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Peter Hudlicka • Feb 5, 2018

# Rear Sprocket Design

I am a mechanical engineering student at the University of Waterloo on the student design team Waterloo Formula Electric SAE.

I'm designing a sprocket for a rear half shaft on our vehicle and was wondering if anyone has experience designing sprockets.

Trying to find the back tension on each tooth of the sprocket, I found the following equation cited in multiple online sources:

Tk=T0*(sinⱷ/sin(ⱷ+2B)^k-1

Tk is the tension on a given engaged tooth

T0 is the maximum tension experienced by the chain

ⱷ is the minimum pitch angle (17-64/N, N being the number of teeth of the sprocket)

2B is a little misleading, thought there is a variable B, the entire expression 2B seems to have a constant value of 360/N

k is the number tooth of the sprocket that is engaged

I have a couple of issues with the equation, aside from the ones mentioned above, I do not understand how it can be applied as it seems that using this equation, the first tooth engaged would take all of the tension of the chain as k-1 --> 1-1 = 0 --> Tk= T0*(sinⱷ/sin(ⱷ+2B)^0 = 1--> Tk = T0

Does anyone know this equation/can you corroborate its accuracy, and or clarify some of my questions about its application?

Thank you!

Peter

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