In a 3D printer (or any other CNC application really) where a lead screw is part of a motion system, there is a design choice to be made. . .
- Drive the lead screw, having the lead screw nut fixed in place.
- Drive the lead screw nut, having the lead screw itself fixed in place.
There are "claimed" pros and cons to each path. Specifically, driving the lead screw is mechanically far simpler (install a flexible coupler between the motor and lead screw, and you're done!) but has apparent problems with accuracy because of shaft wobble, as well as speed because of fighting high rotational inertia. Driving the lead screw nut, on the other hand, is mechanically more complex, but has a fixed (supposedly low!) inertia for any lead screw lengths as well as more manageable wobble characteristics. (It should be noted at this point that most professional, high-performance systems do indeed drive the lead screw nut.)
Operating under the above ostensible wisdom, I was planning a new 3D printer build based on the concept of a lead nut drive. While making an efficient and affordable parts list, I was noting that the taper bearings I found most reasonable to use to make the nut drive, as small as they are, are still quite the mass of steel. Furthermore, the diameter of the rotating bearing mass is quite a bit larger than my preferred lead screw diameter. Since I would assume the radius squared term in the equation for rotational inertia takes some kind of key stand here, and my lead screws themselves could be any conceivable length, I started to question the wisdom that it's "always" more performant to drive the lead nut.
An extreme counter-example is if one used something like two sets of LM67048/LM67010 cone/cup pairs, where a single cone weighs in at >100 g, and has an outer diameter of >16 mm, which ends up being >200 g of rotating mass just in bearings (accounting for two cones), plus the rest of the nut weight. Then, combine this with 300 mm of 8 mm lead screw, which may only weigh ~90 g, and suddenly it just doesn't feel like it would be easier to abruptly accelerate all that nut hardware than it would to just drive the lead screw directly.
I'm at a minor impasse here, because I don't know "for certain" how to go about making the decision in a clear and quantifiable way. Should one just multiply the mass by the diameter squared, to get the rotational inertia, and use that as an apples-to-apples comparison across any body we may want to rotate, i.e. taking the smaller number as the winner? Is that good enough?
