Is there an equation linking belt drive tension to C-C distance?

R

Rodrigo Blakenship

New Member
Hello,

Having checked design manuals (Naismith, gates, SDP/SI) and textbooks like Shigley's I could not find an equation linking the centre to centre distance between two pulleys of a belt drive to the tension in that drive.
The reason why I wanted this equation was because I wanted to pretension my belt using the C-C distance instead of an idler pulley. Although this goes against the valid points that the belt tension will change with time and will need to be re-tensioned, I just wanted to give it a go. Advice I got from this forum and other forums is to apply Hooke's law. Using this approach I found it difficult to calculate the Young's modulus and I was wondering how I should go about doing it.
One method I had is based on the fact that the belt is composed of several fibreglass cords running along the length of the belt covered by neoprene. I am calculating the Young's modulus of the belt using EC = EF VF + EM VM , where VF and VM are the volume fractions of fibers and matrix (neoprene) respectively and EC is the Young's modulus of the belt.

I took this method from a free textbook on composites (https://www.princeton.edu/~maelabs/hpt/materials/composites.htm). Images of the internal structure of the belt can be found here: https://www.gates.com/in/en/power-t...r-synchronous-belts.p.9356-000000-000000.html
I would really appreciate any feedback on this method or any alternative methods..
 
The modulus of the reinforcing cords are much, much higher than the neoprene body. I would neglect the effect of the rubber and model just the cord.
 
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