A semi-analytic method for elastic/plastic shrink-fit analysis and design

Abstract

A semi-analytic method for elastic/plastic shrink-fit analysis and design is developed. In contrast to many available semi-analytic methods, it is assumed that the outer disc obeys the von Mises yield criterion and its associated flow rule. The inner component of the assembly is purely elastic. The complete solution consists of three principal steps. First, the elastic/plastic solution in the outer disc is outlined. The only output of this solution required for the next step is the circumferential strain at the inner radius. It is shown that this strain can be found without having the strain distribution in the plastic region of the disc. This significantly simplifies the design of shrink fits. Moreover, only two parameters related to the outer disc (Poisson’s ratio and the dimensionless inner radius) are involved in numerical part of the elastic/plastic solution in the outer disc. Second, the found circumferential strain at the inner radius is used in conjunction with an analytic solution in the inner component of the assembly to match the two solutions. Any conventional design criterion can be adopted at this stage to determine optimal conditions. The complete solution involves several independent parameters. However, this does not cause any difficulty for design since these parameters are involved in analytic expressions. The final step is only necessary if the distribution of strains in the plastic region of the outer disc should be found.