Minimum coil diameter prior to yield
Minimum coil diameter prior to yield
(OP)
I've got a situation where I need to determine the minimum bend radius a tube can take prior to material yield and I am having a heck of a time getting reasonable results. Something tells me this should be a relatively simple exercise but I am not getting any results that make sense.
My situation is this:
347 stainless tube, 1/4" OD, 3/16" ID being inserted into a slightly larger guide tube. Tube enters verically into a radiused section of the guide path and exists 135 degrees relative to vertical. What is the minimum diameter of curvature the tube can take prior to yield? I've tried reducing the curved section to a situation where I can use a case from Roark's on beams but I am not getting believable results. Roark's states that depth of beam curvature must be less than 1/10th radius of curvature, I think this may have something to do with bad results form this method. Any takers?
Thanks.
My situation is this:
347 stainless tube, 1/4" OD, 3/16" ID being inserted into a slightly larger guide tube. Tube enters verically into a radiused section of the guide path and exists 135 degrees relative to vertical. What is the minimum diameter of curvature the tube can take prior to yield? I've tried reducing the curved section to a situation where I can use a case from Roark's on beams but I am not getting believable results. Roark's states that depth of beam curvature must be less than 1/10th radius of curvature, I think this may have something to do with bad results form this method. Any takers?
Thanks.





RE: Minimum coil diameter prior to yield
Stress = M d/2/I M /E/I = 1/R
Stress = E / R * d/2
Set stress = yield stress - .01 and
solve for R = Radius (to the centerline)
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RE: Minimum coil diameter prior to yield
What is length of pipe your pushing in, the deflection of the pipe be dependant on its length and whether it stays elastic or not.
regards
desertfox
RE: Minimum coil diameter prior to yield
The outer fiber length for the bent tube is the elongated length. The length of the neutral axis is the reference length before bending. The difference between the stretched outer fiber length and the neutral axis length through the same bend angle divided by the neutral axis length equals the strain of the outer fiber. I ran through the equation and rearrange to solve for the bend radius at the neutral axis and got r = OD/(2*strain).
Yield stress for annealed 347 is 30,000 psi.
E = 28 x 10^6 lb/in^2
Yield strain is 0.0011 in/in
OD is .25 in
r = 116.7 in bend radius at yield. That seems large, but it doesn't take much to bend small tube to yield.
What do you think?
Ted
RE: Minimum coil diameter prior to yield
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RE: Minimum coil diameter prior to yield
RE: Minimum coil diameter prior to yield
In this case, r = OD/.004 = 62.5 in.
Ted
RE: Minimum coil diameter prior to yield
It should be r=OD/.004 or even more accurate r = 250.5 x OD. The rest of the formula is an error.
RE: Minimum coil diameter prior to yield
The rule of thumb for pipe bending any diameter of any wall thickness is 1º bend over a length equal to the diameter, which works since c = d/2 is independent of wall thickness and c and I are the same in all directions.
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"What gets us into trouble is not what we don't know, its what we know for sure" - Mark Twain
RE: Minimum coil diameter prior to yield
Thanks for the speedy input. Ted, I particularly like the idea of looking at it from a strain perspective. As far as the 116" bend redius, yes, that seems quite large and in-field practical experience would indicate we can get away with a radius much smaller than that. Could it be possible that as the tube elastically collapses that some additional leeway is possible for a smaller than calculated radius?
To give you an idea of what we can get away with: we routinely get tubing in that's got OD's at or less than .450", .030" wall and less and it comes in 10' coils. It's usually a wee bit set but a little tug with a hydraulic ram (in reverse) at 200lbs and she's as straight as when it came of the draw machine. Most of the tubing we use is Inconel 600/690 and 316L. In fact, one particular I690 tube we use is less than .100" OD x .015 wall and it comes in 18" coils and a small tug gets it nice and straight as well.
This particular application I am posting about is an in-core instrument, a customer is asking us to give them an instrument that can handle under 2' radius bends and desires that without working the material. Experience tells me that's way too small but I know that we can do much better than 116" without issues. This is one of those cases where theory will give us a comfortable margin but doesn't allow us to get an exact practical value.
RE: Minimum coil diameter prior to yield
Using the .2% offset definition for yield, the resulting bend radius limit is 62.5" for the .25 tube. That seems to compare well with your experience. Minimum bend radius to just before yield for the .100 diameter tube would be 25". It must be wound in 18" coils so it stays coiled for handling.
You were asking for bend radius with no yield.
Ted