Mutterings

It seems like I’ve spent a significant amount of time on blogging meta-activities like pressing the button to upgrade each WordPress plugin this year, even though I haven’t posted anything since last August. Oh well, life happens.

I have done a little printing, specifically a couple jobs that came my way via 3D Hubs. At some point I’ll get keen enough to add a button or whatnot here, now that an API for doing that has been made available.

I’ve been very quiet for a long time, but I’m starting to get back into the right mindset.

Jérémie FRANCOIS blogs about 3D printing and has some very neat posts about building one’s own parts, including hotends, that I’m keen to take a closer look at.

It also struck me that I should look into the structural qualities of my printer-to-be to ensure that I’m not setting unreasonable goals for the precision of the finished machine.

The major issue will be with vertical deflection of the horizontal guide rods that make up the bulk of the bridge, and across which the X-carriage travels. Using an online calculator and data references I can see that for 2 steel rods of 12mm diameter with support columns (the vertical threaded rods) separated by 400mm, a X-carriage of 1kg mass should cause deflection of no more than 47 microns. Since the entire mass will not be concentrated at a single point in the centre but distributed across LM12UU bearings at each end of the carriage, and the X-drive motor will be cantilevered outside one end, the actual maximum deflection will be somewhat less than this.

Deflection is proportional to load force so if I can halve the mass of the carriage I’ll halve the deflection. (Halving the acceleration due to gravity would have the same effect, but is significantly less feasible.) A Bowden extruder will help, but multiple extruders (maybe a Kraken) and a mount for my Dremel will take me in the opposite direction.

Deflection is proportional to distance-between-supports cubed and reducing it would have a huge impact. Dropping it from 500mm to 400mm reduced the deflection by almost half. To go any closer will really eat into my print area and I don’t want to do that. This needs serious contemplation, as one of my major goals here is to get significantly better precision than can be achieved with my PrintrBot LC.

Deflection is also inversely proportional to the fourth power of the rods’ diameter, thus using 12mm rods (which I have from several flatbed-scanner-autopsies) gives a 5-fold improvement over 8mm rods. Going bigger again, however, is not really an option at this stage.

My conclusion? 47 microns maximum deflection is probably OK, but it means there’s no point putting work into ultra-fine vertical motion control – 200-step motors directly driving 1mm-pitch threaded rods is already an order of magnitude finer than the possible bend in the rods due to gravity pulling the carriage down.

On the other hand, fine Z control could be used to more-smoothly compensate for beam-deflection by adding some extra Z lift as the carriage moves toward the centre. To do this right, though, would need some seriously good calibration of deflection across the entire X range. So this goes onto the Future Improvements queue.

Earlier I pondered the rarity of worm drive extruders. Upon reflection I can see that at least one reason would be the twisting imposed on the filament by the worm, but this filament-twisting could be eliminated by simply putting a gear driven by the worm between worm and filament. Another experiment joins the queue.

I realise I threw around one particular gear ratio without any explanation.

It is usually considered important to maximise the potential life of 3D-printed gears. If (for example) one tooth happens to be misshapen, then it will apply slightly different pressure to each tooth that it meshes with than will the other teeth on that same gear. If the misshapen tooth meshes with only a subset of the teeth on the other gear then over time those teeth will accumulate a wear pattern different from the others and the motion of the driven gear will become irregular.

To ensure that wear is distributed evenly, we arrange for each tooth on the driving gear to mesh with every tooth on the driven gear once before meshing with any of them a second time. This is not as difficult as it might seem – the numbers of teeth on the two gears simply need to be relatively prime. Neither number need actually be prime, so 10 and 51 (both composite) having no common factors larger than 1 means they qualify, and they are slightly closer to 5:1 than 10 and 49.

Many people choose New Year’s Day to make resolutions; I’m going to get in early by starting this exercise in extraversion today.

One of my motivations is to put down in writing (etc.) the assorted project ideas running around inside my head. Foremost right now is my “build a better RepRap” project, so I’ll dive right in.

A little over 2 years ago I backed Brook Drumm’s KickStarter project and after some months wait I received my Printrbot LC kit. Since first powering it up I’ve made a couple of small modifications to the machine but I want More Awesomeness. I don’t want to sacrifice any of the capability I have now, which means I have to build a second 3D printer while leaving the first untouched. I now have pretty much all of the vitamins except the hotend, and it’s time to get more serious about assembly.

The new machine is to be based on nophead‘s Mendel90 design. My main design goal is improved print resolution and accuracy, building on the serious stability of the Mendel90 frame. Extra features I’m adding in support of this include

• gear reduction (approx. 5:1) in X, Y, and Z drive, to trade off speed for resolution
• belt reduction (2:1) in both X and Y, ditto
• M6 1mm-pitch threaded rod for Z
• T2.5 belts and pulleys; maybe GT2 2mm in some future iteration
• gear reduction (approx. 5:1) and M6 1mm-pitch worm in extruder drive, to better match finest extrusion to finest axial motion
• anti-backlash gears (printed) in each train

Ignoring microstepping for the moment, resolution comes out as:

• X and Y: 200 step-per-rev motor, 51:10 gear, 16 tooth T2.5 pulley, 2:1 belt =>
  (200 step/rev x 51/10 x 2/1) / (16 t/rev x 2.5 mm/t) =>
  51 steps/mm, or 19.6 microns/step
• Z: 200 step-per-rev motor, 51:10 gear, 1mm-pitch thread =>
  (200 step/rev x 51/10) / (1 mm/rev) =>
  1020 steps/mm, or 0.98 microns/step
• extruder: 200 step-per-rev motor, 51:10 gear, 1mm-pitch thread, 3mm diameter filament, 0.4mm diameter nozzle =>
  (200 step/rev x 51/10) / (1 mm/rev) x (0.4 x 0.4)/(3 x 3) =>
  18.13 steps/mm extruded, or 55.15 microns/step

(I don’t plan to rely on microstepping for any increase in resolution, merely for smoothness and noise-reduction.)

I’ve seen a little mention of worm-drive extruders but not a lot about why they seem to have disappeared other than that they’re slow. Since I’m not initially concerned with speed I would like to find out what other disadvantages they have, and if I must I’ll find out by experimentation.