It depends on how much statistical confidence you want/need. A practical lower limit is ~ 12 samples: 4 stress levels with 3 samples per stress level. But this will have very low statistical significance, will not capture the so-called fatigue or endurance limit, will not capture variability in raw material, heat treatment, etc. I recently worked with a test lab on developing some S-N curves, and 39 specimens were chosen for one material/manufacturing method combination: 6 stress levels with 4 samples per stress level, and then an additional 15 specimens for probing the fatigue limit using a staircase method.

Are you interested in surface contact stress fatigue or tensile stress fatigue? Flight critical aircraft gears are designed using L2 life (98% reliability) for tooth bending because a fractured tooth is usually a very nasty type of failure. Flight critical gears and rolling element bearings are designed using L10 life (90% reliability) for surface contact stress because a pitted tooth or bearing race is usually a very benign failure mode that can be detected long before it poses a serious problem.

Other things to consider with tensile fatigue in gear materials is the effect that shot peening or cyclic load reversals can have. For example, AGMA recommends applying a reduction factor of 0.71 to the published tensile fatigue stress limits for a gear tooth (like with an idler gear) subject to fully reverse bending loads. Will the testing consider common factors in gear design like fully reverse bending in idler teeth or the effect of shot peening?

The gears used in aircraft drivetrains often operate at high speeds for thousands of hours, so the number of load cycles they can accumulate over their design life can reach 10^8 or more. It can be time consuming and costly to test a large number of material specimens to this lifecycle. And as TVP noted, the raw material quality and process controls used to produce the gear can have a large effect on fatigue life and reliability. Do you need to consider these factors with your testing?

Thanks #TVP and #tbuelna for your answers, very helpful.

I am not testing gears myself. But I was recently in touch with a gear-testing lab where they have been deriving an S-N curve for a new material. All their tests (almost a 100 specimens) used the same gear exactly (same geometry, material, heat treatment ..etc) and the only variable was the torque applied. I am not sure whether the S-N curve they derived is representative of the material. I mean if you try to design a gear of this material but with bigger geometry, would it be enough to apply the stress correction factors such as size factor ...etc? or should they have included different geometries in their testing?

One more thing please, the ISO standards mention that the long life factor is somewhere between 0.85 and 1 (where 1 is for ideal conditions for which pitting is minimal). The S-N curve derived in the lab I mentioned earlier included values of the long life factor below 0.85, is this ok?