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.
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:
(EDIT: fixed the last observation)
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.
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.
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.
Then you need to get all four bearings very flat at the same time or they will be riding on a point load as well. You still need steel though. I might use a small box for the Zenxy, but not for the LR at any time soon.
I have been doing testing on the old Burly and New gantry on my red and black build. I measure no noticeable deflection at the corner tops, literally none. I guess the looks of them throw people off? People are very determined to redesign the corners but I have never found them to be an issue in any way, even from version 1. I would rather spend my time on the parts that do move.
I measured 0.005mm with 1 kg of load on the end mill, so practically none indeed. The corner pieces just don’t look that beefy, but I agree they are very effective.
The corners have another tube connecting them though. You only get a racking movement (which we agree does not really exist, at least for short legs).
However, if you put an additional straight leg under the center of a frame tube to halve the effective size of the MPCNC, I think it will be less effective at fighting the tube flexing in the XY plane, because there is no tube in the XY plane to help out. I have no idea whether just a straight leg is already good enough, it may very well be.
Wait… I don’t think extra legs will work… it’s the gantry tubes that you need to stop from flexing, not the frame tubes. Extra legs don’t help with that. Though extra clamps for the belts will help with reducing belt stretching, but you can just mount that on the frame tubes, no need for legs.
I have legs that are 27mm of metal showing between foot and lock. With a 4.2kg load on the end mill I show less than, 0.02mm (0.001") at the corner. My dial indicator just shows a hint of a wiggle so I am assuming less a third of that.
With that same load the new center gets 0.2mm (0.01") deflection at the endmill, the burly center takes 2.6kg to move the same amount.
Yes the side rails are under no load axially, and no load side-to-side. The only load is vertical. Additional vertical supports can help reduce sagging in Z and this can make a difference for very large machines.
An extra belt clamp for a reduced workspace is interesting. The belt contribution to deflection could be reduced. Hold the belt and attach to the table, or hold the belt and attach to the side rail (now the rail does have axial load), or hold the belt and attach to the belt elsewhere, like clamping a 2mm rack on the entire unused length.
But more important than all of that is to measure the deflection because if the gantry rails deflect with the cube of the length and the belts deflect linearly with length, you have a good chance of getting no practical improvement even with perfect belts. It is still a fun academic exercise but not a realistic improvement.
True. But a 1 meter 304 stainless steel tube deflects around 0.040mm per kg, while the belts stretch 0.160mm at that 1kg load (assuming both belts take equal load). This is assuming you have a 1x1 meter build, and that you have minimal stick out. At larger stick out, the belt stretch becomes less. But the tubes will also deflect less.
At different sizes there will be different ratios, but 1x1 meter is already a pretty large MPCNC. For a lowrider with a very long Y axis, the difference can be very large with extra clamps.
All that said, I haven’t tried it so it might indeed be academic 
Ah ok, fair enough. I still stand by my statement that measurement is most important, exactly because of stuff like this! 
I’ve tested belt clamps and they work extremely well.
Quick and dirty round 2
Slightly less dirty this time. I just checked SS and 1" EMT…interesting.
4.345kg (9.58lbs)
71" span, simply supported
72", SS 25.55mm OD (the wrong size) , 1.55mm wall thickness (0.060"), 1.65kg = 5mm sag
72", 1" EMT OD (29.6mm) , 1.42mm wall thickness (0.056"), 1.76kg = 3mm sag
So that is not bad, so much cheaper, more rigid and not a huge weight difference. It is still much more rough, but to save that money a little sanding is not a huge ask if needed, but at my local store they all seem to be pretty non-straight and this piece is not too bad at .2mm oval, stainless is about 0.1mm oval. If any of you remember take a look at 1" EMT next time and see how it looks.
What about the “rigid” 3/4" emt? I would guess it is more consistent, since it has outside threads on one end. The OD is 1.05". Is it just too heavy?
