belt conundrum

[derf]

So I've been resto- modding an old Seneca Falls lathe, and I'm working on the drive train, basically putting power to the counter shaft. I came up with a 2 speed arrangement using a 2"& 3" pulley on the motor, and a 9"& 10" on the driven. The 2" on the motor goes to the 10" pulley for 5:1 reduction, and then a 3" pulley to the 9" for a 3:1 reduction. The problem lies in the belt length. Theoretically, the belt length should be same for both speeds, according to my math, BUT.....when set up for the 3"& 9", the belt length is about 1/2 shorter.
I wanted to use a simple belt tensioner so it would be easy to change speeds, but now there is quite a bit of difference in position of the tensioner.
I figured that the pulleys were slightly under/oversize and might account for the discrepancy, so I actually measured the diameter with 12" calipers with the belt on to get a true o.d. When adding the diameters, there is only .015" difference between the 2 combinations. When figuring the circumference, the difference is .048" shorter for the 3&9 combo, but in all reality it is closer to 1/2". I know this by measuring with split v belt made for that purpose.
Am I missing something here? or do these have to be dead nuts on the money to accomplish a simple task?

 

[4GSR]

How about posting some pictures to give us a better idea of what you have there?

 

[derf]

 

[Ulma Doctor]

v belts don't run at the bottom of the pulleys if they are operating correctly.
they have a pitch diameter that is somewhere near the center of the pulley v
my craftsman TH42 had a 2 speed arrangement that was similar.
the motor and gravity was responsible for belt tension.
there was a difference in where my motor sat, dependent on what step i was running

the tensioner is a good idea, but it doesn't have to be super tight to work

 

[francist]

I have a belt calculator app from Gates on my phone, so for kicks I ran your numbers. In both cases, I used a hypothetical 12" center to center distance. The 2" to 10" combination yielded a 44.2" belt length. The 3" to 9" combination yielded a 43.6" belt length. Difference of 0.6". Cannot give you the reason, although it may have something to do with the belt having steeper angles on the 2-10 combination so the travelled distance is longer.

-frank

 

[derf]

Your numbers are almost spot on. The distance between centers is 11.900" and I'm using a 44" belt. The belt would be tight at 12" on center for the 10 and 2, but I left slack to roll it off to the other set. I kind of figured it had something to do with the taper of the v belt, as with the flat belt I used on the cone pulley didn't have that problem.
I guess I never thought about using the Gates calculator......I did on the flat belt. Thanks for answers guys.