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Timing belt tension forces

Hello everyone

Wondering if someone can help me with some calculations which i initially though would be easy but have ended up giving me a bit of trouble.

I have a 2 pulley timing belt system. For calculating purposes 1 pulley can be assumed to be fixed and the other rotate freely. Also the pulleys can be assumed to be infinitely small. I don't need to know the force variation across the timing belt/pulley interface.

At distance x away from the fixed pulley a force acts on the timing belt. Other known values include:

E = Timing belt elasticity

l0 =Timing belt initial length

F0 = Timing belt initial tension

F = Amount of load applied to the timing belt

I want to calculate the slack side tensile force (Fs) and the tight side tensile force (Ft). I am useing a calculator with a solver function so basically i just need to know what assumptions i need to make and the math stuff is easily done.

Assumptions i have done so far:

F=Ft-Fs

Length of belt=l0+l0*F0/E

I have tried ALOT of different assumptions but i'm missing some sort of essensial observation regarding this problem.

If anyone could help me with an approach to the problem or point me towards some online available litterature about the problem i would be really thankfull.

In advance thank you.

Regards Christian

Mehcanical engineering