Are you climb milling or conventional? I would recommend NOT climb milling.
Could be slide way screws to lose or too tight. Be sure to use a torque wrench to tighten ALL slide way screws. Could be servos out of sync. Which tech support should be able to help you with that. How long is your tool sticking out of the tool holder. Choke up tight as you can. Long tools deflect and scream when cutting. Don't know if this helps. But as you can tell there are alot of variables when it comes to tracking down problems. What material are you cutting? What are the speeds and feeds? Whats the tool diameter? Is it with all tools and all ovals? Have you checked your vectors? Do you have steppers or servos? Something may have nothing to do with the problem. Got any pictures? The machine shaking sounds real weird. Are all your screws tight?