Motor stability

I am commisioning a servo system, and I saw some instabbility on a chain driven by a servo motor. Although when I trace the motor speed, at 300 rpm only a fluctuation of about 15 rpm was visible, which could not account for the instabillity on the chain, so it must be the mechanical drive chain.
I was wondering if someone could estimate what 'normal' stability for a good tuned motor is, related to the motor speed. For instance : for a 1500 rpm asynchronous motor :
at 100 rpm : 15 rpm, at 300 rpm : 20 rpm, at 1000 rpm : 12 rpm etc.., and the same for a synchronous servomotor.
What could be the difference between an uncoupled motor and a motor connected to a load?
This information would help me a lot in evaluating the quality of my motor tuning.
Thanks

Please post some screen shots of the trace
Speed contoller and position controller

What could be the difference between an uncoupled motor and a motor connected to a load?
ANSWER the torque demanded by the load.

I think you need to describe what the driven load is and have a good idea of what the changes in the torque demanded by load are.

Dan Bentler