Trying to design a gear with minimum thickness

[mendi1]

Hello,

I am blanking on the equations I should use to calculate the stress through a section of a gear. I would like to be able to calculate the thickness of trepanned gear. Hopefully the attachment helps show what I am looking for. The area between the arrows needs to be minimized.

Thank you

 

[kazx9r]

what the heck is a trepanned gear? is this a helical, straight cut?