Jeshua Lacock wrote: > On Jul 20, 2012, at 6:00 PM, Stephen Dubovsky wrote: > > >> Sag is only the start of the problem. The whip is going to be the real >> problem. >> > > Hi Stephen, > > I am not sure I understand what you mean by "whip"? > > Long, thin shafts tend to "whip" when spun at high speeds. Look up "first critical speed". When the rotation speed matches the first vibrational moment's natural frequency, the vibration can build to enormous magnitude very quickly, permanently bending the shaft. Above the first critical speed, the shaft will rotate about its center of mass. Below that speed, it will rotate around the axis of its support bearings. Most ballscrew manufacturers have charts of critical speed, and you'd be amazed at how low these are for the longer ones, even at 25mm diameter. Also remember that a ballscrew is a lot less stiff than a solid shaft, and so the natural frequency is a lot lower.
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