A generalized theory for shaft-hub couplings

The design of compression-fit joints, based on the theory of thick-walled cylinders, is usually referred to shaft-hub couplings carried out between two elements that have an axial symmetric shape. The stress distributions both inside the elements and on the contact surfaces can be defined by the equilibrium and by the compatibility formulae once the total radial interference and the internal and external pressure (the boundary conditions) are known. The complete tensile state of the coupling is defined by two principal stresses: the radial and the hoop tensions. The present article aims at extending the analytic calculation valid for two elements to a number of n elements by means of a sequential solution of the governing equation system. The elements in contact can rotate at a generic angular velocity and can, also, be made of different materials. The overall solution has been derived starting from the hypothesis of the simultaneous presence of axial symmetric geometries and axial symmetric loads. The mathematical model has been verified by comparing the theoretical results with some finite-element analysis calculations performed on the same coupled elements.