Yay! Measurements!
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I’m thinking this is a bad idea. Under the sagging stresses, the top side of the tubing is under compression and will become the failure point as the tube buckles in on itself. The internal pre-stressed cable would increase the compression and the tubing would most likely buckle sooner.
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Reading through this thread it seems to me like the best two options are to slide some well fitted Woden rods into the conduit Or switch to Stainless.
I can get regular steel EMT at my local big box store for $.65 a foot. So that’s like 1/7 the cost of stainless. For some of us retired guys, that’s meaningful.
Please post your source for 304 stainless as I have not been able to find 1” O.D. in the US for less than $5.20/ft for 0.065” wall and $7.30/ft for 0.120” wall. Thanks!
You’re right, it is probably a bad idea, but for a different reason. I seriously doubt the steel tube will be anywhere near its failure point. I just don’t think the cable is going to reduce sag very much, as it will just stretch as the tubing sags. But I may still try it.
I may have mentioned this before (even in this post 
). I’ve seen Jimmy Diresta put a long flat piece of metal under some square tube. Then he put a screw in the middle pushing up into the square tube until the square tube looked straight. As Jamie said, I bet it would respond to forces the same (similar spring constant), but the gantry would start straighter.
adding material to the center of the tube is very inefficient, especially something other than steel. that being said the best (in terms of effort, bang for buck) way to increase the stiffness of the current design is to increase wall thickness.
the best way to improve the stiffness on a future design is to increase the OD of the tube, imho. if possible, start at the beginning and determine how much deflection is acceptable (maybe easier typed then done), then you can calculate the right size tube.
I’m curious about the original test though…
- if the 1.00in SS was compared to regular 3/4in EMT then OD for that size EMT is about 0.90in, which is significant (the 1.00in will be 22% stiffer, everything else being equal).
- if the stainless is DOM then that also may explain some of the difference in deflection as DOM is stronger due to the process.
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Yes, the tubes will be 700% more expensive, but it only increases the total MPCNC cost by 20-25%. Of course, if you’re looking to save money then the cheaper EMT tubes will also work just fine. I didn’t mean to imply that stainless is necessary and that everyone should buy them. Apologies if my post came across too harsh.
I live in the Netherlands, and I ordered my tubes from here: rvsonline.nl. Typically, when I see U.S. prices they are a little bit or sometimes a lot lower than here, especially for commodity items. Maybe the tubes are an exception.
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I’ve picked up tube from these places for my lowrider.
https://www.metalsupermarkets.com/ << Have one of these about an hour away, so I picked it up in store.
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Well like I said, I think this next version might be better off one size larger in diameter. So…I asked the German crew from Uncle Phil’s FB group and it seems the next size up in conduit over there is similar so hopefully I can do just two versions this time around instead of three. I will need to go geek out at a few hardware stores and check the larger conduit with calipers, as last time I found the larger stuff to vary more.
For a new version it is time to make more than an incremental change I think. The Burly is really capable, compared to what we had early on the Burly is probably at least 4x more rigid. The new center I made Improved on that still, A little bit (I put numbers somewhere around here 5-20% Can’t remember). No harm in me trying a bigger build and giving you all the numbers from a real test.
The burly as is will always exist, so that could give me a little more design freedom to try and make a substantial improvement without a large cost jump with a new version. I love the current price point, especially if you factor in shipping cost between these machines and all others that have to ship large rails, they simply can not compete.
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I’d think that as soon as you crank tension on the cable, the tubing will begin to bow without any sagging load required. You’re essentially trying to pull the ends of the tubing towards each other. Think “bow” and arrow.
Even if it doesn’t bow immediately from the pre-tension of the cable, as soon as the tube sags to anything other than straight, the cable tension would make it “sag” worse, as it would want to pull the ends towards each other.
You know, I was standing in Home Depot about to buy some EMT to test this, and I had the same thought. As soon as there is any bow at all in the pipe,. the stressed rod will just tend to bow it out.
So then I thought, what if I fill the pipe with quickset and a tensioned rod? Except a thicker wall plain pipe will perform just as well, weigh less, and is way easier to make.
Not one of my better ideas, sorry.
Assuming we’re talking about 3/4" EMT, what about getting a 3/4"x1/8" steel rod and sliding it in vertically, maybe with a tack weld (or JBWeld) at the ends? Not as good as a continuous weld, but would that give you more flex resistance, at least along the plane of the insert? I suppose you could also get a square tube that just fits to provide some side-flex support as well…
But I’m a computer scientist, not a mechanical engineer.
This has been done and I think it’s a good alternative if you can’t just buy thick-walled tubing. I think you will want to secure the inner tube along the length, not just at the ends, or else the gap will allow the outer tube to flex the same as before.
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I dug a little deeper into the physics and math behind my own quick and dirty flex measurement. I was also interested in comparing round with square beams.
