###### Abstract  
Gears are one of the the most widespread mechanical components and their design is supported by standard calculation methods. Among all the possible failure modes of gears, tooth root bending is the most critical and could lead to catastrophic failures. In this regard, different surface treatments could be exploited to improve the gear strength. Among them, shot peening is the most common. The aim of this study is to evaluate the effectiveness of shot peening on improving the tooth root bending resistance. This is achieved by exploiting the Finite Element Method (FEM) in combination with advanced multiaxial fatigue criterion based on the critical plane concept. A standard Single Tooth Bending Fatigue test was reproduced numerically via FEM. Beside the wrought gears, shot peened ones were also simulated. The state of stress induced by the shot peening was obtained numerically by simulating the surface treatment itself with non-linear dynamic analyses. The results have shown quantitatively how the residual stresses promote an improvement in the resistance and how the local hardening could lead to different early paths of nucleation and propagation of cracks on the tooth fillet. g 20222010 August 202201  
common ones are the Meshing Gears (MG) test, e.g., [14; 16], the Single Tooth Bending Fatigue (STBF) test, e.g., [17; 18; 19] and the tests on notched specimens, e.g., [20; 21; 22]. In the meshing gears experiments, the specimen is a gear pair manufactured with the material to be characterized. Surface treatments could also be applied. This kind of test reproduces the real loading conditions under operation. The stress cycle in the root region reflects the one that real gears will be subjected to during operation [23; 24]. While this configuration is possibly the one offering the most reliable results, it is time-consuming and expensive. With each gear pair, a single value of \(s_{Film(MG)}\) can be estimated since the test ends with the breakage of (at least) one tooth rendering the specimen unusable for further tests. The testing costs can be significantly reduced using notched specimens instead of meshing gears. While the testing of simple notched samples could be performed on any monoaxial testing device, the absence of meshing limits the reliability of the results that did not include some important influences, e.g., the effect of the manufacturing process, the real surface finishing, the lubrication, etc. To partially counteract this limitation, opportune correction coefficients are used [25]. While this practice could slightly improve the results, they remain far from being as reliable as those obtained with tests on meshing gears. A compromise solution is represented by the Single Tooth Bending Fatigue (STBF) test [17]. STBF relies on the application of two time-dependent coaxial forces to two opposite flanks of teeth of the gear sample. The application of the forces uses two anvils and the Wildhaber distance [1] to ensure equilibrium of the system. This configuration uses (for each test) only two teeth in which final failure does not compromise the entire gear and another teeth pair of the same gear could be used for the successive test. In other words, with the STBF approach, multiple tests could be performed on a single gear (instead of a single test every two gears like in the MG approach). Moreover, STBF tests do not require lubrication thus resulting in low-cost and simple experimentation [26]. While these tests seem to be the best experimental configuration, some problems could arise when the measures in terms of forces have to be converted into the fatigue limit of the material \(\sigma_{Film(STBF)}\). In most cases, this is achieved with an inverse application of the standards. However, this requires the re-definition of some parameters with the consequent introduction of uncertainties.