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Optimum manually fabricated square tube elbow joints...

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I'm hoping there's a MechE or someone out there with a couple cents to spare, might point out what I'm doing wrong or what incorrect assumptions I've made.  I am definately not a MechE and am pretty new to designing/fabricating a part like this.

I'm trying to calculate the optimum cuts to form elbow joints in aluminum square tubing (Al 6063-T5), at various angles.  The important part is keeping the outer tube wall around the bend intact to keep the sections of tube aligned after bending while I'm brazing the joint.  And since I need the joint to be air/water tight, minimizing the bend radius of the outer tube wall to minimize gaps in the side walls is a really good thing...

My setup: For brazing, I'm using an oxypropane mini torch (It's just the cutest wee widdle torch you ever did see, HAH). For cutting, I have a cheapo vertical benchtop bandsaw that cuts ok-ish but the fence and guide are crap, so I'm 3D printing jigs to hold the work piece at the correct position and angle for each cut in the aluminum square tube (one for each specific location and angle = 3 per joint), and the actual cuts appear accurate enough for my needs.

I must be doing something wrong because I either get a gap between the angled cut faces, or the lowest point on the angled cut face touches first and acts a fulcrum and fractures the outer wall while bending.  Or the bend radius of the outer wall is just too small and it fractures for greater than 90deg elbow joints (partially bent back over itself).

So I'm pretty sure the main problems I have is my design of the joint/targeted cuts are just wrong or not dealing with the specific material well enough.

Quick illustration, not proportional, nor accurate, and mating faces should physically touch (but easier to see shape with small gap for illustration):

I'm using 3 cuts:
- 2 angled cuts at A/2 degrees relative to joint cross section, to create the angled mating surfaces of the remaining side wall/tube top surface after the tube is cut and bent.  The angled cuts are aligned to Bz.
- 1 straight "chop" cut parallel to and centered at joint cross section but stopping short of cutting the outer wall, to remove side wall material inside the outer wall's bend radius.  For wider chop cut, I just move the work piece a little left/right over the blade to widen the cut a bit. 

My calculations so far, likely wrong, especially as rusty as my basic geometry is:
A = desired overall angle of elbow joint, where 0deg means straight pipe with no bend, and greater than 90deg starts folding back on itself.

W = tube wall thickness, in this case 1mm.

WC, WS = material (Al 6063-T5) compression zone / strain zone within the outer tube wall resulting from bending.  I am not a MechE, but AFAIK the inner side of the bend gets compressed and the outer side is strained to acheive the bend, and the actual border between the zones forms the effective arc length radius comparable to the un-bent length...  BUT, I'm not a MechE, so I don't know the right way to calculate this.  I'm guestimating WC=WS= 50% of W = 0.5mm.

RI = inner radius of outer wall bend

R = effective bend radius in outer wall bend, = RI + WC

C = chop cut width, *intended* to be equal to the arc length of the resulting bent outer tube wall.  Minimum chop cut is about 0.95mm.
C = A/360 * 2 * PI * R

Bz = z axis coordinate on joint angle bisector to aim the cutting edge at for the angled cuts.  It is not really "z axis" since the work piece is laid on its side for cutting, but it is z-axis in the un-bent illustration.  When I'm designing the 3D printed jigs to guide the cut, I align the near-edge of the cutting blade surface to this point.  Bz=0 is set at the unbent outer tube wall outer surface AKA the surface the unbent tube sits on.
Bz= (RI + WC + WS) - (C/2)/tan(A/2)

Center Point of outer wall bend radius = *intended* to be the corner between the surfaces created by the angle and chop cut.  When the tube is bent, the 2 sides of the joint should meet with this common point as the bend radius.  Emphasis on the word "intended", this has not worked out for me so far and the actual bend radius appears to be anywhere but where I think it should be, but I'm bending the piece by hand, so I can't be sure.

I've tried many iterations: Design jig->3DP->cut tube, but the results are nowhere near what I'm expecting, so either my calc's are waaay off or I've made assumptions that are flat out wrong.

Am I on the right track, do my calc's make any sense?  Any related manual fabrication pointers / math checks / etc is much appreciated.

Robert Smith Eco Warrior:
I shall return to this and try and answer, when I don't have a stinking cold and can concentrate. Today doing maths is a non starter. I just want to sleep...  :=\

Looks like my last post was lost during repair...  Here are sketches again.  Please forgive their crudeness...


Well, the problem is extruded aluminum is not real homogeneous.  I make some L-shaped brackets for mounting PC boards with power transistors, and bend them on a sheet metal brake.  Each one has to be bent to a different angle so that after springing back it ends up at 90 degrees.  Not a huge difference between them, but enough that one bend setting would leave them all different by up to 10 degrees or so.

So, there is likely to be no perfect cutout that gives you the desired bend for brazing.  Maybe if the bend was then done by pressing it into a rigid form they would come out about right.


You make a good point that the material is not very homogeneous, and springback is certainly an issue.

The bigger problem I've been dealing with is that the part fractures into 2 parts during bending, not always but nearly always for greater than 90 bends, and the material is strained/deformed to the point springback doesn't occur, which is not good.  So, I went back to the drawing board, and have been attempting to calculate the ideal cuttout to eliminate fracturing the wall and still get the surfaces to align well enough to braze.

And as soon as I attempted calculating the bend, my results got worse instead of better, thus this thread.

I redesigned my jigs from scratch and have been spending the past few evenings tweaking the acuracey of the whole thing.  Will post results when I get the next set printed and tested.


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