Shaft-hub press fit subjected to bending couples: Analytical evaluation of the shaft-hub detachment couple

A mathematical modelling of a shaft-hub press-fit subjected to bending couples applied to the shaft extremities is developed, and the value of the bending couple inducing an un- desired shaft-hub incipient detachment is analytically determined. The shaft-hub contact is modelled in terms of two elastic Timoshenko beams connected by a distributed elastic spring, whose stiffness is analytically evaluated. Two models of the distributed spring are considered. The first model expresses the combined deformability of both the shaft and the hub cross sections. The second model accounts for the stiffening effect exerted by the shaft portion protruding from the hub on the adjacent shaft part that is in contact with the hub, and, consequently, it assumes only a rigid body motion of the shaft cross section, thus neglecting its deformability. Based upon this beam-like model, the bending couple producing the incipient detach- ment between the shaft and the hub is theoretically determined in term of the shaft-hub geometry, of the initial shaft-hub interference, and of the elastic constants. Comparisons with selected Finite Element (FE) forecasts indicate that the first modelling produces an incipient detachment couple that appreciably overrates the FE forecasts, whereas the sec- ond modelling lowers the error down to technically acceptable predictions.