Estimation of gear SN curve for tooth root bending fatigue by means of maximum likelihood method and statistic of extremes

Gear failure due to tooth root bending fatigue is one of the most dangerous gear failure modes. Therefore, the precise definition of gear bending fatigue strength is a key aspect in gear design. As a matter of fact, in order to assess a gear component, an accurate estimation of the component SN curve is required. This curve must properly take into account three main aspects: the slope of the fatigue strength region, the slope of the region ahead the fatigue knee and the position of the knee itself. In addition, with the aim of being able of considering different reliability levels, a proper estimation of the associated dispersion is required too. Single Tooth Bending Fatigue (STBF) tests are usually used to investigate the tooth load carrying capacity with respect to the bending failure mode. However, due to the test rig configuration, two main differences between test and real case are present. Firstly, the statistical behavior is different, since in the meshing gear the strength is determined by its weakest tooth, while in a STBF test the failing tooth is predetermined. Secondly, the load history is different.Therefore, additional effects have to be taken into account to obtain the gear SN curve starting from STBF tests. In this article, due to its capability of handling interrupted tests (e.g. runouts), Maximum Likelihood Estimation (MLE) has been used to estimate, in the most reliable way, the SN curve from experimental points. SoE (Statistic of Extremes) has been adopted to move from the STBF SN curve to the gear one, as, by means of a simple mathematical passage, SoE enables the estimation of the strength of the weakest tooth among the z gear teeth and, as a consequence, of the gear. The effect of the different load history is considered by adopting a literature-based approach (i.e. use of corrective coefficient). This paper describes in detail the proposed calculation method and shows its application to determine the SN curve in a practical case