Openbeam rigidity for larger frames?

Hey guys, I want to build a CoreXY or Tantillus kind of printer. The length of the beams I will be using is 360mm in all three dimensions.

Does anyone know if the 15x15 extrusions of OpenBeam are rigid enough to keep a square frame? Or am I really bound to 20x20 Misumi extrusions or something like Misumi?

With Openbeam I can buy the corner squares that are designed by openbeam, but besides looking good, it's also quite expensive. If it probably isn't usable with a larger frame, then I will go for the 20x20 extrusions.

In general, profile-ignoring terms, square beam deflection or rigidity goes down with the third power of length and up with the fourth power of thickness, so if you wanted the same deflection with twice the length, you'd need 2^3=8 times the area moment of inertia, which would mean 8^(1/4)=1.7 times the thickness. In other words 20mm versus 15mm would get you (20/15)^(4/3)=145% more length.


In detail, the stiffness of the section is directly related to the Ix & Iy columns on [us.misumi-ec.com] but I'm not sure what the corresponding specs on 1515 openbeam are.

So in an attempt to understand that simply, 1.7X thickness = 2X the length?

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Realizer- One who realizes dreams by making them a reality either by possibility or by completion. Also creating or renewing hopes of dreams.
"keep in mind, even the best printer can not print with the best filament if the user is the problem." -Ohmarinus

I think you have to factor in the smooth rods or whatever else is used aswell. By itself the openbeam is too flexible. I'm building a printer at the moment with 600mm openbeam. The stability comes from 12mm steel rods.

Yeah I completely understand. My current printer is using 8mm hardchromed rods, I will buy the same kind of rods for the new printer. In my current printer the rods are not flexing much, a little bit when I push on them with force, but the amount of force generated by just printing (linear forces) are way lower. The rods don't flex with normal use so I don't think thicker than 8mm is important for this printer.

Also, the rods may be 360mm, but the area of the rods that is hanging free will be less since the sides of the rods will be fixed in holding clamps.

All in all, it seems that the 15x15 openbeams should do. All corners will be fixed with end-connectors and corner connectors. It is a cube-like structure (so it uses 12 beams), and if neccesary I can even print brackets that connect the beams in the corners a bit more.

I can't calculate the things in your link DaveX, I wish I had higher math at school, but I didn't. It's hard for me to read formulas (hence me doing art school I guess..).

I don't personally have a machine with 8mm round Rod but it would be interesting to know how much deflection when printing

Edited 2 time(s). Last edit at 06/02/2014 02:56PM by cnc dick.

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MrDoctorDIV
So in an attempt to understand that simply, 1.7X thickness = 2X the length?

Yes-ish... since the 1.7 factor depends on the doubling of the length. If you quadrupled the length, the thickness would need to be 1.7*1.7, not 1.7*2.


The basic formula is from [en.wikipedia.org] , with the I values based on the thickness from the rectangular entry on [en.wikipedia.org]

Ohminarus, I guess I'm not precisely sure of your question. If you are happy with your current rods and deflections, and you are moving to something with longer spans, you'd need to upgrade the stiffness to to get the same deflection performance. Alternately, if you increase the length without upgrading the stiffness, then you would get larger deflections.

If you increase the length by a factor of X, then, if you don't change the materials, you will get an increase in deflection by a factor of X^3=X*X*X.

You could offset that increase in deflection by a corresponding increase in stiffness (which by [en.wikipedia.org] is is related to h^4 or r^4, would require an increase in diameter or thickness by a factor X^(3/4) ) or by using a stiffer 'E' material.

You could also offset some of the deflections by reducing the forces applied to the beams by reducing moving weights or slowing things down. If you doubled the lengths, you'd need to reduce moving masses or accelerations by a factor of 8 to get the same deflections.

If you are using smaller spans, or better geometries, you get correspondingly stiffer behavior. Stiffening up the joints further from the corners would help. The Mendel 90 is pretty stiff because it uses the width of the sheets as very thick beams

Alright, yes, I am going to make a completely new printer, so it's not something I can compare to what I have now.

My MendelMax 1.5 uses 20x20 beams but also uses strictly printed parts in the connection of those beams. The OpenBeam printer I want to create will use these described L-shape joints:

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OpenBeam's L-shape joining plate is injection molded out of EMS Grivory GVX, a high-performance, high glass fiber reinforced polyamide copolymer that is engineered for metal replacement applications. It has comparible tensile strength to die cast aluminum, at 1/2 the weight.

Indeed my idea was to stiffen up the joints further from the corners too. And I expect a square box to perform better than the MendelMax when it comes to rigidity.

The reason why I want to use OpenBeam is so that I don't have to use T-slots and because I think the construction can be lighter, but I don't know for sure, I mean, I have never built anything similar before.

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DaveX
Yes-ish... since the 1.7 factor depends on the doubling of the length. If you quadrupled the length, the thickness would need to be 1.7*1.7, not 1.7*2.

Yeah, I knew it was relative to current size calculation and not absolute, but good clarifications for others reading.
At least that's one thing down simple in my build planning. Thanks.

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Realizer- One who realizes dreams by making them a reality either by possibility or by completion. Also creating or renewing hopes of dreams.
"keep in mind, even the best printer can not print with the best filament if the user is the problem." -Ohmarinus

80/20 has a claculator which can give you numbers for all of their profiles and you can probably find something pretty close to openbeam. [www.8020.net]

Just to round this off, I've received my 360mm long openbeams today and they feel more than qualified for the job

This is purely with the corner-connectors, so with the extra brackets I'm gonna print this frame will probably be even more rigid than my MendelMax 1.5