Study on the Influence Coefficient of Residual Stress used to Estimate the Stress Life Curve of Gears

This study aims to estimate the gear S-N curve by the influence coefficient m of the residual stress at the root of the gear for providing theoretical basis and experimental support for the study of the bending fatigue performance of the gear. Based on the crack propagation theory and the linear damage accumulation theory, according to the Goodman relation, the residual stress is treated as the average stress. The spatial distribution of the residual stress is considered, and the residual stress is treated as a step function about depth, so the crack propagation process is divided into several stages. Through the fatigue test, the S-N curve of the gear is obtained. In order to avoid the influence of gear material and shape on the coefficient m, the S-N curve after heat treatment is used as the initial S-N curve, and the S-N curve after shot peening is used as the result curve. Through S-N curve, the influence coefficient m of tooth root residual stress is calculated, and the S-N curve of gears after shot peening is deduced by m value, which is compared with the S-N curve obtained by experiment. The influence coefficient m of residual stress calculated by S-N curve is 0.2132. The S-N curve of shot peening derived from m value is lnS=7.6963-0.0821lnN, which is consistent with the trend of S-N curve obtained by experiment, and the calculated data are more secure in the case of high cycle fatigue. The huge capital and labor cost of gear fatigue test can be saved by estimating gear S-N curve more accurately by m value. It provides a theoretical and experimental basis for the study of the influence coefficient of tooth root residual stress, and provides a solution for estimating the gear S-N curve.