Torque Calculations for Vertical Power Screws

Several of the RepRap team are using stepper-driven threaded rods to drive linear positioning axes. Since torque required for the horizontal axes of our RepRaps is proportional to the product of the friction coefficient and the load and since the extruder is very light there is typically not much worry that even the smallest stepper motors salvaged off of printers and disk drives will be up to the job.

The vertical axis is another matter, however. In my own design the vertical axis steppers must lift not only the extruder but also the positioning systems, structural parts and guide rods for the horizontal axes. In other designs being developed the whole working surface plus whatever it is that is being fabricated wants lifting.

After I acquired the high torque NEMA 17 steppers I noticed that the 24 volt power supplies that they needed for achieving their peak torque performance were considerably more expensive than the much more ubiquitous 12 bolt supplies for a given watt rating. Checking with the manufacturer I learned that while there was no real problem with using 12 volt supplies with them I could expect their torque performance to drop off by roughly half with the halving of the voltage supply. I then began to wonder whether the four NEMA 17's operated with 12 volt power were up to the job of moving the vertical axis loads on my very large, heavy RepRap design.

I was able to quickly establish from load tables on screw jacks that they ought to do the job. Shortly afterwards I found a little paper giving a methodology for calculating such torque requirements. I've reworked the methodology therein into the attached paper which you might want to use if you have similar worries about stepper loading.

http://reprapdoc.voodoo.co.nz/pub/Main/FAQ/TorqueCalculations.pdf

I ran several examples and the results agree fairly well with the screw jack tables on the web. There is a worked example at the end of the paper for a 3/8-24 threaded rod. That is a shade bigger than the 8 mm threaded rods that several of you are using but still very similar.

In using this methodology please keep in mind that I make no claims for it's robustness. It has been nearly 40 years since I took dynamics in engineering school and there were several problems in derivations in the source paper that I was able to see that I tried to work around. It might give you an idea whether a stepper's lifting capacity is up to scratch in extreme cases like mine though. I always try to use a 100-250% safety factor when I design things.

If our blogs have any dynamics boffin readers I would appreciate any suggestions or criticisms of what I have cobbled together here.

One last thing, the header rather cheekily refers to the paper as "A Scientific Report". I make no such claims. That is an artifact of the Scientific Notebook template that I used when I put the paper together. I've not yet got sophisticated enough in using the text editing aspect of Scientific Notebook to figure out how to turn that header into something more appropriate.