rob768,
I agree, a deeper case will allow a greater contact stress limit. Of course, the strength of the underlying core material supporting the case also has a significant effect on the allowable contact stress (ie. brinelling). There are also limits (both metalurgical and economical) to how thick a case can be produced. And the exact carburizing, quench and temper process employed determines those properties. The typical case hardening processes for 8620 alloy steel are-
a) carburize and direct quench, followed by tempering, or
b) carburize, cool, reheat, single quench and temper, or
c) carburize, cool, reheat, double quench and temper
These various processes can produce a core hardness that varies from about 120 ksi to 180 ksi, and a case that varies from about .020 to .070 inch thickness.
Also remember that a case hardened gear undergoes significant distortion during the quench, so it must be finished by grinding. The amount of distortion is dependent upon the geometry of the part and whether a quench fixture is employed. The more the part distorts, the more material that must be removed during the finish grind and the thinner the finished case.
The actual level of contact stress that a gear experiences in service can vary greatly, depending upon the accuracy of the manufactured gears, the accuracy of the mounted gears and any deflection of the gears under load and/or thermal displacement. For example, a spur gear mesh has a nice line of contact, in theory. But that quickly becomes a point contact condition (edge loading) with just a couple thousanths of an inch of misalignment. And your contact stresses go up by several factors. That's why the standard formulas you find in Dudley or Buckingham are very conservative.
As for MTPTurbo's original query, you will never really end up with "too thick of a case" on your parts, due to inherent limitations with most commercial carburizing processes. It's typical practice with carburized gears to specify a finished case depth range (after grinding) and hardness and to where it applies (flanks, tips, root fillets, etc.), as well as a minimum core hardness. It's then up to your gear vendor to optimize his processing to meet your finished part requirements. Remember, he's in business to make money, so he won't leave your parts in the carburizing furnace any longer than necessary to produce the requisite case depth (time is money).
Good Luck.
Terry