Timing belt sizing for quadrotor power transmission

Looking for info on designing timing belt power transmissions. Some sites I’ve found of interest:

http://www.roymech.co.uk/Useful_Tables/Drive/Timing_belts.html

http://us.misumi-ec.com/pdf/tech/mech/p2823.pdf

http://www.sdp-si.com/D265/PDF/D265T003.pdf

The tooth profile of the FT2 and HTD belts have a much higher resistance to skipping combined with a higher power transfer.

http://www.hpcgears.com/technical.htm
Technical data on belts, gearing, chains.

http://www.contitech.de/pages/produkte/antriebsriemen/antrieb-industrie/download/TD_Synchrobelt_HTD_en.pdf
HTD belt data sheet

http://www.gates.com/europe/file_display_common.cfm?thispath=Europe%2Fdocuments_module&file=Gates_PU_Catalogue_2012_E2%2Epdf
M
ore HTD belt design data sheet

http://www.skf.com/files/896756.pdf
SKF “Power Transmission Belts” manual ; from page 128 onward for timing belt sizes and calculations

http://www.gates.com/login/register.cfm?requesting=powergripManual
Gates manual for “Powergrip GT2 Belt Drives” (may have to register; it’s free)

http://www.gates.com/login/register.cfm?requesting=llpdesign
Gates design manual for “Light Power and Precision” (may have to register; its free)

SUPPLY

Looking for places to get cheaper timing belts:

http://www.robotdigg.com/category/9/Timing-Pulley&Belt
Chinese outfit. Prices reasonable, minimum order is $25 shipping

http://reprap.org/wiki/Choosing_Belts_and_Pulleys
Supplier list of timing belts and pulleys (bottom of page).

DESIGN

What I learned from going over the SKF and Gates design manuals for timing belts and pulleys: Belts transmit a certain amount of power. That power is based on the rpm of the pulleys. Taking the RPM out of the equation, the force on the belt is relatively constant for (for a certain RPM). The torque varies but only because the gear diameter changes. Between the different timing pulley sizes (at a constant RPM) the torque varies based on the pulley diameter. The force on the belt is relatively constant.

The force on the belt however seems to vary with RPM for some reason. Have to understand why that is. Also have to understand why the belt length affects the force transmitted by the belt.

The torque and power numbers listed in the tables is based on 6 tooth engagement. Less then 6 teeth requires a correction factor.

Going with a GT2 pulley system. It provides a much better power transfer with less skipping. Even a small GT2 2mm pitch belt at 6mm wide will be able to transmit about 70w of power. The 4mm wide belt should transmit about 47W of power.
Equation for Power: P (W) = Torque (N-m) * RPM * (2*pi/60)  (source)

Using the data from the “Gates Light Power/Precision” design manual, a GT2 5mm(pitch) belt can transfer nearly 3 times the power at the same belt width and RPM then a XL belt.

For the GT2 belts, the 3mm pitch belt can carry 4 times the load of the 2mm pitch belt and the 5mm pitch belt can carry 5 times the load of the 3mm belt. So instead of increasing the belt width, you get much more bang for the buck by going to the next size pitch belt.

In contrast with the  Trex450 belt is 2.03mm(MXL) pitch or 0.8 inch pitch, 3mm (1/8″) wide. This MXL belt can transmit about 30W of power.
From THIS POST I was able to get about 700g of thrust = 50ish W with only 5 teeth engaged on the 11T pulley at around 2000RPM. Since only 5 teeth were engaged (6 is minimum) only 80% of the possible power was transmitted, so i could possibly transmit 40ish W with all 6 teeth engaged. I was actually exceeding the design guidelines in terms of power transmitted but only by a little bit.  Going with a larger puley of 19T (see this post) I was able to get 1080g of thrust = 90ish W.
I was pushing the system way beyond its design capabilities. Likely the timing belt design data is conservative.
With a GT2 belt, I should be able to transmit WAY more power with a similar sized belt. With a 14T pulley, at 3600 RPM,

For a 3kg AUW (2kg quad and 1kg payload), I would aim for a 3:1 power to weight ratio, so need to be able to generate 9kg of thrust. Using two 250 blades (250mm long, 22mm chord) I need about 4500RPM at 10deg blade angle to get 9kg of thrust from all 4 rotors. With a 2 bladed rotor I’d be sucking down 911W. Slowing down the rotor to 3500rpm and adding 2 more blades (4 total) 9kg of thrust can be produced at 880W. Goes to show how much drag increases with RPM.
Designing for 3500 RPMs and 1KW power usage (250W per rotor)

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