What is the one variable in the universe of motion control system variables that ties everything together?

Some time ago a friend of mine, Phd Mathematician, wrote a software program that optimized all the variables required to construct an electric motor. The obvious ones are simple physical variables like diameter and length of the motor housing. The issue of motor size can be arbitrary for most applications, but every now and then you get caught in a size constrained application like the well water pump that needs to have a 2″ outside diameter in order to fit inside a 3″ pipe.

Shaft diameter and length, or course, would have to be considered based on the amount of torque that must be transferred. And even though these are simple physical constraints, you caught in a more complex relationship because there is static torque and dynamic torque. In the dynamic consideration there are starting and stopping characteristics, each of which is often unique.

The time displacement curve is the cornerstone of all motion control. You can get pretty fancy with the analysis. You can refer to the first and second derivatives of the motion, acceleration and jerk, and define a lot of boundary performance issues that a target motor and amplifier must be able to provide or the application will not work.

An interesting side note on the time-displacement curve is that you can consider work done as the area under the curve. So integral calculus had some value in the situation.

And we haven’t really addressed the magnetic circuit yet. There are generally 2 magnetic elements in any motor. Usually one is an electromagnet and the other is a permanent magnet. So we need to consider all the associated variables of design in an electromagnet are copper windings on ferromagnetic metal cores. Wire diameter, number of turns, length of turn, length of end turn ( the un-used portion of the copper from a magnetic standpoint), the voltage, current and excitation frequency of the applied current assuming its coming from a PWM based solution.

And we’re just getting started. The magnetic performance of the core material at varying frequencies and temperatures. You get the picture. That nice, neat, simple little starter motor that’s attached to your car engine with two wires from the battery turns out to be pretty complex.

My friend the mathematician said that his program has 23 variables of design that were needed to define the electric motor. Pretty scary if you have to do tradeoff analysis to find the “perfect” design for a specific requirement. But it is way too much work to actually do all this analysis unless you are going to produce a whole lot of one design.

So is there any Unified Field Theory that brings all this stuff together? TIME! The one thing that unifies all motor considerations is time. And by looking at the system from this perspective it is sometimes possible to simplify things a bit, in an otherwise very complex system. We’ll look at this in further detail in the next installment.

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