inertia ratio of servo


Thread Starter


what is inertia ratio of any servo system?

how does it effect on machine? how can we relate it to autotuning?

Ken Emmons Jr.

The inertia ratio is the ratio of load inertia (what gets coupled to the motor) to the inertia of the motor itself. You can't just say X:Y ratio is good for all systems. It depends on the system. If you have a considerable inertia mismatch (over 3:1 or higher let say) You can try this as an experiment, as I have (inadvertently):

- Clamp a circular test mass to your motor with a set screw(s) that simulates the reflected load. This represents a very solid coupling to the motor since it is directly clamped or bolted to the shaft. Tune your motor, or using autotune step up your response until just before things get noisy and ringy.

- Hook up your system with your couplings, gearboxes, and/or ballscrew sliders and your real load. You will not be able to tune as tightly to get the same performance, even with high performance zero backlash ballscrews. This is because of Backlash or spring constant in the system. I think what happens is because of the backlash and spring effect the motor goes from "feeling" the entire inertia of the system to *instantly* "feeling" just its own inertia. The greater the mismatch the worse this effect is.

Unfortunatley you have to consider everything, the stiffness of your couplings, backlash of ballscrews, torsional effects of shafts, etc.

Some people will argue that direct drive motors can handle large inertial mismatches. This is generally true, but if the load is tightly bolted to the motor shaft the motor and load inertia are really one, so the ratio is 1:1. Take that same load on a direct drive motor and put a long skinny shaft adapter between the load and motor mounting face and you will again have problems!

So the long wind response boils down to the fact that there are a lot of "it depends ..." when it comes to inertia matching. If you have the luxury I would experiment with anything over 2:1 or 3:1 if you need high performance. I've had very good luck with THK high precision preloaded ballscrews (around 300-400mm travel) and bellows couplings at over 3:1 ratios using Mitsubishi motors tuned very responsively.


William Sturm

Inertia ratio is the load inertia/motor inertia.  It impacts tuning because the load inertia can go in and out of phase with the motor inertia, especially if it has a flexible coupling.  This causes large changes in the actual inertia and you have to tune for the worst case.

James Ingraham


"what is inertia ratio of any servo system?"

The other responses did a good job of answering this. Your next question might be, "How do I determine this value?" Or even, "What units are we talking about?" This is where the software from the servo manufacturers comes in quite handy.

"how does it effect on machine?"

Also already well-answered, but it goes nicely into:

"how can we relate it to autotuning?"

Basically, as the inertia mismatch gets worse the tuning gets worse. At some point auto-tuning won't even run. Even tuning it manually becomes difficult. You'll especially find it difficult to get good tuning at both high- and low-speed.

For what's it's worth, on the big-ish systems I work on (on the order of several thousand pounds) the servo manufacturer's seem to be telling us 10:1 is pretty good and 20:1 is pushing it. Of course, in the 300mm travel ballscrew mentioned earlier, I imagine they're looking for some very rapid and very stiff movement. And that's the key; as you need more stiffness, you need less inertia mis-match.

-James Ingraham
Sage Automation, Inc.

Peter Nachtwey

Yes, it is the coupling that makes all the difference. All the auto tuning software does is try to find some parameters for an equation that can be used to estimate the actual position given a control signal. If the system is kept mechanically simple and stiff a gain and time constant may be all that is necessary.

If the shaft between the load and the motor twists this introduces two more poles and two more variables to identify, a natural frequency and a damping factor. If the auto tuning software is not designed to find these two extra parameters it will try to use only the gain and time constant to find the best match and not matter what it does it will not be right.
The inertia ratio (or inertia mismatch) is must be taken into account for servo with low mechanical stiffness. Tuning of servo is often difficult due to mechanical resonance in this case. It's true for both high (more than 1:5) and low (less 1:0.5) inertia mismatches.
This is the next question: How can we have good tuning but for different process operating conditions (large ratios of inertia change).

This kind of problem will occur on drives turning a common lineshaft. In a recent job, the inertia ratio was too large and we needed to program adaptive tuning for the servo control. In other words, the controller gain of the servo would be set by an external source (for example,the number of dryer cans connected to the lineshaft)

Ben Janvier

Ken Emmons Jr.

I don't know of any other way to do this than what you have done. Mitsubishi Electric (and others) have an adaptive autotune function for this purpose, but changing the gains yourself if you know what the loads are should work as well.

Can you tune the system down to less sensitive operation for all loads, or do you need the high performance on the lower intertias?

Another thing I have not tried is to connect an inertia damper (flywheel) to the motor shaft. You might have to make a special piece depending on your application, and if you are connected to a gearbox you might not have the room for such a thing. If you do have the room and the mass is tightly coupled it will change your load to motor inertia ratio. I believe some motor manufacturers do this internal to the motor when they offer "low inertia" and "medium inertia" motors.


I read with big interest your answers on the ratio of slowness and servo-motor. I am at present in second year of UNIVERSITY INSTITUTE OF TECHNOLOGY in industrial engineering and Maintenance and during my training course, I have to deal with this subject.

The problem is whom I am far from excelling at the subject.
I would thus have heaps of questions and regrettably, I found only rare answers has these.

My work has to succeed has the realization of a model shaping the unwanted mechanical phenomena bound to the ratio of slowness applied to the axis of transmission of power of a trans-stacker. The steepness of transmission were the one of a spring.

The objective of my study is to define the limits of the report of slowness between the load and the engine according to the organized regulation and the trajectories imposed on the system. The purpose of the study passes by the non-linear consideration of the effects of the games in the transmission, as well as the influence of the frictions.

At the moment I have no sketch of launch while it inspires you, and especially how you would set you there to manage it?