Effect of Gear Design Parameters on Stress Histories Induced by Different Tooth Bending Fatigue Tests: A Numerical-Statistical Investigation

The characterization of new materials for enabling gear design is definitely a fundamental objective in the gear industry and research. Single Tooth Bending Fatigue (STBF) tests can be performed to speed up this process. However, it is well known that STBF tests tend to overestimate material strength compared to tests performed directly on meshing gears (MG) which, in turn, require an excessively long test time. Therefore, it is common practice to use a constant correction factor f(korr) of 0.9 to translate STBF results for designing actual MG (e.g., via ISO 6336). Recent works involving a combination of Finite Element Models (FEM) and multiaxial (non-proportional) fatigue criteria based on the critical plane concept have highlighted that the assumption of considering f(korr) as a constant independent of the gear design parameters leads to inaccurate results. However, in previous studies, no correlation between f(korr) and gear design parameters has emerged. In the present paper, the influence of the normal pressure angle (alpha(n)), the profile shift coefficient (x*), and the normal module (m(n)) on f(korr) was investigated by analyzing FEM simulations with the Findley fatigue criterion. 27 gear geometries were studied by varying the above 3 parameters in 3 levels (full factorial DOE). These geometries were simulated in both MG and STBF configurations. The results of the 54 FEM simulations were analyzed by applying the Findley fatigue criterion and the corresponding f(korr) were calculated. The correlation between f(korr) and alpha(n), x* and m(n) was investigated using the Analysis of Variance (ANOVA) technique. The results show that the only gear design parameter influencing f(korr) is x* hence, a regression model for f(korr) including x* has been developed. This latter has been then adopted for calculating and comparing f(korr) values from other combination of the parameters found in literature, giving good correspondence.