max length of ballscrew

[stirling]

Hi - hope this is the right forum.

Advice needed on max length before sag is a concern with 16mm diam rolled ballscrews (isel). I'm not worried so much about whip as I'll only be driving them Max 5 revs/sec.

Thanks

Ian

[schbrownie]

I looked for a ball screw calculator/formula, but I wasn't able to find one... so we can do a little logical assumption to help you come up with an answer. The stanards book I have says that the root diamater of a 16mm ball screw is about 13.4mm. So, if you do a calculation for the deflection of a 16mm steel shaft and for a 13.4mm steel shaft, the deflection of your screw will fall somewhere inbetween these two numbers.

To play on the safe side, you could just skip doing the 16mm shaft and only do the calculations for the 13.4mm shaft.

Sag = L^4 / S
L = length
S = Sag Coefficient

S = E x I x 384 / (5 x sw)

E = Modulus of Elasticity
sw = PI x diam^2 / (4 x density)

If you want to save yourself some math... pacific bearing's catalog has a lot of the math done for you and it's in chart format. So...

Sag = L^4 / S (getting S from a table)

So.. here are the entries for a 14mm shaft:
S = 2.45 x 10^12 for hardened steel
S = 2.31 x 10^12 for stianless
you pick your material

Don't forget to use millimeters for length.

[ger21]

Originally Posted by stirling Hi - hope this is the right forum. Advice needed on max length before sag is a concern with 16mm diam rolled ballscrews (isel). I'm not worried so much about whip as I'll only be driving them Max 5 revs/sec. Thanks Ian

Use the critical speed calculator here.

http://www.nookindustries.com/ball/BallCalculators.cfm

Put 13 in for the root diameter, and 300rpm, and it'll give you a max length. It varies depending on the mounting.

[stirling]

Thanks to both of you. I calcualted from schbrownie's figures that with a 1m screw I'd have 0.4mm of sag, which is intuitively reasonable I feel. Wheras with a 2m screw (the length I actually need) it shot up to 6.5mm which I think is probably too much - though I don't really know to be honest.

(thought: if I never reach the critical speed - does 6.5mm of sag over 2m actually matter? - maybe that's where compressive force comes in but see fixed-fixed below - wow this gets complicated)

From gerry's calculator (I assume the resonant speed is where whip occurs or perhaps maximises) I'm within bounds. Of course the fact that the sag is probably unacceptable negates this anyway.

Whilst researching this I came accross the four accepted methods of ballscrew support again i.e. the so called fixed-free, simple-simple, fixed-simple and fixed-fixed. I currently use the fixed-simple scheme in the form of a double angular contact bearing for the fixed (driven) end and a fully floating bearing at the other end. I use this because I was told that if you use fixed-fixed then this leaves no mechanism for screw expansion/contraction with temperature change. Any thoughts on this please? I ask because the fixed-fixed system (e.g a double angular contact at both ends) appears from the data to give higher performance for a given screw.

FWIW I looked at techno isel's technical papers but I'm sure there's a problem with their critical speed/screw length/diameter chart. It doesn't appear to make any sense to me at all. For those interested it's at http://www.techno-isel.com/LMC/H860/PDF/H860P019.pdf page 22.

Thanks

Ian