How did this turn out?
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TLDR: I am guessing best case you gained 10% stiffness at a 15% running weight increase. I don’t think running weight will be much more than the spindle and carriage weight so negligible. I wouldn’t recommend it since that is a lot of work to get 10%. I would just buy thicker conduit. Also sorry to 1 month necro but again waiting on parts to print and looking for what people said about the Primo and saw this was brought up to the front and I did not see any maths which made me sad face… see excel in zip.
Full:
Waiting for my Primo parts to print and I saw this thread and thought i could give a quick tip for calculating this yourself since I didn’t see anyone put up the maths. I am assuming you have perfect adhesion between your core and shell which is another can of worms. I also used a very stiff pine value and a light weight just to be as generous as possible for the effects. Don’t use concrete. ^^
The stiffness value is the relationship of the EI.
I, which as someone mentioned up above I is the second moment of inertia and is related to the stress fiber equation of Mc/I. (List of second moments of area - Wikipedia)
E, is the Modulus of elasticity or the stretch-i-ness or stiffness of a material. For E a high value is steel and a low value is rubber.
If you modify the stress max fiber equation to Mc/EI that is the strain in the fiber direction under a bending load. The strain is a useful property because it relates to how much something stretched under load vs its original length. Since these rods are used as a carriage holder they feel a bending load from the trucks on the rail similar to cars on a bridge so EI is an appropriate way to approximate total stiffness of your structure. (If it was a strut you would use EA [area stiffness])
Most of the time you add a core to stabilize the skins or shell of your structure because they are so thin they buckle without out of plane stiffness. Not because the inside is a good place to stuff more stiffness. The opposite is true better stiffness comes from adding thickness to the outside, better to add more steel further away from the center. Why the mechanic will just start welding bar-stock to the outside of a pipe if it starts sagging, I saw you in this thread crazy mechanic. 
Tried attaching excel I made to hide it in zip file to show maths. Should be virus and error free but you get what you pay for… no warranties expressed or implied.
MPCNC_CoreAdd.zip (10.3 KB)
Cheers,
Lucid
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A fin of bar stock off the bottom of the rails, between the bearings, would probably be the best bang for the buck, then. You lose the ability to rotate your rails, but you get perfect adhesion along the length of the stabilizer (full access to the weld joint), and a vertical fin will give you the best resistance to flexing under load. Which is all and good for the outside rails, but you might have to settle for more of a short square bar on the gantry rails (more like a key than a stabilizer), as you have far less open space going through the core. I don’t know if the gains (stiffness) outweigh the costs (weight) at that point. I suppose, if you have the time and energy for it, you could slice a gantry rail along one side, and weld a fin into it, so that the bulk, if not the entirety, is inside the rail. Of course, maintaining a circular rail while slicing it and welding it back together might be… less simple than it sounds. 
If the tube is straight and the bar is straight, couldn’t you just weld it at the end? The tube tapers toward the top, so it’s not like the bar would have reason to flex sideways. Well, under cutting forces, but I think the bigger problem is gravity, right?
Might also just drill some holes in the top and tag the bar in that way. The core bearings are a bit off center, so you wouldn’t even have to grind them back down if you don’t want to.
Or what about a t angle? Wouldn’t that be cool if you could find the right size?
But then, it’s really a poor solution, still, i think.
Sure, but that won’t give you anywhere near the full benefit of the additional bar. It’s the exact same theory as a torsion box in woodworking (well, maybe a close cousin). The pieces have to be continuously joined to reap the full benefits. With torsion boxes, the skin needs to be glued to the framing members, or it’s not nearly as strong. With a stiffening rod/fin, the same holds true. And for any composite material, for that matter. Composite doesn’t have to mean dissimilar materials, just composed of multiple parts.
A bar on the bottom couldn’t be installed in the gantry cross members. The outsides are easy enough to support with mid span supports, and unless you build and enormous machine, they aren’t needed either.
Which you could approach with closer and closer holes drilled for spot welds, no?
That’s why @kvcummins mentioned putting one on the inside
Which is mostly why it’s a poor solution, lol.
Don’t get me wrong, I’m all for people trying things out, especially when I don’t think they’ll work, considering how often I’m wrong about stuff. I certainly don’t think it will work well enough to try it myself unless I come up with suitable scrap AND get bored. I’m only here because I don’t know much about engineering and I learn a bunch from those who do.
