A dial indicator is a little overkill in my books, but be aware its a mechanical system. so tolerances will show you up if you don't account for them.
A fair bit of this is in relation to Delta Printers, but the ascpects overlap.
So as a simple start, a commercial kit or printer will generally not have an error in the angle of the vertical rods, (120 degrees), Its hard to measure and the influence from it is tiny. More likely your rods may not be quite parallel to each other, this causes binding or resistance in the carriages as they move up and down. which causes failures that may be dependent on temperate or minute changes.
Next in the chain is the carriages that travel up and down the vertical rods, depending on the bearings used they can rock side to side, in or out, etc, for a number of these, you can bias the bearing holders to reduce this motion, It is a source of backlash, and sadly most devices don't place the pivot for the diagonal rods at the center of rotation of the carriages, this alone would mostly eliminate it. you may see modders making carriages with more than 2 bearings to remove it, but biasing accomplishes the same task
Ok moving on the diagonal rods, My cheap choice of printer has had the majority of people recieve different length rods, due to the geometry of a delta if they are not very similar in length its impossible to make its travel level, a quick way to see if this is the case without disassembling a delta is to have it move along the A,B and C axis's of travel, the print head should not rotate at all. These rods are also where a number of people have tired to hunt down backlash, generally by rubber banding them, where in reality there issue is generally the metal pieces that attach to the sleeve bearing are not the right length and just need a nick of a file to bring rigid.
And finally all that's left in the middle is the print head plate. the lower the mass here, the less backlash and overshoot on fast direction changes your likely to see, dont go crazy, but lower weight here can mean a faster average print speed without issues like speed wobble as the motion rings out for a few mm past a 90 degree corner. Generally I havent seen things go wrong here, but a metal piece will last far longer than plastic as the hot end will deform it over time.
Ok so moving on to calibration. Delta's are a little hard to visualize at first glance, its part of what makes the math so weird, but in general as long as the build area is dead flat, and secured rigidly, it being perpendicular to the rods is not so critical, 2-3mm out of plane to the vertical rods can be calibrated out just by the end stops.
Ok, so first up, a Delta's true axis's of motion are A, B and C, towards and away from each tower, there may be a Y axis or and X axis depending on your machine but there is never both, 1 is just calculated. as such calibrating on X and Y axis only hides a lot of the information the movement is trying to tell you.
The first thing I adjust on a delta is its tramming per axis, You move it from one end of a towers axis and back again, noting which end it was out of tram, if it was low towards the tower, you want the end stop position higher, and vice verse, you will likely have to run through this step on each axis a few times in a circle, as it does slightly effect the other axis's as you tram one, but it does converge pretty quickly,
Next up is the Delta Radius, The math to convert a delta's radius based motion to XYZ is based upon an assumed radius of motion, If this radius is too high, the print head will raise towards the center of the build area, and fall towards the outside, and vice versa, most open source printer controllers (marlin or repeater firmware) let you correct this, generally saved to eeprom or by uploading a revised program over USB
And finally is build volume height, rather than touch your carefully adjusted end stops, instead lock them down and just tell the printer its taller or shorter to raise or lower the nozzle to the surface.
Now at this point i would always print a filled 1 layer high circle as a confirmation, generally by eye, looking at how translucent a printed piece is you can spot extremely tiny errors, on the level of a few microns, as the amount of smoosh between adjacent lines changes. this allows for some final small tweaking in.
At this point you should be ready to print something to tolerance, PLA loves cooling, ABS loves heating, for pla get some painters tape and a UHU glue stick, smear a very thin layer of the glue over the tape and you will be set, I've done well over 200 prints without applying new glue or changing the tape (I will eventually need to change it, its starting to discolour) For ABS, go with Kapton tape, a mist of Acetone on the build plate a minute or 2 before printing generally gets the level of adhesion i need (trace amounts of abs still embedded on kapton)
Things to be aware of, When you first run filament through a hot end, it will come running out at you, same for when it heats up to temp the expansion will cause some to shoot out the hot end, this is normal, if you can hear it sizzling, its either quite moist (humidity) or your running it too hot, for PLA humidity is generally fine, for ABS its more of a pain in interlayer bonding, so those rolls should be stored with a desiccant if your not using it for more than 2 weeks,
You will through a little bit of trial and error stumble upon the correct speed and temp for a given filament, e.g. the PLA i use reguarly, the white is 217C for speeds up to 50mm/s ramping up to 230C if i wanted to get to 85mm/s (the heat needs to fully melt the center of the filament), while the Black PLA i use, melts just fine at 182C, but I cannot run it faster than 30mm/s without crazy stringing, In both cases it relates to viscosity, but there will generally be a sweet spot that works best for you, both these filaments came shipped as (195C), but its never exact in my experiences.
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