V Pulley to Flat Pulley Drives

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Stan

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All the old common US small lathes used this system which made it possible to change pulleys without adjusting the motor. I have made three, two step V pulleys, last week and cannot get the sizes right so that the belt is the same length on each pair. Logan uses a ratio of 2.1 to 1 to get their speeds evenly spaced but that is not a requirement for me with a DC drive.

The first pulley I made the same as I would a V to V drive and that was a mile out. For the second one I used all the formulas I could find in Machinery Handbook which appear to work out mathematically but the larger pulley is too small. I came to the conclusion that the formula did not allow for the fact that larger V pulleys have bigger included angle and wider at the top which allows the belt to ride lower.

For the third pulley. I made both pulleys with the same angle and top width and made the big pulley .100 bigger than calculated but it it is still a bit too small.

Does anyone have the answer? Here are the numbers I am working with:
2.5" V pulley to 9.5" flat pulley
?? (approx 5.25") V pulley to 7.625" flat pulley
A new Gates B size belt.

The pertinent information I got from the Handbook is that you work with effective diameters which is the OD of a V pulley, and the OD of a flat pulley minus twice the belt thickness.
 

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