Scaling up Kossel Mini January 30, 2014 03:14PM |
Registered: 11 years ago Posts: 471 |
Re: Scaling up Kossel Mini January 31, 2014 11:19AM |
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Re: Scaling up Kossel Mini January 31, 2014 12:03PM |
Registered: 10 years ago Posts: 732 |
Does anybody have information about tensile modulus of GT2 and T2.5?Quote
epicepee
use GT2 belts
Re: Scaling up Kossel Mini February 01, 2014 02:15AM |
Registered: 10 years ago Posts: 1,381 |
Re: Scaling up Kossel Mini February 01, 2014 10:41AM |
Registered: 10 years ago Posts: 732 |
Re: Scaling up Kossel Mini February 01, 2014 01:33PM |
Registered: 10 years ago Posts: 1,381 |
Quote
hercek
Unfortunately I believe insufficient to decide whether to go with glass reenforced belt or steel reenforced belt.
I also think they also significantly understimate the stretching problem.
Re: Scaling up Kossel Mini February 01, 2014 04:11PM |
Registered: 10 years ago Posts: 732 |
Well, as many times as it is below the young modulus, that many times the stretch is less meaningfull for unit length of belt. Anyway this is meaningless claim without some concrete numbers/examples in comparison to our delta bots. At least rmat claims dynamic stretch is a problem. Maybe he bought low quality belts or pulleys. Or maybe it is a real problem.Quote
A2
If your load is well under the young modulus you don't have "meaningful" stretch.
That is about static stretch during wear-in. That is not what I'm concerned about. I believe that is not what rmat was talking about. I was not able to find modulus (or the linear stifness) of the belt itself in the linked PDF. That is what I'm interested in. How does it compare between GT2 (fiber glass reinforcement) and T2.5 (steel reinforcement).Quote
A2
PowerGrip GT2
There is minimal stretching during the wear-in period.
After the burn in period there is no stretching due to wear.
The effects of belt elongation and tooth deflection do not have any influence on the registration accuracy of this type of system.
[www.cad.sun.ac.za]
Note that on page 16 of the paper they explicity take belt stiffness Kr into account when computing the total drive stiffness. So clearly dynamic belt stretching (I do not mean the initial wear-in stretching) needs to be taken into account for precise positioning.Quote
A2
Timing Belt Theory
pg13
the total elongation (deformation) of the belt operating under load is equal to the total belt elongation resulting from the belt pre-tension.
For most practical cases the difference between the deformations of the belt in contact with both pulleys during pretension and during operation is negligible.
Tensile tests show that in the tension range timing belts are used, stress is proportional to strain.
Theoretically, the tooth stiffness increases with increasing belt tension over the tooth, which has also been confirmed empirically.
This results in the practical recommendation for linear actuators to operate under high pre-tension in order to achieve higher stiffness, and hence, better positioning accuracy.
[www.gatesmectrol.com]
Yes, belt modulus for both GT2 and T2.5 is the number I would like to see. Then I would be able to guess whether rmat might have been right with his claim that GT2 is not good since it is too stretchy.Quote
A2
The amount of force to produce a specified stretch is known as the belt modulus.
[www.epi-eng.com]
Re: Scaling up Kossel Mini February 01, 2014 04:15PM |
Registered: 10 years ago Posts: 732 |
Re: Scaling up Kossel Mini February 02, 2014 03:42PM |
Registered: 10 years ago Posts: 153 |
Re: Scaling up Kossel Mini February 02, 2014 05:36PM |
Registered: 10 years ago Posts: 732 |
Re: Scaling up Kossel Mini February 03, 2014 03:18AM |
Registered: 10 years ago Posts: 1,381 |
Quote
hercek
A typicall stepper dynamical force change (usable torque about 0.2 N/m and pulley with 14 mm diameter) can be about 2 * 0.2 / (0.014/2) = 57N.
Quote
hercek
18000/25.4*6*0.82 ≅ 3486.6 lb (or about 15509 N)
Re: Scaling up Kossel Mini February 03, 2014 07:12AM |
Registered: 10 years ago Posts: 732 |
Claim 1 of the document:Quote
A2
I found no contradictions in the Gates chart.
Post the units, and show your work to avoid confusion.
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.Quote
A2
0.2 N/m / .007 m = 28.57 N
28.57 newton = 6.423 pound-force
Belt Elongation = (1.0 meter * 28.57 N) / (124105648 N/meter²)Quote
A2
Belt Elongation = (1.0 meter * 28.57 N) / 124105648 N/meter²
Belt Elongation = 0.00000023 meter = 0.00023 mm = 0.000009 inch
Re: Scaling up Kossel Mini February 03, 2014 09:47AM |
Registered: 10 years ago Posts: 732 |
Re: Scaling up Kossel Mini February 03, 2014 11:47AM |
Registered: 10 years ago Posts: 1,381 |
Quote
hercek
Claim 1 of the document:Quote
A2
I found no contradictions in the Gates chart.
