prym,
What are you trying to accomplish with your analysis? Are you trying to design/optimize the components sizes or materials? Are you trying to model behavior under dynamic loads? Are you trying to get a rough factor of safety or detailed deflections? Knowing your objective may help tailor our advice for you.
If you are simply looking at axial (thrust) loading, you could probably simplify your model by using radial symmetry (e.g. analyze a "pie piece").
However, if you are looking at unbalanced or dynamic loads, you probably need to retain at least half the model. This means a lot more elements and contact surfaces, but it can be done. In any event, I recommend using symmetry as much as possible (this will help with your constraints as well as decrease your model size)
I expect that, whatever your objective, you'll be using a cylindrical coordinate system (r, theta, z).
With regards to constraining the balls, the contact surfaces with the races should be enough to keep them from "flying off". But, if you encounter problems, I have found success with attaching weak ground springs.
Hopefully, some of this gets you started. Feel free to feed back with questions or images and we can help you out.
Pete