I am looking for a formula to increase speed using pulleys using more than one step to increase to final rpm

I am looking for a formula to increase speed using pulleys using more than one step to increase to final rpm

My first pulley is 32″ going to a 5.5″ I will have a larger pulley on this shaft as well and it will go back to a 5.5″ on another shaft with another larger pulley turning the final 5.5″ pulley. If my main pulley is turning at 150rpm what sizes of pulleys will i need to make my final pulley turn 2600 rpm using the two step increase.

Robert:

The ratio between you input and output pulley is

32/5.5 or 5.818:1

The speeds you mention of 2600/150 = 17.333

If you already have the first step the 5.818 reduction your out put speed on that shaft is

150 x 5.818 or 872.72

to get all the way to 2600 you will need an additional increase of

2600/872.2 = 2.979

5.5 x 2.979 = 16.3854 diameter

Alternately you can look at your total ratio. Which is

17.333

if you want to create this speed ratio in two equal steps take the square root of

17.333^(1/2) = 4.164

with a 5.5 in output diameter on both stages the input pulley would be

5.5 * 4.164 = 22.898″

150 * 4.164 = 624.6

624.6 * 4.164 = 2600.834

The slight difference is due to round off error.

Niel