PSI - Issue 17

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

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1. Introduction

Polygon shaft-hub connections (P-SHCs) realize a torsional moment transmission primarily via form locking. In comparison to conventional press fits, their advantage is the transmission of high static torsional moments without slipping through the connection. New manufacturing processes, such as the two-spindle-non-round-lathe technology, allow the cost-effective production of P-SHCs with geometrically similar hypotrochoidal profile shapes. However, a widespread industrial application is limited by the lack of basic concepts for static and fatigue strength calculation. Therefore, the aim of this paper is to provide an approach for durably dimensioning P-SHCs with hypotrochoidal profile shapes under static and high cycle stresses. This approach is based on experimental investigations. Nomenclature diameter of minimal circumscribed circle permissible pressure diameter of maximum inscribed circle survival probability logarithmic staircase factor logarithmic standard deviation mean diameter safety factor eccentricity , Cartesian coordinates generation point resistance moment of bending notch factor resistance moment of torsion 2 static support effect stress concentration factor of torsion joining length twisting angle rotating bending moment interference torsional moment nominal bending fatigue strength load cycle number , basic fatigue strength of tensile- tappet number compression stress ratio ultimate tensile strength tensile yield strength of material torsion mean stress surface roughness polar angle of cross-section 2. Experimental investigations The precondition for the development of an approach for dimensioning P-SHCs under static and high cycle stresses is initially the geometric similarity. According to Ziaei (2002), this allows to transfer experimental investigations to other, but geometrical similar profile types. Therefore, the following experimental investigations were based on previously unstandardized P-SHCs with hypotrochoidal profile shapes. The hypotrochoidal profile shape was generated by rolling a roller circle in a base circle (cf. Fig. 1a). The generation point describes the profile shape during the rolling movement. The generating point has the eccentricity radial to the center of the roller circle. This allows to indicate a parameter description for the profile shape according to equations (1) and (2) in dependence on the polar angle . ( ) = ⁄ 2 ∙ cos( ) + ∙ cos(( − 1) ) (1) ( ) = ⁄ 2 ∙ sin( ) − ∙ sin(( − 1) ) (2) Different types of hypotrochoidal profiles with the parameters according to Table 1 were considered in the experimental investigations. In Fig. 1b the corresponding profile shapes are shown and the minimal circumscribed circle diameter and the maximum inscribed circle diameter were exemplarily marked. All investigated profiles had the same minimal circumscribed circle diameter = 40 . The mean diameter is the average of and 2.1. Geometrical description of P-SHCs