Is there any problem in conducting dynamic balancing of rotor with lower rpm than the rated rpm of the machine? For e.g. for a 3000 rpm motor rotor if we are doing the dynamic balancing @ 750 rpm will it create any vibrational problems. If it is so what is the acceptable speed limit for doing the dynamic balance of 3000 rpm rated motor rotor.
As a minimum, the equipment really should be balanced at operating speed. The "acceptable" capability limit of the facility performing dynamic balancing of a 3000 rpm machine SHOULD be roughly in the 4500-5000 rpm range. This is because when a machine is manufactured to either NEMA or IEC standards, it must be mechanically capable of withstanding a 1.25 per unit over speed condition (e.g. it doesn't come apart and injure adjacent personnel or equipment). The only way some users will validate the design is to actually operate at that kind of speed.
There is a lot that can change between 0.25 and 1.00 pu speed. Aside from the purely mechanical stresses, there are also significant thermal distribution issues - coolant flow is not going to be the same at the slower speed.
Second thought: most of the testers who do this type of "assessment" at reduced speeds have significant experience with how the equipment operates at the actual operating condition and have developed empirical fudge factors to accommodate this.
Knowing nothing else about the test subject (rotor) or the test equipment (the balance machine), I'd estimate that you'd be looking at an upper vibration limit of somewhere in the range of 0.3 to 0.5 mm/sec velocity at 750 rpm to ensure "good" (20 mm/sec) performance at 3000 rpm. And yes - you'd have to be measuring velocity or acceleration - not displacement.
Best bet - if your facility does not have the capability for appropriate testing, find someone who does and CONTRACT OUT THE WORK. It will save you immense headaches and possible lawsuits later on.