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3D printer use stepper motors for moving print head and extruding filament. They need to have good torque and resolution.

Microstepping improves resolution as much as 32 fold (I think) but reduces torque the higher you microstep.

So...

  1. Why not rotate the motor with microstepping at high RPM (which also reduces torque) and increase the torque by heavy gear reduction using a worm gear?

  2. Won't the movement of printhead be even smoother and small errors in microstepping and unevenness of gears be averaged out using high RPM and gear reduction approach?

  3. Does microstepping indeed provide accurate divisions of steps?

  4. Can we get by with weaker motors because torque will be increased by gear reduction?

  5. Can we get by with 48 step stepper motors instead of 200 step because gear reduction provides increased resolution?

  6. There are extruders that use flex shaft to turn worm gear in direct extruder while motor is mounted on frame which turns flex shaft (zesty nimble comes to mind). Why don't they just use smallest possible stepper motor to rotate worm gear directly, instead?

Increasing motor RPM and using gear reduction should preserve the precision and torque, letting you use weaker, lighter motors, potentially reducing granularity of movement. I thought this was simpler approach and I wanted to understand what would I be losing as trade offs. I had considered more friction at worm gear and wear, higher heating of motor etc. But may be it's like "don't fix what ain't broken". 3D printers aren't that costly nowadays. I just wish they were even cheaper.

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    $\begingroup$ Engineering is the act of selecting trade-offs. While your idea would certainly work, it imposes it's own (rather large) set of tradeoffs. Among these: more complex, more wear, more potential harm from inadvertent axis moves, each moving interface either lowers precision or increases friction, fast printing with high RPMs would generate more heat, there's limits on how precise one can even work soggy plastic - no matter the precision of the machine, etc. $\endgroup$
    – dandavis
    Jun 15 at 16:19
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To answer each point:

  • Microstepping improves resolution as much as 32 fold (I think) but reduces torque the higher you micro-step.

Torque is not reduced by micro-stepping. Torque reduction only occurs when you are moving at high RPMs. The motor's phase resistance has to be conducive to the target RPM's (or step rate). Further, micro-stepping can go as has as 1/256, and I have personally used 1/128. Some will say that all higher micro-stepping does is improve smoothness not accuracy. I have personally tested 1/128 micro-stepping over a 17-inch long axis. I was able to achieve accuracy and repeatability to within 5 microns.

  • Why not rotate the motor with micro-stepping at high RPM (which also reduces torque) and increase the torque by heavy gear reduction using a worm gear?

Backlash! The whole point of stepper motors is that they produce backlash-free movement. Putting a transmission between the electromagnetic and the end effector will create backlash that has to be compensated for during the movement. Modern CNC systems account for this in their movement profiles and incorporate automatic backlash compensation (e.g. Mach3)

  • Won't the movement of printhead be even smoother and small errors in microstepping and unevenness of gears be averaged out using high RPM and gear reduction approach?

It is already smooth enough with 1/64th or greater micro-stepping. The extrusion nozzle only goes down to 2mm.

  • Does microstepping indeed provide accurate divisions of steps?

Yes. Yes, it does.

  • Can we get by with weaker motors because torque will be increased by gear reduction?

No, because it will just stall.

  • Can we get by with 48 step stepper motors instead of 200 step because gear reduction provides increased resolution?

Apart from the fact that no one makes 48 steps per revolution motors, using a gear reduction would be counterintuitive. Currently, there are 400 steps per revolution motors, which actually increase accuracy without any torque losses.

  • There are extruders that use flex shaft to turn worm gear in direct extruder while motor is mounted on frame which turns flex shaft (zesty nimble comes to mind). Why don't they just use smallest possible stepper motor to rotate worm gear directly, instead?

Torque! If they used a small motor to drive the extruder they would have to compensate for the torque loss with higher power (i.e. voltages). This would lead to cooling issues for that motor.

Bottom line is that if you size the motors and design the system correctly then a transmission is not needed. If you want more torque, get bigger motors. If the gantry needs to be light weight, then use a delta or corexy mechanism.

