Many sources of shape change but in my view the order of importance in terms of their effects are.
1)Material variability - analysis, source and processing
2)Material variability - heat treat/residual stress condition prior to carburizing
3)Shape change during quench
4)Shape change (creep) during carburizing.

Work done 25 years ago at the University of Aston in England and repeated more recently at Illinois Institute of Technology shows that more random variation in shape is caused by variations in batch chemical analysis than any other factor.

Having reduced variability in analysis as much as possible then prior treatment should involve normalize and temper of all material and maybe even stress relief

The quench severity needs to be reduced to the minimum capable of producing the required properties hence the current interest in vacuum carburizing and gas quenching

Finally the parts need to be racked and supported to minimise creep during carburize.

You might want to try 4340
and see if you do not get less
distortion.  You might want to
consider flame hardening
quench and temper and then
stress relief.  .010 per side
does seem excessive even with
carburized material.
Are you cutting the blank oversize
to allow for the shrinkage?

Diamondjim: Customer specified material is 8620. So the option of using 4340 is presently not under active consideration. But if nothing works then we would have to try that.

We are cutting blanks oversize so that heat treat distortion is taken care of in finish hobbing after heat treatment.

Carburize: Thanks for the feedback. I would try to contact Illinois institute of technology to check if they have any specification for material, for heat treatment process which gives less distortion.

You could try vacuum carburizing, using a high pressure gas quench, or a quench containing hydrogen if necessary.  Email me and I can suggest a company to work with.  They have been successful in reducing distortion for the auto companies.

Another way of reducing distortion during heat treat is to cryogenically treat the item before heat treat.  This assumes true cryogenics, not the -110 F cold treatment.

 Of course, the advice about material given in the postings above is operative.  If you start out with or induce high residual stresses in the metal, ther is not much you can do about the distortion they cause as they relieve.

Ways of minimizing distortion on 8620 Material:

1) rough machine - stress relieve - machine - carburize

2) marquench (use hot oil)

3) quench plug or tool for carburizing

4) vacuum carburize