Re: Scaling up Kossel Mini

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hercek

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A2
I found no contradictions in the Gates chart.
Post the units, and show your work to avoid confusion.

Claim 1 of the document:
The last column of the table specifies unit as lb/in² for 1" wide belt.
Claim 2 of the document:
Note 7 specifies the formula for the belt elongation computation as BeltElongation = (BeltLength * TensileLoad) / TensileModulus.
Lets specify what should be the units for all the terms of this equation except the TensileModulus:

• for BeltElongation it is in
• for BeltLength it is in
• for TensileLoad it is lb

Lets put the units into the equation and derive the unit for their TensilaModulus:
in = (in*lb)/TensileModulus
TensileModulus = (in*lb)/in
TensileModulus = lb
That means that from the Note 7 we can deduce that their unit for TensileModulus is actually lb.

Claim 1 is different from Calim 2 because lb ≠ lb/in².
That is the contradicition in the document. The problem with contradictions is that anything can be deduced from them. I interpreted it one way and deduced elongation of about 1.85 mm (If I would assume load of only 29N instead of 57N), you interpreted it another way and deduced elongation of 230 nm which is about a wavelength of ultraviolet light. What interpretation sounds more probable?

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A2
0.2 N/m / .007 m = 28.57 N
28.57 newton = 6.423 pound-force

I multiplied 28.57N by 2 and got about 57N becasue the stepper can produce the force of 28.57N (ignoring the stepper rotor inertial forces) in one direction and (with big enough jerk) in the opposite direciton too just a moment later. So once we have force on the belt of +28.57N and the moment later -28.58N. The difference is about 57N. I did it this way to get the worst ever possible situation. If the worst possible situation would lead to neglible elongation then I would know this is not something to be concerned about. But I easily grant you that we should use number 28.57N ... really this does not matter much. My computation ingnores so many things that factor of 2 is almost nothing compared to other possible errors. But I would start to be concerned at about factor of 10 and more.

As for as the rest of your computaion. It is correct. You just selected the other interpretaion of the document with condtradictions.
Except the last step. You have the last step wrong. If you would bother to continue to folow also the units in the very last step you would even notice the contradiction in the document since:

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A2
Belt Elongation = (1.0 meter * 28.57 N) / 124105648 N/meter²
Belt Elongation = 0.00000023 meter = 0.00023 mm = 0.000009 inch

Belt Elongation = (1.0 meter * 28.57 N) / (124105648 N/meter²)
Belt Elongation = 230e-9 * (meter*N) / (N/meter²)
Belt Elongation = 230e-9 * meter / (1/meter²)
Belt Elongation = 230e-9 * meter³
Ooops, belt elongation in cubic meters? Does not sound right to me.

Anyway, in the absence of more data, I'm tempted to think that my interpretation of the contradictory document is the correct one. Especialy because it is about the same as the estimation I did here for my T2.5 belts with steel core. There can be a big error in my estimation because I more or less guessed the steel core filament diameter in my belt (there was no easy way to measure it without cutting off and dismantling a piece of the belt). But I doublt I guessed it wrong by 3 orders of magnitude.

Uff, I do not like imperial units. They are a mess. And I do not have experience with them. And I do not even want the experience. People who use them (like the authors of the document) should at least use them right so that they do not confuse the hell out of us SI users who want to keep it simple.

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hercek
Lets put the units into the equation and derive the unit for their TensilaModulus:
in = (in*lb)/TensileModulus
TensileModulus = (in*lb)/in
TensileModulus = lb
That means that from the Note 7 we can deduce that their unit for TensileModulus is actually lb.

Belt Elongation = (1.0 meter * 28.57 N) / (124105648 N/meter²)
Belt Elongation = 230e-9 * (meter*N) / (N/meter²)
Belt Elongation = 230e-9 * meter / (1/meter²)
Belt Elongation = 230e-9 * meter³
Ooops, belt elongation in cubic meters? Does not sound right to me.

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hercek

Anyway, in the absence of more data, I'm tempted to think that my interpretation of the contradictory document is the correct one.
... And I do not even want the experience.

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hercek
I multiplied 28.57N by 2 and got about 57N becasue the stepper can produce the force of 28.57N (ignoring the stepper rotor inertial forces) in one direction and (with big enough jerk) in the opposite direciton too just a moment later.

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hercek
I do not have a guess how big it is without putting down some equations though.