PSI - Issue 37

752 Sebastian Vetter et al. / Procedia Structural Integrity 37 (2022) 746–754 Sebastian Vetter / Structural Integrity Procedia 00 (2019) 000 – 000 7 Under the assumption that the parameters stress state due to external load, residual stress, surface factor and local hardness do not scatter within their assigned reference areas , the parameter sets can be obtained for discrete areas. The determination of the assigned parameter set is based on the random drawing of values according to the distribution of a parameter within a shaft. Thus, the inherent scatter of the shaft is modeled. The parameter sets , which represent the scatter-influencing parameters of the shaft surface, are input to the local strength approach. The application of this approach for all surfaces leads to a statement of whether the local stress is less than or equal to the local fatigue limit. If the stress is less than or equal to the fatigue limit for all surfaces, the shaft will be able to withstand the nominal stress . In this case, there is a run out. If this inequality is not fulfilled, there is a failure. The result obtained must be noted in the S – N curve for the corresponding nominal stress level . In the further procedure, it is necessary to determine the results (run out or failure) in the S – N curve for nominal stress levels for the shaft already randomly generated. For this purpose, the stress states , must be reduced by a stress multiplier. The stress multiplier describes the ratio of a newly selected nominal stress level 1 and the nominal stress level for which a result has already been determined. The described procedure for the stochastic generation of single shafts is repeated for a total of shafts. In this way, the scatter between the shafts is modelled. For each nominal stress level, a survival probability can be determined based on the ratio of run outs to the number of shafts, . Based on the nominal stresses and their survival probabilities, the location and scattering parameter and of the fatigue strength can be determined by fitting the value pairs for a normal distribution. 5. Validation In the following, the probabilistic method for determining the distribution of the fatigue strength is validated in experimental tests. Shafts as shown in Fig. 3 are used for this purpose. The shafts are loaded with a rotating bending stress. The material is quenched and tempered 42CrMo4+QT (1.7225).

Fig. 3. Sketch of the specimen used for validation.

5.1. Implementation of probabilistic model The necessary parameters for the probabilistic model were determined for the experimentally tested shafts, which represent the population. These include the values listed in Table 1 for the distribution parameters of the scatter influencing parameters. To describe the external shape in terms of the diameter, 22 shafts were measured. The parameters of the distribution of the radius could be derived based on the tolerance width of 2 mm given on the technical drawing and a process capability of 1.33. For the description of the influencing parameter of the surface condition, 12 measuring sections on different shafts, each with more than 40 grooves, were examined to describe the surface topography. Based on this, the distribution parameters for the groove depth and the groove radius of the surface grooves were obtained. It was found that the distance between two grooves is equal to the groove width . In addition, the groove width showed almost no scatter. Therefore, the groove width should be included in the model as a non-scattering parameter (see Table 2). Residual stress measurements have shown that the residual stresses decrease with increasing number of load cycles. Therefore, neither axial nor tangential residual stresses are considered in the model. In order to describe the influencing parameter of material condition on the basis of the local hardness, 10 hardness measurements according to HV10 were carried out on each of 25 shafts at the critical diameter. Based on these measurements, the parameters of the distribution of the local hardness could be fitted.