Constitutive Equations for Joints with Clearance

Abstract

The small displacements notion is widely used in tolerancing, particularly to describe the kinematics of joints with clearance. But this purely geometrical approach does not take into account the joint forces description. Our paper aims at examining the consequences of such an approach on the forces representation. After a brief reminder of the constitutive equations of perfect f joints, our interest will focus on joints with clearance. We demonstrate that the forces in such joints have the same expression as the forces in the corresponding perfect joints. But their components do not have any value any longer, they must match some inequalities depending on the displacements actual value. The main interest of the proposed approach is to determine the joint forces properties by considering only the geometrical study, well mastered by now.