Mike,
Great question!! The balancing process is indeed accomplished at a fixed RPM, because the belt drive motors on the balancing machines are generally fractional horsepower AC induction types.
Both the situations you describe can and do cause apparent imbalances. The machine uses the amplified signals it receives from its vibration sensors to synch a strobe to whatever speed the arm is being driven, so that small variations in the test RPM due to arm diameter variations can be ignored. The 'filter' adjustment control furthur refines this parameter. Anotherwords, the imbalances due to non-concentricity are not speed sensitive. They are of greater amplitude at higher speeds, but still entirely proportional to the rotation speed/frequency.
Balance corrections (drilled holes) are therefore effective in resolving imbalances due to non-concentricity of the laminations. Bent shafts, on the other hand, manifest themselves in varying degrees based on where the armature is supported. If I carefully balance an arm with a bent shaft, it will appear to fall out of balance as soon as the vee blocks are spread differently. Shafts that change diameter due to wear behave the same way. The sad fact is that MOST arm shafts are bent to a small extent, the only real question being "how much?" When operating the balancing equipment, the operator soon learns that an arm which simply won't come down to a good reading almost always IS bent!
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