iucu-
It would help if you would provide more details. Based on your limited description, it sounds like you have either a dynamic imbalance issue or a rotor/shaft dynamics issue.
To keep things simple I'll assume your shaft is operating at a safe margin (maybe 25%) below its critical speed. However, one thing that can affect critical speed is stiffness of the shaft bearing system, and bearing preload will usually increase shaft critical speed. Your deep groove ball bearings probably operate with some internal radial clearance and are not preloaded. So Tmoose's suggestion to use a pair of angular contact ball bearings axially preloaded with a wave spring is definitely worth considering if critical speed is a concern
Dynamic imbalance is fairly easy to resolve. You simply need to dynamically balance your rotating assembly. Take a look at
ISO 1940/1 for details of the procedure. Your application sounds like it would require balancing in two planes to quality grade G6.3 or G2.5.
If the vibration is due to excitation of some structural mode (torsion, bending, whirling, etc) in the rotating assembly, resolving the problem may require much more effort. As BrianE22 suggests, before making any changes the first thing you need to do is diagnose the existing situation. Measure the vibration characteristics of your operating system. Calculate the operating frequency range of all potential sources of excitation in the system, such as gear/belt/chain meshing frequencies, bearing element passing frequencies, input/output forces acting on the rotor, etc. And if you have the capability, perform an analysis to determine if your rotating assembly has any structural modes that might couple with the excitation frequencies. Resolving this type of issue can usually be achieved by modifying the rotating component size/shape/section to shift the particular structural mode outside of the operating range, by using larger/stiffer shaft bearings with increased preload, or by modifying associated drivetrain component characteristics (such as meshing or passing frequencies) to eliminate the source of excitation.