# Torque and Pulley Ratios

#### billinr

I would like to ask if anyone could explain how torque is consumed through a reduction ratio - in this case pulleys on a common shaft.

I have a three shaft system, joined by belts.
The motor pulley is 25.4mm, turning at 100 rpm, with an available 1.4Nm torque. This is connected to the second shaft via belt. The second shaft has an input pulley of 82.5mm.

Also on the second shaft is another pulley of 24.5mm. This pulley is connected via belt to a third shaft with a 40.6mm pulley.

My question is: If the final pulley makes use of 100% of the torque available, how would I calculate how much of the torque is used at the jack shaft? If I negate any losses from bearings, does the ratio have any effect on the torque or is the intermediate shaft just going along for the ride?

On the other side, does the ratio change the torque that is available at the third shaft?

Thanks

#### SystemTheory

From the belt ratios you should be able to find the angular speed at each shaft in rpm. If the belts don't slip, there is no loss of speed. If you neglect friction in the system, there is no loss of torque in the driveline. Convert shaft speeds to radian per second. The power at every shaft, computed as torque times speed (in watts), would then be constant due to conservation of power at each instant of time. Since you know the input power, you can find torque at each shaft from the power and radian shaft speed.

Edit: torque input equals torque output on the jack shaft when power is conserved, but force obviously differs in each belt operating at a different radius.

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#### billinr

SystemTheory
Thank you for the reply. This is making a bit more sense.

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