Post the units, and show your work to avoid confusion.
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:
Lets put the units into the equation and derive the unit for their TensilaModulus:
- for BeltElongation it is in
- for BeltLength it is in
- for TensileLoad it is lb
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?
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.Quote
A2
0.2 N/m / .007 m = 28.57 N
28.57 newton = 6.423 pound-force
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:
Belt Elongation = (1.0 meter * 28.57 N) / (124105648 N/meter²)Quote
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 = 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.
Quote
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.
Quote
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.
Quote
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.
I'm looking forward to your equations.Quote
hercek
I do not have a guess how big it is without putting down some equations though.
Re: Scaling up Kossel Mini February 03, 2014 01:38PM |
Registered: 10 years ago Posts: 732 |
zsh> maxima Maxima 5.32.1 [maxima.sourceforge.net] using Lisp SBCL 1.1.14 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) A: 1.0 * meter * 28.57 * Newton / (124105648 * Newton / meter^2); (%o1) 2.302070893663115e-7 meter^3 (%i2) ^D zsh>If you still do not believe it then use the function bug_report().
Re: Scaling up Kossel Mini February 03, 2014 04:00PM |
Registered: 10 years ago Posts: 1,381 |
Quote
A2
Using a 6 mm wide GT2 belt with a 28.57 newton-force (6.42 pound-force),
there is 0.00023 mm (0.000009 inch) of belt stretch.
For all practical purposes, this is equivalent to zero stretch.
A: 1.0 * meter * 28.57 * Newton ; B: 124105648 * Newton * meter^2 ; C: A / B ;
Re: Scaling up Kossel Mini February 06, 2014 01:22PM |
Registered: 10 years ago Posts: 732 |
Re: Scaling up Kossel Mini February 06, 2014 04:05PM |
Registered: 10 years ago Posts: 1,381 |
Gates claims their GT2 belt has zero stretch, you "deduced" that the stretch is 1.85 mm.Quote
hercek
I interpreted it one way and deduced elongation of about 1.85 mm
Quote
A2
0.2 N/m / .007 m = 28.57 N
28.57 newton = 6.423 pound-force
Quote
hercek
A2, I needed a break from this discussion. But I'll give you one more chance. Maybe you made only a mistake (maybe you are not trolling me).
Why should I use a script which is different from mine and from the one specified in the Note 7 of the Gates document. In your script, the definition of B should have been: 124105648 * Newton / meter²; (Because the unit for their "modulus" was lb/in². Because you changed the problem without any explanation why you are doing so, it looks like you are trying to pull out a Straw Man.
Quote
hercek
Even If I would try to use your script (exactly as you have written it), notice that you got the final unit of elongation (meter) in the position of a denominator. That means that you are actually proposing to measure distances in units of 1/meter. Does it not sound bad to you? Distances are typically measured in units of meter, not 1/meter.
Re: Scaling up Kossel Mini February 06, 2014 05:36PM |
Registered: 10 years ago Posts: 732 |
Re: Scaling up Kossel Mini February 06, 2014 07:58PM |
Registered: 10 years ago Posts: 1,381 |
Quote
hercek
Uff, ok, I took apart the rostock here and I measured the T2.5 belt with steel core.
I pre-tensioned the 1.48m long belt with force of 190N.
Then I needed to increase the force to 280N to make it longer by about 2.5mm (one belt teeth span).
That corresponds to elontagion of about 0.02mm per 1 meter of belt and 1 newton of force.
Quote
hercek
That corresponds to elontagion of about 0.02mm per 1 meter of belt and 1 newton of force.
Quote
hercek
Which line corresponds to the script you entered in Maxima?
Re: Scaling up Kossel Mini February 07, 2014 05:50AM |
Registered: 10 years ago Posts: 732 |
I do not have specification of the belt. The seller did not specify the producer. The Gates document does not mention T2.5 belts so I cannot use that as an approximation. (Regardless we do not agree how to interpret the Gates document.) It was a T2.5 belt. Its width was 6mm. Its length was 1.480m when it was tensioned with force of 190N. Then I increased the force to 280N. That made the belt to stretch to the final length of 1.4825m (1.4825m - 1.480m = 0.0025m = 2.5mm). So how much would this belt stretch if it was 1m long and the applied force was 1N? For that we need to divide the measured elongation of 2.5mm by the force difference and the length of the belt.Quote
A2
Did you mean:
A 1.0 meter span, of a T2.5 belt, with a 280 N tensile force (62.95 pound-force) elongated by 2.5 mm?
