Servo motor. Load Inertia-to-rotor inertia ratio

A little OT.

What should the 'load inertia-to-rotor inertia' ratio be for a properly designed servo system.

I am working on a system that has 7 servo motors. Three of them have a ratio of about 0.63:1 and four others have 24:1.
It is difficult to tune them and I am wondering if it is a mechanical problem or my lack of knowledge on these Bosch EcoDrive Cs with Sercos drives.

For the 24:1 cases, from my experience the stiffness of the coupling is an important factor. What sort of couplings do you have ?

For the 24:1 cases, from my experience the stiffness of the coupling is an important factor. What sort of couplings do you have ?

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For this case, the rotary motion of motor is changed to linear. The motor has a small pulley driving a timing belt. The load moves on a linear bearing and the load is coupled to the timing belt. The motor only can turn 3/4 of a turn.

There are many 'rules of thumb'
Generally a 1:1 ratio is considered ideal.
As the ratio of reflected load:rotor inertia goes up, the system gets progressively harder to tune for performance.
Some people recommend max. 3:1, some max. 6:1, others 10:1.
It is really just an indicator.

Stiffness (or, inversely, compliance) of the coupling also plays a part and you can typically relax the rule for inertia ratio if the coupling is stiff.

A timing belt is not considered stiff in this context. Coupled with a 24:1 inertia ratio, it would be very difficult to get any significant accel/decel out of the system and still maintain control.

I have a lot of experience with EcoDrives. My distributor would not have sold us the servos if they knew I had a 24:1 ratio.

Gerry has it right on all counts. You will not likely have success getting performance out of that system. If you have belts, can you get a better pulley ratio to improve your ratio?

YOu need a gear box to reduce the reflected inertia

The gear box ratio should be sqrt(Jl/Jm) is the ratio of the teeth on the motor gear to the teeth on the load gear. This gears the motor down so in can make more turns and makes the inertia look lower.

Peter Nachtwey said:

The gear box ratio should be sqrt(Jl/Jm) is the ratio of the teeth on the motor gear to the teeth on the load gear. This gears the motor down so in can make more turns and makes the inertia look lower.

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Yes, and a low backlash gearbox to keep your positioning accuracy...

It really is all about system stiffness. Rick, if you are using EcoDrives you must be dealing with the guys at CMA. Those guys are applying frameless motors directly to printer impression rolls very successfully. This mechanical package yields inertial mismatches in the 100:1 to 1000:1 range. They can do this because the motor rotor is locked onto the roll shaft. The motor to load stiffness is extremely high. Additionally the available torque is very high due to the motor construction.

While belt systems can be made to work you need to be disproportionately careful when applying them. You need to use the stiffest belt available (something like a Gates PolyChain). Upsize the belt at least one size from what the torque requirement calls for. Use the largest diameter sprockets you possible can. As you can see, as you do this the system inertia starts to climb. That is one of the reasons people use gearboxes in these situations; high stiffenss and low inertia in a small package.

Keith

A couple of relevant documents to aid in understanding

Either case is not ideal.
In the 0.63 to 1 you are using more current to move the rotor interia than load. Those axes should not be an issue to tune.
24 to 1 is not an acceptable mismatch. Your only possiblity with a mismatch that high is a constant velocity application, with very stiff mechanical transmission elements.
When it comes to tuning Ecodrives are very forgiving, but not 24 to 1 forgiving. Time to add a gearbox or upsize the motor.