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# Flow Calculations

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Posted · Flow Calculations
2 hours ago, gr5 said:

So Cura does care if the filament is round versus if the filament is square because it calculates the flow coming out of the nozzle assuming that it knows the diameter of the filament going into the feeder and it knows the linear distance the filament has moved so it calculates the volume of filament extruding that way.

Cura doesn't care about the diameter of the nozzle - it assumes that the volume of filament going through the feeder matches that coming out of the nozzle (no leaks).

This is absolutely true.  Cura relies on you telling it a reasonable value for line width.  A value similar to your nozzle width.

Yes, cura does care about the shape of the filament.  Instead of asking for filament diameter, a more accurate question would be 'filament cross-sectional area'.  So, if you were to use square filament for whatever reason, you can rearrange the equation below to solve for D, or equivalent diameter, and that would produce exactly equal G Code values.

Equating the diameter of the nozzle to the length of a side for a square nozzle does not make a lot of sense.  The key parameter here is area.

Remember, we want the volumetric flow rate to be equal. So, for a nozzle with diameter, D, the equivalent square nozzle would have side length S equal to:

S = D*sqrt(pi/4)

So when you say 'the lines require slightly different amounts plastic', it is because the dimensions of the square nozzle are incorrect to begin with.  According to this equation, for any linear distance of extruded filament, the amount of material will be exactly the same.

The shape of the extrusion will be slightly different of course, but that is beyond the topic of this thread I think. That is a much more complex issue.  From a slicing perspective, the calculation is important to determine the rate and distances of the extruded filament in the gcode.

The biggest issues would be at the start and stop points, but the differences can be fixed or 'covered up' by adjusting your overlap percentages.

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Posted · Flow Calculations
On 6/21/2019 at 1:44 PM, yellowshark said:

Thanks for that @gr5. I am not sure the sonotube/shute point is relevant to the point I was trying to make, which is that firstly you need more concrete to build a rectangular column than a circular column of the same dimension. A 15ft circular column with a diameter of 2 ft needs 47.1 cubic feet of concrete . A 2 ft square column needs 60 cubic feet.

So if Cura uses a rectangular profile when doing its calculations – which was the stated point that I was questioning, it was not my point – then with a circular delivery profile (fine maybe it is elliptical but lol it looks circular to me) then are you not over-extruding by 27%?

Also I remain dubious that 0.8mm nozzle would draw a 0.4mm line. A couple of years back I discovered my printer was drawing 0.45mm lines - with everything in Cura setup for 0.4mm lines - which I assumed was due to either wear and tear or manufacturing tolerance and so I changed Cura to 0.45 nozzle and line width and improved my prints.

When you say 'and improved my prints', what were the symptoms? What looked bad before and what is the appearance now that it looks better?

The extrusion width will always be greater than the nozzle diameter, unless the layer height is close to the nozzle diameter.  By changing from 0.4 to 0.45 in Cura, you actually changed the path spacing as well as the amount of plastic being pushed into the nozzle. Path spacing = width for the Cura engine.

So I would guess you had too much overlap between adjacent passes. You should also adjust the extrusion multiplier for even better prints, if you want to be super calibrated.

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Posted · Flow Calculations

The point I was attempting to make is that the flow rate (volume of material per distance travelled) is independent of nozzle shape. Circle, square, ant convex polygon.

The key to accurate computation of the volume extruded is to accurately model the shape of the sausage, I used ideal shapes above for the thought experiment.

Furthermore a square would be a poor choice for a nozzle because the minimum line width would be different depending on the motion vector.

As for the area of the nozzles being different, that only affects the velocity of the plastic going through the nozzle.

Imagine a 0.1 nozzle with the same external geometry (flat nozzle surface 1mm wide). If you extrude the same volume of plastic through it as the 0.4 nozzle, it will produce the same line width. But for the same head speed, the velocity of the plastic through the nozzle would be 16x faster. The extruded sausage would be the same shape because the formation it is dependent upon the shape of the bed (or prior layers), the bottom of the nozzle, and the surface tension of the plastic that constrains the sides.

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• 3 months later...
Posted (edited) · Flow Calculations
On 6/20/2019 at 9:32 AM, gr5 said:

@yellowshark - Cura doesn't care if the nozzle is round, square, star shaped nor what it's cross section is when calculating the amount of filament needed to extrude a line of filament.  If the nozzle diameter is 0.8 but the line width is 0.4 it will extrude the right amount to fill the volume of that printed "line" of filament.

Back to your concrete analogy - if you are pouring concrete into a sonotube, it doesn't matter how big the chute is - it matters how much volume the sonutube takes up.  The nozzle in this analogy is the chute only.

In real life of course it matters a little but Cura doesn't worry about nozzle shape.

Also note that the spacing of the "lines" is equal to the line width.  So with 100% fill it should work very well.

Edited.  Question asked in separate topic.

Edited by Reywas
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• 1 year later...
Posted · Flow Calculations

I'm personnaly using this formula to calculate not the flow but the "real" wall thickness , and it's rather correct.

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