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I came across this suggestion on the klipper github, https://www.facebook.com/groups/Hypercube.Evo/permalink/192106034761003/. In order to reduce the stretching in the bowden tube you can add fiberglass packaging tape lengthwise along the tube. This would decrease the elasticity while still allowing the plastic filament to run through it. Allowing you to reduce the retraction length and have better control over the amount of plastic being extruded.

Is there any reasons that this would not work or actually decrease the performance of the bowden tube?

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    $\begingroup$ seems to be that was reduced the vibration in the extruder but not related with the fiber on the tube. the wavy corners is due some object is pulling the extruder while printing, so the nozzle can't be accurate on printing. This happens when the reel is too tight or even the wiring $\endgroup$ – Fernando Baltazar Aug 10 '18 at 7:22
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    $\begingroup$ the tube doesn't really stretch under normal operation, so it's a solution in search of a problem $\endgroup$ – dandavis Aug 10 '18 at 22:34
  • $\begingroup$ I quite agree with Dan's comment, if, when the printer is designed/built, the Bowden tube is of a length such that it reaches the extreme (i.e. maximum/minimum x, y, z) positions of the extruder, and then some, then the Bowden tube shouldn't be stretched at all, in normal operation, and assuming that it doesn't catch upon any protuberance at any point along its length. $\endgroup$ – Greenonline Aug 12 '18 at 21:42
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The question seems to be built on a false premise, namely that the major extrude/retract errors in a Bowden design come from tube stretch. The PTFE tube is not significantly elastic, actually it is reasonably stiff so there is minimal scope for improvement here.

A longer tube will contribute to degraded precision, but slack in the filament/tube gap is roughly as significant as stretch (and filament compression). Constraining the tube path may help marginally (but there is no need to 'bond' the tube). There is not much you can to to reduce the gap between filament and tube, but this will dominate the error for a long tube.

The most obvious weak point is the clip used to secure the tube at each end. I saw a review of a recent Prusa design where high quality clips were called out as making a big improvement to securing each end of the tube.

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The most common setup is 1.75 mm filament inside PTFE tube with 2 mm internal diameter and 4 mm outside diameter. The 4 mm outside diameter goes inside pneumatic push in 4 mm tube connector with 1/8 BSP thread that goes somewhere like E3D extruder.

It is very arguable if PTFE tube not significantly elastic. Apart from elasticity the filament some kind of compressing inside forming the sinus like line along the tube. And it has several places where it pushes at the tube wall and this deforms it slightly from circular to ellipse shape. All these effects accumulates with the length of the tube.

But in theory all these have minor effect if the feed rate is around the same value (the first order forces equalize and effect could be eliminated with proper retraction value). The bigger effect will be if feed rate changes and as result internal compression in the tube will vary and as result the melted filament will go out slightly off time. And this will affect quality but slightly and in some places of the print. Basically the motion variance will do some kind of coloring of the print.

I am personally recommend to use reinforced tube. The best tube I found is 5 mm bike gear outer cable. It is steel reinforced with internal PTFE lining that perfectly suits 1.75 mm filament. Also it has outer layer of some kind of plastic that fit really well inside 5 mm push fit connector. The only problem is that 5 mm push fit connectors not common but you could find them on ebay as I did. Another advantage of this cable is that you could cut out couple of centimetres of outer plastic at one end and the result steel shell will be 4 mm in diameter and goes deep inside E3D extruder. The steel layer of this cable is actually spring and it makes this cable really perfect for 3D printer.

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The Young modulus of PTFE is about 500 MPa and the surface of a PTFE tube for 1.75 mm filament is about 9.4 mm2.

The Young modulus of PLA is variable, between 350 and 2800 MPa, let's say 2000 MPa. The filament surface is 2.4 mm2.

The ratio is about 1 because the surface ratio is 4x and the Young's modulus ratio 1/4x. As result, the stretching of PTFE is about similar to the compression of PLA inside it (of course they sum, since they go in opposite directions). PLA is very stiff: other materials will compress much more and make the stretching of PTFE less relevant.

However the filament is thinner than the tube, so it will curl a bit, which increases its contraction much more! It is likely that even for PLA the stretching of the PTFE is much less relevant than the compression of the filament.

Anyway, fiberglass has a Young's modulus of about 80 GPa (150 times PTFE), but its thickness is what? 0.1 mm? That bring a surface of 2 mm2 at most (and I'm very optimistic, more likely much less than 1 mm2). Fiberglass helps to strengthen PTFE by a factor of surely less than 30, more likely 10 or less (will the glue hold or slide?).

As result, PTFE, from a contribution to the overall stretching/compression of 50 % (in fact, much less due to curling), will be reduced to about 5 %. It is good, but this is an optimistic value.

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