Einblick in die Festigkeitsberechnung nach DIN 3689 genormter hypotrochoidischer Welle-Nabe-Verbindungen unter reiner Torsionsbeanspruchung

In the field of modern drive technology, ever higher power densities are required, which is why conventional form-fit shaft-hub connections are increasingly reaching their mechanical limits. Against this backdrop, in November 2021 the DIN 3689 Part 1 standard for hypotrochoidal profile geometry appeared as a promising alternative, which was given the abbreviation H‑profile in the aforementioned standard. Based on extensive component tests using the staircase method, their dynamic load-bearing behaviour under a torsional load was investigated. The experimental fatigue notch factors and bearable torsional moment amplitudes determined using this procedure provide a first insight into the dynamic torsional load-bearing capacity in dependence of the profile parameters number of corners and profile eccentricity. The influence of the shaft material was also analysed.

Reliable calculation equations based on an analytical method already exist for the hypotrochoidal shaft without hub. These equations have already been verified experimentally for the static load case. The results for pure torsional loading are presented in this article and will be incorporated into calculation part 2 of the DIN 3689 standard in the near future. This will provide the designer with a tool that he can use in future to design hypotrochoidal shafts and calculate the required static safety factors. In order to estimate the dynamic torsional load-bearing capacity, purely theoretical fatigue notch factors of the investigated hypotrochoidal shafts are presented, the comparison of which with the experimental values of the connection also shows the effect of the tribological stress in the contact between shaft and hub on the fatigue strength.

The comparatively low fatigue notch factors of the stand alone hypotrochoidal shafts and also of the connections with hub compared to conventional form-fit connections due to the geometry-related lower notch effect, in combination with the economical manufacturability of hypotrchoidal profiles, suggest a promising future.