TheTechnicalNoob: thanks for the link.
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).
Ok, so for GT2 belt it would be 18000 lb for 1" wide belt. Based on note 4, that is 18000/25.4*6*0.82 ≅ 3486.6 lb (or about 15509 N) for the common 6mm belt repraps often use. That means the elongation for 1m long belt and 57N force change is 1 * 57 / 15509 ≅ 0.0037 m = 3.7 mm.
That is quite a lot but suprisingly near to the value I estimated before for the glass core (which was 3mm). Probably just a luck since I was only guessing what the glass core cross section may be. Anyway, it is good sign that it does not differ by order or more orders of magnitude.
That indicates that young modulus may not be that different for a string of twisted fibers compared to a single fiber. That indicates that the individual filaments are barely twisted around themselves when spun to the reinforcement string of a belt and/or that a good pretension is applied when the belt is produced.
Anyway, 3.7mm per metre is a lot! Even if we decide that printers typically use only 1/10 of the needed stepper torque when changing direction of movement, even with this assumption we get 0.37 mm tower position error which will lead to about the same errors in the effector movement. And only due to the belt elasticity. That also means that printed part errors we see around corners may be also because of belt elasticity (and not only because of the surface tension and contraction of the cooling plastic).
Now we only need the same data for the belts with a steel core. They should be better by at least 1/3.
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).
Ok, so for GT2 belt it would be 18000 lb for 1" wide belt. Based on note 4, that is 18000/25.4*6*0.82 ≅ 3486.6 lb (or about 15509 N) for the common 6mm belt repraps often use. That means the elongation for 1m long belt and 57N force change is 1 * 57 / 15509 ≅ 0.0037 m = 3.7 mm.
That is quite a lot but suprisingly near to the value I estimated before for the glass core (which was 3mm). Probably just a luck since I was only guessing what the glass core cross section may be. Anyway, it is good sign that it does not differ by order or more orders of magnitude.
That indicates that young modulus may not be that different for a string of twisted fibers compared to a single fiber. That indicates that the individual filaments are barely twisted around themselves when spun to the reinforcement string of a belt and/or that a good pretension is applied when the belt is produced.
Anyway, 3.7mm per metre is a lot! Even if we decide that printers typically use only 1/10 of the needed stepper torque when changing direction of movement, even with this assumption we get 0.37 mm tower position error which will lead to about the same errors in the effector movement. And only due to the belt elasticity. That also means that printed part errors we see around corners may be also because of belt elasticity (and not only because of the surface tension and contraction of the cooling plastic).
Now we only need the same data for the belts with a steel core. They should be better by at least 1/3.