We are doing gear hobbing, then case carburizing followed by oil quench and temper. Post heat treat, we perform gear grinding. If, for example, we have achieved a Gear Class of “7” during hobbing (for both profile as well as helix), what could be the best class after heat treatment? Is it possible to contain the distortion within “1 class” (i.e. “8”) for this case? What is your experience in this regard?
If you are grinding the gears after carburizing, are using the correct rough-hobbing size (form) and leave the right amount of stock on for post-heat-treatment grinding, you should expect to be able to grind your gears to the class you desire. In my opinion, however, you can't make a blanket statement saying that controlling the size to a specific class before heat treating will yield a specific class afterwards. There are too many variables involved. However, you could possibly make trial runs to statistically predict the distortion due to the influence of the gear shape and size.
Taking normal proper care in processing (good normalizing to blanks, proper fixturing in the furnace and correct cooling rate in quench), you should be able to manage (minimize) distortion. And obviously the size of the gear and shape play a large role in the results. Then there are always some "tricks" that can be used on difficult gear shapes. For example, painting some areas with carburizing stop-off paint to control stresses or machining out bores or other surfaces after carburizing that do not need to be carburized. Another example would be a gear with large lightening holes in the web that cause the gear geometry to "dive in" above the holes. Painting the inside of the drilled holes will keep carburized compressive stresses from the holes affecting the gear geometry above them.
Toyota, for example, also controls the material Jominy (DI values) closer on specific gears for repeatability. On one style gear they might require their steelmaker to control the Jominy within only 1 HRC point throughout the whole Jominy range. Some American automakers purchase gear steel to extremely tight DI values to achieve the same consistency from lot to lot. If the material hardenability is not controlled, the distortion will vary from lot to lot (even assuming the heat treating is closely controlled).