An Elasto-Plastic Analytical Solution for the Shrink-Fit Problem with a Thin Strain-Hardening Hub and an Elastic Solid Shaft

Abstract

An analytical solution is obtained in this article for the axisymmetric shrink fit problem with a thin strain hardening hub and an elastic solid shaft. The solution is based on the deformation theory of Hencky, the yield criterion of von Mises, and the assumption of infinitesimal deformations. An elastic power law plastic material model is employed to represent the stressstrain relation of the hub material, with the compressibility of material being included. The solution is derived by using a stress formulation and with the help of a modified Nadai's auxiliary variable method and the extended Michell theorem. All expressions for the stress, strain, and displacement components are derived in explicit forms in terms of an auxiliary variable and four constant parameters that are determined from given boundary conditions by an iterative process. Three specific solutions are presented as limiting cases of the solution. Numerical results are also provided to show quantitatively applications of the solution. This solution, together with the related specific solutions and numerical results, furnishes a new theoretical basis for the mechanical design of shrink-fit sets.