There is wealth of literature on the subject of single (or uni-) directional gear tooth bending stress and lifte
relationships (i.e., S-N curves) that has been published in various journals and handbooks over past decades.
Several of them were adopted as industrial standards by different gear societies worldwide. However, they
have limited information regarding the fluctuating bi-directional (reversed) gear tooth bending fatigue life
prediction. To fill in this gap for practical applications, the author first intended to apply traditional fatigue
theories such as modified Goodman, Gerber and Morrow to derive a series of S-N equations. Upon
correlation of these equations with the regressed test results, significant deviations were found. From the
observation of test results, it was found that the slopes and endurance limits on the fitted S-N curves from
several different tested conditions were reasonably similar, if the test gears had been made from the same
batch of material and manufacturing process. Based on the above observation, the author proposed a new
approach to reduce the deviation from the above theories.

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