there is nothing intrinisically wrong with long lead screws as long as they are correctly supported in tension by appropriate supports and of sufficient diameter. Making them larger pitch reduces the revs needed which also alleviate whipping. The issue then becomes one of inertia; a long, thick screw has high inertia needing lots of torque to accelerate it, but again that can be offset by a larger pitch...
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.
Wouldn't a hollow ballcrew have a greater moment of inertia, which would affect the acceleration?
Otherwise it sounds like a good idea, if you've got a nice long drill :lol:
Cant see why that is not possible.. Would just need to have one thread cut and ground from a high carbon steel tube... I think Jonathan, (aint no expert) that the inertia is a function of mass, which would be considerably less with a tube...
P.S. Am starting to wander away from rack & pinion..
I'm no expert either! But the moment of inertia, I, of a tube is 0.5*pi*(R^4-r^4), where R is outer radius and r is inner radius. From that you can easily see that the further out the mass is distributed the higher I gets. In a tube all the mass is far out...
I'm not sure without working it out properly - what diameter solid ballscrew would be equivalent to what diameter tube, that's the question.
This may be straying into the realm of the theoretical, not sure such a thing as a hollow lead screw exists.. But I do see your point although the inner mass of a solid would still require movement and account for some of the power required to rotate it.. Just checked florins posted specs and he has used 25mm dia leadscrews, and 2 nema 34 12N motors to power them.. Those motors would probably pull my car up a hill..!
We're deviating from Steve's original topic, but you need to compare like with like diameters. If you start with a solid 16mm dia ballscrew, and compare it to a 16mm dia hollow ballscrew (theoretical) with say a 10mm dia bore, you will find it has less inertia. The reduction is only small because you are taking it away from the middle, where it has less effect.
In your equation R is fixed at 16mm and r varies from 0 to 10mm (in this example). So R^4 - r^4 gets smaller, and the inertia goes down.
the fallacy is that a 20mm screw on a 5mm pitch has a minor diameter of 15mm which means the inner bore couldnt be more than 10mm, so the stiffness would be the same as a 19.5mm solid screw and the inertia similarly.. i.e. boring a 10mm hole reduces the inertia by 7%... hardly worth the effort.
On a 40mm dia, 40mm pitch screw the thread minor dia is 35mm so a 25mm bore might be possible... about a 16% reductoin in inertia... might be worth it in some scenarios
but overall, not worth the trouble, which is why you never see them
The inertia benefit is marginal, but it's interesting to compare a 20mm dia solid with a 20mm dia tube with 15mm bore which shows ~28% increase in natural frequency, so potentially a 28% increase in rpm before whipping . . .
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