Dimensioning motor for motion control

I was told that in the ideal case the inertia of the motor is equal to the inertia of the mechanical system.
That a higher inertia for the mechanical system then for the motor would be worse, I can understand. But what if the inertia of the mechanical system is (much) smaller the inertia of the motor, why would this be worse for the system then a 1:1 ratio? What is the phylosofy behind this one to one relationship of the inertias of motor and mechanical system?

that is as myth due to ignorance of the real problem

The real problem is stiffness or lack of it when the load inertia is high relative to the motor or actuator. I/we often control loads MUCH bigger than the motor in hydraulics. When the load is relatively big and not stiff extra control features are needed to control an under damped system.

In your case where the load is smaller you will be OK but the inertia of the motor will limit performance.

The motor must be able to meet the demands of the load. In all cases one demand is torque - if the motor cannot equal or exceed torque demanded by load it is overloaded and if severe enough will stall. Torque demand by load can be easily measured with a torque wrench or lever arm and weights - this applies to constant torque loads only (conveyers hoists trolleys etc)

Pumps and blowers are "increasing torque" loads because of the affinity curves - torque goes up as speed goes up. For this type of load refer to manufacturer curves.

The second demand of a load can be inertia for example large flywheel. I think you not only need to evaluate inertia when starting but also and maybe more important when slowing or braking with the motor. Consider pushing a car into garage - not too bad to get it rolling but you better know when to put on the brakes to avoid going thru the back wall - especially when YOU are the brake.

It seems to me that if the motor is oversized reasonably say 10% for both torque and inertia and will always operate at 95% averaged load then you should be OK.

I need to learn more about this myself and the calcs needed to approximate so really hope an expert will come riding and decrease our lack of expertise.

Dan Bentler

Peter Nachtwey said:

In your case where the load is smaller you will be OK but the inertia of the motor will limit performance.

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I was thinking about the case where you choose an oversized servomotor compared to the calculations, or the proposed type from the supplier. That oversized motor would have more torque, but as it is bigger also a higher inertia.
So, in this case why would it lead to a limited performance.
In the same margin I would ask, where do you make a choice between a 'slow' servomotor with a nominal speed of f.i. 1500 rmp and a gearbox of i=10 or a 'fast' servomotor with a nominal speed of 6000 rpm and a gearbox of i=40?

Plc_User said:

What is the phylosofy behind this one to one relationship of the inertias of motor and mechanical system?

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For a given motor/gearbox/load, maximum load acceleration is achieved when the gearbox ratio is chosen so that the load inertia seen by the motor is the same as the motor inertia.

(A typical example of using differentiation for finding the max/min of a function)

The reflected inertia is the inertial load that the motor sees through the system's drive train. That is the concern.
Here is a very good paper but it will make your eyes glaze over:

http://www.kollmorgen.com/website/c...t/KOL_MotorInertiaMismatch_Brief_08_12_10.pdf

Plc_User said:

I was thinking about the case where you choose an oversized servomotor compared to the calculations, or the proposed type from the supplier. That oversized motor would have more torque, but as it is bigger also a higher inertia.

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You didn't mention the amount of torque in your first post. That is OK but if you need to accelerate quickly you need to maximize the torque to total inertia.

For a given motor/gearbox/load, maximum load acceleration is achieved when the gearbox ratio is chosen so that the load inertia seen by the motor is the same as the motor inertia.

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AngularAcceleration=Torque/TotalInertia
If the setting the load inertia to the motor inertia doesn't minimize the TotalInertia then it doesn't provide maximum acceleration does it?

The Kollmorgan link shows that they don't think the inertia ratios need to be match but they don't say why. I have a link to a pdf that says why.
http://www.ecst.csuchico.edu/~repanich/Technical_Tools/The Myth of Inertia Matching.pdf

I wonder how all those hydraulic motor applications worked . No gear box and inertia mistmatches. Actually I wonder why the servo motor people haven't asked why the hydraulic people don't worry about matching inertia. Often hydraulic motors are chosen because they provide high torque with low inertia and don't need gear boxes.

I remember googling this a little while ago. The answer that I came to, as peter stated, is that inertia matching a myth.

My guess how this came up in the first place was just a general guideline for picking motors when the application was trivial.

In general I think you'll find inertia is loosely proportional to torque.

Peter Nachtwey said:

AngularAcceleration=Torque/TotalInertia
If the setting the load inertia to the motor inertia doesn't minimize the TotalInertia then it doesn't provide maximum acceleration does it?

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Are you agreeing or disagreeing ?

I thought it was obvious

L D[AR2 said:

Are you agreeing or disagreeing ?

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Matching inertia doesn't maximize angular acceleration does it? Reducing total inertia does.

If you reduce the inertia, then you can always select a gearbox ratio that will result in maximum accel of the load.

You are defining in a vacuum with that example. You aren't considering design practicality. The same can be said of audio amplifiers and speakers but no one I know of has developed a speaker with perfectly flat impedence from 20-20K Hz. It's the sama mathematical exercise, by the way.

The PDF Peter linked touches on the genesis of this issue. It really started back in the stepper motor days. It's one thing to go over torque on a closed loop servo system. It is completely another to go over torque on an open loop stepper system. It you took the torque shots the author talks about in a stepper system you will verly likely start losing steps.

You should look into what machinery manifacturers are doing with direct drive motors today. 1000:1 inertia ratios are no big deal. It comes back to what Peter said. If you have the torque you are in good shape.

Keith

Your math is good

L D[AR2 said:

If you reduce the inertia, then you can always select a gearbox ratio that will result in maximum accel of the load.

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Yes, your solution provides maximum acceleration rates if torque is limited but at some point there is more than enough torque without the gear box.

The point is that having a little more torque as in Plc_User's case isn't a problem. The inertias don't have to match.

kamenges said:

You are defining in a vacuum with that example.

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See post #1 then #5 - does anyone have any alternative answers to the posters original question ?

While what you state is true, I don't believe that your answer is the historical philosophy behind maintaining the inertia match. It does correctly identify why, in the absence of other limits, 1:1 is the ideal limit.

I think the historical genesis of the 1:1 matching is pretty well explained in the two links provided.

Keith