A Phd mathematician friend once told me, after several years of work doing his dissertation, that electric motor design is a system in which there are 22 variables that are linked together in complex relationships. Since the human mind is not capable of operating at this level of complexity with all the variables simultaneously, we model these complex systems in groups of variables and perform boundary searches looking for relative optimum solutions.

That’s kind of how it is working in motion control systems. Generally there are many variables competing simultaneously within a project. The hardest thing to do is group the variables together logically and put them in order of priority. But this effort early in a given project will help you guide the project to completion even if you have to make changes as the project progresses. Staying focused on the most important objective will help to prevent becoming distracted by side issues and will help you get more done in less time.

But the really big thing is looking at operating conditions in terms of their relationship to time. And there are some interesting insights from looking at things with respect to time.

Simple things like understanding the relationship of the forces acting in the system from **F=ma**, in which acceleration has a time component in the denominator. In the scalar value, as the time constraint for a move decreases, the force required is increasing arithmetically. Sizing of a servo motor, for example, can quickly reach limits because the increasing force needed to accelerate the load increases the size of the motor. The motor’s own inertia now becomes a constraint working against the desired performance. And there applications where the last 10 milliseconds of move time will cause the motor sizing application to fail.

Even more interesting, and hopefully more useful, is considering the derivative of time. Not so much because of the numerical value, which isn’t as helpful, but because the first derivative of time shows up in a number of critical relationships.

The current flowing through a power mosfet has a limit of di/dt which defines the breakdown limit of the device. This is the instantaneous current rate or the rate at which the mosfet can increase the current in a specific amount of time. This limit also governs the acceleration rate of the motor. The motor acceleration can be considered the sum of the inertia of the rotor and the ability of the amplifier to put current through the stator winding.

Reversal stress in a mechanical transmission line is also limited by dT/dt, the instantaneous change in torque over a change in time. Think about the change in the drive train of a wind turbine gear reducer. The gears may be unloaded when the propellers are not turning. Then the wind comes along and pushes the propellers and sends an impulse force pushing the gears into mesh at full load in a very short amount of time. This is a bit like hammering the gears and will cause catastrophic failure.

Similarly in servo systems, reversal stress creates the same conditions every time a load is reversed. How much, if any, dwell time is allowed for the system to pause before reversing? In the metals industry, high speed stamping and forming is done with continuously rotating inertia wheels which allow the impact to occur through linking arms because the direct stress at the multi-ton force levels cannot be controlled. The same is true considering the motion of the pumping jack using in oil & gas production.

More next week.

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