Thread: Hi all
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29-12-2009 #7
I have done some thinking and reading around timing pulleys and belts. It all comes down to the shear force on the teeth. The load has three components - static force, cutting force and inertia.
The static force is given by F = m * u where m is mass and u is friction coeff.. for ball races say 0.01, and lets say gantry is 30kg so F = 0.3N.
Cutting force for most woods would be 5N. Inertia is given by F = m * a. we want to accelerate to maximum speed in 0.02sec (for a medium spec machine). maximum speed for cutting is, say, 1200 mm/min = 0.02m/s. The acceleration therefore is .02m/s divided by 0.02 sec = 1m/sec^2 so F = 30 * 1 = 30N
so our pulley has to push on the belt with a force of 0.3 + 5 + 30 = 35N (ignore the 0.3, its noise!).
At 1200mm/min the pulley revs, for a 10 tooth pulley on 5mm pitch will be 1200/(5 * 10) = 24rpm = 0.4rps (2.5rads/sec)
The diameter of a 10tooth pulley on a 5mm HTD is 15mm so the radius is 7.5mm and the torque therefore is 35N @ 7.5mm radius = 0.26Nm
Power = Torque * rads/sec = 0.26 * 2.5 = 0.65W
From ther HPCGears catalog pages 787-790 the required HTD belt can be calculated as follows. Choose service factor c0 as 2.0, calculate c2 = c0 + c3 + c6 = 2.0, taking C3 and C6 both = 0. Pb = Power x C2 =.65 x 2 = 1.3W, which means from Graph 1 (page 788) aN 8M belt is needed.
there is one tooth in mesh so C1 factor is 0.1 and C7 taken as 0.8, therefore Pu > Pb and Pu = Pn * c1 * c7 so Pn > pb/(c1 * c7) = 1.3/(.1 * .8) = 16.25W which suggests a 15mm wide belt minimum. Note however that the torque load of a 15mm dia pully is a bit high.
A better choice would be a 20 tooth pulley, with a OD of 32mm, radius 16mm, torque 35N @ 16mm = 0.56Nm and Pb = 0.56 * 1.25rads/sec^2 = 0.67W so Pn>16W as before. This also needs a 15mm wide belt but is more in the sweet spot in the belt tables.
Now, 1 rev of pulley = 100mm movement, and assuming we want 0.05mm resolution we need 1 rev of motor = 10mm so we need 10:1 gearing, so motor speed at 1200mm/min = 2 revs/sec or 400 steps/sec.
So motor needs 10tooth, driving 100tooth/20tooth compound gear driving against the belt. Mechanically could be tricky to arrange.
On this basis only a tiny motor would be required due to the gearing... It doesn't look quite right to me, I need to think it through more...
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