Belt C-C distance to Tension

[RodrigoBlakenship]

TL;DR

Is there a known equation relating tension to C-C distance?

Hi all,
I've looked through design manuals (SDP/SI, Gates, Naismith) and textbooks like Shigley's, but haven't found an equation linking initial belt tension to pulley center-to-center distance for a timing belt. I understand initial tension is typically based on the applied load, but I'm curious:
A) Is there a known equation relating tension to C-C distance?
B) If not, how might one go about deriving it?

Thanks in advance!

 

[Baluncore]

A) Is there a known equation relating tension to C-C distance?
B) If not, how might one go about deriving it?

In theory, given the C-C distance, the zero length of the belt path can be computed. Knowing the initial belt length, Hook's law, and also the spring constant, allows tension to be computed, in proportion to extension.

In practice, the tension will be different in different parts of the belt, and there will be dynamic harmonics present. The belt will be a V-belt, and the sectional width of the V will be reduced by tension, so that it will drop and wedge deeper into the V of the pulley, increasing grip, while changing the computed zero tension length. That will rapidly become too complex to compute.

In real applications, a mechanical tensioner is employed with belts to maintain a specified tension in the belt, independent of variations in belt path length, wear, or aging of the belt.

 

[Lnewqban]

TL;DR: Is there a known equation relating tension to C-C distance?
A) Is there a known equation relating tension to C-C distance?
B) If not, how might one go about deriving it?

Thanks in advance!

Welcome!
What makes you believe that a relation exists between those two parameters?
The C-C distance is determined by the internal architecture of the engine (locations of crank and cam shafts).