Reflected Inertia?

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Posted by Paul Copioli at 04/25/2001 1:00 PM EST


Engineer on team #217, Team Macomb - Royal Fusion, from Utica Schools, Fraser Schools, Warren Cons. School and Ford Motor Company.


In Reply to: Reflected Inertia?
Posted by ChrisH on 04/24/2001 11:27 AM EST:



: Can any of you motor gurus tell me what this is and how to calculate it? None of our technical people have ever heard of it.

Chris,


I am an engineer at FANUC Robotics (Roch Hills, MI) and I work with servo motors every day. Reflected inertia is especially important when dealing with servo motors in order to manage control system stability. Anyway, P.J. is correct about reflected inertia, but I will get more specific.

Let's take a motor connected to a spur gear set with a 4:1 ratio (pinion pitch diameter is 25mm and output gear is 100mm). An arm is attached directly to the output gear and has a length L with a mass Marm. The arm has an inertia about its CG, Iarm and the CG is located at L/2. The inertia at the spur gear output is Itot=Iarm + Marm*(L/2)^2. That, however, is not the inertia seen at the motor.

Itot@mot = Itot/(GR^2) 'Inertia seen at motor

GR is the gear ratio. I define gear ratio as the number of turns of the MOTOR per 1 turn of the output.

The output gear also has an Inertia which needs to be reflected in the same way (Igear@mot = Igear/[GR^2]).

If you have multiple stages, then each stage is reflected to the previous stage by dividing the inertia by (GRstage^2).

After the Inertia from each component is reflected to the motor, you add them all up and compare the total reflected inertia to the motor rotor inertia. Like P.J. said, ideally, you would like to keep the ratio at 1:1, but most digital servo motors can handle 10:1 Load to rotor ratio.

If you are using pots for arm feedback on FIRST robots, we have found that minimizing the load-to-rotor ratio helps in controllability.

Any questions or if you want the derivation, just ask.

-Paul