Any chance you have part numbers for your motors/drives handy? I'd look closely at that backlash figure and work out what it means in terms of position error after it's converted to linear motion. 7-10 arcminutes is a pretty large amount of backlash and may cause issues when interpolating holes or otherwise changing directions. Which is a twofold problem: 1) accuracy and 2) sudden increases in chipload that can break small endmills. But if your 6 micron number is correct, the gearbox backlash would be roughly half that figure. Not the end of the world in that case.
Personally I don't think steppers are nearly as bad as it's being portrayed here. There's a big difference between an Arduino + a $15 Amazon stepper (aka the experience of 99% of the people who have used steppers) and a closed-loop industrial stepper + matching drive. I also doubt there is enough rigidity in the structure and control authority in the steppers for the individual steps to be visible on the part unless you're running glacial feedrates where the motors actually come to a complete stop (or slow significantly) between micro-steps.
As you said: servos are definitely better but does it
really matter for this application with this machine? I doubt it. Motors are also the easiest thing to replace so if you do decide you need them, you can spend the money and replace them later.
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One suggestion (with some caveats) that may help improve the rigidity of the aluminum structure: don't bolt the end plates (which support the ballscrews) into the track of the aluminum extrusion directly below them, if you can avoid it. It'd be better to bolt them all the way
through the extrusion. I.e. run a threaded rod all the way through the extrusion to the opposite side and put a nut on either end. This distributes the load a bit so it's not all just getting levered against a nut held in place by a thin lip of aluminum. A given load concentrated into a small volume = higher strain = higher stress. It'll also serve to pre-tension the aluminum a bit. Both will reduce the deflection of those supports in response to applied loads.
Crappy illustration here that should get the idea across. The green lines would be threaded rods (and inside the extrusion) with nuts on either end.
Speaking of pre-stressing, I think it's a pretty neat idea. It's something I would try if I was building this. Run several threaded rods through each extrusion (one per opening in the cross-section) and tighten them all an equivalent amount to compress the extrusion. Since you have steel plates on the ends of all your extrusions, you can just pass them through those and use them as bearing surfaces for the nuts.
The big upside of this is that it can substantially increases the rigidity of the structure. It will deflect less for a given external load. Perhaps not as much as as cast iron or steel...but more than the original aluminum. The big downside is that more care in assembly and more upfront calculation will be involved to settle on an appropriate amount of pre-tension, and crucially to minimize tweaking the members and distorting their shapes which
will happen and may make your alignment task harder. That's always a risk when you intentionally add stress. Ideally you'd do this
before it's assembled. Even more ideally you'd also send the individual members out, pre-stressed, to have reference surfaces for each member post-machined. Removing as little material as possible - just enough to get a clean reference surface. Goes without saying that the internal rods should be considered permanent and can never be loosened/tightened/disassembled or it's all for naught.
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One thing I didn't see in your OP are locating features. Take for example your ballscrew supports for the X-axis. How will you align them to one another? If you're using the standard extrusion t-slots/holes to do it, you don't really get any say in the alignment - it is what it is when you assemble it. Maybe they can tolerate the potential misalignment, but if they can't then consider separating those brackets into two parts - one bracket that bolts to the extrusion, and another bracket that contains the ballscrew support and is bolted to the first bracket. That way you have some ability to align the ballscrew supports independently of the attachment to the extrusion.
Another crappy picture to make it clearer - red lines are the potential separation points.
It looks like you have a couple areas where you have extrusions bolted to one another. Those would be weak points for sure. Hard to tell without more CAD views!
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Personally I'm not on board with the idea that the smart businessman thing to do is to turn your <$10k side-project into a mound of obligations and debt by 10-xing your budget and signing a multi-year lease on an industrial space that's an hour+ away. That might make sense if you were trying to make this your primary source of income ASAP and have no issue paying those expenses out of pocket for the next couple of years.
I get a similar thing when it comes to housing as I also live in a ludicrously expensive place. "There's gotta be a cheaper place! You're just not looking that hard!" I just tell them you know what...hop on Zillow or Craigslist and find one. They never do. They just say it and then carry on believing there are heaps of houses sitting around here that are equivalent to mine but 50% below market value. Likewise I've been told "just rent an industrial space" for the sake of saving 100 square feet in my garage, as if those spaces don't cost $30/SF/year around here.
This is a common line of questioning/lecturing when it comes to those living in expensive areas. There are those who can't wrap their heads around the idea that not everybody wants to completely upend their life, quit their jobs, move their SO/kids, leave their friends, etc. just for the sake of moving to Wisconsin to score some cheap real estate. It's easier to just...do the thing and try it out. If you love it and want to pursue it, great. If you don't, you're only out the money you spent + what it'll cost to have someone pick up your machine and haul it to a scrapyard.
To each their own I guess. I wouldn't stress about it though.