This does not make sense, show your math.Quote
hercek
That corresponds to elontagion of about 0.02mm per 1 meter of belt and 1 newton of force.
Yes, it is about 5 grade math and you are doing it wrong.Quote
A2
FYI: this is 5th grade math.
Since the equivalence relation is transitive we can deduce (I assume N stands for Newton):Quote
A2
B: 124105648 * Newton * meter^2 ; = ( Tensile Modulus ) = 124105648 N/meter².
Re: Scaling up Kossel Mini February 07, 2014 05:32PM |
Registered: 10 years ago Posts: 1,381 |
Quote
hercek
steel crosssection area is about 0.28 mm²
Quote
hercek
Since the equivalence relation is transitive we can deduce (I assume N stands for Newton):
124105648 * Newton * meter² = 124105648 * Newton/meter²
Now we can devide by 124105648*Newton:
meter² = 1/meter²
Now we can multiply by meter²:
meter⁴ = 1
Which is a contradiction.
I proofed by contradiction that what you have writen for expression B is not correct.
Re: Scaling up Kossel Mini February 08, 2014 06:11AM |
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Re: Scaling up Kossel Mini February 08, 2014 06:42AM |
Registered: 10 years ago Posts: 1,381 |
Re: Scaling up Kossel Mini February 08, 2014 06:48AM |
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Re: Scaling up Kossel Mini February 08, 2014 06:55AM |
Admin Registered: 17 years ago Posts: 7,879 |
Re: Scaling up Kossel Mini February 08, 2014 07:00AM |
Registered: 10 years ago Posts: 732 |
You are confused so much here that it is starting to be funny.Quote
A2
The only way you can get the units to work out using the new input of cross-sectional area is to proportionalize
the area of the glass fiber bundles over 1 square inch before multiplying by the modulus of the belt, i.e. (1* inch * inch /(0.000434 * inch * inch)).
If you don't do that you get meter3, which is a bogus conclusion.
So the final proper term for yung modulus in the maxima script should be (10000000 * pound / (inch*inch)).Quote
A2
Fiberglass
Tensile Strength 350,000 lbs/in^2
Elongation at break 2.5 – 3.5%
Modulus 10,000,000 lbs/in^2
zsh> rmaxima Maxima 5.32.1 [maxima.sourceforge.net] using Lisp SBCL 1.1.14 Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) A: (6.423*pound) * (39.37*inch); (%o1) 252.87351 inch pound (%i2) B: (Notice also that I got the result in a nice unit which is inch. It makes sense to measure elongation in inches. Notice you got the resutl in 1/inch (your inch is in denominator). How could you measure elongation (i.e. length) in (1/inch)?1510000000*pound/(inch*inch))*(0.000434*inch*inch); (%o2)6514340.0 pound (%i3) A/B; (%o3).03884385714285714.05826578571428571 inch (%i4) ^D zsh>
No, I'm not. * means multiplication in maxima. It is no special kind of placeholder. It is the sign for multiplication in maxima. So you did not show my proof of you being wrong to be incorrect.Quote
A2
You are confusing wxMaxima place holder (*) as multiplication.
Do not make things up! I did not say the Gates equation is wrong. I saied there is a contradiction in the document.Quote
A2
hercek, you continue to claim that the Gates equation is wrong, then why don't you show us the correct equation?
I said that either their formula is wrong or the unit for their special kind of modulus is wrong. Here I even posted a proof that their document contains a contradiction: [forums.reprap.org]Quote
hercek
Hell, that documents must be writen by heretics of physics. Not only the authors use "hogshead" units, but they cannot even get it right, even with them. Ok, so they define modulus as lb/in² but (based on the formula (in note 7) for ussage of their modulus values) the unit is actually only lb. Or at least I hope this is what they intended (one cannot be completely sure when they have contradictions even in such a simple document).
Re: Scaling up Kossel Mini February 08, 2014 07:10AM |
Registered: 10 years ago Posts: 1,381 |
Re: Scaling up Kossel Mini February 08, 2014 10:56PM |
Registered: 10 years ago Posts: 732 |
Sorry. I did not even know nophead joined the discussion at the time I was writing my last response. Once I started to write it I did not see the thread progress. However I'm glad nophead was better at explaining what is wrong. I was trying to do it in a more formal way (without actually modeling it in a proof assistant like COQ or Isabelle) to build a more precise argument showing where the errors are (so that they can be understood and corrected). Nophead stated how it should be. I would not accept it myself if it would not already map perfectly at what I believed it worked like. It would be merely another hypothesis to me. The question which hypothesis is the right one would still be open.Quote
A2
Why didn't you pick up on this, and point it out?
Re: Scaling up Kossel Mini February 14, 2014 08:33AM |
Registered: 10 years ago Posts: 7 |