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  • $\begingroup$ 28BYJ-48 is common 48 steps motor in diy robotics. The info on microstepping is very confusing on internet. I've read that even half step microstepping doesn't ensure precisely half movement of a full step. You're saying microstepping offers all the precision and torque needed, in which case it seems I'm trying to solve a problem that doesn't exist. I don't understand however, why you're saying a weaker motor with gear reduction will stall. Doesn't gear reduction increase torque? $\endgroup$ Jun 15 at 17:36
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    $\begingroup$ @MiteshPatel, A weaker motor with gear reduction still has to overcome the friction in the transmission system. Further, unless that "weaker" motor is sized correctly when it is spinning at a higher RPM it is more prone to stalling, due to Back EMF, causing a torque reduction. $\endgroup$
    – user77232
    Jun 16 at 13:28
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There's an old rule that says "If the question starts with 'Why don't they,' the answer is most likely 'money.'"

In this case, the issue is the cost of worm gears. Properly mating worm gears are much more expensive to make than common spur gears. That probably accounts for most of it -- not to mention the 200 step motors we see on most FDM printers are a very common item, and the more you make of something the less each one costs.

Beyond that, you can't back-drive most worm gears (especially those with a high reduction ratio). That wouldn't affect an extruder (or would it? I've seen a lot of Things for knobs to go on the extruder motor shaft), but if I couldn't back-drive my X or Y axes I'd be very annoyed (having to use the manual motion control in the firmware for everything like bed tramming) -- even the lead screw Z axis can be back-driven without undue effort.

So, bottom line, what we have now works well enough and making it (maybe a very little bit) better would cost more than what we gain would be worth. IMO.

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  • $\begingroup$ Thanks for your answer. You're of course right about prohibitive high costs of precise worm gears, but zesty nimble folks are already using plastic worm gears. Seems, with 1:40 reduction precision is non issue. Nema 17 motors used in most 3D printers are not very costly but using smaller, faster motors can be even cheaper. I'm thinking of same precision, but cheaper, not seeking more precision. Also, worm gears can be driven forward and backward by motor, but load can't back drive worm, which is advantage IMO. $\endgroup$ Jun 15 at 16:23
  • $\begingroup$ I say again -- if I can't back-drive at least my X, Y, and Z axes, there will be some pretty sudden retrofitting going on. "Back-drive" is the load end driving the motor, not direction of the motor driving the gear. Most worm gears (even at only 40:1) can't be driven from the output shaft due to friction angles. $\endgroup$
    – Zeiss Ikon
    Jun 15 at 16:30
  • $\begingroup$ I don't understand why should load back drive motor. I think I'm missing something essential here. Is it so that if inertia of load is so much that if motor doesn't yield, something in the power train would break, most probably worm gear? I agree that load can't back drive a worm gear, but I was thinking that would make the mechanism stiffer and motor won't have to fight inertia of print head when changing direction. Worm gear would insulate motor from inertia of print head. $\endgroup$ Jun 15 at 16:45
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    $\begingroup$ When I "level" my bed, I auto home, set my Z offset to the thickness of the feeler gage I use, and then disable steppers. It would take several times as long if I had to go from X to Y "Move Axis" menus repeatedly to move the bed and hotend because I couldn't drive the (idle) stepper by pushing on the load. Extruder is the one place a worm gear might not cause trouble -- but I don't see us needing that level of leverage there; existing geared extruders use 2:1 or 3:1 gearing and change the steps per millimeter in the firmware. $\endgroup$
    – Zeiss Ikon
    Jun 15 at 16:53
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  1. There are extruders that use flex shaft to turn worm gear in direct extruder while motor is mounted on frame which turns flex shaft (zesty nimble comes to mind). Why don't they just use smallest possible stepper motor to rotate worm gear directly, instead?

The Flex3Drive, from which the Zesty was purportedly cloned, does admit using a very small NEMA-8 motor directly coupled to the worm gear in place of a flex shaft. This still adds a considerable (from the standpoint of machines aiming for 40 m/s² acceleration and such) amount of mass to the toolhead, and I'm not clear what E-axis speed/acceleration is attainable with 40:1 reduction and a low-power motor like that.

While the larger steppers typically used in 3D printers are perfectly capable of any plausible E-axis speed or acceleration you could want without gearing or with small reduction (e.g. 2:1 or 3:1), once you get up to worm gear level ratios, it's a question of the properties of your specific motor whether you can get enough speed for acceptable retraction performance or even normal print moves at very high speeds. For example, I have a Flex3Drive G5 and the orignal NEMA-17 E-stepper from my Ender 3 does not work well with it without further gearing on the motor side of the shaft. However, a "high RPM stepper" like you suggest should manage just fine with worm gear reduction.

Now, is there any reason to do this? If you're transmitting the force in a manner that can't deal with high torque, like a flex shaft, yes. Otherwise, no. As others have said, modern microstepping is ridiculously accurate.

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