optimization of spur gear design 1

[james80]

I am working on multiobjective optimization problem for
multistage spur gear reduction units.
I trying to incorporate case depth or case hardness and core hardness into the constraint equation as two separate design variables or adding another constraint equation relating the two hardness. Unfortunately, I couldnt come up with any such relation

Could anyone give me some suggestions on this?

 

[Carburize]

Check AGMA 2001 which gives fundamental rating factors for gear teeth, there is information on tooth loading limts for various levels of hardness of through-hardened material and data on case carburized teeth.