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16-09-2010 #12
I believe that whip occurs when the shaft rotation speed equals the natural bending frequency. So a ballscrew with a 20Hz nat frequency would whip at 1200rpm (=20 Hz[cycles per second] x 60 seconds per minute).
Natural frequency is related to SQRT(k/m) where k is stiffness and m is mass. Therefore in principle a hollow ballscrew, with slightly lower stiffness, but much lower mass, would give a high frequency and could rev higher before whipping, all else being equal. It would also have a slightly lower inertia, allowing slightly higher accelerations etc.
But never seen a hollow ballscrew, so either they are rare, or not worth the expense.
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