred sixty. The result was astounding. If you consider the three sine waves to represent the magnetic fields generated by three sets of stator windings whose poles are equally spaced around the circumference of the motor the result is... a
constant amplitude magnetic field
that rotates in space!
Motors and generators using commutators were extremely successful commercially by the time Tesla (and others) discovered the principle of using the rotating magnetic field to create an induction motor. The construction of electrically-excited stator magnetic poles and rotating armatures was an established part of the budding field of electrical engineering. All anyone had to do to make a working induction motor
that did not require a mechanical commutator was to change how the stator poles were excited, and use the transformer principle (also newly discovered at the time) to excite the rotor from the alternating current in the stator windings. It didn't take long (as far as historical things go) for engineers to accept and build on the concept.
From the beginning, induction motors had one wee bit of a problem: the speed of the rotating magnetic field depended on the frequency of the alternating current excitation. That meant that, unlike DC motors, the speed of an AC motor was not easily varied. Another problem that occurred immediately was the general non-availability of three-phase power from public utilities. It costs a lot more money to distribute low-voltage three-phase power than it does to distribute low-voltage single-phase power. Three "pole pig" transformers, instead of just one, for every ten or so houses on a street meant that homes did not receive three-phase power. Only factories, with large motor horsepower requirements, could afford the "new" three-phase power distribution. Still, there was (and is) a huge consumer market for fractional horsepower electric motors. Attempts to satisfy this market led to a range of design concepts, all efforts to create a rotating magnetic field from a single-phase alternating current source.
The constant speed problem has never been efficiently addressed with mass-produced fractional horsepower motors. Spatially rotating magnetic fields are simple to produce with three-phase power sources, but rotating magnetic fields can also be produced from two-phase power sources. The magnetic fields from a two-phase source do rotate in space, but they also vary in amplitude and this produces unwanted variations in motor torque. Not a big problem with fractional horsepower motors used for fans: the inertia of the fan "smooths" out the torque variations.
There are only a few simple ways to generate a two-phase power source, with the requisite difference in phase to create a rotating magnetic field, from a si
ngle-phase source. For fan motors, the shaded pole technique works well enough, although it is horribly inefficient. Capacitors can be used to provide a phase shift necessary to generate two-phase power, and hence a rotating magnetic field. They are typically found in larger motor applications, up to about one horsepower, for such things as refrigerator compressors, water pumps, and saws. Sometimes two capacitors are needed: one to provide starting torque and another to provide running torque with a centrifugal switch "cutting out" the starter capacitor when operating speed is reached. However, none of these techniques addresses the speed control problem.
There is a
short thread on Stack Exchange that addresses speed control of shaded-pole motors
only. And
here is a link with some "simple" math that explains how shaded-pole motors work. Your best bet might be to experiment with an ordinary wall-mounted "light dimmer" to see if it will provide a satisfactory range of control.
Or maybe turn instead to modern 21st Century technology. It appears we have come full circle and are back to DC motors, but without mechanical commutators. Electronics to the rescue! Pulse-width modulation! Variable frequency excitation! Hall-effect and current sensors for electrical commutation with MOSFETs and IGFETs and all manner of other semiconductor devices! It is a Brave New World for the current generation of engineers!
For a "solution" to your problem, I would recommend that you try powering the fan from a cheap wall-mounted light dimmer first because it could get very expensive trying to lower the voltage sufficiently, while still maintaining enough torque to turn the fan blades, using
non-polarized AC motor capacitors. Those puppies are expensive!