I want to make 100% clear that I do NOT want to stop anyone from trying any of the hare-brained ideas that come up in this forum (except when those ideas are prima facie dangerous, illegal, or otherwise overwhelmingly stupid; i.e., usually my ideas). I love a good game of What-If and How-About, and talking about these things, including poking at them with (intellectually) sharp sticks is what keeps creative works happening. Some of us are just better at being stodgy old coots who don’t like brash young punks comin’ in and makin’ a ruckus with their newfangled thinkin’s… 
On the inside I think a tube-in-tube idea, secured periodically with jbweld, is still one of the best I’ve seen. It’s bit heavier than a vertical fin for a given thickness but I think it still might be more weight efficient because like an I-beam more of the mass is near the top and bottom extremes. So if you were to choose a tube and a fin of equal weight, the tube would contribute more stiffness.
Or you can just start with thicker wall tube in the first place. In the end for a given weight I think thick-wall tube is really hard to beat.
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It’s kinda like fail in cad or fail in wood, right? Find the flaws in an idea with other people’s expertise vs just pissing on the electrical fence to see what happens.
Depends on your target audience…
Tragedy is when I cut my finger. Comedy is when you fall into an open sewer and die.
Mel Brooks
I am sorry I didn’t mean to drag this into pro’s and con’s of welding angle inside or out with a side comment. I just love the mornings where I come into the shop and see that angle bar has been welded onto something that just wasn’t stiff enough for the machinists tastes. Like a cheap lamp that is also acting as a tool holder. Warms the cockles of me heart, even better when duct tape is involved. I saw that idea in this thread and it once again made me smile. I love that machinist ingenuity that works. Keep in mind that tool holder dimensional tolerance requirements are “meh looks ok”. (+/-0.500)
If you do weld a bar on to your 20 dollars of conduit (must be continuous or spot welded at a pitch per natural diameter) don’t forget to hot straighten and re-anneal/heat treat to get your properties and dimensional tolerances back since welding could warp in the 10 thou range. There are some back shops that can do that for you for less than $1000 in my area if you are looking at the +/-10 thou range. 
I kid I kid.
If money is no option but re-straightening is a bridge to far can i interest you in some industry level rods:
These would shoot your rod stiffness up size-ably, but i think the rest of the system is your weak link just like before when you were using good and cheap conduit with no wood core. I will give Ryan credit, when i free bodied his system i liked how most of the forces balanced out. Also the material selection is available, but like my Mcmaster car link above you can always throw more money at it with industry level parts but at that point you should just order a expensive CnC kit that would include industry level guides and blocks. I do all sorts of stupid tinkering on the side knowing its not going to do much but it does improve my ability to design and build which is still something that is useful for my next project. Just don’t go bankrupt doing it.
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I think you shouldn’t be welding conduit. The coating is toxic. But maybe glue would be good for an experiment.
Wait, this actually happens?
100% Dom, though…
Hmm, titanium rod isn’t all that much heavier than stainless steel tubing… It should be fairly rigid, right?
I agree you shouldn’t inhale welding fumes unless they are organically sourced free range billets.
Also glues fumes can also be troubling unless they come from a good vintage. I think we can all agree that markers are just too good not to sniff regardless of pedigree.
(100% trolling. Drugs are bad. Please use appropriate ventilation and personal protection.)
I am sorry when i read that comment that is the first thing that came to my mind and i had to share. 
It is interesting what you learn later in life about how bad somethings are like CAD plating. I will be done waiting on parts soon and will go back to just lurking.
Alas, not. Check out the section “But what about titanium?” in the below primer:
There are prop 65 types of dangers (which are real but not immediate), but there are also mixing ammonia and bleach and getting killed by chlorine gas kind of dangers. Welding galvanized steel releases dangerous poison (zinc oxide).
I have definitely inhaled occasional mdf dust and solder fumes, which I shouldn’t. But this is a different kind of warning.
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I have heard mixed reports on zinc oxide. From what I’ve gathered, it will definitely lay you out with a flu-like fever, but it’s not long-lasting or cumulative like lead poisoning or silica dust. Still not eager to weld galvanized without a stiff breeze, but not the end of the world. That is, if you accept poisoning advice from random people on the internet.
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I’ve welded lots of galvanized stell over the years. First off, you can’t weld it unless you grind away the galvanizing, or it just spits. If some of the galvanizing does get in the weld it’ll puff out white, it stinks bad, so i just have a natural reaction not to breathe the stuff.
Muratic acid will strip galvanize off real quick, but that stuff is far worse to breathe. I don’t see how anyone could actually inhale enough of it to be harmful though. I’ve just been physically unable to breathe at the slightest wiff of it.