Threadless Ballscrew Nut (5 degree tilt for 16mm shaft)

This is another design for threadless ballscrew nut.

The nut relies on friction of the shaft and bearings to grip, and move by turning the nut or the shaft.

You'll need:

1. M6 x 47mm screws x3
2. M6 x 20mm screw x1
3. M6 x 11mm x 1mm spacers x6
4. M6 nuts x3 (or x6 if you want to "lock" the nuts in place)
5. M6 square nut x1
6. 626 bearings x6

You want to print 2 identical pieces and put the back-to-back, place the square nut in the slot for the adjustment screw, and screw the bearings and "tension adjustment screw" in.

To make spacers, I just pick up some M6 washers, secure a stack of them onto a M6 screw with nut, put them on a drill, and turn down the outer diameter with a grinder.
If you don't have a grinder, you can use some sandpaper to do the job.

You want the spacers to avoid the outer bearing ring (and maybe the sealing cap?) to grind against the printed ballscrew nut, and with some support under the bearing you can tighten the screws with greater force, thus better secure the nuts in place.

The 2 screw holes for the fixed bearings are a bit tight, you just tap them when you screw them in.

as a bonus, you can loosen the adjustment screws so you can slide the nut around the shaft, acts as a "quick release" like what you have on a lathe :-D

The tested nut

The nut I printed (shown in the picture) sustained my full body weight (approx 55kg), I can't get it to slip even I apply nearly my full weight onto it.

It's 5 degree tilt angle on a 16mm shaft, according to calculation it should travel about 4.397mm per revolution, with my (cheap Chinese) digital caliper it traveled around 4.66mm per revolution, I think the error is introduced by:

1. the play on the bearing
2. resolution of the printing (I'm printing with 0.2mm layer height on a Flashforge Creator Pro)
3. the cheap Chinese caliper... got it for like USD$15...... you can't really count on that.

The math behind revolution and nut movement:

1. let the tilt angle of the ball bearing be ϴ
2. let the diameter of the shaft be D
3. the circumferences of the shaft be C = D x π
4. the movement of the nut after full revolution be H

given the angle ϴ and shaft diameter D

the movement of the nut per revolution is:
H = tan(ϴ) x D x π

for example:

1. a 8mm shaft with 20 degree ball bearing angle will travel
   H= tan(20 degree) x 8mm * π ~= 0.364 x 8mm x 3.1415 ~= 9.147mm
   after a full revolution.
2. a 8mm shaft with 10 degree ball bearing angle will travel
   H = tan(10 degree) x 8mm * π ~= 0.176 x 8mm x 3.1415 ~= 4.4315mm
   after a full revolution.
3. a 16mm shaft with 10 degree ball bearing angle will travel
   H = tan(10 degree) x 16mm x π ~= 0.176 x 16mm x 3.1415 ~= 8.8631mm
   after a full revolution.

given the shaft diameter D and desired travel distance H

the tilt angle of the ball bearing should be
ϴ = tan^-1(H / (D x π))

for example,

1. you want the nut to travel 4mm after a full revolution with a 16mm shaft, go for
   ϴ = tan^-1(4 / (16 x π)) ~= tan^-1(0.00795) ~= 4.55 degree