PSI - Issue 17

Sebastian Vetter et al. / Procedia Structural Integrity 17 (2019) 90–97 Sebastian Vetter/ Structural Integrity Procedia 00 (2019) 000 – 000

95

6

The fatigue strength of the P-SHCs was evaluated by using the modified staircase method from Hück (1983). It is particularly suitable for reliably determining an average strength value with just a few tests. The logarithmic staircase factor describes the ratio between two neighboring stress levels. It is determined by an expected logarithmic standard deviation as = 10 . The logarithmic standard deviation = 0.0321 specified in Vetter et al. (2018) for shaft-hub connections was used for this purpose. Due to the existing contact between shaft and hub, the endurance limit was set to 10 million load cycles. The test frequency was approximately 15 Hz. The evaluated nominal bending fatigue strength values determined for 50 % survival probability are given in Table 4. Table 4. Specification of investigated P-SHCs with experimentally determined rotating bending moments and nominal bending fatigue strength values (interference = 0.5‰ ; relative joining length / = 1 ; survival probability = 50 % ). Test series Profil shape Material of shaft and hub Stress ratio / Number of evaluated tests Bending moment [Nm] Nominal bending fatigue strength [MPa] a) H3-convex C45E+N 0 8 618 121 b) H3-convex C45E+N 1 7 532 104 c) H3-convex 42CrMo4+QT 1 7 558 109 d) H7-concave C45E+N 0 7 624 117 e) H7-concave C45E+N 1 4 544 102 Based on the limits of torsional moments and the case distinction according to the associated failure locations in Table 3, an approach to dimension P-SHCs regarding static stresses will be developed subsequently. The failure in the contact joint occurs when a permissible pressure at the tappet of the shaft is exceeded by the caused pressure due to the torsional moment. In the following, the permissible and existing pressure is described in analogy to the design of feather key connections according to DIN 6892 (2012) and ANSI/AGMA 6101-E08 (2008). The permissible pressure describes the limit at which plasticization occurs between shaft and hub. The permissible pressure can be defined according to equation (5) using the yield strength of the shaft material. = 0.9 ∙ (5) The existing pressure is determined by the torsional moment and its lever arm /2 , the number of tappets , the eccentricity and the joining length . The limit of torsional moment of the contact joint can be calculated according to equation (6) under the condition that the permissible and existing pressure are equal. , = ∙ ∙ ∙ ∙ (6) A failure through permanent deformation at the free shaft occurs when the locale stress exceeds the yield strength of the material. The dimensioning of shaft components regarding permanent deformation can be adapted from the German national standard DIN 743 (2012) for P-SHCs. The static torsion can be converted with the factor √3 into an equivalent normal stress by using the von-Mises equation for ductile steels. The stress concentration caused by the profile shape is represented by the stress concentration factors of torsion according to Table 1. The diameter of inscribed circle must be selected for the calculation of the equivalent resistance moment for torsion. The static support effect for torsion is taken into account by the factor 2 = 1.2 . Thus the limit of torsional moment with regard to permanent deformation of the shaft can be calculated according to equation (7). , ℎ = ∙ 2 ∙ ∙ 3 16 ∙ √3 ∙ (7) 3. Approach for the dimensioning of P-SHCs 3.1. Dimensioning for static stresses