The material selected by Boundary Lubrication Systems is a 4140 heat treat that has good wear characteristics, excellent fatigue characteristics, a high working temperature, and high yield strengths. 

Service Properties

table of normal service limits - how long will gears last and how hot can you run them

table of normal service limits - how long will gears last and how hot can you run them

In service properties, the most important features are hardness for long term wear resistance and service temperature to make sure the part doesn't weaken over time and eventually fail.

We ruled out 9310, because according to NASA:

 Source NASA: "However, because AISI 9310 loses much of its hardness at temperatures beyond 250’ F (ref. 3), its application to advanced aircraft systems may be limited." http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19790006218.pdf

Mechanical Properties:

Table of Mechnaical material properties

Table of Mechnaical material properties

Yield strength is basically how far you can bend the material before it becomes permanently bent, and this is the most important property for this application because once the gears are bent they will not spin. 4140 has excellent yield strengths that are just 3% under 4340. Meanwhile, 4140 is cheaper and easier to machine.

Price isn't the only reason:

Metal fatigue properties for machined steel components are the best at approximately 30 HRc hardness. Once you get above 30 HRc the gears will become more and more brittle. Our proprietary heat treat is just above this, and is the farthest we would recommend for this application. Hardening gears above this could cause them to shatter with repeated high stresses.