Bending Stresses and Deformations in Prismatic Profiled Shafts with Noncircular Contours Based on Higher Hybrid Trochoids

Abstract

This paper presents an analytical method for determining the bending stresses and deformations in prismatic, noncircular profile shafts with trochoidal cross sections. The so-called higher trochoids can be used as form-fit shaft-hub connections. Hybrid (mixed) higher trochoids (M-profiles) were developed for the special application as a profile contour for the form-fit shaft and hub connections in an earlier work by the author. M-profiles combine the advantages of the two standardised polygonal and spline contours, which are used as shaft-hub connections for the transmission of high torques. In this study, the geometric and mechanical properties of the higher hybrid trochoids were investigated using complex functions to simplify the calculations. The pure bending stress and shaft deflection were determined for M-profiles using bending theory based on the theory of mathematical elasticity. The loading cases consisted of static and rotating bends. Analytical, numerical, and experimental results agreed well. The calculation formulas developed in this work enable reliable and low-cost dimensioning with regard to the stresses and elastic deformations of profile shafts subjected to bending loads.