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Sizing: Load to rotor inertia matching

We’re continuing our discussion about stepper motor ringing and inertia matching. We had established the following load-to-rotor inertia ratios:

Inertia Mathing
Figure 1: Inertia Matching in stepper Motors

  • 1:1 load-to-rotor inertia as an ideal ratio.
  • Greater than 1:1 and up to 5:1, with the load inertia being higher than the rotor’s inertia, as good.
  • Greater than 5:1 and up to 10:1 as okay.
  • Greater than 10:1, try to avoid.

I remember an application where the customer wanted to use the smallest step motor possible at the end of a robotic arm to position a sensor. The sensor was mounted directly to a single stack motor and presented a load-to-rotor inertia of about 20:1. Higher than the 10:1 load-to-rotor inertia ratio that I try to avoid. The weight of the step motor was important, though because it had an impact on a second motor that controlled the robotic arm. I had cautioned them that the ringing at the end of the move was going to be significant, but they were caught up with the weight issue and wanted to try it to see how it would work.

Well, the step motor made an accurate move, but when the move was finished the load rang for about two seconds. I think it was as close to a tuning fork that I’ve ever seen. We weighed (pun intended) two solutions. One was to increase the size of the motor to get a better load-to-rotor inertia ratio and the other was to add a gearbox. Gearboxes reduce the inertia by the inverse square of its gear ratio, This lower inertia that the gearbox presents to the motor’s shaft is called the reflected inertia, but more on that in another posting. The weight of the larger motor was less than the weight of the smaller motor and a gearbox. Plus the larger motor was less expensive than, the smaller motor and gearbox combination, so the larger motor was used.

Conveyor Inertia Matching Graphic
Figure 2: Inertias for a conveyor system

A two stack motor would reduce the load-to-rotor inertia ratio to 10:1 and a triple stack motor would reduce it to 6.67:1  A triple stack motor was used and the ringing amplitude and time was significantly reduced.

In addition to getting the proper load-to-rotor inertia match, one usually has to connect the shaft of the motor to the load’s shaft. A coupling that has lots of torsional compliance or springiness can create even more ringing problems even if the load-to-rotor inertia match is 1:1

Picture a plastic tube with an inside diameter that fits snuggly over the motor’s shaft and the load’s shaft and doesn’t slip on either one of the shafts. Let’s make the plastic tube one inch long with almost a half inch on both shafts. Let’s also assume we have a 1:1 load-to-rotor inertia match and that this is a good coupling with no torsional windup. Make a move and the load follows the motor’s shaft and the system has a slight ring at the end of the move.

Now make the coupling two inches long and perform our move/ringing test again. The load-to-rotor inertia is still the same, but the load isn’t as tightly connected to the motor’s shaft because there is some torsional windup in the two-inch-long plastic tube. The motor shaft moves and twists or “winds up” the tubing before the load starts to move.  When the motor stops the plastic tube will still be “wound up” so it will impart its stored energy to the load and ring back and forth until all the energy in the tube is dissipated.

Let’s get a bit ridiculous and make the tube a foot long. Can you imagine the torsional windup that this system would have? The motor might take a step but the load wouldn’t know about it for about half an hour.

More next time.

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LMD Linear

Liberty MDrive (LMD) Linear Actuator products integrate a 1.8° 2-phase stepper motor, external shaft linear mechanicals and drive electronics to deliver long life, high accuracy, and repeatability in compact, low cost packages.

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