Some recent responses to the last post on tradeoff analysis made me think about the complex math behind the design of electric motors. Its way more complex than you would think. Not because I know anything about it, but a good friend of mine Dr. Hao Huang, did an incredible job of building an inclusive model of the electric motor and an optimization program as his doctoral thesis. Its an incredible piece of programming, dare I say art?, that took an entire case of paper to print out.

In the electric motor, its not just torque and speed. Its all the other things that have to be addressed simultaneously in order to produce the torque and speed.

From a purely electrical perspective you have the voltage, excitation frequency, current, winding resistance, ampere turns, wire gauge, fill factor, end turn losses, and the electrical time constant for establishing a charge in the winding. There might be more variable to consider here, but even if that’s everything, think about the complexity of the rules of interaction and tradeoffs just in this group alone.

Then there is the electromagnetic group, mostly around the production of magnetic flux in the core material. So there is the permeability curve of the core based on how much electrostatic charge is imparted from the winding, the time constant of the creating a magnetic field, what frequency the motor operates at and the most important area of all; the losses in the material. Loss in the core is from the bulk magnetization of the material and varies at different frequencies.

There is also the eddy current loss which is a function of how large the material is. This is where the idea of laminations comes from. The thinner the lamination steel, the less the eddy current loss. But, at the same time, the less steel is in the core, due to air gaps created by insulation coatings and slight variances in the flatness of the laminations. That’s why some motor make weird noises when you apply a voltage to them.

The core and copper losses are manifested as heat. And this is actually the ultimate limit in any conversation about motors. You can make a 1HP motor do the work of a 3 horsepower motor as long as you can get the heat out. Insulation material are the final defense against damaging the winding, so the thermal limits have to be respected.

And that’s where priorities must be established. Some applications require lower operating temperatures. Some applications require high efficiency. So which variable is the most important? And what is the order of priorities for the other variables.

I recently ran into an application that was size constrained 2.25″ OD maximum AND no forced air cooling. Dr. Huang’s optimization software allowed input of a size or temperature constraint along with up to 10 user defined variables that were in a priority list, and the software would conduct a boundary search to find the best solution optimized for the stated inputs. Pretty incredible. Not something that can be solved with known tools.

Hao, if you read this please contact me. I would like to catch up with you.

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