Gear root bending strength: statistical treatment of Single Tooth Bending Fatigue tests results

Abstract

Gear tooth failure due to tooth root bending fatigue is one of the most dangerous failure modes in gears. Therefore, the precise definition of gear bending fatigue strength is a key aspect. Furthermore, in order to calculate the service life of a gear component, an accurate estimation of the S‑N curve is required. This curve must properly account for the slope of the fatigue strength region, the slope of the region ahead the fatigue knee, as well as the position of the knee itself. Hence, in order obtain a curve at different reliability levels, a proper estimation of the dispersion associated with the experimental points is required. Usually, Single Tooth Bending Fatigue (STBF) tests are used to investigate the gear load carrying capacity with respect to the bending failure mode. Then, starting from the gear specimen test data, the S‑N curve that has to be used in the rating method has to be determined. Maximum Likelihood Estimation (MLE), a statistical tool capable of considering also interrupted tests (e.g. runouts) has been used to estimate, in the most reliable way, the S‑N curve from experimental points. Furthermore, if the STBF test is performed in a symmetrical configuration, i.e. two teeth loaded at the same time, also the survival of one of the two teeth represents an information that can be taken into account thanks to MLE.Moreover, additional effects must be considered to obtain the S‑N curve of a real component starting from STBF tests. In reality, the load history and the statistical behaviour are different, since in a meshing gear the strength is determined by its weakest tooth, while in a STBF test the failing tooth is predetermined. The latter effect is considered by means of the statistic of extremes, which enables the estimation of the strength of the weakest tooth and therefore of the gear. This paper describes in detail the proposed calculation method and explains its application to determine the S‑N curve in practical cases.