I think the design has several other issues:

There appears to be a pretty large imbalance between the motor inertia and axis 
inertia. You can fix this by using a reduction on the jackshaft. For reference, 
some of the older Stratasys systems have a nearly identical arrangement. They 
use about 3/4" steel tube as a shaft and a 3:1 belt reduction from the motor to 
the shaft. They also use the same reduction on the X axis.


The bigger issue, in my mind, is the lightweight frame.
Your motors might have around 2NM torque which translates to about 45 
pound-force on a 3/4” drive pulley. If you apply 45lbs of force to the side of 
the printer, it will bend sideways a lot. Add a 3:1 reduction to it and you get 
over 100lbf of side load at the top of a lightweight frame—that is if you 
actually use 2nm torque during acceleration. For reference, the Stratasys 
printers I refer to weigh around 150lbs and still the entire thing sways on its 
rubber feet when the axis motion syncs up with the machine resonance. And they 
do use stepper motors. This also illustrates why the humble stepper is still a 
good fit for lightweight printer frames. 


> On Dec 5, 2022, at 8:08 AM, gene heskett <ghesk...@shentel.net> wrote:
> 
> On 12/5/22 06:59, andy pugh wrote:
>> On Mon, 5 Dec 2022 at 02:20, Chris Albertson <albertson.ch...@gmail.com>
>> wrote:
>>> and we don't even know the exact kind of steel in the rod.  Without
>> knowing more it is a toss-up.
>> You don't need to know, all iron alloys have the same stiffness (to within
>> a couple of percent).
>> The shear modulus (G) for steel is 80 and for carbon fibre is around 5.
>> Steel is a lot stiffer than CF.
>> Anyway, with a 2Nm motor you might see 1.7 degrees of twist in an 8mm steel
>> shaft which is 500mm long.
>> Playing with numbers it would be 3 x less with a steel tube 12mm dia and
>> 1mm wall thickness.
>> To match the stiffness of the steel bar with a _round_ carbon tube it would
>> need to be 20mm dia and 1.5mm wall thickness.
>> https://amesweb.info/Torsion/torsion-of-shaft-calculator.aspx
>> Note that there is only any torsional load on the shaft when accelerating,
>> so the extruder will generally not deviate from the path very much, but
>> will be lagging along the correct path.
>> (This is true of milling machines too, the f-error is typically
>> approximately along the path, so has less effect on part geometry than the
>> raw numbers would indicate)
> 
> Thank you Andy. Bearing the difference in torsional rigidity of sq vs round 
> in mind, I just ordered, be here the 7nth, a 4 pack of 23x25x500mm round cf 
> tubes, one of which will replace the looooong coupling rod with the puny 
> motor in the middle of it, across the rear of an Ender5+, some pulleys I can 
> machine away half the weight of, some belt clamps, and a 10M roll of gt2 belt 
> 6mm wide. I'll put one of the 1NM 3 phase stepper/servo motors in the inside 
> corner of the frame with the controller close by, driving one end of this 
> tube. Not the middle.
> 
> FWIW, I'm fond of the gyroid pattern infill but its jiggle will be distorted 
> by the torsion give, so while I've got room for 2" tube, the biggest I can 
> buy seems to be 1", or 23x25. 2" would probably begin to affect inertia with 
> its weight, so 1mm wall, 25mm OD may be the best balance point.
> 
> All I need to do is get the step & dir out of an BTT Octopus-pro, which I'm 
> sure I can do. The belting will replace the x drive belt after I figure out 
> how to route one run of it thru the square cf tube. Different piece of the 
> project IOW.
> 
> Take care & stay well.
> 
> In the realm of motor theory, a chance reading of one of stepperonline's 
> .pdf's, explains better how they work, and its the same for 2 phase as 3 
> phase, they cannot lose home unless they can't move the load, AND will issue 
> an alm contact if they lose a step/home. I've got that rigged in .hal to stop 
> LCNC in about a millisecond everyplace I'm using them. Sweet.
> 
> Cheers, Gene Heskett.
> -- 
> "There are four boxes to be used in defense of liberty:
> soap, ballot, jury, and ammo. Please use in that order."
> -Ed Howdershelt (Author, 1940)
> If we desire respect for the law, we must first make the law respectable.
> - Louis D. Brandeis
> Genes Web page <http://geneslinuxbox.net:6309/ 
> <http://geneslinuxbox.net:6309/>>
> 
> 
> 
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