Simplified Lamé’s equations to determine contact pressure and hoop stress in thin-walled press-fits

Abstract

A simplification of Lamé’s equation to determine radial and hoop stress due to interference on press-fits is introduced. The two novel simplified equations introduced in this paper provide a method to quickly and accurately calculate the contact pressure (radial stress) and hoop stress between two contacting surfaces with alike material properties. The simplified equations assume that the press-fit joining method is applied to thin-walled cylindrical components. Additionally, the simplified equations introduced in this paper greatly summarize the mechanics of the press-fit joint assembly allowing a more general engineering and construction application easily understood by the layman. First, this paper shows the derivation of the simplified equations departing from Lamé’s equation. The simplified equations are then validated by comparing them to predictions obtained through Finite Element Analysis and other scholars’ analytical solutions. In addition to the simplified equations, this study reveals that the thickness (i.e. inner and outer diameter) of the press-fit components does not play a significant role when calculating hoop stress in thin-walled press-fit components, contrary to current solutions which depend on the thickness to determine hoop stress.