inertia matching servo motor to gearbox

[Roachman]

I need to know the formula for matching a servo motor to a gearbox (planetary in this particular case) given the moments of inertia for both units. I suspect that the reduction ratio and possibly other factors will influence the outcome. Would appreciate help.

 

[EnglishMuffin]

Reflect the system moment of inertia back to the motor shaft. This involves knowing the speed ratios and moment of inertias of the various intermediate shafts.
Ireflected = Inertia *(N1/N2)^2
Where N2 = speed of shaft to which you are refecting
N1 = speed of inertia you are relecting back
There's an old "rule of thumb" that the momemt of inertia of the load reflected back to the motor should not exceed twice the motor inertia. But what really matters is the mechanical torsional natural frequency of the complete system versus the electrical bandwidth of the servo system. So you really need the torsional stiffnesses to do it properly.

 

[SERVOCAM]

I have always used the "rule of thumb" that the inertia of you load must not be 10 times greater than the load for servo systems (an like said, it depends on the system and desired performance).

Inertia of the load is reduced by the square of the ratio of the gearbox.

Jreduction = Jload / ratio^2

(J = Inertia)

Must remember that your output torque does not exceed the gearbox rating, and the motor speed does not excede the input rating of the gearbox. Also take into consideration the gearbox efficiency for your sizing and the gearbox inertia.

Speed is decreaded by the ratio
Torque is increased by the ratio
Inertia is decreaded by the square of the ratio



Cameron Anderson - Sales & Applications Engineer
Aerotech, Inc. -

http://www.aerotech.com

"Dedicated to the Science of Motion"

 

[EnglishMuffin]

Servocam : do you mean "10 times greater than the motor inertia"? If so - all I can say is - I'm speechless! (of course, its the natural frequency that really matters).

 

[SERVOCAM]

Yes, 10 (ten) times. In general motion control applictions it really isn't critical that the inertia be matched that close. Today's servo controllers and motors have the capability to handle larger mismatches. I have felt safe with up to 20:1 with one Mfgs drives. Once (for temp use so customer could demonstrate) I had a system at 115:1 inertia mismatch and could get it work fine with a little tunning.

On high performance precision applications, matching the inertia down is more important. But like any application, the inertia matchine will depend on many factors.



Cameron Anderson - Sales & Applications Engineer
Aerotech, Inc. -

http://www.aerotech.com

"Dedicated to the Science of Motion"

 

[EnglishMuffin]

Well, if you had a stiff system, it would work. But I can think of a number of applications from my own experience where 4:1 wouldn't work - so for a general rule of thumb (which is all it is), I think 10:1 is a bit much. As I say, its really the natural frequency of the system that matters. Also, for many applications, you also have to consider the absolute acceleration capability of the system. So I'll admit that rules of thumb are probably not very advisable here - its too complicated for that.

 

[CMcF]

So how do you calculate the natural frequency of the system?

 

[EnglishMuffin]

Look in a text that covers torsional vibration of a multi inertia system. Even that approach is a rule of thumb, however - it just gives you a rough idea whether you are likely to have problems. Of course, the fully correct approach is to write the differential equations of the system and use control theory to study the performance. Of course, then you will probably find that you need to know all kinds of details about the servo control system and motor that you probably don't have and can't easily get, so you end up giving the data to the servo control system manufacturer(s) and/or using their application software, if available.