Calculating the radius of multiple rope pulleys

[odinengineer]

I am trying to calculate the radiuses of the different pulleys. It is a modification of a double tackle block and tackle pulley. On a typical pulley all of the radius are the same and can spin freely. To save cost and space I wanted to combine the four separate pulley wheels in to two multi pitched pulley wheels. I need help trying to figure out what all the radiuses should be so that there is no rope slippage. Does anyone knows of the equations or formulas for this style of pulley. My first attempt was close but I am still getting rope slippage.

 

[btrueblood]

You need to include the stretch vs. tensile load characteristic of the rope.

 

[odinengineer]

ok, how do I do that?

I am using Commercial Grade Nylon-coated Ss Wire Rope, 3x7 Hollow Core, .032" - .037",110# Brk Strg,25'l

 

[MikeHalloran]

It can't work as drawn.

It can work if the two pulleys on each axle are independent of each other and can rotate at different speeds.



Mike Halloran
Pembroke Pines, FL, USA

 

[odinengineer]

I know it will work if each wheel can rotate independently of the others. I did not want the wheels to move independently. What I am trying to figure out is how I could change the radiuses to create the different speeds. Pulleys of different radiuses have different belt speeds while still maintaining the same RPM’s. The speeds per wheel should be constant, right. So how do I calculate the belt speed to Radiuses of a pulley gear train?

 

[hydtools]

Belt speed is 2*r*pi*rpm.

Ted

 

[btrueblood]

Ah, missed that (wheels are fixed to each other), thanks Mike. I think Mr. Halloran is right, again, as usual.

 

[MikeHalloran]

Mr. Halloran has spent a great many years doing things wrong, or somewhat less than completely right, and has slowly developed a fine-tuned sense of 'Deja Uh-Oh'.

Thank you for the kind words anyway.


Mike Halloran
Pembroke Pines, FL, USA

 

[Compositepro]

Listen to Mike's advice. While it is theoretically possible to do it, it isn't practical. You would need to factor in the stretch of the rope and its change with tension, the diameter of the rope and its change with tension, the distance between pulleys, etc. You will never get it right, so performance will always suffer compared to separate bearings. It would also probably actually cost more.