We encounter mechanical phenomena all the time. We see things move, fall, spin, oscillate, break, etc. Electrical phenomena, on the other hand, are not always visible. Therefore, it has become a common practice to use mechanical analogies to explain and teach less visible concepts.

We compare electrons to water when explaining voltage, current, and Ohm’s law. The inductor is often compared to a spring, and the capacitor to a mass/inertia. The electrical resonance can then be compared to the mechanical resonance.

Even control engineers use mechanical analogies to illustrate their concepts; the proportional-derivative controller is nothing but a mass-damper system in that sense.

The theory of AC motors involves many difficult concepts, often explained with mathematical formulas and graphs. This is an obstacle to effective teaching and vulgarization. In this post, I propose 3 ideas to make the teaching of AC motors more fun. My goal is to stimulate more ideas and analogies; if you have some, please share them.

# The rotating magnetic field — a traveling wave

The rotating magnetic field is one of the basic concepts in the field of AC machines. It is a 140-year-old concept, often referred to in the French literature as the “theorem of Ferraris”, after the Italian scientist Galileo Ferraris. In a sentence, the rotating magnetic field is a traveling wave that is generated from 3 (or more) stationary sine waves in a given spatial configuration.

This concept is still often conveyed using equations and animated signals. But this is not fun! How about explaining it as a wave in a stadium! It becomes much more intuitive. Here is, for example, a full turn rotation: Youtube link.

# The synchronous reference frame — field orientation

The concept of a synchronous reference frame ensues directly from the rotating magnetic field concept. The analysis of AC motors in the natural (stationary) reference frame is tedious. Engineers and scientists have long used the rotation transformation to express the motor equations in the synchronous reference frame.

We can use the analogy of taking a photo of someone on a carousel, in both stationary and rotating references. The picture below is from a training presentation by Dave Wilson. To my knowledge, Dave is the only one who uses this analogy to explain this concept. This is literally fun!

I think that this analogy can be pushed a little further, to explain the cross-coupling terms in the dq-reference frame.

# The slip frequency — blowing in the wind

The concept of slip frequency in induction AC motors is also tricky for beginners and non-specialists. How would you explain it? Here is an idea.

Imagine a boat, very basic with a simple sail. The boat moves only in one direction, and the wind is blowing in that same direction. The force of the wind pushes the boat forward. When the speed of the boat achieves the wind speed, the sail feels no more force, so the boat decelerates. When it decelerates (because of the resistive force of the water which is opposite to the direction of movement), its speed becomes less than the wind speed, and the speed difference makes the boat speed up again. In steady-state, the boat will move at a speed slower than the wind speed. The difference between the speeds is directly related to the resistive force.

You can imagine that a shark is pushing the boat in the same direction as the wind until it makes it move faster than the wind. This is equivalent to the negative slip frequency of an induction motor in the generator mode.

**Disclaimer**: Analogies are an effective teaching tool, as long as we know their limits and we state them. An analogy that is pushed beyond its limit becomes a sophism.