I found a calculator for maximum displacement given a couple of inputs. It boils down to the following formula:
maximum displacement (meters) = P * (L^3) / (48 * E * I)
where P is the load in Newton (1 kg is 9.81 newton), L is the length of the beam in meters, E is young’s modulus in Pascal (190,000,000,000 to 200,000,000,000 for 304 stainless steel), and I is the moment of inertia in meters^4. In the case of a round tube with a 25mm OD and 2mm wall thickness, I is equal to 3.22e-8.
Plugging in those numbers gives a maximum displacement of 0.033mm. It’s at least in the ball park of my measurement.
I found two different formulas for the moment of inertia I. You can find the formulas for different shapes and sizes on this page. (If the page starts complaining about creating an account, you can reset your cookies or open the page in a ‘private window’ or ‘incognito mode’ or something). Ixc computes it from the center of the beam, Ix computes it from the outside of the beam I think. I used Ix instead of Ixc, and it was 3.3 times higher than Ixc.
Some observations:
- Flex increases with length to the power of 3!
- A round tube with 25mm OD and 2mm thickness weighs the same as a square tube of 20x20mm with the same 2mm wall thickness. The Ix of a round tube is around 1.4 to 1.5 times higher than that of the square tube of the same weight. If you use Ixc this factor is around 1.2. (The square tube also has different Ix values depending on the angle of the load, in contrast to the round tube. I don’t know how to calculate the Ix depending on the load angle.)
- If you increase the thickness of the round tube, the Ix increases, but the weight also increases. The relationship is not exactly linear, but pretty close in the 1mm - 5mm range. So you don’t really get more “stiffness per kg of weight of the tube”. Thickness equal to the radius (no hollow tube) is a bad idea. It’s better to have a thinner wall with a larger diameter for a given weight.
- Stiffness increases roughly with the 3rd power of the radius (!) if you keep the thickness constant. (Note that weight roughly increases linearly only). A 50mm OD round tube is about 8 or 9 times stiffer and only just over twice as heavy as a 25mm tube.
(EDIT: fixed the last observation)
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Crazy awesome right! I think I agree with all of that. Main take away, Larger diameter is best. Now the trick is to balance everything else that goes with it. The larger the diameter the larger the printed pieces have to be to hold them, the larger the box needs to be to ship them, most importantly the larger the footprint needs to be to accommodate the larger diameter that also increase the length of the tubes (rigidity decreases by a factor of three).
I guess another way to say that is a little more rigid requires a lot more everything, diminishing returns. I will give these larger EMT some test to see if they are worth it or not, but hey will need to be significantly better for me to sacrifice all of that for a little speed (which is what rigidity gets you, added depth or linear speed).
Now you can see why even a $400k machine does not seem to have super mind blowing specs, they are just better (maybe 100x faster) but not 100,000x faster, diminishing returns.
If you add in square tubes are also heavier for the same rigidity, plus they require 1/3 more hardware which also adds to the weight, you see why I chose round.
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Agree 100% and it also reemphasizes the importance of building as small as you can get away with. Building a machine 2x bigger “just in case” will produce 1/8th the stiffness of the rails, which can mean the difference between success and failure depending what you’re doing.
Just to round out the picture, two other major factors are z height and belt stretch. Stiffness decreases quadratically with z height but it has a (relatively) lower stiffness constant to begin with. Belt stiffness decreases linearly with x or y length. At small sizes beam deflection is more or less balanced with these other factors, but as the size increases the beam deflection gets worse faster than the other effects.
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Indeed. I think 0.030mm to 0.050mm of flex per 1 meter tube is already very good. According to my measurements today, the z height and belt stretch are much more dominant factors at this point.
Aluminum instead of steel could even be awesomer! At least rigidity-wise. Consider this: aluminum is roughly 3 times less dense than steel. A 25mm OD steel tube is the same weight as a 75mm OD aluminum tube at the same wall thickness. That means the Ix is 3^3 = 27 times higher. Young’s modulus of aluminum is only around 70 GPa instead of 200 GPa for steel. But adjusting for that, its stiffness is still 9x better for the same weight!
A quick google shows that a 75x2mm aluminum tube is roughly the same price as a 25x2mm 304 stainless steel tube.
Of course, like you said, everything would need to be bigger. And, I know, bearings sink in. But it does make me wonder whether a rectangular aluminum “box” style for the lowrider would make sense, where you’d use one large rectangular tube with bearings on the outside of it. Maybe with steel strips for the bearings to roll over. Not something you’d pick up at the local hardware store though.
Agreed.
But couldn’t you use temporary braces or something for when you want to machine something small on a large machine?
Let’s say your frame is 1000x1000mm, workspace is 700x700mm or so. If you want to machine some aluminum that is only 100x100mm, couldn’t you make some legs that you install temporarily at X=400mm and at Y=400mm? (You could move them to any location, to make the effective workspace any size you want.)
Bonus points for making the legs a “triangle” shape, and even more bonus points for clamping your belts at that point too, so their effective length is also reduced.