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Introduction: Threadless Ballscrew - 3D Printed

OK, so I found this on thingiverse and made a little testprint myself.

Basically you take at least three ball-bearings and group them around a plain steel rod - but skewed.

That skew will generate a linear motion when the rod is turned.

Pros of this approach are:

+ Almost no backlash.

+ Use stuff that you have laying around / can obtain for cheap to make something you usually have to order.

+ Travel-per-turn is variable! It depends on the skew angle and the diameter of rod and bearings (not sure on the exact math here). It seems that 20° will travel about double the same bearing-rod-combo would at 10° skew.

+ You can use multiple "speeds" on one rod at the same time.

+ Travel-direction is determined by nut-orientation. You can have multiple nuts with opposing directions on one rod.

Cons are:

- Holding-force is obviously much lower than with a thread-based system.

Shaft is a 4mm Fischertechnik axle, the bearings are 3x7x3mm and 4x8x3mm RC-hobby bearings.

I printed the centerpieces on my UP! mini at 0.25mm layer-height. Threads for the screws are cut directly into the PLA.

The purple one has a skew angle of 10°, the transparent one 20°

Here's a little video on YouTube.

Embedding videos here is crap by the way…

Step 1: Some Files…

OK, by popular demand - the STLs for the three ballnuts you see above…

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Questions

math behind traveling distance calculation:

given the diameter of the shaft D, and bearing angle ϴ, how far does it travel if the shaft takes a full turn?

the bearing travels a helical path alone the center of the shaft
if we expand the cylinder (the shaft often has a cylindrical shape... if yours doesn't, you're in trouble.) into a plane, we get a right triangle with it's hypotenus equals the circumferences of the cylinder C, distance traveled by the ball bearing alone the helical path T, the angle towards the direction of movement ϴ, and movement along the shaft h.

the shaft with diameter D has a circumferences of C = D * π, the distance the nut has traveled is:

h = tan(ϴ) * D * π

for example,
1. a 8mm shaft with 20 degree ball bearing angle will travel

h = tan(20 degree) * 8mm * π ~= 0.364 * 8mm * 3.1415 ~= 9.147mm

after a full turn.

2. a 8mm shaft with 10 degree ball bearing angle will travel

h = tan(10 degree) * 8mm * π ~= 0.176 * 8mm * 3.1415 ~= 4.4315mm

after a full turn.

3. a 16mm shaft with 10 degree ball bearing angle will travel

h = tan(10 degree) * 16mm* π ~= 0.176 * 16mm * 3.1415 ~= 8.8631mm

after a full turn.

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now, say you want the nut to travel h mm after a full turn of the shaft, how do you calculate the correct angle for it?

taken the above equation

h = tan(ϴ) * D * π,

rearrange that

tan(ϴ) = h / (D * π),

ϴ = tan^-1(h / (D * π))

for example, you want the nut to travel 4mm alone a 16mm shaft:

ϴ = tan^-1(4 / (16 * π)) ~= tan^-1(0.00795) ~= 4.55 degree

=============

HOWEVER,

1. bearings got play and tolerance
2. shafts got tolerance
3. 3D printed parts got tolerance
4. friction of "steel against steel" is not very high...

how long a specific "ball bearing bearing nut" will travel per shaft turn may vary from nut to nut.

the above equations just give you an idea on how to design your own nut, for precision cnc you ALWAYS has to calibrate your machine.

=============

dunno if we have something like rubber coated bearings or not?

I know there're POM bearing wheel out there (such as the wheel used in V-slot or other aluminium extrusions), but POM is a low friction (ie, slippery) material...

maybe i'll get the tires from those mini 4WD and try them out...

2 replies

@palatis

Cool stuff bro, thanks for the math!

I am sure this will help a lot of people.

damn where does the image go?

@palatis

Cool stuff bro, thanks for the math!

I am sure this will help a lot of people.

This is really cool! Do you have the files of this part? And embedding YouTube videos is really easy. If you just copy and paste the URL (while on the computer) and hit enter you're all done. That easy!

2 replies

Alright, here you go.

The M3 holes are Ø 2.5mm for proper threadcutting.

The M4 ones are Ø 3.6mm since I have no M4 cutter, so I just used the screw itself to cut a thread. Make sure to do it properly and at the right angle or the rod won't be centered.

Look on thingiverse for "Threadless Ballscrew".

There is a customizable one on there somewhere - fitting whatever parts you have at home.

Also i tried all possible ways to embed the video, neither of them works.

Maybe it's a problem with the latest Safari…