PSI - Issue 17

96 Sebastian Vetter et al. / Procedia Structural Integrity 17 (2019) 90–97 Sebastian Vetter/ Structural Integrity Procedia 00 (2019) 000 – 000 7 Based on a case distinction, equation (8) can be used to estimate the limit of torsional moment , that can be transmitted through the P-SHC with a hypotrochoidal profile shape. , = min( , ; , ℎ ) (8) Fig. 4 illustrates the limits of torsional moments evaluated experimentally and in addition the calculated one for those P-SHCs according to equation (8). Due to the maximum error of the calculation compared to the experiment, a minimal safety factor of = 1.2 is recommended for the limit of permissible static torsional moment , (cf. equation (9)). , = , (9)

Fig. 4. Experimental investigated limits of torsional moments and specific curves of plasticization for free shafts and the corresponding contact

3.2. Dimensioning for high cycle fatigue

In the following, an approach for dimensioning P-SHCs with a hypotrochoidal profile shape based on existing nominal stress concepts will be developed. Thus the nominal stress concepts according to the American national Standard ANSI/AGMA 6101-E08 (2008), the German national standard DIN 743 (2012) or the FKM guideline from Rennert et al. (2012) can be used. In order to enable the dimensioning of the P-SHCs according to nominal stress concepts, the results of the high cycle fatigue test series from Table 4 are used to determine notch factors for rotating bending (cf. Table 5). The notch factors for the profile shapes H3-convex and H7-concave can be calculated using the FKM guideline with equation (10). The FKM guideline defines the basic bending fatigue strength of the material as equal to the tensile-compression fatigue strength , according to Table 2. = , (10) Using the tests with rotating bending and static torsion, the mean stress effect can be evaluated for the H3-convex and H7-concave profile shapes. For this purpose, an equivalent mean normal stress with , = √3 is calculated concerning the ratio / = 1 by using the von-Mises equation for ductile steels. Hence, the corresponding stress ratio results from lowest to highest stress to = 0,3 . For pure rotating bending, the stress ratio is = −1 . If the mean stress effect is defined as an increase in the linear equation of the relationship between stress amplitude and mean stress according to Schütz (1965), the mean stress effect can be calculated with equation (11). = , =−1 − , =0,3 √3 = , =−1 − , =0,3 √3 , =0,3 (11) The Notch factor for the profile shape H3-convex made of the material 42CrMo4+QT (test series c) must be calculated. According to the investigations of Neikes et al. (2019), it can be assumed that the mean stress effect is not significantly influenced by the material. Therefore, a theoretically high cycle load capacity for the stress ratio = −1 can be calculated with the mean stress effect of the H3-convex profile. This results in a notch factor = 3.5 for the material 42CrMo4+QT according to the tensile-compression fatigue strength , (cf. Table 2).