Shear and Bending Stresses in Prismatic, Non-Circular-Profile Shafts with Epitrochoidal Contours Under Shear Force Loading

In the field of modern drive technology, conventional form-fit shaft-hub connections, such as the standardized keyway connection, are reaching their mechanical limits due to the space-saving design. The trochoidal profiles are elegant modern shaft-hub connections with a compact design for high-power transmission. This article deals with an analytical approach to determining the stress state in trochoidal profiles under shear bending. The solution completes the existing analytical attempts at the load cases of pure bending and torsion. Similar to the torsional loading case, a conformal mapping must be found that can completely transform the unit circle to the non-circle profile area. The conformal mapping function is deduced from the contour equation of the profile. To check the analytical results, in addition, numerical investigations were carried out. The results of the complementary numerical studies show very good agreement with the analytical solutions. The equations derived for the maximum stresses enable a reliable and cost-effective design of the profile shafts subjected to shear force loading.