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# Servo motor inertia ratio

## Servo motor inertia ratio

(OP)
Hey all,

I understand that inertia ratio between the load and the rotor can be a good guideline for how to size a servo motor and gearbox.

From what I have seen as a general rule of thumb, people suggest a load:rotor ratio of less than 10:1 or as close to 1:1 as possible.
I am wondering if there would be any harm in gearing down to be less than 1:1, like 1:10.

I imagine there would be no issues, as it would reduce the load on the motor or improve the acceleration of the load up to operating speed.

I should say, this servo is just being used to index a rotary table.

What thoughts do you have?

### RE: Servo motor inertia ratio

Although it seems sensible that a 1:1 inertia ratio will be the target, it is not always feasible or cost-effective. Many servo motor manufacturers recommend keeping the inertia ratio at or below 10:1, although there are many applications that work well at much higher ratios.

The best inertia ratio for an application is the dynamics of the step and the accuracy needed.

### RE: Servo motor inertia ratio

There's probably been more nonsense offered about "inertial matching" issues than any other in all the years I have been in servo control. There is really nothing "optimal" about a 1:1 ratio.

In the real world, what you typically need to worry about most is how your resonant and anti-resonant frequencies of the load-coupling-load system vary with changing ratios. Increasing the load inertia too much can lower these sqrt(k/J) frequencies into the zones you want actual operation, which is problematic.

The 10:1 ratio limit is simply a common rule of thumb to keep you out of trouble in common systems, mainly rotary servo motors with a small-diameter helical coupling to the load. On the other hand, with direct-drive motors where the "coupling" has the full diameter of the motor, resulting in a very high stiffness "k", you can successfully use a ratio of hundreds to one.

There are some secondary issues that get worse with high inertia ratios. If you have the system tuned well with a large load attached, you may get bad behavior with the load unattached, even just for test purposes. If you have backlash, the load is effectively unattached during the transition, and you can get problematic behavior then as well.

There is absolutely no problem here in going below a 1:1 ratio if it helps other system goals.

Curt Wilson
Omron Delta Tau

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